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test_pie/external/alglib-3.16.0/interpolation.cpp
Timo Menzel d20d85177b Add texturemerge code.
2023-09-14 11:12:02 +02:00

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/*************************************************************************
ALGLIB 3.16.0 (source code generated 2019-12-19)
Copyright (c) Sergey Bochkanov (ALGLIB project).
>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#ifdef _MSC_VER
#define _CRT_SECURE_NO_WARNINGS
#endif
#include "stdafx.h"
#include "interpolation.h"
// disable some irrelevant warnings
#if (AE_COMPILER==AE_MSVC) && !defined(AE_ALL_WARNINGS)
#pragma warning(disable:4100)
#pragma warning(disable:4127)
#pragma warning(disable:4611)
#pragma warning(disable:4702)
#pragma warning(disable:4996)
#endif
/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS IMPLEMENTATION OF C++ INTERFACE
//
/////////////////////////////////////////////////////////////////////////
namespace alglib
{
#if defined(AE_COMPILE_IDW) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_RATINT) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_FITSPHERE) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_INTFITSERV) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_SPLINE1D) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_PARAMETRIC) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_SPLINE3D) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_POLINT) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_LSFIT) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_RBFV2) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_SPLINE2D) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_RBFV1) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_RBF) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_INTCOMP) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_IDW) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Buffer object which is used to perform evaluation requests in the
multithreaded mode (multiple threads working with same IDW object).
This object should be created with idwcreatecalcbuffer().
*************************************************************************/
_idwcalcbuffer_owner::_idwcalcbuffer_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_idwcalcbuffer_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::idwcalcbuffer*)alglib_impl::ae_malloc(sizeof(alglib_impl::idwcalcbuffer), &_state);
memset(p_struct, 0, sizeof(alglib_impl::idwcalcbuffer));
alglib_impl::_idwcalcbuffer_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_idwcalcbuffer_owner::_idwcalcbuffer_owner(const _idwcalcbuffer_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_idwcalcbuffer_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: idwcalcbuffer copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::idwcalcbuffer*)alglib_impl::ae_malloc(sizeof(alglib_impl::idwcalcbuffer), &_state);
memset(p_struct, 0, sizeof(alglib_impl::idwcalcbuffer));
alglib_impl::_idwcalcbuffer_init_copy(p_struct, const_cast<alglib_impl::idwcalcbuffer*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_idwcalcbuffer_owner& _idwcalcbuffer_owner::operator=(const _idwcalcbuffer_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: idwcalcbuffer assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: idwcalcbuffer assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_idwcalcbuffer_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::idwcalcbuffer));
alglib_impl::_idwcalcbuffer_init_copy(p_struct, const_cast<alglib_impl::idwcalcbuffer*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_idwcalcbuffer_owner::~_idwcalcbuffer_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_idwcalcbuffer_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::idwcalcbuffer* _idwcalcbuffer_owner::c_ptr()
{
return p_struct;
}
alglib_impl::idwcalcbuffer* _idwcalcbuffer_owner::c_ptr() const
{
return const_cast<alglib_impl::idwcalcbuffer*>(p_struct);
}
idwcalcbuffer::idwcalcbuffer() : _idwcalcbuffer_owner()
{
}
idwcalcbuffer::idwcalcbuffer(const idwcalcbuffer &rhs):_idwcalcbuffer_owner(rhs)
{
}
idwcalcbuffer& idwcalcbuffer::operator=(const idwcalcbuffer &rhs)
{
if( this==&rhs )
return *this;
_idwcalcbuffer_owner::operator=(rhs);
return *this;
}
idwcalcbuffer::~idwcalcbuffer()
{
}
/*************************************************************************
IDW (Inverse Distance Weighting) model object.
*************************************************************************/
_idwmodel_owner::_idwmodel_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_idwmodel_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::idwmodel*)alglib_impl::ae_malloc(sizeof(alglib_impl::idwmodel), &_state);
memset(p_struct, 0, sizeof(alglib_impl::idwmodel));
alglib_impl::_idwmodel_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_idwmodel_owner::_idwmodel_owner(const _idwmodel_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_idwmodel_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: idwmodel copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::idwmodel*)alglib_impl::ae_malloc(sizeof(alglib_impl::idwmodel), &_state);
memset(p_struct, 0, sizeof(alglib_impl::idwmodel));
alglib_impl::_idwmodel_init_copy(p_struct, const_cast<alglib_impl::idwmodel*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_idwmodel_owner& _idwmodel_owner::operator=(const _idwmodel_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: idwmodel assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: idwmodel assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_idwmodel_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::idwmodel));
alglib_impl::_idwmodel_init_copy(p_struct, const_cast<alglib_impl::idwmodel*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_idwmodel_owner::~_idwmodel_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_idwmodel_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::idwmodel* _idwmodel_owner::c_ptr()
{
return p_struct;
}
alglib_impl::idwmodel* _idwmodel_owner::c_ptr() const
{
return const_cast<alglib_impl::idwmodel*>(p_struct);
}
idwmodel::idwmodel() : _idwmodel_owner()
{
}
idwmodel::idwmodel(const idwmodel &rhs):_idwmodel_owner(rhs)
{
}
idwmodel& idwmodel::operator=(const idwmodel &rhs)
{
if( this==&rhs )
return *this;
_idwmodel_owner::operator=(rhs);
return *this;
}
idwmodel::~idwmodel()
{
}
/*************************************************************************
Builder object used to generate IDW (Inverse Distance Weighting) model.
*************************************************************************/
_idwbuilder_owner::_idwbuilder_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_idwbuilder_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::idwbuilder*)alglib_impl::ae_malloc(sizeof(alglib_impl::idwbuilder), &_state);
memset(p_struct, 0, sizeof(alglib_impl::idwbuilder));
alglib_impl::_idwbuilder_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_idwbuilder_owner::_idwbuilder_owner(const _idwbuilder_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_idwbuilder_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: idwbuilder copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::idwbuilder*)alglib_impl::ae_malloc(sizeof(alglib_impl::idwbuilder), &_state);
memset(p_struct, 0, sizeof(alglib_impl::idwbuilder));
alglib_impl::_idwbuilder_init_copy(p_struct, const_cast<alglib_impl::idwbuilder*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_idwbuilder_owner& _idwbuilder_owner::operator=(const _idwbuilder_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: idwbuilder assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: idwbuilder assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_idwbuilder_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::idwbuilder));
alglib_impl::_idwbuilder_init_copy(p_struct, const_cast<alglib_impl::idwbuilder*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_idwbuilder_owner::~_idwbuilder_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_idwbuilder_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::idwbuilder* _idwbuilder_owner::c_ptr()
{
return p_struct;
}
alglib_impl::idwbuilder* _idwbuilder_owner::c_ptr() const
{
return const_cast<alglib_impl::idwbuilder*>(p_struct);
}
idwbuilder::idwbuilder() : _idwbuilder_owner()
{
}
idwbuilder::idwbuilder(const idwbuilder &rhs):_idwbuilder_owner(rhs)
{
}
idwbuilder& idwbuilder::operator=(const idwbuilder &rhs)
{
if( this==&rhs )
return *this;
_idwbuilder_owner::operator=(rhs);
return *this;
}
idwbuilder::~idwbuilder()
{
}
/*************************************************************************
IDW fitting report:
rmserror RMS error
avgerror average error
maxerror maximum error
r2 coefficient of determination, R-squared, 1-RSS/TSS
*************************************************************************/
_idwreport_owner::_idwreport_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_idwreport_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::idwreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::idwreport), &_state);
memset(p_struct, 0, sizeof(alglib_impl::idwreport));
alglib_impl::_idwreport_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_idwreport_owner::_idwreport_owner(const _idwreport_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_idwreport_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: idwreport copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::idwreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::idwreport), &_state);
memset(p_struct, 0, sizeof(alglib_impl::idwreport));
alglib_impl::_idwreport_init_copy(p_struct, const_cast<alglib_impl::idwreport*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_idwreport_owner& _idwreport_owner::operator=(const _idwreport_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: idwreport assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: idwreport assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_idwreport_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::idwreport));
alglib_impl::_idwreport_init_copy(p_struct, const_cast<alglib_impl::idwreport*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_idwreport_owner::~_idwreport_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_idwreport_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::idwreport* _idwreport_owner::c_ptr()
{
return p_struct;
}
alglib_impl::idwreport* _idwreport_owner::c_ptr() const
{
return const_cast<alglib_impl::idwreport*>(p_struct);
}
idwreport::idwreport() : _idwreport_owner() ,rmserror(p_struct->rmserror),avgerror(p_struct->avgerror),maxerror(p_struct->maxerror),r2(p_struct->r2)
{
}
idwreport::idwreport(const idwreport &rhs):_idwreport_owner(rhs) ,rmserror(p_struct->rmserror),avgerror(p_struct->avgerror),maxerror(p_struct->maxerror),r2(p_struct->r2)
{
}
idwreport& idwreport::operator=(const idwreport &rhs)
{
if( this==&rhs )
return *this;
_idwreport_owner::operator=(rhs);
return *this;
}
idwreport::~idwreport()
{
}
/*************************************************************************
This function serializes data structure to string.
Important properties of s_out:
* it contains alphanumeric characters, dots, underscores, minus signs
* these symbols are grouped into words, which are separated by spaces
and Windows-style (CR+LF) newlines
* although serializer uses spaces and CR+LF as separators, you can
replace any separator character by arbitrary combination of spaces,
tabs, Windows or Unix newlines. It allows flexible reformatting of
the string in case you want to include it into text or XML file.
But you should not insert separators into the middle of the "words"
nor you should change case of letters.
* s_out can be freely moved between 32-bit and 64-bit systems, little
and big endian machines, and so on. You can serialize structure on
32-bit machine and unserialize it on 64-bit one (or vice versa), or
serialize it on SPARC and unserialize on x86. You can also
serialize it in C++ version of ALGLIB and unserialize in C# one,
and vice versa.
*************************************************************************/
void idwserialize(idwmodel &obj, std::string &s_out)
{
jmp_buf _break_jump;
alglib_impl::ae_state state;
alglib_impl::ae_serializer serializer;
alglib_impl::ae_int_t ssize;
alglib_impl::ae_state_init(&state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&state, &_break_jump);
alglib_impl::ae_serializer_init(&serializer);
alglib_impl::ae_serializer_alloc_start(&serializer);
alglib_impl::idwalloc(&serializer, obj.c_ptr(), &state);
ssize = alglib_impl::ae_serializer_get_alloc_size(&serializer);
s_out.clear();
s_out.reserve((size_t)(ssize+1));
alglib_impl::ae_serializer_sstart_str(&serializer, &s_out);
alglib_impl::idwserialize(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_stop(&serializer, &state);
alglib_impl::ae_assert( s_out.length()<=(size_t)ssize, "ALGLIB: serialization integrity error", &state);
alglib_impl::ae_serializer_clear(&serializer);
alglib_impl::ae_state_clear(&state);
}
/*************************************************************************
This function unserializes data structure from string.
*************************************************************************/
void idwunserialize(const std::string &s_in, idwmodel &obj)
{
jmp_buf _break_jump;
alglib_impl::ae_state state;
alglib_impl::ae_serializer serializer;
alglib_impl::ae_state_init(&state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&state, &_break_jump);
alglib_impl::ae_serializer_init(&serializer);
alglib_impl::ae_serializer_ustart_str(&serializer, &s_in);
alglib_impl::idwunserialize(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_stop(&serializer, &state);
alglib_impl::ae_serializer_clear(&serializer);
alglib_impl::ae_state_clear(&state);
}
/*************************************************************************
This function serializes data structure to C++ stream.
Data stream generated by this function is same as string representation
generated by string version of serializer - alphanumeric characters,
dots, underscores, minus signs, which are grouped into words separated by
spaces and CR+LF.
We recommend you to read comments on string version of serializer to find
out more about serialization of AlGLIB objects.
*************************************************************************/
void idwserialize(idwmodel &obj, std::ostream &s_out)
{
jmp_buf _break_jump;
alglib_impl::ae_state state;
alglib_impl::ae_serializer serializer;
alglib_impl::ae_state_init(&state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&state, &_break_jump);
alglib_impl::ae_serializer_init(&serializer);
alglib_impl::ae_serializer_alloc_start(&serializer);
alglib_impl::idwalloc(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_get_alloc_size(&serializer); // not actually needed, but we have to ask
alglib_impl::ae_serializer_sstart_stream(&serializer, &s_out);
alglib_impl::idwserialize(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_stop(&serializer, &state);
alglib_impl::ae_serializer_clear(&serializer);
alglib_impl::ae_state_clear(&state);
}
/*************************************************************************
This function unserializes data structure from stream.
*************************************************************************/
void idwunserialize(const std::istream &s_in, idwmodel &obj)
{
jmp_buf _break_jump;
alglib_impl::ae_state state;
alglib_impl::ae_serializer serializer;
alglib_impl::ae_state_init(&state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&state, &_break_jump);
alglib_impl::ae_serializer_init(&serializer);
alglib_impl::ae_serializer_ustart_stream(&serializer, &s_in);
alglib_impl::idwunserialize(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_stop(&serializer, &state);
alglib_impl::ae_serializer_clear(&serializer);
alglib_impl::ae_state_clear(&state);
}
/*************************************************************************
This function creates buffer structure which can be used to perform
parallel IDW model evaluations (with one IDW model instance being
used from multiple threads, as long as different threads use different
instances of buffer).
This buffer object can be used with idwtscalcbuf() function (here "ts"
stands for "thread-safe", "buf" is a suffix which denotes function which
reuses previously allocated output space).
How to use it:
* create IDW model structure or load it from file
* call idwcreatecalcbuffer(), once per thread working with IDW model (you
should call this function only AFTER model initialization, see below for
more information)
* call idwtscalcbuf() from different threads, with each thread working
with its own copy of buffer object.
INPUT PARAMETERS
S - IDW model
OUTPUT PARAMETERS
Buf - external buffer.
IMPORTANT: buffer object should be used only with IDW model object which
was used to initialize buffer. Any attempt to use buffer with
different object is dangerous - you may get memory violation
error because sizes of internal arrays do not fit to dimensions
of the IDW structure.
IMPORTANT: you should call this function only for model which was built
with model builder (or unserialized from file). Sizes of some
internal structures are determined only after model is built,
so buffer object created before model construction stage will
be useless (and any attempt to use it will result in exception).
-- ALGLIB --
Copyright 22.10.2018 by Sergey Bochkanov
*************************************************************************/
void idwcreatecalcbuffer(const idwmodel &s, idwcalcbuffer &buf, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwcreatecalcbuffer(const_cast<alglib_impl::idwmodel*>(s.c_ptr()), const_cast<alglib_impl::idwcalcbuffer*>(buf.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine creates builder object used to generate IDW model from
irregularly sampled (scattered) dataset. Multidimensional scalar/vector-
-valued are supported.
Builder object is used to fit model to data as follows:
* builder object is created with idwbuildercreate() function
* dataset is added with idwbuildersetpoints() function
* one of the modern IDW algorithms is chosen with either:
* idwbuildersetalgomstab() - Multilayer STABilized algorithm (interpolation)
Alternatively, one of the textbook algorithms can be chosen (not recommended):
* idwbuildersetalgotextbookshepard() - textbook Shepard algorithm
* idwbuildersetalgotextbookmodshepard()-textbook modified Shepard algorithm
* finally, model construction is performed with idwfit() function.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
NX - dimensionality of the argument, NX>=1
NY - dimensionality of the function being modeled, NY>=1;
NY=1 corresponds to classic scalar function, NY>=1 corresponds
to vector-valued function.
OUTPUT PARAMETERS:
State- builder object
-- ALGLIB PROJECT --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildercreate(const ae_int_t nx, const ae_int_t ny, idwbuilder &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwbuildercreate(nx, ny, const_cast<alglib_impl::idwbuilder*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function changes number of layers used by IDW-MSTAB algorithm.
The more layers you have, the finer details can be reproduced with IDW
model. The less layers you have, the less memory and CPU time is consumed
by the model.
Memory consumption grows linearly with layers count, running time grows
sub-linearly.
The default number of layers is 16, which allows you to reproduce details
at distance down to SRad/65536. You will rarely need to change it.
INPUT PARAMETERS:
State - builder object
NLayers - NLayers>=1, the number of layers used by the model.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetnlayers(const idwbuilder &state, const ae_int_t nlayers, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwbuildersetnlayers(const_cast<alglib_impl::idwbuilder*>(state.c_ptr()), nlayers, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function adds dataset to the builder object.
This function overrides results of the previous calls, i.e. multiple calls
of this function will result in only the last set being added.
INPUT PARAMETERS:
State - builder object
XY - points, array[N,NX+NY]. One row corresponds to one point
in the dataset. First NX elements are coordinates, next
NY elements are function values. Array may be larger than
specified, in this case only leading [N,NX+NY] elements
will be used.
N - number of points in the dataset, N>=0.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetpoints(const idwbuilder &state, const real_2d_array &xy, const ae_int_t n, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwbuildersetpoints(const_cast<alglib_impl::idwbuilder*>(state.c_ptr()), const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), n, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function adds dataset to the builder object.
This function overrides results of the previous calls, i.e. multiple calls
of this function will result in only the last set being added.
INPUT PARAMETERS:
State - builder object
XY - points, array[N,NX+NY]. One row corresponds to one point
in the dataset. First NX elements are coordinates, next
NY elements are function values. Array may be larger than
specified, in this case only leading [N,NX+NY] elements
will be used.
N - number of points in the dataset, N>=0.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void idwbuildersetpoints(const idwbuilder &state, const real_2d_array &xy, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
n = xy.rows();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwbuildersetpoints(const_cast<alglib_impl::idwbuilder*>(state.c_ptr()), const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), n, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This function sets IDW model construction algorithm to the Multilayer
Stabilized IDW method (IDW-MSTAB), a latest incarnation of the inverse
distance weighting interpolation which fixes shortcomings of the original
and modified Shepard's variants.
The distinctive features of IDW-MSTAB are:
1) exact interpolation is pursued (as opposed to fitting and noise
suppression)
2) improved robustness when compared with that of other algorithms:
* MSTAB shows almost no strange fitting artifacts like ripples and
sharp spikes (unlike N-dimensional splines and HRBFs)
* MSTAB does not return function values far from the interval spanned
by the dataset; say, if all your points have |f|<=1, you can be sure
that model value won't deviate too much from [-1,+1]
3) good model construction time competing with that of HRBFs and bicubic
splines
4) ability to work with any number of dimensions, starting from NX=1
The drawbacks of IDW-MSTAB (and all IDW algorithms in general) are:
1) dependence of the model evaluation time on the search radius
2) bad extrapolation properties, models built by this method are usually
conservative in their predictions
Thus, IDW-MSTAB is a good "default" option if you want to perform
scattered multidimensional interpolation. Although it has its drawbacks,
it is easy to use and robust, which makes it a good first step.
INPUT PARAMETERS:
State - builder object
SRad - initial search radius, SRad>0 is required. A model value
is obtained by "smart" averaging of the dataset points
within search radius.
NOTE 1: IDW interpolation can correctly handle ANY dataset, including
datasets with non-distinct points. In case non-distinct points are
found, an average value for this point will be calculated.
NOTE 2: the memory requirements for model storage are O(NPoints*NLayers).
The model construction needs twice as much memory as model storage.
NOTE 3: by default 16 IDW layers are built which is enough for most cases.
You can change this parameter with idwbuildersetnlayers() method.
Larger values may be necessary if you need to reproduce extrafine
details at distances smaller than SRad/65536. Smaller value may
be necessary if you have to save memory and computing time, and
ready to sacrifice some model quality.
ALGORITHM DESCRIPTION
ALGLIB implementation of IDW is somewhat similar to the modified Shepard's
method (one with search radius R) but overcomes several of its drawbacks,
namely:
1) a tendency to show stepwise behavior for uniform datasets
2) a tendency to show terrible interpolation properties for highly
nonuniform datasets which often arise in geospatial tasks
(function values are densely sampled across multiple separated
"tracks")
IDW-MSTAB method performs several passes over dataset and builds a sequence
of progressively refined IDW models (layers), which starts from one with
largest search radius SRad and continues to smaller search radii until
required number of layers is built. Highest layers reproduce global
behavior of the target function at larger distances whilst lower layers
reproduce fine details at smaller distances.
Each layer is an IDW model built with following modifications:
* weights go to zero when distance approach to the current search radius
* an additional regularizing term is added to the distance: w=1/(d^2+lambda)
* an additional fictional term with unit weight and zero function value is
added in order to promote continuity properties at the isolated and
boundary points
By default, 16 layers is built, which is enough for most cases. You can
change this parameter with idwbuildersetnlayers() method.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetalgomstab(const idwbuilder &state, const double srad, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwbuildersetalgomstab(const_cast<alglib_impl::idwbuilder*>(state.c_ptr()), srad, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets IDW model construction algorithm to the textbook
Shepard's algorithm with custom (user-specified) power parameter.
IMPORTANT: we do NOT recommend using textbook IDW algorithms because they
have terrible interpolation properties. Use MSTAB in all cases.
INPUT PARAMETERS:
State - builder object
P - power parameter, P>0; good value to start with is 2.0
NOTE 1: IDW interpolation can correctly handle ANY dataset, including
datasets with non-distinct points. In case non-distinct points are
found, an average value for this point will be calculated.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetalgotextbookshepard(const idwbuilder &state, const double p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwbuildersetalgotextbookshepard(const_cast<alglib_impl::idwbuilder*>(state.c_ptr()), p, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets IDW model construction algorithm to the 'textbook'
modified Shepard's algorithm with user-specified search radius.
IMPORTANT: we do NOT recommend using textbook IDW algorithms because they
have terrible interpolation properties. Use MSTAB in all cases.
INPUT PARAMETERS:
State - builder object
R - search radius
NOTE 1: IDW interpolation can correctly handle ANY dataset, including
datasets with non-distinct points. In case non-distinct points are
found, an average value for this point will be calculated.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetalgotextbookmodshepard(const idwbuilder &state, const double r, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwbuildersetalgotextbookmodshepard(const_cast<alglib_impl::idwbuilder*>(state.c_ptr()), r, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets prior term (model value at infinity) as user-specified
value.
INPUT PARAMETERS:
S - spline builder
V - value for user-defined prior
NOTE: for vector-valued models all components of the prior are set to same
user-specified value
-- ALGLIB --
Copyright 29.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetuserterm(const idwbuilder &state, const double v, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwbuildersetuserterm(const_cast<alglib_impl::idwbuilder*>(state.c_ptr()), v, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets constant prior term (model value at infinity).
Constant prior term is determined as mean value over dataset.
INPUT PARAMETERS:
S - spline builder
-- ALGLIB --
Copyright 29.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetconstterm(const idwbuilder &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwbuildersetconstterm(const_cast<alglib_impl::idwbuilder*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets zero prior term (model value at infinity).
INPUT PARAMETERS:
S - spline builder
-- ALGLIB --
Copyright 29.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetzeroterm(const idwbuilder &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwbuildersetzeroterm(const_cast<alglib_impl::idwbuilder*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
IDW interpolation: scalar target, 1-dimensional argument
NOTE: this function modifies internal temporaries of the IDW model, thus
IT IS NOT THREAD-SAFE! If you want to perform parallel model
evaluation from the multiple threads, use idwtscalcbuf() with per-
thread buffer object.
INPUT PARAMETERS:
S - IDW interpolant built with IDW builder
X0 - argument value
Result:
IDW interpolant S(X0)
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
double idwcalc1(const idwmodel &s, const double x0, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::idwcalc1(const_cast<alglib_impl::idwmodel*>(s.c_ptr()), x0, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
IDW interpolation: scalar target, 2-dimensional argument
NOTE: this function modifies internal temporaries of the IDW model, thus
IT IS NOT THREAD-SAFE! If you want to perform parallel model
evaluation from the multiple threads, use idwtscalcbuf() with per-
thread buffer object.
INPUT PARAMETERS:
S - IDW interpolant built with IDW builder
X0, X1 - argument value
Result:
IDW interpolant S(X0,X1)
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
double idwcalc2(const idwmodel &s, const double x0, const double x1, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::idwcalc2(const_cast<alglib_impl::idwmodel*>(s.c_ptr()), x0, x1, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
IDW interpolation: scalar target, 3-dimensional argument
NOTE: this function modifies internal temporaries of the IDW model, thus
IT IS NOT THREAD-SAFE! If you want to perform parallel model
evaluation from the multiple threads, use idwtscalcbuf() with per-
thread buffer object.
INPUT PARAMETERS:
S - IDW interpolant built with IDW builder
X0,X1,X2- argument value
Result:
IDW interpolant S(X0,X1,X2)
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
double idwcalc3(const idwmodel &s, const double x0, const double x1, const double x2, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::idwcalc3(const_cast<alglib_impl::idwmodel*>(s.c_ptr()), x0, x1, x2, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
This function calculates values of the IDW model at the given point.
This is general function which can be used for arbitrary NX (dimension of
the space of arguments) and NY (dimension of the function itself). However
when you have NY=1 you may find more convenient to use idwcalc1(),
idwcalc2() or idwcalc3().
NOTE: this function modifies internal temporaries of the IDW model, thus
IT IS NOT THREAD-SAFE! If you want to perform parallel model
evaluation from the multiple threads, use idwtscalcbuf() with per-
thread buffer object.
INPUT PARAMETERS:
S - IDW model
X - coordinates, array[NX]. X may have more than NX elements,
in this case only leading NX will be used.
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is out-parameter and will be
reallocated after call to this function. In case you want
to reuse previously allocated Y, you may use idwcalcbuf(),
which reallocates Y only when it is too small.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwcalc(const idwmodel &s, const real_1d_array &x, real_1d_array &y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwcalc(const_cast<alglib_impl::idwmodel*>(s.c_ptr()), const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates values of the IDW model at the given point.
Same as idwcalc(), but does not reallocate Y when in is large enough to
store function values.
NOTE: this function modifies internal temporaries of the IDW model, thus
IT IS NOT THREAD-SAFE! If you want to perform parallel model
evaluation from the multiple threads, use idwtscalcbuf() with per-
thread buffer object.
INPUT PARAMETERS:
S - IDW model
X - coordinates, array[NX]. X may have more than NX elements,
in this case only leading NX will be used.
Y - possibly preallocated array
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is not reallocated when it
is larger than NY.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwcalcbuf(const idwmodel &s, const real_1d_array &x, real_1d_array &y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwcalcbuf(const_cast<alglib_impl::idwmodel*>(s.c_ptr()), const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates values of the IDW model at the given point, using
external buffer object (internal temporaries of IDW model are not
modified).
This function allows to use same IDW model object in different threads,
assuming that different threads use different instances of the buffer
structure.
INPUT PARAMETERS:
S - IDW model, may be shared between different threads
Buf - buffer object created for this particular instance of IDW
model with idwcreatecalcbuffer().
X - coordinates, array[NX]. X may have more than NX elements,
in this case only leading NX will be used.
Y - possibly preallocated array
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is not reallocated when it
is larger than NY.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void idwtscalcbuf(const idwmodel &s, const idwcalcbuffer &buf, const real_1d_array &x, real_1d_array &y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwtscalcbuf(const_cast<alglib_impl::idwmodel*>(s.c_ptr()), const_cast<alglib_impl::idwcalcbuffer*>(buf.c_ptr()), const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function fits IDW model to the dataset using current IDW construction
algorithm. A model being built and fitting report are returned.
INPUT PARAMETERS:
State - builder object
OUTPUT PARAMETERS:
Model - an IDW model built with current algorithm
Rep - model fitting report, fields of this structure contain
information about average fitting errors.
NOTE: although IDW-MSTAB algorithm is an interpolation method, i.e. it
tries to fit the model exactly, it can handle datasets with non-
distinct points which can not be fit exactly; in such cases least-
squares fitting is performed.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwfit(const idwbuilder &state, idwmodel &model, idwreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::idwfit(const_cast<alglib_impl::idwbuilder*>(state.c_ptr()), const_cast<alglib_impl::idwmodel*>(model.c_ptr()), const_cast<alglib_impl::idwreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
#if defined(AE_COMPILE_RATINT) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Barycentric interpolant.
*************************************************************************/
_barycentricinterpolant_owner::_barycentricinterpolant_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_barycentricinterpolant_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::barycentricinterpolant*)alglib_impl::ae_malloc(sizeof(alglib_impl::barycentricinterpolant), &_state);
memset(p_struct, 0, sizeof(alglib_impl::barycentricinterpolant));
alglib_impl::_barycentricinterpolant_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_barycentricinterpolant_owner::_barycentricinterpolant_owner(const _barycentricinterpolant_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_barycentricinterpolant_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: barycentricinterpolant copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::barycentricinterpolant*)alglib_impl::ae_malloc(sizeof(alglib_impl::barycentricinterpolant), &_state);
memset(p_struct, 0, sizeof(alglib_impl::barycentricinterpolant));
alglib_impl::_barycentricinterpolant_init_copy(p_struct, const_cast<alglib_impl::barycentricinterpolant*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_barycentricinterpolant_owner& _barycentricinterpolant_owner::operator=(const _barycentricinterpolant_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: barycentricinterpolant assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: barycentricinterpolant assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_barycentricinterpolant_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::barycentricinterpolant));
alglib_impl::_barycentricinterpolant_init_copy(p_struct, const_cast<alglib_impl::barycentricinterpolant*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_barycentricinterpolant_owner::~_barycentricinterpolant_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_barycentricinterpolant_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::barycentricinterpolant* _barycentricinterpolant_owner::c_ptr()
{
return p_struct;
}
alglib_impl::barycentricinterpolant* _barycentricinterpolant_owner::c_ptr() const
{
return const_cast<alglib_impl::barycentricinterpolant*>(p_struct);
}
barycentricinterpolant::barycentricinterpolant() : _barycentricinterpolant_owner()
{
}
barycentricinterpolant::barycentricinterpolant(const barycentricinterpolant &rhs):_barycentricinterpolant_owner(rhs)
{
}
barycentricinterpolant& barycentricinterpolant::operator=(const barycentricinterpolant &rhs)
{
if( this==&rhs )
return *this;
_barycentricinterpolant_owner::operator=(rhs);
return *this;
}
barycentricinterpolant::~barycentricinterpolant()
{
}
/*************************************************************************
Rational interpolation using barycentric formula
F(t) = SUM(i=0,n-1,w[i]*f[i]/(t-x[i])) / SUM(i=0,n-1,w[i]/(t-x[i]))
Input parameters:
B - barycentric interpolant built with one of model building
subroutines.
T - interpolation point
Result:
barycentric interpolant F(t)
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
double barycentriccalc(const barycentricinterpolant &b, const double t, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::barycentriccalc(const_cast<alglib_impl::barycentricinterpolant*>(b.c_ptr()), t, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
Differentiation of barycentric interpolant: first derivative.
Algorithm used in this subroutine is very robust and should not fail until
provided with values too close to MaxRealNumber (usually MaxRealNumber/N
or greater will overflow).
INPUT PARAMETERS:
B - barycentric interpolant built with one of model building
subroutines.
T - interpolation point
OUTPUT PARAMETERS:
F - barycentric interpolant at T
DF - first derivative
NOTE
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentricdiff1(const barycentricinterpolant &b, const double t, double &f, double &df, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::barycentricdiff1(const_cast<alglib_impl::barycentricinterpolant*>(b.c_ptr()), t, &f, &df, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Differentiation of barycentric interpolant: first/second derivatives.
INPUT PARAMETERS:
B - barycentric interpolant built with one of model building
subroutines.
T - interpolation point
OUTPUT PARAMETERS:
F - barycentric interpolant at T
DF - first derivative
D2F - second derivative
NOTE: this algorithm may fail due to overflow/underflor if used on data
whose values are close to MaxRealNumber or MinRealNumber. Use more robust
BarycentricDiff1() subroutine in such cases.
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentricdiff2(const barycentricinterpolant &b, const double t, double &f, double &df, double &d2f, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::barycentricdiff2(const_cast<alglib_impl::barycentricinterpolant*>(b.c_ptr()), t, &f, &df, &d2f, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine performs linear transformation of the argument.
INPUT PARAMETERS:
B - rational interpolant in barycentric form
CA, CB - transformation coefficients: x = CA*t + CB
OUTPUT PARAMETERS:
B - transformed interpolant with X replaced by T
-- ALGLIB PROJECT --
Copyright 19.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentriclintransx(const barycentricinterpolant &b, const double ca, const double cb, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::barycentriclintransx(const_cast<alglib_impl::barycentricinterpolant*>(b.c_ptr()), ca, cb, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine performs linear transformation of the barycentric
interpolant.
INPUT PARAMETERS:
B - rational interpolant in barycentric form
CA, CB - transformation coefficients: B2(x) = CA*B(x) + CB
OUTPUT PARAMETERS:
B - transformed interpolant
-- ALGLIB PROJECT --
Copyright 19.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentriclintransy(const barycentricinterpolant &b, const double ca, const double cb, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::barycentriclintransy(const_cast<alglib_impl::barycentricinterpolant*>(b.c_ptr()), ca, cb, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Extracts X/Y/W arrays from rational interpolant
INPUT PARAMETERS:
B - barycentric interpolant
OUTPUT PARAMETERS:
N - nodes count, N>0
X - interpolation nodes, array[0..N-1]
F - function values, array[0..N-1]
W - barycentric weights, array[0..N-1]
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentricunpack(const barycentricinterpolant &b, ae_int_t &n, real_1d_array &x, real_1d_array &y, real_1d_array &w, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::barycentricunpack(const_cast<alglib_impl::barycentricinterpolant*>(b.c_ptr()), &n, const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Rational interpolant from X/Y/W arrays
F(t) = SUM(i=0,n-1,w[i]*f[i]/(t-x[i])) / SUM(i=0,n-1,w[i]/(t-x[i]))
INPUT PARAMETERS:
X - interpolation nodes, array[0..N-1]
F - function values, array[0..N-1]
W - barycentric weights, array[0..N-1]
N - nodes count, N>0
OUTPUT PARAMETERS:
B - barycentric interpolant built from (X, Y, W)
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentricbuildxyw(const real_1d_array &x, const real_1d_array &y, const real_1d_array &w, const ae_int_t n, barycentricinterpolant &b, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::barycentricbuildxyw(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), n, const_cast<alglib_impl::barycentricinterpolant*>(b.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Rational interpolant without poles
The subroutine constructs the rational interpolating function without real
poles (see 'Barycentric rational interpolation with no poles and high
rates of approximation', Michael S. Floater. and Kai Hormann, for more
information on this subject).
Input parameters:
X - interpolation nodes, array[0..N-1].
Y - function values, array[0..N-1].
N - number of nodes, N>0.
D - order of the interpolation scheme, 0 <= D <= N-1.
D<0 will cause an error.
D>=N it will be replaced with D=N-1.
if you don't know what D to choose, use small value about 3-5.
Output parameters:
B - barycentric interpolant.
Note:
this algorithm always succeeds and calculates the weights with close
to machine precision.
-- ALGLIB PROJECT --
Copyright 17.06.2007 by Bochkanov Sergey
*************************************************************************/
void barycentricbuildfloaterhormann(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t d, barycentricinterpolant &b, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::barycentricbuildfloaterhormann(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, d, const_cast<alglib_impl::barycentricinterpolant*>(b.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
#if defined(AE_COMPILE_FITSPHERE) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Fits least squares (LS) circle (or NX-dimensional sphere) to data (a set
of points in NX-dimensional space).
Least squares circle minimizes sum of squared deviations between distances
from points to the center and some "candidate" radius, which is also
fitted to the data.
INPUT PARAMETERS:
XY - array[NPoints,NX] (or larger), contains dataset.
One row = one point in NX-dimensional space.
NPoints - dataset size, NPoints>0
NX - space dimensionality, NX>0 (1, 2, 3, 4, 5 and so on)
OUTPUT PARAMETERS:
CX - central point for a sphere
R - radius
-- ALGLIB --
Copyright 07.05.2018 by Bochkanov Sergey
*************************************************************************/
void fitspherels(const real_2d_array &xy, const ae_int_t npoints, const ae_int_t nx, real_1d_array &cx, double &r, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::fitspherels(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), npoints, nx, const_cast<alglib_impl::ae_vector*>(cx.c_ptr()), &r, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Fits minimum circumscribed (MC) circle (or NX-dimensional sphere) to data
(a set of points in NX-dimensional space).
INPUT PARAMETERS:
XY - array[NPoints,NX] (or larger), contains dataset.
One row = one point in NX-dimensional space.
NPoints - dataset size, NPoints>0
NX - space dimensionality, NX>0 (1, 2, 3, 4, 5 and so on)
OUTPUT PARAMETERS:
CX - central point for a sphere
RHi - radius
NOTE: this function is an easy-to-use wrapper around more powerful "expert"
function fitspherex().
This wrapper is optimized for ease of use and stability - at the
cost of somewhat lower performance (we have to use very tight
stopping criteria for inner optimizer because we want to make sure
that it will converge on any dataset).
If you are ready to experiment with settings of "expert" function,
you can achieve ~2-4x speedup over standard "bulletproof" settings.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void fitspheremc(const real_2d_array &xy, const ae_int_t npoints, const ae_int_t nx, real_1d_array &cx, double &rhi, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::fitspheremc(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), npoints, nx, const_cast<alglib_impl::ae_vector*>(cx.c_ptr()), &rhi, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Fits maximum inscribed circle (or NX-dimensional sphere) to data (a set of
points in NX-dimensional space).
INPUT PARAMETERS:
XY - array[NPoints,NX] (or larger), contains dataset.
One row = one point in NX-dimensional space.
NPoints - dataset size, NPoints>0
NX - space dimensionality, NX>0 (1, 2, 3, 4, 5 and so on)
OUTPUT PARAMETERS:
CX - central point for a sphere
RLo - radius
NOTE: this function is an easy-to-use wrapper around more powerful "expert"
function fitspherex().
This wrapper is optimized for ease of use and stability - at the
cost of somewhat lower performance (we have to use very tight
stopping criteria for inner optimizer because we want to make sure
that it will converge on any dataset).
If you are ready to experiment with settings of "expert" function,
you can achieve ~2-4x speedup over standard "bulletproof" settings.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void fitspheremi(const real_2d_array &xy, const ae_int_t npoints, const ae_int_t nx, real_1d_array &cx, double &rlo, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::fitspheremi(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), npoints, nx, const_cast<alglib_impl::ae_vector*>(cx.c_ptr()), &rlo, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Fits minimum zone circle (or NX-dimensional sphere) to data (a set of
points in NX-dimensional space).
INPUT PARAMETERS:
XY - array[NPoints,NX] (or larger), contains dataset.
One row = one point in NX-dimensional space.
NPoints - dataset size, NPoints>0
NX - space dimensionality, NX>0 (1, 2, 3, 4, 5 and so on)
OUTPUT PARAMETERS:
CX - central point for a sphere
RLo - radius of inscribed circle
RHo - radius of circumscribed circle
NOTE: this function is an easy-to-use wrapper around more powerful "expert"
function fitspherex().
This wrapper is optimized for ease of use and stability - at the
cost of somewhat lower performance (we have to use very tight
stopping criteria for inner optimizer because we want to make sure
that it will converge on any dataset).
If you are ready to experiment with settings of "expert" function,
you can achieve ~2-4x speedup over standard "bulletproof" settings.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void fitspheremz(const real_2d_array &xy, const ae_int_t npoints, const ae_int_t nx, real_1d_array &cx, double &rlo, double &rhi, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::fitspheremz(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), npoints, nx, const_cast<alglib_impl::ae_vector*>(cx.c_ptr()), &rlo, &rhi, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Fitting minimum circumscribed, maximum inscribed or minimum zone circles
(or NX-dimensional spheres) to data (a set of points in NX-dimensional
space).
This is expert function which allows to tweak many parameters of
underlying nonlinear solver:
* stopping criteria for inner iterations
* number of outer iterations
* penalty coefficient used to handle nonlinear constraints (we convert
unconstrained nonsmooth optimization problem ivolving max() and/or min()
operations to quadratically constrained smooth one).
You may tweak all these parameters or only some of them, leaving other
ones at their default state - just specify zero value, and solver will
fill it with appropriate default one.
These comments also include some discussion of approach used to handle
such unusual fitting problem, its stability, drawbacks of alternative
methods, and convergence properties.
INPUT PARAMETERS:
XY - array[NPoints,NX] (or larger), contains dataset.
One row = one point in NX-dimensional space.
NPoints - dataset size, NPoints>0
NX - space dimensionality, NX>0 (1, 2, 3, 4, 5 and so on)
ProblemType-used to encode problem type:
* 0 for least squares circle
* 1 for minimum circumscribed circle/sphere fitting (MC)
* 2 for maximum inscribed circle/sphere fitting (MI)
* 3 for minimum zone circle fitting (difference between
Rhi and Rlo is minimized), denoted as MZ
EpsX - stopping condition for NLC optimizer:
* must be non-negative
* use 0 to choose default value (1.0E-12 is used by default)
* you may specify larger values, up to 1.0E-6, if you want
to speed-up solver; NLC solver performs several
preconditioned outer iterations, so final result
typically has precision much better than EpsX.
AULIts - number of outer iterations performed by NLC optimizer:
* must be non-negative
* use 0 to choose default value (20 is used by default)
* you may specify values smaller than 20 if you want to
speed up solver; 10 often results in good combination of
precision and speed; sometimes you may get good results
with just 6 outer iterations.
Ignored for ProblemType=0.
Penalty - penalty coefficient for NLC optimizer:
* must be non-negative
* use 0 to choose default value (1.0E6 in current version)
* it should be really large, 1.0E6...1.0E7 is a good value
to start from;
* generally, default value is good enough
Ignored for ProblemType=0.
OUTPUT PARAMETERS:
CX - central point for a sphere
RLo - radius:
* for ProblemType=2,3, radius of the inscribed sphere
* for ProblemType=0 - radius of the least squares sphere
* for ProblemType=1 - zero
RHo - radius:
* for ProblemType=1,3, radius of the circumscribed sphere
* for ProblemType=0 - radius of the least squares sphere
* for ProblemType=2 - zero
NOTE: ON THE UNIQUENESS OF SOLUTIONS
ALGLIB provides solution to several related circle fitting problems: MC
(minimum circumscribed), MI (maximum inscribed) and MZ (minimum zone)
fitting, LS (least squares) fitting.
It is important to note that among these problems only MC and LS are
convex and have unique solution independently from starting point.
As for MI, it may (or may not, depending on dataset properties) have
multiple solutions, and it always has one degenerate solution C=infinity
which corresponds to infinitely large radius. Thus, there are no guarantees
that solution to MI returned by this solver will be the best one (and no
one can provide you with such guarantee because problem is NP-hard). The
only guarantee you have is that this solution is locally optimal, i.e. it
can not be improved by infinitesimally small tweaks in the parameters.
It is also possible to "run away" to infinity when started from bad
initial point located outside of point cloud (or when point cloud does not
span entire circumference/surface of the sphere).
Finally, MZ (minimum zone circle) stands somewhere between MC and MI in
stability. It is somewhat regularized by "circumscribed" term of the merit
function; however, solutions to MZ may be non-unique, and in some unlucky
cases it is also possible to "run away to infinity".
NOTE: ON THE NONLINEARLY CONSTRAINED PROGRAMMING APPROACH
The problem formulation for MC (minimum circumscribed circle; for the
sake of simplicity we omit MZ and MI here) is:
[ [ ]2 ]
min [ max [ XY[i]-C ] ]
C [ i [ ] ]
i.e. it is unconstrained nonsmooth optimization problem of finding "best"
central point, with radius R being unambiguously determined from C. In
order to move away from non-smoothness we use following reformulation:
[ ] [ ]2
min [ R ] subject to R>=0, [ XY[i]-C ] <= R^2
C,R [ ] [ ]
i.e. it becomes smooth quadratically constrained optimization problem with
linear target function. Such problem statement is 100% equivalent to the
original nonsmooth one, but much easier to approach. We solve it with
MinNLC solver provided by ALGLIB.
NOTE: ON INSTABILITY OF SEQUENTIAL LINEARIZATION APPROACH
ALGLIB has nonlinearly constrained solver which proved to be stable on
such problems. However, some authors proposed to linearize constraints in
the vicinity of current approximation (Ci,Ri) and to get next approximate
solution (Ci+1,Ri+1) as solution to linear programming problem. Obviously,
LP problems are easier than nonlinearly constrained ones.
Indeed, such approach to MC/MI/MZ resulted in ~10-20x increase in
performance (when compared with NLC solver). However, it turned out that
in some cases linearized model fails to predict correct direction for next
step and tells us that we converged to solution even when we are still 2-4
digits of precision away from it.
It is important that it is not failure of LP solver - it is failure of the
linear model; even when solved exactly, it fails to handle subtle
nonlinearities which arise near the solution. We validated it by comparing
results returned by ALGLIB linear solver with that of MATLAB.
In our experiments with linearization:
* MC failed most often, at both realistic and synthetic datasets
* MI sometimes failed, but sometimes succeeded
* MZ often succeeded; our guess is that presence of two independent sets
of constraints (one set for Rlo and another one for Rhi) and two terms
in the target function (Rlo and Rhi) regularizes task, so when linear
model fails to handle nonlinearities from Rlo, it uses Rhi as a hint
(and vice versa).
Because linearization approach failed to achieve stable results, we do not
include it in ALGLIB.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void fitspherex(const real_2d_array &xy, const ae_int_t npoints, const ae_int_t nx, const ae_int_t problemtype, const double epsx, const ae_int_t aulits, const double penalty, real_1d_array &cx, double &rlo, double &rhi, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::fitspherex(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), npoints, nx, problemtype, epsx, aulits, penalty, const_cast<alglib_impl::ae_vector*>(cx.c_ptr()), &rlo, &rhi, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
#if defined(AE_COMPILE_INTFITSERV) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_SPLINE1D) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
1-dimensional spline interpolant
*************************************************************************/
_spline1dinterpolant_owner::_spline1dinterpolant_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_spline1dinterpolant_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::spline1dinterpolant*)alglib_impl::ae_malloc(sizeof(alglib_impl::spline1dinterpolant), &_state);
memset(p_struct, 0, sizeof(alglib_impl::spline1dinterpolant));
alglib_impl::_spline1dinterpolant_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_spline1dinterpolant_owner::_spline1dinterpolant_owner(const _spline1dinterpolant_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_spline1dinterpolant_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: spline1dinterpolant copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::spline1dinterpolant*)alglib_impl::ae_malloc(sizeof(alglib_impl::spline1dinterpolant), &_state);
memset(p_struct, 0, sizeof(alglib_impl::spline1dinterpolant));
alglib_impl::_spline1dinterpolant_init_copy(p_struct, const_cast<alglib_impl::spline1dinterpolant*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_spline1dinterpolant_owner& _spline1dinterpolant_owner::operator=(const _spline1dinterpolant_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: spline1dinterpolant assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: spline1dinterpolant assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_spline1dinterpolant_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::spline1dinterpolant));
alglib_impl::_spline1dinterpolant_init_copy(p_struct, const_cast<alglib_impl::spline1dinterpolant*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_spline1dinterpolant_owner::~_spline1dinterpolant_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_spline1dinterpolant_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::spline1dinterpolant* _spline1dinterpolant_owner::c_ptr()
{
return p_struct;
}
alglib_impl::spline1dinterpolant* _spline1dinterpolant_owner::c_ptr() const
{
return const_cast<alglib_impl::spline1dinterpolant*>(p_struct);
}
spline1dinterpolant::spline1dinterpolant() : _spline1dinterpolant_owner()
{
}
spline1dinterpolant::spline1dinterpolant(const spline1dinterpolant &rhs):_spline1dinterpolant_owner(rhs)
{
}
spline1dinterpolant& spline1dinterpolant::operator=(const spline1dinterpolant &rhs)
{
if( this==&rhs )
return *this;
_spline1dinterpolant_owner::operator=(rhs);
return *this;
}
spline1dinterpolant::~spline1dinterpolant()
{
}
/*************************************************************************
Spline fitting report:
RMSError RMS error
AvgError average error
AvgRelError average relative error (for non-zero Y[I])
MaxError maximum error
Fields below are filled by obsolete functions (Spline1DFitCubic,
Spline1DFitHermite). Modern fitting functions do NOT fill these fields:
TaskRCond reciprocal of task's condition number
*************************************************************************/
_spline1dfitreport_owner::_spline1dfitreport_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_spline1dfitreport_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::spline1dfitreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::spline1dfitreport), &_state);
memset(p_struct, 0, sizeof(alglib_impl::spline1dfitreport));
alglib_impl::_spline1dfitreport_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_spline1dfitreport_owner::_spline1dfitreport_owner(const _spline1dfitreport_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_spline1dfitreport_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: spline1dfitreport copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::spline1dfitreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::spline1dfitreport), &_state);
memset(p_struct, 0, sizeof(alglib_impl::spline1dfitreport));
alglib_impl::_spline1dfitreport_init_copy(p_struct, const_cast<alglib_impl::spline1dfitreport*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_spline1dfitreport_owner& _spline1dfitreport_owner::operator=(const _spline1dfitreport_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: spline1dfitreport assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: spline1dfitreport assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_spline1dfitreport_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::spline1dfitreport));
alglib_impl::_spline1dfitreport_init_copy(p_struct, const_cast<alglib_impl::spline1dfitreport*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_spline1dfitreport_owner::~_spline1dfitreport_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_spline1dfitreport_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::spline1dfitreport* _spline1dfitreport_owner::c_ptr()
{
return p_struct;
}
alglib_impl::spline1dfitreport* _spline1dfitreport_owner::c_ptr() const
{
return const_cast<alglib_impl::spline1dfitreport*>(p_struct);
}
spline1dfitreport::spline1dfitreport() : _spline1dfitreport_owner() ,taskrcond(p_struct->taskrcond),rmserror(p_struct->rmserror),avgerror(p_struct->avgerror),avgrelerror(p_struct->avgrelerror),maxerror(p_struct->maxerror)
{
}
spline1dfitreport::spline1dfitreport(const spline1dfitreport &rhs):_spline1dfitreport_owner(rhs) ,taskrcond(p_struct->taskrcond),rmserror(p_struct->rmserror),avgerror(p_struct->avgerror),avgrelerror(p_struct->avgrelerror),maxerror(p_struct->maxerror)
{
}
spline1dfitreport& spline1dfitreport::operator=(const spline1dfitreport &rhs)
{
if( this==&rhs )
return *this;
_spline1dfitreport_owner::operator=(rhs);
return *this;
}
spline1dfitreport::~spline1dfitreport()
{
}
/*************************************************************************
This subroutine builds linear spline interpolant
INPUT PARAMETERS:
X - spline nodes, array[0..N-1]
Y - function values, array[0..N-1]
N - points count (optional):
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
OUTPUT PARAMETERS:
C - spline interpolant
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
-- ALGLIB PROJECT --
Copyright 24.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dbuildlinear(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, spline1dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dbuildlinear(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine builds linear spline interpolant
INPUT PARAMETERS:
X - spline nodes, array[0..N-1]
Y - function values, array[0..N-1]
N - points count (optional):
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
OUTPUT PARAMETERS:
C - spline interpolant
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
-- ALGLIB PROJECT --
Copyright 24.06.2007 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dbuildlinear(const real_1d_array &x, const real_1d_array &y, spline1dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dbuildlinear': looks like one of arguments has wrong size");
n = x.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dbuildlinear(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This subroutine builds cubic spline interpolant.
INPUT PARAMETERS:
X - spline nodes, array[0..N-1].
Y - function values, array[0..N-1].
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
OUTPUT PARAMETERS:
C - spline interpolant
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dbuildcubic(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t boundltype, const double boundl, const ae_int_t boundrtype, const double boundr, spline1dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dbuildcubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, boundltype, boundl, boundrtype, boundr, const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine builds cubic spline interpolant.
INPUT PARAMETERS:
X - spline nodes, array[0..N-1].
Y - function values, array[0..N-1].
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
OUTPUT PARAMETERS:
C - spline interpolant
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dbuildcubic(const real_1d_array &x, const real_1d_array &y, spline1dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t boundltype;
double boundl;
ae_int_t boundrtype;
double boundr;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dbuildcubic': looks like one of arguments has wrong size");
n = x.length();
boundltype = 0;
boundl = 0;
boundrtype = 0;
boundr = 0;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dbuildcubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, boundltype, boundl, boundrtype, boundr, const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This function solves following problem: given table y[] of function values
at nodes x[], it calculates and returns table of function derivatives d[]
(calculated at the same nodes x[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - spline nodes
Y - function values
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
OUTPUT PARAMETERS:
D - derivative values at X[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Derivative values are correctly reordered on return, so D[I] is always
equal to S'(X[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
void spline1dgriddiffcubic(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t boundltype, const double boundl, const ae_int_t boundrtype, const double boundr, real_1d_array &d, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dgriddiffcubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, boundltype, boundl, boundrtype, boundr, const_cast<alglib_impl::ae_vector*>(d.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function solves following problem: given table y[] of function values
at nodes x[], it calculates and returns table of function derivatives d[]
(calculated at the same nodes x[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - spline nodes
Y - function values
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
OUTPUT PARAMETERS:
D - derivative values at X[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Derivative values are correctly reordered on return, so D[I] is always
equal to S'(X[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dgriddiffcubic(const real_1d_array &x, const real_1d_array &y, real_1d_array &d, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t boundltype;
double boundl;
ae_int_t boundrtype;
double boundr;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dgriddiffcubic': looks like one of arguments has wrong size");
n = x.length();
boundltype = 0;
boundl = 0;
boundrtype = 0;
boundr = 0;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dgriddiffcubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, boundltype, boundl, boundrtype, boundr, const_cast<alglib_impl::ae_vector*>(d.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This function solves following problem: given table y[] of function values
at nodes x[], it calculates and returns tables of first and second
function derivatives d1[] and d2[] (calculated at the same nodes x[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - spline nodes
Y - function values
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
OUTPUT PARAMETERS:
D1 - S' values at X[]
D2 - S'' values at X[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Derivative values are correctly reordered on return, so D[I] is always
equal to S'(X[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
void spline1dgriddiff2cubic(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t boundltype, const double boundl, const ae_int_t boundrtype, const double boundr, real_1d_array &d1, real_1d_array &d2, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dgriddiff2cubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, boundltype, boundl, boundrtype, boundr, const_cast<alglib_impl::ae_vector*>(d1.c_ptr()), const_cast<alglib_impl::ae_vector*>(d2.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function solves following problem: given table y[] of function values
at nodes x[], it calculates and returns tables of first and second
function derivatives d1[] and d2[] (calculated at the same nodes x[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - spline nodes
Y - function values
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
OUTPUT PARAMETERS:
D1 - S' values at X[]
D2 - S'' values at X[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Derivative values are correctly reordered on return, so D[I] is always
equal to S'(X[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dgriddiff2cubic(const real_1d_array &x, const real_1d_array &y, real_1d_array &d1, real_1d_array &d2, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t boundltype;
double boundl;
ae_int_t boundrtype;
double boundr;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dgriddiff2cubic': looks like one of arguments has wrong size");
n = x.length();
boundltype = 0;
boundl = 0;
boundrtype = 0;
boundr = 0;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dgriddiff2cubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, boundltype, boundl, boundrtype, boundr, const_cast<alglib_impl::ae_vector*>(d1.c_ptr()), const_cast<alglib_impl::ae_vector*>(d2.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This function solves following problem: given table y[] of function values
at old nodes x[] and new nodes x2[], it calculates and returns table of
function values y2[] (calculated at x2[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - old spline nodes
Y - function values
X2 - new spline nodes
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points from X/Y are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
N2 - new points count:
* N2>=2
* if given, only first N2 points from X2 are used
* if not given, automatically detected from X2 size
OUTPUT PARAMETERS:
F2 - function values at X2[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Function values are correctly reordered on return, so F2[I] is always
equal to S(X2[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
void spline1dconvcubic(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t boundltype, const double boundl, const ae_int_t boundrtype, const double boundr, const real_1d_array &x2, const ae_int_t n2, real_1d_array &y2, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dconvcubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, boundltype, boundl, boundrtype, boundr, const_cast<alglib_impl::ae_vector*>(x2.c_ptr()), n2, const_cast<alglib_impl::ae_vector*>(y2.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function solves following problem: given table y[] of function values
at old nodes x[] and new nodes x2[], it calculates and returns table of
function values y2[] (calculated at x2[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - old spline nodes
Y - function values
X2 - new spline nodes
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points from X/Y are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
N2 - new points count:
* N2>=2
* if given, only first N2 points from X2 are used
* if not given, automatically detected from X2 size
OUTPUT PARAMETERS:
F2 - function values at X2[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Function values are correctly reordered on return, so F2[I] is always
equal to S(X2[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dconvcubic(const real_1d_array &x, const real_1d_array &y, const real_1d_array &x2, real_1d_array &y2, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t boundltype;
double boundl;
ae_int_t boundrtype;
double boundr;
ae_int_t n2;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dconvcubic': looks like one of arguments has wrong size");
n = x.length();
boundltype = 0;
boundl = 0;
boundrtype = 0;
boundr = 0;
n2 = x2.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dconvcubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, boundltype, boundl, boundrtype, boundr, const_cast<alglib_impl::ae_vector*>(x2.c_ptr()), n2, const_cast<alglib_impl::ae_vector*>(y2.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This function solves following problem: given table y[] of function values
at old nodes x[] and new nodes x2[], it calculates and returns table of
function values y2[] and derivatives d2[] (calculated at x2[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - old spline nodes
Y - function values
X2 - new spline nodes
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points from X/Y are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
N2 - new points count:
* N2>=2
* if given, only first N2 points from X2 are used
* if not given, automatically detected from X2 size
OUTPUT PARAMETERS:
F2 - function values at X2[]
D2 - first derivatives at X2[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Function values are correctly reordered on return, so F2[I] is always
equal to S(X2[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
void spline1dconvdiffcubic(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t boundltype, const double boundl, const ae_int_t boundrtype, const double boundr, const real_1d_array &x2, const ae_int_t n2, real_1d_array &y2, real_1d_array &d2, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dconvdiffcubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, boundltype, boundl, boundrtype, boundr, const_cast<alglib_impl::ae_vector*>(x2.c_ptr()), n2, const_cast<alglib_impl::ae_vector*>(y2.c_ptr()), const_cast<alglib_impl::ae_vector*>(d2.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function solves following problem: given table y[] of function values
at old nodes x[] and new nodes x2[], it calculates and returns table of
function values y2[] and derivatives d2[] (calculated at x2[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - old spline nodes
Y - function values
X2 - new spline nodes
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points from X/Y are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
N2 - new points count:
* N2>=2
* if given, only first N2 points from X2 are used
* if not given, automatically detected from X2 size
OUTPUT PARAMETERS:
F2 - function values at X2[]
D2 - first derivatives at X2[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Function values are correctly reordered on return, so F2[I] is always
equal to S(X2[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dconvdiffcubic(const real_1d_array &x, const real_1d_array &y, const real_1d_array &x2, real_1d_array &y2, real_1d_array &d2, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t boundltype;
double boundl;
ae_int_t boundrtype;
double boundr;
ae_int_t n2;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dconvdiffcubic': looks like one of arguments has wrong size");
n = x.length();
boundltype = 0;
boundl = 0;
boundrtype = 0;
boundr = 0;
n2 = x2.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dconvdiffcubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, boundltype, boundl, boundrtype, boundr, const_cast<alglib_impl::ae_vector*>(x2.c_ptr()), n2, const_cast<alglib_impl::ae_vector*>(y2.c_ptr()), const_cast<alglib_impl::ae_vector*>(d2.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This function solves following problem: given table y[] of function values
at old nodes x[] and new nodes x2[], it calculates and returns table of
function values y2[], first and second derivatives d2[] and dd2[]
(calculated at x2[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - old spline nodes
Y - function values
X2 - new spline nodes
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points from X/Y are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
N2 - new points count:
* N2>=2
* if given, only first N2 points from X2 are used
* if not given, automatically detected from X2 size
OUTPUT PARAMETERS:
F2 - function values at X2[]
D2 - first derivatives at X2[]
DD2 - second derivatives at X2[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Function values are correctly reordered on return, so F2[I] is always
equal to S(X2[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
void spline1dconvdiff2cubic(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t boundltype, const double boundl, const ae_int_t boundrtype, const double boundr, const real_1d_array &x2, const ae_int_t n2, real_1d_array &y2, real_1d_array &d2, real_1d_array &dd2, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dconvdiff2cubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, boundltype, boundl, boundrtype, boundr, const_cast<alglib_impl::ae_vector*>(x2.c_ptr()), n2, const_cast<alglib_impl::ae_vector*>(y2.c_ptr()), const_cast<alglib_impl::ae_vector*>(d2.c_ptr()), const_cast<alglib_impl::ae_vector*>(dd2.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function solves following problem: given table y[] of function values
at old nodes x[] and new nodes x2[], it calculates and returns table of
function values y2[], first and second derivatives d2[] and dd2[]
(calculated at x2[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - old spline nodes
Y - function values
X2 - new spline nodes
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points from X/Y are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
N2 - new points count:
* N2>=2
* if given, only first N2 points from X2 are used
* if not given, automatically detected from X2 size
OUTPUT PARAMETERS:
F2 - function values at X2[]
D2 - first derivatives at X2[]
DD2 - second derivatives at X2[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Function values are correctly reordered on return, so F2[I] is always
equal to S(X2[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dconvdiff2cubic(const real_1d_array &x, const real_1d_array &y, const real_1d_array &x2, real_1d_array &y2, real_1d_array &d2, real_1d_array &dd2, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t boundltype;
double boundl;
ae_int_t boundrtype;
double boundr;
ae_int_t n2;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dconvdiff2cubic': looks like one of arguments has wrong size");
n = x.length();
boundltype = 0;
boundl = 0;
boundrtype = 0;
boundr = 0;
n2 = x2.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dconvdiff2cubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, boundltype, boundl, boundrtype, boundr, const_cast<alglib_impl::ae_vector*>(x2.c_ptr()), n2, const_cast<alglib_impl::ae_vector*>(y2.c_ptr()), const_cast<alglib_impl::ae_vector*>(d2.c_ptr()), const_cast<alglib_impl::ae_vector*>(dd2.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This subroutine builds Catmull-Rom spline interpolant.
INPUT PARAMETERS:
X - spline nodes, array[0..N-1].
Y - function values, array[0..N-1].
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundType - boundary condition type:
* -1 for periodic boundary condition
* 0 for parabolically terminated spline (default)
Tension - tension parameter:
* tension=0 corresponds to classic Catmull-Rom spline (default)
* 0<tension<1 corresponds to more general form - cardinal spline
OUTPUT PARAMETERS:
C - spline interpolant
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dbuildcatmullrom(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t boundtype, const double tension, spline1dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dbuildcatmullrom(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, boundtype, tension, const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine builds Catmull-Rom spline interpolant.
INPUT PARAMETERS:
X - spline nodes, array[0..N-1].
Y - function values, array[0..N-1].
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundType - boundary condition type:
* -1 for periodic boundary condition
* 0 for parabolically terminated spline (default)
Tension - tension parameter:
* tension=0 corresponds to classic Catmull-Rom spline (default)
* 0<tension<1 corresponds to more general form - cardinal spline
OUTPUT PARAMETERS:
C - spline interpolant
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dbuildcatmullrom(const real_1d_array &x, const real_1d_array &y, spline1dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t boundtype;
double tension;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dbuildcatmullrom': looks like one of arguments has wrong size");
n = x.length();
boundtype = 0;
tension = 0;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dbuildcatmullrom(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, boundtype, tension, const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This subroutine builds Hermite spline interpolant.
INPUT PARAMETERS:
X - spline nodes, array[0..N-1]
Y - function values, array[0..N-1]
D - derivatives, array[0..N-1]
N - points count (optional):
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
OUTPUT PARAMETERS:
C - spline interpolant.
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
-- ALGLIB PROJECT --
Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dbuildhermite(const real_1d_array &x, const real_1d_array &y, const real_1d_array &d, const ae_int_t n, spline1dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dbuildhermite(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(d.c_ptr()), n, const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine builds Hermite spline interpolant.
INPUT PARAMETERS:
X - spline nodes, array[0..N-1]
Y - function values, array[0..N-1]
D - derivatives, array[0..N-1]
N - points count (optional):
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
OUTPUT PARAMETERS:
C - spline interpolant.
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
-- ALGLIB PROJECT --
Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dbuildhermite(const real_1d_array &x, const real_1d_array &y, const real_1d_array &d, spline1dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
if( (x.length()!=y.length()) || (x.length()!=d.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dbuildhermite': looks like one of arguments has wrong size");
n = x.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dbuildhermite(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(d.c_ptr()), n, const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This subroutine builds Akima spline interpolant
INPUT PARAMETERS:
X - spline nodes, array[0..N-1]
Y - function values, array[0..N-1]
N - points count (optional):
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
OUTPUT PARAMETERS:
C - spline interpolant
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
-- ALGLIB PROJECT --
Copyright 24.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dbuildakima(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, spline1dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dbuildakima(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine builds Akima spline interpolant
INPUT PARAMETERS:
X - spline nodes, array[0..N-1]
Y - function values, array[0..N-1]
N - points count (optional):
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
OUTPUT PARAMETERS:
C - spline interpolant
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
-- ALGLIB PROJECT --
Copyright 24.06.2007 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dbuildakima(const real_1d_array &x, const real_1d_array &y, spline1dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dbuildakima': looks like one of arguments has wrong size");
n = x.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dbuildakima(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This subroutine calculates the value of the spline at the given point X.
INPUT PARAMETERS:
C - spline interpolant
X - point
Result:
S(x)
-- ALGLIB PROJECT --
Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
double spline1dcalc(const spline1dinterpolant &c, const double x, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::spline1dcalc(const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), x, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
This subroutine differentiates the spline.
INPUT PARAMETERS:
C - spline interpolant.
X - point
Result:
S - S(x)
DS - S'(x)
D2S - S''(x)
-- ALGLIB PROJECT --
Copyright 24.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1ddiff(const spline1dinterpolant &c, const double x, double &s, double &ds, double &d2s, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1ddiff(const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), x, &s, &ds, &d2s, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine unpacks the spline into the coefficients table.
INPUT PARAMETERS:
C - spline interpolant.
X - point
OUTPUT PARAMETERS:
Tbl - coefficients table, unpacked format, array[0..N-2, 0..5].
For I = 0...N-2:
Tbl[I,0] = X[i]
Tbl[I,1] = X[i+1]
Tbl[I,2] = C0
Tbl[I,3] = C1
Tbl[I,4] = C2
Tbl[I,5] = C3
On [x[i], x[i+1]] spline is equals to:
S(x) = C0 + C1*t + C2*t^2 + C3*t^3
t = x-x[i]
NOTE:
You can rebuild spline with Spline1DBuildHermite() function, which
accepts as inputs function values and derivatives at nodes, which are
easy to calculate when you have coefficients.
-- ALGLIB PROJECT --
Copyright 29.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dunpack(const spline1dinterpolant &c, ae_int_t &n, real_2d_array &tbl, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dunpack(const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), &n, const_cast<alglib_impl::ae_matrix*>(tbl.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine performs linear transformation of the spline argument.
INPUT PARAMETERS:
C - spline interpolant.
A, B- transformation coefficients: x = A*t + B
Result:
C - transformed spline
-- ALGLIB PROJECT --
Copyright 30.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dlintransx(const spline1dinterpolant &c, const double a, const double b, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dlintransx(const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), a, b, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine performs linear transformation of the spline.
INPUT PARAMETERS:
C - spline interpolant.
A, B- transformation coefficients: S2(x) = A*S(x) + B
Result:
C - transformed spline
-- ALGLIB PROJECT --
Copyright 30.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dlintransy(const spline1dinterpolant &c, const double a, const double b, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dlintransy(const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), a, b, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine integrates the spline.
INPUT PARAMETERS:
C - spline interpolant.
X - right bound of the integration interval [a, x],
here 'a' denotes min(x[])
Result:
integral(S(t)dt,a,x)
-- ALGLIB PROJECT --
Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
double spline1dintegrate(const spline1dinterpolant &c, const double x, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::spline1dintegrate(const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), x, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
Fitting by smoothing (penalized) cubic spline.
This function approximates N scattered points (some of X[] may be equal to
each other) by cubic spline with M nodes at equidistant grid spanning
interval [min(x,xc),max(x,xc)].
The problem is regularized by adding nonlinearity penalty to usual least
squares penalty function:
MERIT_FUNC = F_LS + F_NL
where F_LS is a least squares error term, and F_NL is a nonlinearity
penalty which is roughly proportional to LambdaNS*integral{ S''(x)^2*dx }.
Algorithm applies automatic renormalization of F_NL which makes penalty
term roughly invariant to scaling of X[] and changes in M.
This function is a new edition of penalized regression spline fitting,
a fast and compact one which needs much less resources that its previous
version: just O(maxMN) memory and O(maxMN*log(maxMN)) time.
NOTE: it is OK to run this function with both M<<N and M>>N; say, it is
possible to process 100 points with 1000-node spline.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
N - number of points (optional):
* N>0
* if given, only first N elements of X/Y are processed
* if not given, automatically determined from lengths
M - number of basis functions ( = number_of_nodes), M>=4.
LambdaNS - LambdaNS>=0, regularization constant passed by user.
It penalizes nonlinearity in the regression spline.
Possible values to start from are 0.00001, 0.1, 1
OUTPUT PARAMETERS:
S - spline interpolant.
Rep - Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
-- ALGLIB PROJECT --
Copyright 27.08.2019 by Bochkanov Sergey
*************************************************************************/
void spline1dfit(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t m, const double lambdans, spline1dinterpolant &s, spline1dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dfit(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, m, lambdans, const_cast<alglib_impl::spline1dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline1dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Fitting by smoothing (penalized) cubic spline.
This function approximates N scattered points (some of X[] may be equal to
each other) by cubic spline with M nodes at equidistant grid spanning
interval [min(x,xc),max(x,xc)].
The problem is regularized by adding nonlinearity penalty to usual least
squares penalty function:
MERIT_FUNC = F_LS + F_NL
where F_LS is a least squares error term, and F_NL is a nonlinearity
penalty which is roughly proportional to LambdaNS*integral{ S''(x)^2*dx }.
Algorithm applies automatic renormalization of F_NL which makes penalty
term roughly invariant to scaling of X[] and changes in M.
This function is a new edition of penalized regression spline fitting,
a fast and compact one which needs much less resources that its previous
version: just O(maxMN) memory and O(maxMN*log(maxMN)) time.
NOTE: it is OK to run this function with both M<<N and M>>N; say, it is
possible to process 100 points with 1000-node spline.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
N - number of points (optional):
* N>0
* if given, only first N elements of X/Y are processed
* if not given, automatically determined from lengths
M - number of basis functions ( = number_of_nodes), M>=4.
LambdaNS - LambdaNS>=0, regularization constant passed by user.
It penalizes nonlinearity in the regression spline.
Possible values to start from are 0.00001, 0.1, 1
OUTPUT PARAMETERS:
S - spline interpolant.
Rep - Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
-- ALGLIB PROJECT --
Copyright 27.08.2019 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dfit(const real_1d_array &x, const real_1d_array &y, const ae_int_t m, const double lambdans, spline1dinterpolant &s, spline1dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dfit': looks like one of arguments has wrong size");
n = x.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dfit(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, m, lambdans, const_cast<alglib_impl::spline1dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline1dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This function builds monotone cubic Hermite interpolant. This interpolant
is monotonic in [x(0),x(n-1)] and is constant outside of this interval.
In case y[] form non-monotonic sequence, interpolant is piecewise
monotonic. Say, for x=(0,1,2,3,4) and y=(0,1,2,1,0) interpolant will
monotonically grow at [0..2] and monotonically decrease at [2..4].
INPUT PARAMETERS:
X - spline nodes, array[0..N-1]. Subroutine automatically
sorts points, so caller may pass unsorted array.
Y - function values, array[0..N-1]
N - the number of points(N>=2).
OUTPUT PARAMETERS:
C - spline interpolant.
-- ALGLIB PROJECT --
Copyright 21.06.2012 by Bochkanov Sergey
*************************************************************************/
void spline1dbuildmonotone(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, spline1dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dbuildmonotone(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function builds monotone cubic Hermite interpolant. This interpolant
is monotonic in [x(0),x(n-1)] and is constant outside of this interval.
In case y[] form non-monotonic sequence, interpolant is piecewise
monotonic. Say, for x=(0,1,2,3,4) and y=(0,1,2,1,0) interpolant will
monotonically grow at [0..2] and monotonically decrease at [2..4].
INPUT PARAMETERS:
X - spline nodes, array[0..N-1]. Subroutine automatically
sorts points, so caller may pass unsorted array.
Y - function values, array[0..N-1]
N - the number of points(N>=2).
OUTPUT PARAMETERS:
C - spline interpolant.
-- ALGLIB PROJECT --
Copyright 21.06.2012 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dbuildmonotone(const real_1d_array &x, const real_1d_array &y, spline1dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dbuildmonotone': looks like one of arguments has wrong size");
n = x.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dbuildmonotone(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::spline1dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
#endif
#if defined(AE_COMPILE_PARAMETRIC) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Parametric spline inteprolant: 2-dimensional curve.
You should not try to access its members directly - use PSpline2XXXXXXXX()
functions instead.
*************************************************************************/
_pspline2interpolant_owner::_pspline2interpolant_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_pspline2interpolant_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::pspline2interpolant*)alglib_impl::ae_malloc(sizeof(alglib_impl::pspline2interpolant), &_state);
memset(p_struct, 0, sizeof(alglib_impl::pspline2interpolant));
alglib_impl::_pspline2interpolant_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_pspline2interpolant_owner::_pspline2interpolant_owner(const _pspline2interpolant_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_pspline2interpolant_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: pspline2interpolant copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::pspline2interpolant*)alglib_impl::ae_malloc(sizeof(alglib_impl::pspline2interpolant), &_state);
memset(p_struct, 0, sizeof(alglib_impl::pspline2interpolant));
alglib_impl::_pspline2interpolant_init_copy(p_struct, const_cast<alglib_impl::pspline2interpolant*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_pspline2interpolant_owner& _pspline2interpolant_owner::operator=(const _pspline2interpolant_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: pspline2interpolant assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: pspline2interpolant assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_pspline2interpolant_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::pspline2interpolant));
alglib_impl::_pspline2interpolant_init_copy(p_struct, const_cast<alglib_impl::pspline2interpolant*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_pspline2interpolant_owner::~_pspline2interpolant_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_pspline2interpolant_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::pspline2interpolant* _pspline2interpolant_owner::c_ptr()
{
return p_struct;
}
alglib_impl::pspline2interpolant* _pspline2interpolant_owner::c_ptr() const
{
return const_cast<alglib_impl::pspline2interpolant*>(p_struct);
}
pspline2interpolant::pspline2interpolant() : _pspline2interpolant_owner()
{
}
pspline2interpolant::pspline2interpolant(const pspline2interpolant &rhs):_pspline2interpolant_owner(rhs)
{
}
pspline2interpolant& pspline2interpolant::operator=(const pspline2interpolant &rhs)
{
if( this==&rhs )
return *this;
_pspline2interpolant_owner::operator=(rhs);
return *this;
}
pspline2interpolant::~pspline2interpolant()
{
}
/*************************************************************************
Parametric spline inteprolant: 3-dimensional curve.
You should not try to access its members directly - use PSpline3XXXXXXXX()
functions instead.
*************************************************************************/
_pspline3interpolant_owner::_pspline3interpolant_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_pspline3interpolant_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::pspline3interpolant*)alglib_impl::ae_malloc(sizeof(alglib_impl::pspline3interpolant), &_state);
memset(p_struct, 0, sizeof(alglib_impl::pspline3interpolant));
alglib_impl::_pspline3interpolant_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_pspline3interpolant_owner::_pspline3interpolant_owner(const _pspline3interpolant_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_pspline3interpolant_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: pspline3interpolant copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::pspline3interpolant*)alglib_impl::ae_malloc(sizeof(alglib_impl::pspline3interpolant), &_state);
memset(p_struct, 0, sizeof(alglib_impl::pspline3interpolant));
alglib_impl::_pspline3interpolant_init_copy(p_struct, const_cast<alglib_impl::pspline3interpolant*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_pspline3interpolant_owner& _pspline3interpolant_owner::operator=(const _pspline3interpolant_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: pspline3interpolant assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: pspline3interpolant assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_pspline3interpolant_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::pspline3interpolant));
alglib_impl::_pspline3interpolant_init_copy(p_struct, const_cast<alglib_impl::pspline3interpolant*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_pspline3interpolant_owner::~_pspline3interpolant_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_pspline3interpolant_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::pspline3interpolant* _pspline3interpolant_owner::c_ptr()
{
return p_struct;
}
alglib_impl::pspline3interpolant* _pspline3interpolant_owner::c_ptr() const
{
return const_cast<alglib_impl::pspline3interpolant*>(p_struct);
}
pspline3interpolant::pspline3interpolant() : _pspline3interpolant_owner()
{
}
pspline3interpolant::pspline3interpolant(const pspline3interpolant &rhs):_pspline3interpolant_owner(rhs)
{
}
pspline3interpolant& pspline3interpolant::operator=(const pspline3interpolant &rhs)
{
if( this==&rhs )
return *this;
_pspline3interpolant_owner::operator=(rhs);
return *this;
}
pspline3interpolant::~pspline3interpolant()
{
}
/*************************************************************************
This function builds non-periodic 2-dimensional parametric spline which
starts at (X[0],Y[0]) and ends at (X[N-1],Y[N-1]).
INPUT PARAMETERS:
XY - points, array[0..N-1,0..1].
XY[I,0:1] corresponds to the Ith point.
Order of points is important!
N - points count, N>=5 for Akima splines, N>=2 for other types of
splines.
ST - spline type:
* 0 Akima spline
* 1 parabolically terminated Catmull-Rom spline (Tension=0)
* 2 parabolically terminated cubic spline
PT - parameterization type:
* 0 uniform
* 1 chord length
* 2 centripetal
OUTPUT PARAMETERS:
P - parametric spline interpolant
NOTES:
* this function assumes that there all consequent points are distinct.
I.e. (x0,y0)<>(x1,y1), (x1,y1)<>(x2,y2), (x2,y2)<>(x3,y3) and so on.
However, non-consequent points may coincide, i.e. we can have (x0,y0)=
=(x2,y2).
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline2build(const real_2d_array &xy, const ae_int_t n, const ae_int_t st, const ae_int_t pt, pspline2interpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::pspline2build(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), n, st, pt, const_cast<alglib_impl::pspline2interpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function builds non-periodic 3-dimensional parametric spline which
starts at (X[0],Y[0],Z[0]) and ends at (X[N-1],Y[N-1],Z[N-1]).
Same as PSpline2Build() function, but for 3D, so we won't duplicate its
description here.
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline3build(const real_2d_array &xy, const ae_int_t n, const ae_int_t st, const ae_int_t pt, pspline3interpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::pspline3build(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), n, st, pt, const_cast<alglib_impl::pspline3interpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function builds periodic 2-dimensional parametric spline which
starts at (X[0],Y[0]), goes through all points to (X[N-1],Y[N-1]) and then
back to (X[0],Y[0]).
INPUT PARAMETERS:
XY - points, array[0..N-1,0..1].
XY[I,0:1] corresponds to the Ith point.
XY[N-1,0:1] must be different from XY[0,0:1].
Order of points is important!
N - points count, N>=3 for other types of splines.
ST - spline type:
* 1 Catmull-Rom spline (Tension=0) with cyclic boundary conditions
* 2 cubic spline with cyclic boundary conditions
PT - parameterization type:
* 0 uniform
* 1 chord length
* 2 centripetal
OUTPUT PARAMETERS:
P - parametric spline interpolant
NOTES:
* this function assumes that there all consequent points are distinct.
I.e. (x0,y0)<>(x1,y1), (x1,y1)<>(x2,y2), (x2,y2)<>(x3,y3) and so on.
However, non-consequent points may coincide, i.e. we can have (x0,y0)=
=(x2,y2).
* last point of sequence is NOT equal to the first point. You shouldn't
make curve "explicitly periodic" by making them equal.
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline2buildperiodic(const real_2d_array &xy, const ae_int_t n, const ae_int_t st, const ae_int_t pt, pspline2interpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::pspline2buildperiodic(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), n, st, pt, const_cast<alglib_impl::pspline2interpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function builds periodic 3-dimensional parametric spline which
starts at (X[0],Y[0],Z[0]), goes through all points to (X[N-1],Y[N-1],Z[N-1])
and then back to (X[0],Y[0],Z[0]).
Same as PSpline2Build() function, but for 3D, so we won't duplicate its
description here.
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline3buildperiodic(const real_2d_array &xy, const ae_int_t n, const ae_int_t st, const ae_int_t pt, pspline3interpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::pspline3buildperiodic(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), n, st, pt, const_cast<alglib_impl::pspline3interpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function returns vector of parameter values correspoding to points.
I.e. for P created from (X[0],Y[0])...(X[N-1],Y[N-1]) and U=TValues(P) we
have
(X[0],Y[0]) = PSpline2Calc(P,U[0]),
(X[1],Y[1]) = PSpline2Calc(P,U[1]),
(X[2],Y[2]) = PSpline2Calc(P,U[2]),
...
INPUT PARAMETERS:
P - parametric spline interpolant
OUTPUT PARAMETERS:
N - array size
T - array[0..N-1]
NOTES:
* for non-periodic splines U[0]=0, U[0]<U[1]<...<U[N-1], U[N-1]=1
* for periodic splines U[0]=0, U[0]<U[1]<...<U[N-1], U[N-1]<1
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline2parametervalues(const pspline2interpolant &p, ae_int_t &n, real_1d_array &t, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::pspline2parametervalues(const_cast<alglib_impl::pspline2interpolant*>(p.c_ptr()), &n, const_cast<alglib_impl::ae_vector*>(t.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function returns vector of parameter values correspoding to points.
Same as PSpline2ParameterValues(), but for 3D.
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline3parametervalues(const pspline3interpolant &p, ae_int_t &n, real_1d_array &t, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::pspline3parametervalues(const_cast<alglib_impl::pspline3interpolant*>(p.c_ptr()), &n, const_cast<alglib_impl::ae_vector*>(t.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates the value of the parametric spline for a given
value of parameter T
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-position
Y - Y-position
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline2calc(const pspline2interpolant &p, const double t, double &x, double &y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::pspline2calc(const_cast<alglib_impl::pspline2interpolant*>(p.c_ptr()), t, &x, &y, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates the value of the parametric spline for a given
value of parameter T.
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-position
Y - Y-position
Z - Z-position
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline3calc(const pspline3interpolant &p, const double t, double &x, double &y, double &z, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::pspline3calc(const_cast<alglib_impl::pspline3interpolant*>(p.c_ptr()), t, &x, &y, &z, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates tangent vector for a given value of parameter T
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-component of tangent vector (normalized)
Y - Y-component of tangent vector (normalized)
NOTE:
X^2+Y^2 is either 1 (for non-zero tangent vector) or 0.
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline2tangent(const pspline2interpolant &p, const double t, double &x, double &y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::pspline2tangent(const_cast<alglib_impl::pspline2interpolant*>(p.c_ptr()), t, &x, &y, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates tangent vector for a given value of parameter T
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-component of tangent vector (normalized)
Y - Y-component of tangent vector (normalized)
Z - Z-component of tangent vector (normalized)
NOTE:
X^2+Y^2+Z^2 is either 1 (for non-zero tangent vector) or 0.
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline3tangent(const pspline3interpolant &p, const double t, double &x, double &y, double &z, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::pspline3tangent(const_cast<alglib_impl::pspline3interpolant*>(p.c_ptr()), t, &x, &y, &z, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates derivative, i.e. it returns (dX/dT,dY/dT).
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-value
DX - X-derivative
Y - Y-value
DY - Y-derivative
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline2diff(const pspline2interpolant &p, const double t, double &x, double &dx, double &y, double &dy, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::pspline2diff(const_cast<alglib_impl::pspline2interpolant*>(p.c_ptr()), t, &x, &dx, &y, &dy, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates derivative, i.e. it returns (dX/dT,dY/dT,dZ/dT).
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-value
DX - X-derivative
Y - Y-value
DY - Y-derivative
Z - Z-value
DZ - Z-derivative
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline3diff(const pspline3interpolant &p, const double t, double &x, double &dx, double &y, double &dy, double &z, double &dz, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::pspline3diff(const_cast<alglib_impl::pspline3interpolant*>(p.c_ptr()), t, &x, &dx, &y, &dy, &z, &dz, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates first and second derivative with respect to T.
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-value
DX - derivative
D2X - second derivative
Y - Y-value
DY - derivative
D2Y - second derivative
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline2diff2(const pspline2interpolant &p, const double t, double &x, double &dx, double &d2x, double &y, double &dy, double &d2y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::pspline2diff2(const_cast<alglib_impl::pspline2interpolant*>(p.c_ptr()), t, &x, &dx, &d2x, &y, &dy, &d2y, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates first and second derivative with respect to T.
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-value
DX - derivative
D2X - second derivative
Y - Y-value
DY - derivative
D2Y - second derivative
Z - Z-value
DZ - derivative
D2Z - second derivative
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline3diff2(const pspline3interpolant &p, const double t, double &x, double &dx, double &d2x, double &y, double &dy, double &d2y, double &z, double &dz, double &d2z, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::pspline3diff2(const_cast<alglib_impl::pspline3interpolant*>(p.c_ptr()), t, &x, &dx, &d2x, &y, &dy, &d2y, &z, &dz, &d2z, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates arc length, i.e. length of curve between t=a
and t=b.
INPUT PARAMETERS:
P - parametric spline interpolant
A,B - parameter values corresponding to arc ends:
* B>A will result in positive length returned
* B<A will result in negative length returned
RESULT:
length of arc starting at T=A and ending at T=B.
-- ALGLIB PROJECT --
Copyright 30.05.2010 by Bochkanov Sergey
*************************************************************************/
double pspline2arclength(const pspline2interpolant &p, const double a, const double b, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::pspline2arclength(const_cast<alglib_impl::pspline2interpolant*>(p.c_ptr()), a, b, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
This function calculates arc length, i.e. length of curve between t=a
and t=b.
INPUT PARAMETERS:
P - parametric spline interpolant
A,B - parameter values corresponding to arc ends:
* B>A will result in positive length returned
* B<A will result in negative length returned
RESULT:
length of arc starting at T=A and ending at T=B.
-- ALGLIB PROJECT --
Copyright 30.05.2010 by Bochkanov Sergey
*************************************************************************/
double pspline3arclength(const pspline3interpolant &p, const double a, const double b, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::pspline3arclength(const_cast<alglib_impl::pspline3interpolant*>(p.c_ptr()), a, b, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
This subroutine fits piecewise linear curve to points with Ramer-Douglas-
Peucker algorithm. This function performs PARAMETRIC fit, i.e. it can be
used to fit curves like circles.
On input it accepts dataset which describes parametric multidimensional
curve X(t), with X being vector, and t taking values in [0,N), where N is
a number of points in dataset. As result, it returns reduced dataset X2,
which can be used to build parametric curve X2(t), which approximates
X(t) with desired precision (or has specified number of sections).
INPUT PARAMETERS:
X - array of multidimensional points:
* at least N elements, leading N elements are used if more
than N elements were specified
* order of points is IMPORTANT because it is parametric
fit
* each row of array is one point which has D coordinates
N - number of elements in X
D - number of dimensions (elements per row of X)
StopM - stopping condition - desired number of sections:
* at most M sections are generated by this function
* less than M sections can be generated if we have N<M
(or some X are non-distinct).
* zero StopM means that algorithm does not stop after
achieving some pre-specified section count
StopEps - stopping condition - desired precision:
* algorithm stops after error in each section is at most Eps
* zero Eps means that algorithm does not stop after
achieving some pre-specified precision
OUTPUT PARAMETERS:
X2 - array of corner points for piecewise approximation,
has length NSections+1 or zero (for NSections=0).
Idx2 - array of indexes (parameter values):
* has length NSections+1 or zero (for NSections=0).
* each element of Idx2 corresponds to same-numbered
element of X2
* each element of Idx2 is index of corresponding element
of X2 at original array X, i.e. I-th row of X2 is
Idx2[I]-th row of X.
* elements of Idx2 can be treated as parameter values
which should be used when building new parametric curve
* Idx2[0]=0, Idx2[NSections]=N-1
NSections- number of sections found by algorithm, NSections<=M,
NSections can be zero for degenerate datasets
(N<=1 or all X[] are non-distinct).
NOTE: algorithm stops after:
a) dividing curve into StopM sections
b) achieving required precision StopEps
c) dividing curve into N-1 sections
If both StopM and StopEps are non-zero, algorithm is stopped by the
FIRST criterion which is satisfied. In case both StopM and StopEps
are zero, algorithm stops because of (c).
-- ALGLIB --
Copyright 02.10.2014 by Bochkanov Sergey
*************************************************************************/
void parametricrdpfixed(const real_2d_array &x, const ae_int_t n, const ae_int_t d, const ae_int_t stopm, const double stopeps, real_2d_array &x2, integer_1d_array &idx2, ae_int_t &nsections, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::parametricrdpfixed(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), n, d, stopm, stopeps, const_cast<alglib_impl::ae_matrix*>(x2.c_ptr()), const_cast<alglib_impl::ae_vector*>(idx2.c_ptr()), &nsections, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
#if defined(AE_COMPILE_SPLINE3D) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
3-dimensional spline inteprolant
*************************************************************************/
_spline3dinterpolant_owner::_spline3dinterpolant_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_spline3dinterpolant_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::spline3dinterpolant*)alglib_impl::ae_malloc(sizeof(alglib_impl::spline3dinterpolant), &_state);
memset(p_struct, 0, sizeof(alglib_impl::spline3dinterpolant));
alglib_impl::_spline3dinterpolant_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_spline3dinterpolant_owner::_spline3dinterpolant_owner(const _spline3dinterpolant_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_spline3dinterpolant_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: spline3dinterpolant copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::spline3dinterpolant*)alglib_impl::ae_malloc(sizeof(alglib_impl::spline3dinterpolant), &_state);
memset(p_struct, 0, sizeof(alglib_impl::spline3dinterpolant));
alglib_impl::_spline3dinterpolant_init_copy(p_struct, const_cast<alglib_impl::spline3dinterpolant*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_spline3dinterpolant_owner& _spline3dinterpolant_owner::operator=(const _spline3dinterpolant_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: spline3dinterpolant assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: spline3dinterpolant assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_spline3dinterpolant_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::spline3dinterpolant));
alglib_impl::_spline3dinterpolant_init_copy(p_struct, const_cast<alglib_impl::spline3dinterpolant*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_spline3dinterpolant_owner::~_spline3dinterpolant_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_spline3dinterpolant_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::spline3dinterpolant* _spline3dinterpolant_owner::c_ptr()
{
return p_struct;
}
alglib_impl::spline3dinterpolant* _spline3dinterpolant_owner::c_ptr() const
{
return const_cast<alglib_impl::spline3dinterpolant*>(p_struct);
}
spline3dinterpolant::spline3dinterpolant() : _spline3dinterpolant_owner()
{
}
spline3dinterpolant::spline3dinterpolant(const spline3dinterpolant &rhs):_spline3dinterpolant_owner(rhs)
{
}
spline3dinterpolant& spline3dinterpolant::operator=(const spline3dinterpolant &rhs)
{
if( this==&rhs )
return *this;
_spline3dinterpolant_owner::operator=(rhs);
return *this;
}
spline3dinterpolant::~spline3dinterpolant()
{
}
/*************************************************************************
This subroutine calculates the value of the trilinear or tricubic spline at
the given point (X,Y,Z).
INPUT PARAMETERS:
C - coefficients table.
Built by BuildBilinearSpline or BuildBicubicSpline.
X, Y,
Z - point
Result:
S(x,y,z)
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
double spline3dcalc(const spline3dinterpolant &c, const double x, const double y, const double z, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::spline3dcalc(const_cast<alglib_impl::spline3dinterpolant*>(c.c_ptr()), x, y, z, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
This subroutine performs linear transformation of the spline argument.
INPUT PARAMETERS:
C - spline interpolant
AX, BX - transformation coefficients: x = A*u + B
AY, BY - transformation coefficients: y = A*v + B
AZ, BZ - transformation coefficients: z = A*w + B
OUTPUT PARAMETERS:
C - transformed spline
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline3dlintransxyz(const spline3dinterpolant &c, const double ax, const double bx, const double ay, const double by, const double az, const double bz, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline3dlintransxyz(const_cast<alglib_impl::spline3dinterpolant*>(c.c_ptr()), ax, bx, ay, by, az, bz, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine performs linear transformation of the spline.
INPUT PARAMETERS:
C - spline interpolant.
A, B- transformation coefficients: S2(x,y) = A*S(x,y,z) + B
OUTPUT PARAMETERS:
C - transformed spline
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline3dlintransf(const spline3dinterpolant &c, const double a, const double b, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline3dlintransf(const_cast<alglib_impl::spline3dinterpolant*>(c.c_ptr()), a, b, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Trilinear spline resampling
INPUT PARAMETERS:
A - array[0..OldXCount*OldYCount*OldZCount-1], function
values at the old grid, :
A[0] x=0,y=0,z=0
A[1] x=1,y=0,z=0
A[..] ...
A[..] x=oldxcount-1,y=0,z=0
A[..] x=0,y=1,z=0
A[..] ...
...
OldZCount - old Z-count, OldZCount>1
OldYCount - old Y-count, OldYCount>1
OldXCount - old X-count, OldXCount>1
NewZCount - new Z-count, NewZCount>1
NewYCount - new Y-count, NewYCount>1
NewXCount - new X-count, NewXCount>1
OUTPUT PARAMETERS:
B - array[0..NewXCount*NewYCount*NewZCount-1], function
values at the new grid:
B[0] x=0,y=0,z=0
B[1] x=1,y=0,z=0
B[..] ...
B[..] x=newxcount-1,y=0,z=0
B[..] x=0,y=1,z=0
B[..] ...
...
-- ALGLIB routine --
26.04.2012
Copyright by Bochkanov Sergey
*************************************************************************/
void spline3dresampletrilinear(const real_1d_array &a, const ae_int_t oldzcount, const ae_int_t oldycount, const ae_int_t oldxcount, const ae_int_t newzcount, const ae_int_t newycount, const ae_int_t newxcount, real_1d_array &b, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline3dresampletrilinear(const_cast<alglib_impl::ae_vector*>(a.c_ptr()), oldzcount, oldycount, oldxcount, newzcount, newycount, newxcount, const_cast<alglib_impl::ae_vector*>(b.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine builds trilinear vector-valued spline.
INPUT PARAMETERS:
X - spline abscissas, array[0..N-1]
Y - spline ordinates, array[0..M-1]
Z - spline applicates, array[0..L-1]
F - function values, array[0..M*N*L*D-1]:
* first D elements store D values at (X[0],Y[0],Z[0])
* next D elements store D values at (X[1],Y[0],Z[0])
* next D elements store D values at (X[2],Y[0],Z[0])
* ...
* next D elements store D values at (X[0],Y[1],Z[0])
* next D elements store D values at (X[1],Y[1],Z[0])
* next D elements store D values at (X[2],Y[1],Z[0])
* ...
* next D elements store D values at (X[0],Y[0],Z[1])
* next D elements store D values at (X[1],Y[0],Z[1])
* next D elements store D values at (X[2],Y[0],Z[1])
* ...
* general form - D function values at (X[i],Y[j]) are stored
at F[D*(N*(M*K+J)+I)...D*(N*(M*K+J)+I)+D-1].
M,N,
L - grid size, M>=2, N>=2, L>=2
D - vector dimension, D>=1
OUTPUT PARAMETERS:
C - spline interpolant
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline3dbuildtrilinearv(const real_1d_array &x, const ae_int_t n, const real_1d_array &y, const ae_int_t m, const real_1d_array &z, const ae_int_t l, const real_1d_array &f, const ae_int_t d, spline3dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline3dbuildtrilinearv(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), m, const_cast<alglib_impl::ae_vector*>(z.c_ptr()), l, const_cast<alglib_impl::ae_vector*>(f.c_ptr()), d, const_cast<alglib_impl::spline3dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine calculates bilinear or bicubic vector-valued spline at the
given point (X,Y,Z).
INPUT PARAMETERS:
C - spline interpolant.
X, Y,
Z - point
F - output buffer, possibly preallocated array. In case array size
is large enough to store result, it is not reallocated. Array
which is too short will be reallocated
OUTPUT PARAMETERS:
F - array[D] (or larger) which stores function values
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline3dcalcvbuf(const spline3dinterpolant &c, const double x, const double y, const double z, real_1d_array &f, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline3dcalcvbuf(const_cast<alglib_impl::spline3dinterpolant*>(c.c_ptr()), x, y, z, const_cast<alglib_impl::ae_vector*>(f.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine calculates trilinear or tricubic vector-valued spline at the
given point (X,Y,Z).
INPUT PARAMETERS:
C - spline interpolant.
X, Y,
Z - point
OUTPUT PARAMETERS:
F - array[D] which stores function values. F is out-parameter and
it is reallocated after call to this function. In case you
want to reuse previously allocated F, you may use
Spline2DCalcVBuf(), which reallocates F only when it is too
small.
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline3dcalcv(const spline3dinterpolant &c, const double x, const double y, const double z, real_1d_array &f, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline3dcalcv(const_cast<alglib_impl::spline3dinterpolant*>(c.c_ptr()), x, y, z, const_cast<alglib_impl::ae_vector*>(f.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine unpacks tri-dimensional spline into the coefficients table
INPUT PARAMETERS:
C - spline interpolant.
Result:
N - grid size (X)
M - grid size (Y)
L - grid size (Z)
D - number of components
SType- spline type. Currently, only one spline type is supported:
trilinear spline, as indicated by SType=1.
Tbl - spline coefficients: [0..(N-1)*(M-1)*(L-1)*D-1, 0..13].
For T=0..D-1 (component index), I = 0...N-2 (x index),
J=0..M-2 (y index), K=0..L-2 (z index):
Q := T + I*D + J*D*(N-1) + K*D*(N-1)*(M-1),
Q-th row stores decomposition for T-th component of the
vector-valued function
Tbl[Q,0] = X[i]
Tbl[Q,1] = X[i+1]
Tbl[Q,2] = Y[j]
Tbl[Q,3] = Y[j+1]
Tbl[Q,4] = Z[k]
Tbl[Q,5] = Z[k+1]
Tbl[Q,6] = C000
Tbl[Q,7] = C100
Tbl[Q,8] = C010
Tbl[Q,9] = C110
Tbl[Q,10]= C001
Tbl[Q,11]= C101
Tbl[Q,12]= C011
Tbl[Q,13]= C111
On each grid square spline is equals to:
S(x) = SUM(c[i,j,k]*(x^i)*(y^j)*(z^k), i=0..1, j=0..1, k=0..1)
t = x-x[j]
u = y-y[i]
v = z-z[k]
NOTE: format of Tbl is given for SType=1. Future versions of
ALGLIB can use different formats for different values of
SType.
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline3dunpackv(const spline3dinterpolant &c, ae_int_t &n, ae_int_t &m, ae_int_t &l, ae_int_t &d, ae_int_t &stype, real_2d_array &tbl, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline3dunpackv(const_cast<alglib_impl::spline3dinterpolant*>(c.c_ptr()), &n, &m, &l, &d, &stype, const_cast<alglib_impl::ae_matrix*>(tbl.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
#if defined(AE_COMPILE_POLINT) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Conversion from barycentric representation to Chebyshev basis.
This function has O(N^2) complexity.
INPUT PARAMETERS:
P - polynomial in barycentric form
A,B - base interval for Chebyshev polynomials (see below)
A<>B
OUTPUT PARAMETERS
T - coefficients of Chebyshev representation;
P(x) = sum { T[i]*Ti(2*(x-A)/(B-A)-1), i=0..N-1 },
where Ti - I-th Chebyshev polynomial.
NOTES:
barycentric interpolant passed as P may be either polynomial obtained
from polynomial interpolation/ fitting or rational function which is
NOT polynomial. We can't distinguish between these two cases, and this
algorithm just tries to work assuming that P IS a polynomial. If not,
algorithm will return results, but they won't have any meaning.
-- ALGLIB --
Copyright 30.09.2010 by Bochkanov Sergey
*************************************************************************/
void polynomialbar2cheb(const barycentricinterpolant &p, const double a, const double b, real_1d_array &t, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialbar2cheb(const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), a, b, const_cast<alglib_impl::ae_vector*>(t.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Conversion from Chebyshev basis to barycentric representation.
This function has O(N^2) complexity.
INPUT PARAMETERS:
T - coefficients of Chebyshev representation;
P(x) = sum { T[i]*Ti(2*(x-A)/(B-A)-1), i=0..N },
where Ti - I-th Chebyshev polynomial.
N - number of coefficients:
* if given, only leading N elements of T are used
* if not given, automatically determined from size of T
A,B - base interval for Chebyshev polynomials (see above)
A<B
OUTPUT PARAMETERS
P - polynomial in barycentric form
-- ALGLIB --
Copyright 30.09.2010 by Bochkanov Sergey
*************************************************************************/
void polynomialcheb2bar(const real_1d_array &t, const ae_int_t n, const double a, const double b, barycentricinterpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialcheb2bar(const_cast<alglib_impl::ae_vector*>(t.c_ptr()), n, a, b, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Conversion from Chebyshev basis to barycentric representation.
This function has O(N^2) complexity.
INPUT PARAMETERS:
T - coefficients of Chebyshev representation;
P(x) = sum { T[i]*Ti(2*(x-A)/(B-A)-1), i=0..N },
where Ti - I-th Chebyshev polynomial.
N - number of coefficients:
* if given, only leading N elements of T are used
* if not given, automatically determined from size of T
A,B - base interval for Chebyshev polynomials (see above)
A<B
OUTPUT PARAMETERS
P - polynomial in barycentric form
-- ALGLIB --
Copyright 30.09.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void polynomialcheb2bar(const real_1d_array &t, const double a, const double b, barycentricinterpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
n = t.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialcheb2bar(const_cast<alglib_impl::ae_vector*>(t.c_ptr()), n, a, b, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Conversion from barycentric representation to power basis.
This function has O(N^2) complexity.
INPUT PARAMETERS:
P - polynomial in barycentric form
C - offset (see below); 0.0 is used as default value.
S - scale (see below); 1.0 is used as default value. S<>0.
OUTPUT PARAMETERS
A - coefficients, P(x) = sum { A[i]*((X-C)/S)^i, i=0..N-1 }
N - number of coefficients (polynomial degree plus 1)
NOTES:
1. this function accepts offset and scale, which can be set to improve
numerical properties of polynomial. For example, if P was obtained as
result of interpolation on [-1,+1], you can set C=0 and S=1 and
represent P as sum of 1, x, x^2, x^3 and so on. In most cases you it
is exactly what you need.
However, if your interpolation model was built on [999,1001], you will
see significant growth of numerical errors when using {1, x, x^2, x^3}
as basis. Representing P as sum of 1, (x-1000), (x-1000)^2, (x-1000)^3
will be better option. Such representation can be obtained by using
1000.0 as offset C and 1.0 as scale S.
2. power basis is ill-conditioned and tricks described above can't solve
this problem completely. This function will return coefficients in
any case, but for N>8 they will become unreliable. However, N's
less than 5 are pretty safe.
3. barycentric interpolant passed as P may be either polynomial obtained
from polynomial interpolation/ fitting or rational function which is
NOT polynomial. We can't distinguish between these two cases, and this
algorithm just tries to work assuming that P IS a polynomial. If not,
algorithm will return results, but they won't have any meaning.
-- ALGLIB --
Copyright 30.09.2010 by Bochkanov Sergey
*************************************************************************/
void polynomialbar2pow(const barycentricinterpolant &p, const double c, const double s, real_1d_array &a, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialbar2pow(const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), c, s, const_cast<alglib_impl::ae_vector*>(a.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Conversion from barycentric representation to power basis.
This function has O(N^2) complexity.
INPUT PARAMETERS:
P - polynomial in barycentric form
C - offset (see below); 0.0 is used as default value.
S - scale (see below); 1.0 is used as default value. S<>0.
OUTPUT PARAMETERS
A - coefficients, P(x) = sum { A[i]*((X-C)/S)^i, i=0..N-1 }
N - number of coefficients (polynomial degree plus 1)
NOTES:
1. this function accepts offset and scale, which can be set to improve
numerical properties of polynomial. For example, if P was obtained as
result of interpolation on [-1,+1], you can set C=0 and S=1 and
represent P as sum of 1, x, x^2, x^3 and so on. In most cases you it
is exactly what you need.
However, if your interpolation model was built on [999,1001], you will
see significant growth of numerical errors when using {1, x, x^2, x^3}
as basis. Representing P as sum of 1, (x-1000), (x-1000)^2, (x-1000)^3
will be better option. Such representation can be obtained by using
1000.0 as offset C and 1.0 as scale S.
2. power basis is ill-conditioned and tricks described above can't solve
this problem completely. This function will return coefficients in
any case, but for N>8 they will become unreliable. However, N's
less than 5 are pretty safe.
3. barycentric interpolant passed as P may be either polynomial obtained
from polynomial interpolation/ fitting or rational function which is
NOT polynomial. We can't distinguish between these two cases, and this
algorithm just tries to work assuming that P IS a polynomial. If not,
algorithm will return results, but they won't have any meaning.
-- ALGLIB --
Copyright 30.09.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void polynomialbar2pow(const barycentricinterpolant &p, real_1d_array &a, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
double c;
double s;
c = 0;
s = 1;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialbar2pow(const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), c, s, const_cast<alglib_impl::ae_vector*>(a.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Conversion from power basis to barycentric representation.
This function has O(N^2) complexity.
INPUT PARAMETERS:
A - coefficients, P(x) = sum { A[i]*((X-C)/S)^i, i=0..N-1 }
N - number of coefficients (polynomial degree plus 1)
* if given, only leading N elements of A are used
* if not given, automatically determined from size of A
C - offset (see below); 0.0 is used as default value.
S - scale (see below); 1.0 is used as default value. S<>0.
OUTPUT PARAMETERS
P - polynomial in barycentric form
NOTES:
1. this function accepts offset and scale, which can be set to improve
numerical properties of polynomial. For example, if you interpolate on
[-1,+1], you can set C=0 and S=1 and convert from sum of 1, x, x^2,
x^3 and so on. In most cases you it is exactly what you need.
However, if your interpolation model was built on [999,1001], you will
see significant growth of numerical errors when using {1, x, x^2, x^3}
as input basis. Converting from sum of 1, (x-1000), (x-1000)^2,
(x-1000)^3 will be better option (you have to specify 1000.0 as offset
C and 1.0 as scale S).
2. power basis is ill-conditioned and tricks described above can't solve
this problem completely. This function will return barycentric model
in any case, but for N>8 accuracy well degrade. However, N's less than
5 are pretty safe.
-- ALGLIB --
Copyright 30.09.2010 by Bochkanov Sergey
*************************************************************************/
void polynomialpow2bar(const real_1d_array &a, const ae_int_t n, const double c, const double s, barycentricinterpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialpow2bar(const_cast<alglib_impl::ae_vector*>(a.c_ptr()), n, c, s, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Conversion from power basis to barycentric representation.
This function has O(N^2) complexity.
INPUT PARAMETERS:
A - coefficients, P(x) = sum { A[i]*((X-C)/S)^i, i=0..N-1 }
N - number of coefficients (polynomial degree plus 1)
* if given, only leading N elements of A are used
* if not given, automatically determined from size of A
C - offset (see below); 0.0 is used as default value.
S - scale (see below); 1.0 is used as default value. S<>0.
OUTPUT PARAMETERS
P - polynomial in barycentric form
NOTES:
1. this function accepts offset and scale, which can be set to improve
numerical properties of polynomial. For example, if you interpolate on
[-1,+1], you can set C=0 and S=1 and convert from sum of 1, x, x^2,
x^3 and so on. In most cases you it is exactly what you need.
However, if your interpolation model was built on [999,1001], you will
see significant growth of numerical errors when using {1, x, x^2, x^3}
as input basis. Converting from sum of 1, (x-1000), (x-1000)^2,
(x-1000)^3 will be better option (you have to specify 1000.0 as offset
C and 1.0 as scale S).
2. power basis is ill-conditioned and tricks described above can't solve
this problem completely. This function will return barycentric model
in any case, but for N>8 accuracy well degrade. However, N's less than
5 are pretty safe.
-- ALGLIB --
Copyright 30.09.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void polynomialpow2bar(const real_1d_array &a, barycentricinterpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
double c;
double s;
n = a.length();
c = 0;
s = 1;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialpow2bar(const_cast<alglib_impl::ae_vector*>(a.c_ptr()), n, c, s, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Lagrange intepolant: generation of the model on the general grid.
This function has O(N^2) complexity.
INPUT PARAMETERS:
X - abscissas, array[0..N-1]
Y - function values, array[0..N-1]
N - number of points, N>=1
OUTPUT PARAMETERS
P - barycentric model which represents Lagrange interpolant
(see ratint unit info and BarycentricCalc() description for
more information).
-- ALGLIB --
Copyright 02.12.2009 by Bochkanov Sergey
*************************************************************************/
void polynomialbuild(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, barycentricinterpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialbuild(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Lagrange intepolant: generation of the model on the general grid.
This function has O(N^2) complexity.
INPUT PARAMETERS:
X - abscissas, array[0..N-1]
Y - function values, array[0..N-1]
N - number of points, N>=1
OUTPUT PARAMETERS
P - barycentric model which represents Lagrange interpolant
(see ratint unit info and BarycentricCalc() description for
more information).
-- ALGLIB --
Copyright 02.12.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void polynomialbuild(const real_1d_array &x, const real_1d_array &y, barycentricinterpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'polynomialbuild': looks like one of arguments has wrong size");
n = x.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialbuild(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Lagrange intepolant: generation of the model on equidistant grid.
This function has O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
Y - function values at the nodes, array[0..N-1]
N - number of points, N>=1
for N=1 a constant model is constructed.
OUTPUT PARAMETERS
P - barycentric model which represents Lagrange interpolant
(see ratint unit info and BarycentricCalc() description for
more information).
-- ALGLIB --
Copyright 03.12.2009 by Bochkanov Sergey
*************************************************************************/
void polynomialbuildeqdist(const double a, const double b, const real_1d_array &y, const ae_int_t n, barycentricinterpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialbuildeqdist(a, b, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Lagrange intepolant: generation of the model on equidistant grid.
This function has O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
Y - function values at the nodes, array[0..N-1]
N - number of points, N>=1
for N=1 a constant model is constructed.
OUTPUT PARAMETERS
P - barycentric model which represents Lagrange interpolant
(see ratint unit info and BarycentricCalc() description for
more information).
-- ALGLIB --
Copyright 03.12.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void polynomialbuildeqdist(const double a, const double b, const real_1d_array &y, barycentricinterpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
n = y.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialbuildeqdist(a, b, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Lagrange intepolant on Chebyshev grid (first kind).
This function has O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
Y - function values at the nodes, array[0..N-1],
Y[I] = Y(0.5*(B+A) + 0.5*(B-A)*Cos(PI*(2*i+1)/(2*n)))
N - number of points, N>=1
for N=1 a constant model is constructed.
OUTPUT PARAMETERS
P - barycentric model which represents Lagrange interpolant
(see ratint unit info and BarycentricCalc() description for
more information).
-- ALGLIB --
Copyright 03.12.2009 by Bochkanov Sergey
*************************************************************************/
void polynomialbuildcheb1(const double a, const double b, const real_1d_array &y, const ae_int_t n, barycentricinterpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialbuildcheb1(a, b, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Lagrange intepolant on Chebyshev grid (first kind).
This function has O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
Y - function values at the nodes, array[0..N-1],
Y[I] = Y(0.5*(B+A) + 0.5*(B-A)*Cos(PI*(2*i+1)/(2*n)))
N - number of points, N>=1
for N=1 a constant model is constructed.
OUTPUT PARAMETERS
P - barycentric model which represents Lagrange interpolant
(see ratint unit info and BarycentricCalc() description for
more information).
-- ALGLIB --
Copyright 03.12.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void polynomialbuildcheb1(const double a, const double b, const real_1d_array &y, barycentricinterpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
n = y.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialbuildcheb1(a, b, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Lagrange intepolant on Chebyshev grid (second kind).
This function has O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
Y - function values at the nodes, array[0..N-1],
Y[I] = Y(0.5*(B+A) + 0.5*(B-A)*Cos(PI*i/(n-1)))
N - number of points, N>=1
for N=1 a constant model is constructed.
OUTPUT PARAMETERS
P - barycentric model which represents Lagrange interpolant
(see ratint unit info and BarycentricCalc() description for
more information).
-- ALGLIB --
Copyright 03.12.2009 by Bochkanov Sergey
*************************************************************************/
void polynomialbuildcheb2(const double a, const double b, const real_1d_array &y, const ae_int_t n, barycentricinterpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialbuildcheb2(a, b, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Lagrange intepolant on Chebyshev grid (second kind).
This function has O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
Y - function values at the nodes, array[0..N-1],
Y[I] = Y(0.5*(B+A) + 0.5*(B-A)*Cos(PI*i/(n-1)))
N - number of points, N>=1
for N=1 a constant model is constructed.
OUTPUT PARAMETERS
P - barycentric model which represents Lagrange interpolant
(see ratint unit info and BarycentricCalc() description for
more information).
-- ALGLIB --
Copyright 03.12.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void polynomialbuildcheb2(const double a, const double b, const real_1d_array &y, barycentricinterpolant &p, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
n = y.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialbuildcheb2(a, b, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Fast equidistant polynomial interpolation function with O(N) complexity
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
F - function values, array[0..N-1]
N - number of points on equidistant grid, N>=1
for N=1 a constant model is constructed.
T - position where P(x) is calculated
RESULT
value of the Lagrange interpolant at T
IMPORTANT
this function provides fast interface which is not overflow-safe
nor it is very precise.
the best option is to use PolynomialBuildEqDist()/BarycentricCalc()
subroutines unless you are pretty sure that your data will not result
in overflow.
-- ALGLIB --
Copyright 02.12.2009 by Bochkanov Sergey
*************************************************************************/
double polynomialcalceqdist(const double a, const double b, const real_1d_array &f, const ae_int_t n, const double t, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::polynomialcalceqdist(a, b, const_cast<alglib_impl::ae_vector*>(f.c_ptr()), n, t, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
Fast equidistant polynomial interpolation function with O(N) complexity
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
F - function values, array[0..N-1]
N - number of points on equidistant grid, N>=1
for N=1 a constant model is constructed.
T - position where P(x) is calculated
RESULT
value of the Lagrange interpolant at T
IMPORTANT
this function provides fast interface which is not overflow-safe
nor it is very precise.
the best option is to use PolynomialBuildEqDist()/BarycentricCalc()
subroutines unless you are pretty sure that your data will not result
in overflow.
-- ALGLIB --
Copyright 02.12.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
double polynomialcalceqdist(const double a, const double b, const real_1d_array &f, const double t, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
n = f.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::polynomialcalceqdist(a, b, const_cast<alglib_impl::ae_vector*>(f.c_ptr()), n, t, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
#endif
/*************************************************************************
Fast polynomial interpolation function on Chebyshev points (first kind)
with O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
F - function values, array[0..N-1]
N - number of points on Chebyshev grid (first kind),
X[i] = 0.5*(B+A) + 0.5*(B-A)*Cos(PI*(2*i+1)/(2*n))
for N=1 a constant model is constructed.
T - position where P(x) is calculated
RESULT
value of the Lagrange interpolant at T
IMPORTANT
this function provides fast interface which is not overflow-safe
nor it is very precise.
the best option is to use PolIntBuildCheb1()/BarycentricCalc()
subroutines unless you are pretty sure that your data will not result
in overflow.
-- ALGLIB --
Copyright 02.12.2009 by Bochkanov Sergey
*************************************************************************/
double polynomialcalccheb1(const double a, const double b, const real_1d_array &f, const ae_int_t n, const double t, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::polynomialcalccheb1(a, b, const_cast<alglib_impl::ae_vector*>(f.c_ptr()), n, t, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
Fast polynomial interpolation function on Chebyshev points (first kind)
with O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
F - function values, array[0..N-1]
N - number of points on Chebyshev grid (first kind),
X[i] = 0.5*(B+A) + 0.5*(B-A)*Cos(PI*(2*i+1)/(2*n))
for N=1 a constant model is constructed.
T - position where P(x) is calculated
RESULT
value of the Lagrange interpolant at T
IMPORTANT
this function provides fast interface which is not overflow-safe
nor it is very precise.
the best option is to use PolIntBuildCheb1()/BarycentricCalc()
subroutines unless you are pretty sure that your data will not result
in overflow.
-- ALGLIB --
Copyright 02.12.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
double polynomialcalccheb1(const double a, const double b, const real_1d_array &f, const double t, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
n = f.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::polynomialcalccheb1(a, b, const_cast<alglib_impl::ae_vector*>(f.c_ptr()), n, t, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
#endif
/*************************************************************************
Fast polynomial interpolation function on Chebyshev points (second kind)
with O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
F - function values, array[0..N-1]
N - number of points on Chebyshev grid (second kind),
X[i] = 0.5*(B+A) + 0.5*(B-A)*Cos(PI*i/(n-1))
for N=1 a constant model is constructed.
T - position where P(x) is calculated
RESULT
value of the Lagrange interpolant at T
IMPORTANT
this function provides fast interface which is not overflow-safe
nor it is very precise.
the best option is to use PolIntBuildCheb2()/BarycentricCalc()
subroutines unless you are pretty sure that your data will not result
in overflow.
-- ALGLIB --
Copyright 02.12.2009 by Bochkanov Sergey
*************************************************************************/
double polynomialcalccheb2(const double a, const double b, const real_1d_array &f, const ae_int_t n, const double t, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::polynomialcalccheb2(a, b, const_cast<alglib_impl::ae_vector*>(f.c_ptr()), n, t, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
Fast polynomial interpolation function on Chebyshev points (second kind)
with O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
F - function values, array[0..N-1]
N - number of points on Chebyshev grid (second kind),
X[i] = 0.5*(B+A) + 0.5*(B-A)*Cos(PI*i/(n-1))
for N=1 a constant model is constructed.
T - position where P(x) is calculated
RESULT
value of the Lagrange interpolant at T
IMPORTANT
this function provides fast interface which is not overflow-safe
nor it is very precise.
the best option is to use PolIntBuildCheb2()/BarycentricCalc()
subroutines unless you are pretty sure that your data will not result
in overflow.
-- ALGLIB --
Copyright 02.12.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
double polynomialcalccheb2(const double a, const double b, const real_1d_array &f, const double t, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
n = f.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::polynomialcalccheb2(a, b, const_cast<alglib_impl::ae_vector*>(f.c_ptr()), n, t, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
#endif
#endif
#if defined(AE_COMPILE_LSFIT) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Polynomial fitting report:
TaskRCond reciprocal of task's condition number
RMSError RMS error
AvgError average error
AvgRelError average relative error (for non-zero Y[I])
MaxError maximum error
*************************************************************************/
_polynomialfitreport_owner::_polynomialfitreport_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_polynomialfitreport_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::polynomialfitreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::polynomialfitreport), &_state);
memset(p_struct, 0, sizeof(alglib_impl::polynomialfitreport));
alglib_impl::_polynomialfitreport_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_polynomialfitreport_owner::_polynomialfitreport_owner(const _polynomialfitreport_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_polynomialfitreport_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: polynomialfitreport copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::polynomialfitreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::polynomialfitreport), &_state);
memset(p_struct, 0, sizeof(alglib_impl::polynomialfitreport));
alglib_impl::_polynomialfitreport_init_copy(p_struct, const_cast<alglib_impl::polynomialfitreport*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_polynomialfitreport_owner& _polynomialfitreport_owner::operator=(const _polynomialfitreport_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: polynomialfitreport assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: polynomialfitreport assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_polynomialfitreport_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::polynomialfitreport));
alglib_impl::_polynomialfitreport_init_copy(p_struct, const_cast<alglib_impl::polynomialfitreport*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_polynomialfitreport_owner::~_polynomialfitreport_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_polynomialfitreport_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::polynomialfitreport* _polynomialfitreport_owner::c_ptr()
{
return p_struct;
}
alglib_impl::polynomialfitreport* _polynomialfitreport_owner::c_ptr() const
{
return const_cast<alglib_impl::polynomialfitreport*>(p_struct);
}
polynomialfitreport::polynomialfitreport() : _polynomialfitreport_owner() ,taskrcond(p_struct->taskrcond),rmserror(p_struct->rmserror),avgerror(p_struct->avgerror),avgrelerror(p_struct->avgrelerror),maxerror(p_struct->maxerror)
{
}
polynomialfitreport::polynomialfitreport(const polynomialfitreport &rhs):_polynomialfitreport_owner(rhs) ,taskrcond(p_struct->taskrcond),rmserror(p_struct->rmserror),avgerror(p_struct->avgerror),avgrelerror(p_struct->avgrelerror),maxerror(p_struct->maxerror)
{
}
polynomialfitreport& polynomialfitreport::operator=(const polynomialfitreport &rhs)
{
if( this==&rhs )
return *this;
_polynomialfitreport_owner::operator=(rhs);
return *this;
}
polynomialfitreport::~polynomialfitreport()
{
}
/*************************************************************************
Barycentric fitting report:
RMSError RMS error
AvgError average error
AvgRelError average relative error (for non-zero Y[I])
MaxError maximum error
TaskRCond reciprocal of task's condition number
*************************************************************************/
_barycentricfitreport_owner::_barycentricfitreport_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_barycentricfitreport_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::barycentricfitreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::barycentricfitreport), &_state);
memset(p_struct, 0, sizeof(alglib_impl::barycentricfitreport));
alglib_impl::_barycentricfitreport_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_barycentricfitreport_owner::_barycentricfitreport_owner(const _barycentricfitreport_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_barycentricfitreport_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: barycentricfitreport copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::barycentricfitreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::barycentricfitreport), &_state);
memset(p_struct, 0, sizeof(alglib_impl::barycentricfitreport));
alglib_impl::_barycentricfitreport_init_copy(p_struct, const_cast<alglib_impl::barycentricfitreport*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_barycentricfitreport_owner& _barycentricfitreport_owner::operator=(const _barycentricfitreport_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: barycentricfitreport assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: barycentricfitreport assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_barycentricfitreport_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::barycentricfitreport));
alglib_impl::_barycentricfitreport_init_copy(p_struct, const_cast<alglib_impl::barycentricfitreport*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_barycentricfitreport_owner::~_barycentricfitreport_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_barycentricfitreport_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::barycentricfitreport* _barycentricfitreport_owner::c_ptr()
{
return p_struct;
}
alglib_impl::barycentricfitreport* _barycentricfitreport_owner::c_ptr() const
{
return const_cast<alglib_impl::barycentricfitreport*>(p_struct);
}
barycentricfitreport::barycentricfitreport() : _barycentricfitreport_owner() ,taskrcond(p_struct->taskrcond),dbest(p_struct->dbest),rmserror(p_struct->rmserror),avgerror(p_struct->avgerror),avgrelerror(p_struct->avgrelerror),maxerror(p_struct->maxerror)
{
}
barycentricfitreport::barycentricfitreport(const barycentricfitreport &rhs):_barycentricfitreport_owner(rhs) ,taskrcond(p_struct->taskrcond),dbest(p_struct->dbest),rmserror(p_struct->rmserror),avgerror(p_struct->avgerror),avgrelerror(p_struct->avgrelerror),maxerror(p_struct->maxerror)
{
}
barycentricfitreport& barycentricfitreport::operator=(const barycentricfitreport &rhs)
{
if( this==&rhs )
return *this;
_barycentricfitreport_owner::operator=(rhs);
return *this;
}
barycentricfitreport::~barycentricfitreport()
{
}
/*************************************************************************
Least squares fitting report. This structure contains informational fields
which are set by fitting functions provided by this unit.
Different functions initialize different sets of fields, so you should
read documentation on specific function you used in order to know which
fields are initialized.
TaskRCond reciprocal of task's condition number
IterationsCount number of internal iterations
VarIdx if user-supplied gradient contains errors which were
detected by nonlinear fitter, this field is set to
index of the first component of gradient which is
suspected to be spoiled by bugs.
RMSError RMS error
AvgError average error
AvgRelError average relative error (for non-zero Y[I])
MaxError maximum error
WRMSError weighted RMS error
CovPar covariance matrix for parameters, filled by some solvers
ErrPar vector of errors in parameters, filled by some solvers
ErrCurve vector of fit errors - variability of the best-fit
curve, filled by some solvers.
Noise vector of per-point noise estimates, filled by
some solvers.
R2 coefficient of determination (non-weighted, non-adjusted),
filled by some solvers.
*************************************************************************/
_lsfitreport_owner::_lsfitreport_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_lsfitreport_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::lsfitreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::lsfitreport), &_state);
memset(p_struct, 0, sizeof(alglib_impl::lsfitreport));
alglib_impl::_lsfitreport_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_lsfitreport_owner::_lsfitreport_owner(const _lsfitreport_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_lsfitreport_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: lsfitreport copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::lsfitreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::lsfitreport), &_state);
memset(p_struct, 0, sizeof(alglib_impl::lsfitreport));
alglib_impl::_lsfitreport_init_copy(p_struct, const_cast<alglib_impl::lsfitreport*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_lsfitreport_owner& _lsfitreport_owner::operator=(const _lsfitreport_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: lsfitreport assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: lsfitreport assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_lsfitreport_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::lsfitreport));
alglib_impl::_lsfitreport_init_copy(p_struct, const_cast<alglib_impl::lsfitreport*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_lsfitreport_owner::~_lsfitreport_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_lsfitreport_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::lsfitreport* _lsfitreport_owner::c_ptr()
{
return p_struct;
}
alglib_impl::lsfitreport* _lsfitreport_owner::c_ptr() const
{
return const_cast<alglib_impl::lsfitreport*>(p_struct);
}
lsfitreport::lsfitreport() : _lsfitreport_owner() ,taskrcond(p_struct->taskrcond),iterationscount(p_struct->iterationscount),varidx(p_struct->varidx),rmserror(p_struct->rmserror),avgerror(p_struct->avgerror),avgrelerror(p_struct->avgrelerror),maxerror(p_struct->maxerror),wrmserror(p_struct->wrmserror),covpar(&p_struct->covpar),errpar(&p_struct->errpar),errcurve(&p_struct->errcurve),noise(&p_struct->noise),r2(p_struct->r2)
{
}
lsfitreport::lsfitreport(const lsfitreport &rhs):_lsfitreport_owner(rhs) ,taskrcond(p_struct->taskrcond),iterationscount(p_struct->iterationscount),varidx(p_struct->varidx),rmserror(p_struct->rmserror),avgerror(p_struct->avgerror),avgrelerror(p_struct->avgrelerror),maxerror(p_struct->maxerror),wrmserror(p_struct->wrmserror),covpar(&p_struct->covpar),errpar(&p_struct->errpar),errcurve(&p_struct->errcurve),noise(&p_struct->noise),r2(p_struct->r2)
{
}
lsfitreport& lsfitreport::operator=(const lsfitreport &rhs)
{
if( this==&rhs )
return *this;
_lsfitreport_owner::operator=(rhs);
return *this;
}
lsfitreport::~lsfitreport()
{
}
/*************************************************************************
Nonlinear fitter.
You should use ALGLIB functions to work with fitter.
Never try to access its fields directly!
*************************************************************************/
_lsfitstate_owner::_lsfitstate_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_lsfitstate_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::lsfitstate*)alglib_impl::ae_malloc(sizeof(alglib_impl::lsfitstate), &_state);
memset(p_struct, 0, sizeof(alglib_impl::lsfitstate));
alglib_impl::_lsfitstate_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_lsfitstate_owner::_lsfitstate_owner(const _lsfitstate_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_lsfitstate_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: lsfitstate copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::lsfitstate*)alglib_impl::ae_malloc(sizeof(alglib_impl::lsfitstate), &_state);
memset(p_struct, 0, sizeof(alglib_impl::lsfitstate));
alglib_impl::_lsfitstate_init_copy(p_struct, const_cast<alglib_impl::lsfitstate*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_lsfitstate_owner& _lsfitstate_owner::operator=(const _lsfitstate_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: lsfitstate assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: lsfitstate assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_lsfitstate_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::lsfitstate));
alglib_impl::_lsfitstate_init_copy(p_struct, const_cast<alglib_impl::lsfitstate*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_lsfitstate_owner::~_lsfitstate_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_lsfitstate_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::lsfitstate* _lsfitstate_owner::c_ptr()
{
return p_struct;
}
alglib_impl::lsfitstate* _lsfitstate_owner::c_ptr() const
{
return const_cast<alglib_impl::lsfitstate*>(p_struct);
}
lsfitstate::lsfitstate() : _lsfitstate_owner() ,needf(p_struct->needf),needfg(p_struct->needfg),needfgh(p_struct->needfgh),xupdated(p_struct->xupdated),c(&p_struct->c),f(p_struct->f),g(&p_struct->g),h(&p_struct->h),x(&p_struct->x)
{
}
lsfitstate::lsfitstate(const lsfitstate &rhs):_lsfitstate_owner(rhs) ,needf(p_struct->needf),needfg(p_struct->needfg),needfgh(p_struct->needfgh),xupdated(p_struct->xupdated),c(&p_struct->c),f(p_struct->f),g(&p_struct->g),h(&p_struct->h),x(&p_struct->x)
{
}
lsfitstate& lsfitstate::operator=(const lsfitstate &rhs)
{
if( this==&rhs )
return *this;
_lsfitstate_owner::operator=(rhs);
return *this;
}
lsfitstate::~lsfitstate()
{
}
/*************************************************************************
This subroutine fits piecewise linear curve to points with Ramer-Douglas-
Peucker algorithm, which stops after generating specified number of linear
sections.
IMPORTANT:
* it does NOT perform least-squares fitting; it builds curve, but this
curve does not minimize some least squares metric. See description of
RDP algorithm (say, in Wikipedia) for more details on WHAT is performed.
* this function does NOT work with parametric curves (i.e. curves which
can be represented as {X(t),Y(t)}. It works with curves which can be
represented as Y(X). Thus, it is impossible to model figures like
circles with this functions.
If you want to work with parametric curves, you should use
ParametricRDPFixed() function provided by "Parametric" subpackage of
"Interpolation" package.
INPUT PARAMETERS:
X - array of X-coordinates:
* at least N elements
* can be unordered (points are automatically sorted)
* this function may accept non-distinct X (see below for
more information on handling of such inputs)
Y - array of Y-coordinates:
* at least N elements
N - number of elements in X/Y
M - desired number of sections:
* at most M sections are generated by this function
* less than M sections can be generated if we have N<M
(or some X are non-distinct).
OUTPUT PARAMETERS:
X2 - X-values of corner points for piecewise approximation,
has length NSections+1 or zero (for NSections=0).
Y2 - Y-values of corner points,
has length NSections+1 or zero (for NSections=0).
NSections- number of sections found by algorithm, NSections<=M,
NSections can be zero for degenerate datasets
(N<=1 or all X[] are non-distinct).
NOTE: X2/Y2 are ordered arrays, i.e. (X2[0],Y2[0]) is a first point of
curve, (X2[NSection-1],Y2[NSection-1]) is the last point.
-- ALGLIB --
Copyright 02.10.2014 by Bochkanov Sergey
*************************************************************************/
void lstfitpiecewiselinearrdpfixed(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t m, real_1d_array &x2, real_1d_array &y2, ae_int_t &nsections, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lstfitpiecewiselinearrdpfixed(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, m, const_cast<alglib_impl::ae_vector*>(x2.c_ptr()), const_cast<alglib_impl::ae_vector*>(y2.c_ptr()), &nsections, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine fits piecewise linear curve to points with Ramer-Douglas-
Peucker algorithm, which stops after achieving desired precision.
IMPORTANT:
* it performs non-least-squares fitting; it builds curve, but this curve
does not minimize some least squares metric. See description of RDP
algorithm (say, in Wikipedia) for more details on WHAT is performed.
* this function does NOT work with parametric curves (i.e. curves which
can be represented as {X(t),Y(t)}. It works with curves which can be
represented as Y(X). Thus, it is impossible to model figures like circles
with this functions.
If you want to work with parametric curves, you should use
ParametricRDPFixed() function provided by "Parametric" subpackage of
"Interpolation" package.
INPUT PARAMETERS:
X - array of X-coordinates:
* at least N elements
* can be unordered (points are automatically sorted)
* this function may accept non-distinct X (see below for
more information on handling of such inputs)
Y - array of Y-coordinates:
* at least N elements
N - number of elements in X/Y
Eps - positive number, desired precision.
OUTPUT PARAMETERS:
X2 - X-values of corner points for piecewise approximation,
has length NSections+1 or zero (for NSections=0).
Y2 - Y-values of corner points,
has length NSections+1 or zero (for NSections=0).
NSections- number of sections found by algorithm,
NSections can be zero for degenerate datasets
(N<=1 or all X[] are non-distinct).
NOTE: X2/Y2 are ordered arrays, i.e. (X2[0],Y2[0]) is a first point of
curve, (X2[NSection-1],Y2[NSection-1]) is the last point.
-- ALGLIB --
Copyright 02.10.2014 by Bochkanov Sergey
*************************************************************************/
void lstfitpiecewiselinearrdp(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const double eps, real_1d_array &x2, real_1d_array &y2, ae_int_t &nsections, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lstfitpiecewiselinearrdp(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, eps, const_cast<alglib_impl::ae_vector*>(x2.c_ptr()), const_cast<alglib_impl::ae_vector*>(y2.c_ptr()), &nsections, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Fitting by polynomials in barycentric form. This function provides simple
unterface for unconstrained unweighted fitting. See PolynomialFitWC() if
you need constrained fitting.
Task is linear, so linear least squares solver is used. Complexity of this
computational scheme is O(N*M^2), mostly dominated by least squares solver
SEE ALSO:
PolynomialFitWC()
NOTES:
you can convert P from barycentric form to the power or Chebyshev
basis with PolynomialBar2Pow() or PolynomialBar2Cheb() functions from
POLINT subpackage.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
N - number of points, N>0
* if given, only leading N elements of X/Y are used
* if not given, automatically determined from sizes of X/Y
M - number of basis functions (= polynomial_degree + 1), M>=1
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearW() subroutine:
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
P - interpolant in barycentric form.
Rep - report, same format as in LSFitLinearW() subroutine.
Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
-- ALGLIB PROJECT --
Copyright 10.12.2009 by Bochkanov Sergey
*************************************************************************/
void polynomialfit(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t m, ae_int_t &info, barycentricinterpolant &p, polynomialfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialfit(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, m, &info, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), const_cast<alglib_impl::polynomialfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Fitting by polynomials in barycentric form. This function provides simple
unterface for unconstrained unweighted fitting. See PolynomialFitWC() if
you need constrained fitting.
Task is linear, so linear least squares solver is used. Complexity of this
computational scheme is O(N*M^2), mostly dominated by least squares solver
SEE ALSO:
PolynomialFitWC()
NOTES:
you can convert P from barycentric form to the power or Chebyshev
basis with PolynomialBar2Pow() or PolynomialBar2Cheb() functions from
POLINT subpackage.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
N - number of points, N>0
* if given, only leading N elements of X/Y are used
* if not given, automatically determined from sizes of X/Y
M - number of basis functions (= polynomial_degree + 1), M>=1
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearW() subroutine:
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
P - interpolant in barycentric form.
Rep - report, same format as in LSFitLinearW() subroutine.
Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
-- ALGLIB PROJECT --
Copyright 10.12.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void polynomialfit(const real_1d_array &x, const real_1d_array &y, const ae_int_t m, ae_int_t &info, barycentricinterpolant &p, polynomialfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'polynomialfit': looks like one of arguments has wrong size");
n = x.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialfit(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, m, &info, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), const_cast<alglib_impl::polynomialfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Weighted fitting by polynomials in barycentric form, with constraints on
function values or first derivatives.
Small regularizing term is used when solving constrained tasks (to improve
stability).
Task is linear, so linear least squares solver is used. Complexity of this
computational scheme is O(N*M^2), mostly dominated by least squares solver
SEE ALSO:
PolynomialFit()
NOTES:
you can convert P from barycentric form to the power or Chebyshev
basis with PolynomialBar2Pow() or PolynomialBar2Cheb() functions from
POLINT subpackage.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
W - weights, array[0..N-1]
Each summand in square sum of approximation deviations from
given values is multiplied by the square of corresponding
weight. Fill it by 1's if you don't want to solve weighted
task.
N - number of points, N>0.
* if given, only leading N elements of X/Y/W are used
* if not given, automatically determined from sizes of X/Y/W
XC - points where polynomial values/derivatives are constrained,
array[0..K-1].
YC - values of constraints, array[0..K-1]
DC - array[0..K-1], types of constraints:
* DC[i]=0 means that P(XC[i])=YC[i]
* DC[i]=1 means that P'(XC[i])=YC[i]
SEE BELOW FOR IMPORTANT INFORMATION ON CONSTRAINTS
K - number of constraints, 0<=K<M.
K=0 means no constraints (XC/YC/DC are not used in such cases)
M - number of basis functions (= polynomial_degree + 1), M>=1
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearW() subroutine:
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
-3 means inconsistent constraints
P - interpolant in barycentric form.
Rep - report, same format as in LSFitLinearW() subroutine.
Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
SETTING CONSTRAINTS - DANGERS AND OPPORTUNITIES:
Setting constraints can lead to undesired results, like ill-conditioned
behavior, or inconsistency being detected. From the other side, it allows
us to improve quality of the fit. Here we summarize our experience with
constrained regression splines:
* even simple constraints can be inconsistent, see Wikipedia article on
this subject: http://en.wikipedia.org/wiki/Birkhoff_interpolation
* the greater is M (given fixed constraints), the more chances that
constraints will be consistent
* in the general case, consistency of constraints is NOT GUARANTEED.
* in the one special cases, however, we can guarantee consistency. This
case is: M>1 and constraints on the function values (NOT DERIVATIVES)
Our final recommendation is to use constraints WHEN AND ONLY when you
can't solve your task without them. Anything beyond special cases given
above is not guaranteed and may result in inconsistency.
-- ALGLIB PROJECT --
Copyright 10.12.2009 by Bochkanov Sergey
*************************************************************************/
void polynomialfitwc(const real_1d_array &x, const real_1d_array &y, const real_1d_array &w, const ae_int_t n, const real_1d_array &xc, const real_1d_array &yc, const integer_1d_array &dc, const ae_int_t k, const ae_int_t m, ae_int_t &info, barycentricinterpolant &p, polynomialfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialfitwc(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(xc.c_ptr()), const_cast<alglib_impl::ae_vector*>(yc.c_ptr()), const_cast<alglib_impl::ae_vector*>(dc.c_ptr()), k, m, &info, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), const_cast<alglib_impl::polynomialfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Weighted fitting by polynomials in barycentric form, with constraints on
function values or first derivatives.
Small regularizing term is used when solving constrained tasks (to improve
stability).
Task is linear, so linear least squares solver is used. Complexity of this
computational scheme is O(N*M^2), mostly dominated by least squares solver
SEE ALSO:
PolynomialFit()
NOTES:
you can convert P from barycentric form to the power or Chebyshev
basis with PolynomialBar2Pow() or PolynomialBar2Cheb() functions from
POLINT subpackage.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
W - weights, array[0..N-1]
Each summand in square sum of approximation deviations from
given values is multiplied by the square of corresponding
weight. Fill it by 1's if you don't want to solve weighted
task.
N - number of points, N>0.
* if given, only leading N elements of X/Y/W are used
* if not given, automatically determined from sizes of X/Y/W
XC - points where polynomial values/derivatives are constrained,
array[0..K-1].
YC - values of constraints, array[0..K-1]
DC - array[0..K-1], types of constraints:
* DC[i]=0 means that P(XC[i])=YC[i]
* DC[i]=1 means that P'(XC[i])=YC[i]
SEE BELOW FOR IMPORTANT INFORMATION ON CONSTRAINTS
K - number of constraints, 0<=K<M.
K=0 means no constraints (XC/YC/DC are not used in such cases)
M - number of basis functions (= polynomial_degree + 1), M>=1
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearW() subroutine:
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
-3 means inconsistent constraints
P - interpolant in barycentric form.
Rep - report, same format as in LSFitLinearW() subroutine.
Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
SETTING CONSTRAINTS - DANGERS AND OPPORTUNITIES:
Setting constraints can lead to undesired results, like ill-conditioned
behavior, or inconsistency being detected. From the other side, it allows
us to improve quality of the fit. Here we summarize our experience with
constrained regression splines:
* even simple constraints can be inconsistent, see Wikipedia article on
this subject: http://en.wikipedia.org/wiki/Birkhoff_interpolation
* the greater is M (given fixed constraints), the more chances that
constraints will be consistent
* in the general case, consistency of constraints is NOT GUARANTEED.
* in the one special cases, however, we can guarantee consistency. This
case is: M>1 and constraints on the function values (NOT DERIVATIVES)
Our final recommendation is to use constraints WHEN AND ONLY when you
can't solve your task without them. Anything beyond special cases given
above is not guaranteed and may result in inconsistency.
-- ALGLIB PROJECT --
Copyright 10.12.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void polynomialfitwc(const real_1d_array &x, const real_1d_array &y, const real_1d_array &w, const real_1d_array &xc, const real_1d_array &yc, const integer_1d_array &dc, const ae_int_t m, ae_int_t &info, barycentricinterpolant &p, polynomialfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t k;
if( (x.length()!=y.length()) || (x.length()!=w.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'polynomialfitwc': looks like one of arguments has wrong size");
if( (xc.length()!=yc.length()) || (xc.length()!=dc.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'polynomialfitwc': looks like one of arguments has wrong size");
n = x.length();
k = xc.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::polynomialfitwc(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(xc.c_ptr()), const_cast<alglib_impl::ae_vector*>(yc.c_ptr()), const_cast<alglib_impl::ae_vector*>(dc.c_ptr()), k, m, &info, const_cast<alglib_impl::barycentricinterpolant*>(p.c_ptr()), const_cast<alglib_impl::polynomialfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This function calculates value of four-parameter logistic (4PL) model at
specified point X. 4PL model has following form:
F(x|A,B,C,D) = D+(A-D)/(1+Power(x/C,B))
INPUT PARAMETERS:
X - current point, X>=0:
* zero X is correctly handled even for B<=0
* negative X results in exception.
A, B, C, D- parameters of 4PL model:
* A is unconstrained
* B is unconstrained; zero or negative values are handled
correctly.
* C>0, non-positive value results in exception
* D is unconstrained
RESULT:
model value at X
NOTE: if B=0, denominator is assumed to be equal to 2.0 even for zero X
(strictly speaking, 0^0 is undefined).
NOTE: this function also throws exception if all input parameters are
correct, but overflow was detected during calculations.
NOTE: this function performs a lot of checks; if you need really high
performance, consider evaluating model yourself, without checking
for degenerate cases.
-- ALGLIB PROJECT --
Copyright 14.05.2014 by Bochkanov Sergey
*************************************************************************/
double logisticcalc4(const double x, const double a, const double b, const double c, const double d, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::logisticcalc4(x, a, b, c, d, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
This function calculates value of five-parameter logistic (5PL) model at
specified point X. 5PL model has following form:
F(x|A,B,C,D,G) = D+(A-D)/Power(1+Power(x/C,B),G)
INPUT PARAMETERS:
X - current point, X>=0:
* zero X is correctly handled even for B<=0
* negative X results in exception.
A, B, C, D, G- parameters of 5PL model:
* A is unconstrained
* B is unconstrained; zero or negative values are handled
correctly.
* C>0, non-positive value results in exception
* D is unconstrained
* G>0, non-positive value results in exception
RESULT:
model value at X
NOTE: if B=0, denominator is assumed to be equal to Power(2.0,G) even for
zero X (strictly speaking, 0^0 is undefined).
NOTE: this function also throws exception if all input parameters are
correct, but overflow was detected during calculations.
NOTE: this function performs a lot of checks; if you need really high
performance, consider evaluating model yourself, without checking
for degenerate cases.
-- ALGLIB PROJECT --
Copyright 14.05.2014 by Bochkanov Sergey
*************************************************************************/
double logisticcalc5(const double x, const double a, const double b, const double c, const double d, const double g, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::logisticcalc5(x, a, b, c, d, g, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
This function fits four-parameter logistic (4PL) model to data provided
by user. 4PL model has following form:
F(x|A,B,C,D) = D+(A-D)/(1+Power(x/C,B))
Here:
* A, D - unconstrained (see LogisticFit4EC() for constrained 4PL)
* B>=0
* C>0
IMPORTANT: output of this function is constrained in such way that B>0.
Because 4PL model is symmetric with respect to B, there is no
need to explore B<0. Constraining B makes algorithm easier
to stabilize and debug.
Users who for some reason prefer to work with negative B's
should transform output themselves (swap A and D, replace B by
-B).
4PL fitting is implemented as follows:
* we perform small number of restarts from random locations which helps to
solve problem of bad local extrema. Locations are only partially random
- we use input data to determine good initial guess, but we include
controlled amount of randomness.
* we perform Levenberg-Marquardt fitting with very tight constraints on
parameters B and C - it allows us to find good initial guess for the
second stage without risk of running into "flat spot".
* second Levenberg-Marquardt round is performed without excessive
constraints. Results from the previous round are used as initial guess.
* after fitting is done, we compare results with best values found so far,
rewrite "best solution" if needed, and move to next random location.
Overall algorithm is very stable and is not prone to bad local extrema.
Furthermore, it automatically scales when input data have very large or
very small range.
INPUT PARAMETERS:
X - array[N], stores X-values.
MUST include only non-negative numbers (but may include
zero values). Can be unsorted.
Y - array[N], values to fit.
N - number of points. If N is less than length of X/Y, only
leading N elements are used.
OUTPUT PARAMETERS:
A, B, C, D- parameters of 4PL model
Rep - fitting report. This structure has many fields, but ONLY
ONES LISTED BELOW ARE SET:
* Rep.IterationsCount - number of iterations performed
* Rep.RMSError - root-mean-square error
* Rep.AvgError - average absolute error
* Rep.AvgRelError - average relative error (calculated for
non-zero Y-values)
* Rep.MaxError - maximum absolute error
* Rep.R2 - coefficient of determination, R-squared. This
coefficient is calculated as R2=1-RSS/TSS (in case
of nonlinear regression there are multiple ways to
define R2, each of them giving different results).
NOTE: for stability reasons the B parameter is restricted by [1/1000,1000]
range. It prevents algorithm from making trial steps deep into the
area of bad parameters.
NOTE: after you obtained coefficients, you can evaluate model with
LogisticCalc4() function.
NOTE: if you need better control over fitting process than provided by this
function, you may use LogisticFit45X().
NOTE: step is automatically scaled according to scale of parameters being
fitted before we compare its length with EpsX. Thus, this function
can be used to fit data with very small or very large values without
changing EpsX.
-- ALGLIB PROJECT --
Copyright 14.02.2014 by Bochkanov Sergey
*************************************************************************/
void logisticfit4(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, double &a, double &b, double &c, double &d, lsfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::logisticfit4(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, &a, &b, &c, &d, const_cast<alglib_impl::lsfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function fits four-parameter logistic (4PL) model to data provided
by user, with optional constraints on parameters A and D. 4PL model has
following form:
F(x|A,B,C,D) = D+(A-D)/(1+Power(x/C,B))
Here:
* A, D - with optional equality constraints
* B>=0
* C>0
IMPORTANT: output of this function is constrained in such way that B>0.
Because 4PL model is symmetric with respect to B, there is no
need to explore B<0. Constraining B makes algorithm easier
to stabilize and debug.
Users who for some reason prefer to work with negative B's
should transform output themselves (swap A and D, replace B by
-B).
4PL fitting is implemented as follows:
* we perform small number of restarts from random locations which helps to
solve problem of bad local extrema. Locations are only partially random
- we use input data to determine good initial guess, but we include
controlled amount of randomness.
* we perform Levenberg-Marquardt fitting with very tight constraints on
parameters B and C - it allows us to find good initial guess for the
second stage without risk of running into "flat spot".
* second Levenberg-Marquardt round is performed without excessive
constraints. Results from the previous round are used as initial guess.
* after fitting is done, we compare results with best values found so far,
rewrite "best solution" if needed, and move to next random location.
Overall algorithm is very stable and is not prone to bad local extrema.
Furthermore, it automatically scales when input data have very large or
very small range.
INPUT PARAMETERS:
X - array[N], stores X-values.
MUST include only non-negative numbers (but may include
zero values). Can be unsorted.
Y - array[N], values to fit.
N - number of points. If N is less than length of X/Y, only
leading N elements are used.
CnstrLeft- optional equality constraint for model value at the left
boundary (at X=0). Specify NAN (Not-a-Number) if you do
not need constraint on the model value at X=0 (in C++ you
can pass alglib::fp_nan as parameter, in C# it will be
Double.NaN).
See below, section "EQUALITY CONSTRAINTS" for more
information about constraints.
CnstrRight- optional equality constraint for model value at X=infinity.
Specify NAN (Not-a-Number) if you do not need constraint
on the model value (in C++ you can pass alglib::fp_nan as
parameter, in C# it will be Double.NaN).
See below, section "EQUALITY CONSTRAINTS" for more
information about constraints.
OUTPUT PARAMETERS:
A, B, C, D- parameters of 4PL model
Rep - fitting report. This structure has many fields, but ONLY
ONES LISTED BELOW ARE SET:
* Rep.IterationsCount - number of iterations performed
* Rep.RMSError - root-mean-square error
* Rep.AvgError - average absolute error
* Rep.AvgRelError - average relative error (calculated for
non-zero Y-values)
* Rep.MaxError - maximum absolute error
* Rep.R2 - coefficient of determination, R-squared. This
coefficient is calculated as R2=1-RSS/TSS (in case
of nonlinear regression there are multiple ways to
define R2, each of them giving different results).
NOTE: for stability reasons the B parameter is restricted by [1/1000,1000]
range. It prevents algorithm from making trial steps deep into the
area of bad parameters.
NOTE: after you obtained coefficients, you can evaluate model with
LogisticCalc4() function.
NOTE: if you need better control over fitting process than provided by this
function, you may use LogisticFit45X().
NOTE: step is automatically scaled according to scale of parameters being
fitted before we compare its length with EpsX. Thus, this function
can be used to fit data with very small or very large values without
changing EpsX.
EQUALITY CONSTRAINTS ON PARAMETERS
4PL/5PL solver supports equality constraints on model values at the left
boundary (X=0) and right boundary (X=infinity). These constraints are
completely optional and you can specify both of them, only one - or no
constraints at all.
Parameter CnstrLeft contains left constraint (or NAN for unconstrained
fitting), and CnstrRight contains right one. For 4PL, left constraint
ALWAYS corresponds to parameter A, and right one is ALWAYS constraint on
D. That's because 4PL model is normalized in such way that B>=0.
-- ALGLIB PROJECT --
Copyright 14.02.2014 by Bochkanov Sergey
*************************************************************************/
void logisticfit4ec(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const double cnstrleft, const double cnstrright, double &a, double &b, double &c, double &d, lsfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::logisticfit4ec(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, cnstrleft, cnstrright, &a, &b, &c, &d, const_cast<alglib_impl::lsfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function fits five-parameter logistic (5PL) model to data provided
by user. 5PL model has following form:
F(x|A,B,C,D,G) = D+(A-D)/Power(1+Power(x/C,B),G)
Here:
* A, D - unconstrained
* B - unconstrained
* C>0
* G>0
IMPORTANT: unlike in 4PL fitting, output of this function is NOT
constrained in such way that B is guaranteed to be positive.
Furthermore, unlike 4PL, 5PL model is NOT symmetric with
respect to B, so you can NOT transform model to equivalent one,
with B having desired sign (>0 or <0).
5PL fitting is implemented as follows:
* we perform small number of restarts from random locations which helps to
solve problem of bad local extrema. Locations are only partially random
- we use input data to determine good initial guess, but we include
controlled amount of randomness.
* we perform Levenberg-Marquardt fitting with very tight constraints on
parameters B and C - it allows us to find good initial guess for the
second stage without risk of running into "flat spot". Parameter G is
fixed at G=1.
* second Levenberg-Marquardt round is performed without excessive
constraints on B and C, but with G still equal to 1. Results from the
previous round are used as initial guess.
* third Levenberg-Marquardt round relaxes constraints on G and tries two
different models - one with B>0 and one with B<0.
* after fitting is done, we compare results with best values found so far,
rewrite "best solution" if needed, and move to next random location.
Overall algorithm is very stable and is not prone to bad local extrema.
Furthermore, it automatically scales when input data have very large or
very small range.
INPUT PARAMETERS:
X - array[N], stores X-values.
MUST include only non-negative numbers (but may include
zero values). Can be unsorted.
Y - array[N], values to fit.
N - number of points. If N is less than length of X/Y, only
leading N elements are used.
OUTPUT PARAMETERS:
A,B,C,D,G- parameters of 5PL model
Rep - fitting report. This structure has many fields, but ONLY
ONES LISTED BELOW ARE SET:
* Rep.IterationsCount - number of iterations performed
* Rep.RMSError - root-mean-square error
* Rep.AvgError - average absolute error
* Rep.AvgRelError - average relative error (calculated for
non-zero Y-values)
* Rep.MaxError - maximum absolute error
* Rep.R2 - coefficient of determination, R-squared. This
coefficient is calculated as R2=1-RSS/TSS (in case
of nonlinear regression there are multiple ways to
define R2, each of them giving different results).
NOTE: for better stability B parameter is restricted by [+-1/1000,+-1000]
range, and G is restricted by [1/10,10] range. It prevents algorithm
from making trial steps deep into the area of bad parameters.
NOTE: after you obtained coefficients, you can evaluate model with
LogisticCalc5() function.
NOTE: if you need better control over fitting process than provided by this
function, you may use LogisticFit45X().
NOTE: step is automatically scaled according to scale of parameters being
fitted before we compare its length with EpsX. Thus, this function
can be used to fit data with very small or very large values without
changing EpsX.
-- ALGLIB PROJECT --
Copyright 14.02.2014 by Bochkanov Sergey
*************************************************************************/
void logisticfit5(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, double &a, double &b, double &c, double &d, double &g, lsfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::logisticfit5(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, &a, &b, &c, &d, &g, const_cast<alglib_impl::lsfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function fits five-parameter logistic (5PL) model to data provided
by user, subject to optional equality constraints on parameters A and D.
5PL model has following form:
F(x|A,B,C,D,G) = D+(A-D)/Power(1+Power(x/C,B),G)
Here:
* A, D - with optional equality constraints
* B - unconstrained
* C>0
* G>0
IMPORTANT: unlike in 4PL fitting, output of this function is NOT
constrained in such way that B is guaranteed to be positive.
Furthermore, unlike 4PL, 5PL model is NOT symmetric with
respect to B, so you can NOT transform model to equivalent one,
with B having desired sign (>0 or <0).
5PL fitting is implemented as follows:
* we perform small number of restarts from random locations which helps to
solve problem of bad local extrema. Locations are only partially random
- we use input data to determine good initial guess, but we include
controlled amount of randomness.
* we perform Levenberg-Marquardt fitting with very tight constraints on
parameters B and C - it allows us to find good initial guess for the
second stage without risk of running into "flat spot". Parameter G is
fixed at G=1.
* second Levenberg-Marquardt round is performed without excessive
constraints on B and C, but with G still equal to 1. Results from the
previous round are used as initial guess.
* third Levenberg-Marquardt round relaxes constraints on G and tries two
different models - one with B>0 and one with B<0.
* after fitting is done, we compare results with best values found so far,
rewrite "best solution" if needed, and move to next random location.
Overall algorithm is very stable and is not prone to bad local extrema.
Furthermore, it automatically scales when input data have very large or
very small range.
INPUT PARAMETERS:
X - array[N], stores X-values.
MUST include only non-negative numbers (but may include
zero values). Can be unsorted.
Y - array[N], values to fit.
N - number of points. If N is less than length of X/Y, only
leading N elements are used.
CnstrLeft- optional equality constraint for model value at the left
boundary (at X=0). Specify NAN (Not-a-Number) if you do
not need constraint on the model value at X=0 (in C++ you
can pass alglib::fp_nan as parameter, in C# it will be
Double.NaN).
See below, section "EQUALITY CONSTRAINTS" for more
information about constraints.
CnstrRight- optional equality constraint for model value at X=infinity.
Specify NAN (Not-a-Number) if you do not need constraint
on the model value (in C++ you can pass alglib::fp_nan as
parameter, in C# it will be Double.NaN).
See below, section "EQUALITY CONSTRAINTS" for more
information about constraints.
OUTPUT PARAMETERS:
A,B,C,D,G- parameters of 5PL model
Rep - fitting report. This structure has many fields, but ONLY
ONES LISTED BELOW ARE SET:
* Rep.IterationsCount - number of iterations performed
* Rep.RMSError - root-mean-square error
* Rep.AvgError - average absolute error
* Rep.AvgRelError - average relative error (calculated for
non-zero Y-values)
* Rep.MaxError - maximum absolute error
* Rep.R2 - coefficient of determination, R-squared. This
coefficient is calculated as R2=1-RSS/TSS (in case
of nonlinear regression there are multiple ways to
define R2, each of them giving different results).
NOTE: for better stability B parameter is restricted by [+-1/1000,+-1000]
range, and G is restricted by [1/10,10] range. It prevents algorithm
from making trial steps deep into the area of bad parameters.
NOTE: after you obtained coefficients, you can evaluate model with
LogisticCalc5() function.
NOTE: if you need better control over fitting process than provided by this
function, you may use LogisticFit45X().
NOTE: step is automatically scaled according to scale of parameters being
fitted before we compare its length with EpsX. Thus, this function
can be used to fit data with very small or very large values without
changing EpsX.
EQUALITY CONSTRAINTS ON PARAMETERS
5PL solver supports equality constraints on model values at the left
boundary (X=0) and right boundary (X=infinity). These constraints are
completely optional and you can specify both of them, only one - or no
constraints at all.
Parameter CnstrLeft contains left constraint (or NAN for unconstrained
fitting), and CnstrRight contains right one.
Unlike 4PL one, 5PL model is NOT symmetric with respect to change in sign
of B. Thus, negative B's are possible, and left constraint may constrain
parameter A (for positive B's) - or parameter D (for negative B's).
Similarly changes meaning of right constraint.
You do not have to decide what parameter to constrain - algorithm will
automatically determine correct parameters as fitting progresses. However,
question highlighted above is important when you interpret fitting results.
-- ALGLIB PROJECT --
Copyright 14.02.2014 by Bochkanov Sergey
*************************************************************************/
void logisticfit5ec(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const double cnstrleft, const double cnstrright, double &a, double &b, double &c, double &d, double &g, lsfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::logisticfit5ec(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, cnstrleft, cnstrright, &a, &b, &c, &d, &g, const_cast<alglib_impl::lsfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This is "expert" 4PL/5PL fitting function, which can be used if you need
better control over fitting process than provided by LogisticFit4() or
LogisticFit5().
This function fits model of the form
F(x|A,B,C,D) = D+(A-D)/(1+Power(x/C,B)) (4PL model)
or
F(x|A,B,C,D,G) = D+(A-D)/Power(1+Power(x/C,B),G) (5PL model)
Here:
* A, D - unconstrained
* B>=0 for 4PL, unconstrained for 5PL
* C>0
* G>0 (if present)
INPUT PARAMETERS:
X - array[N], stores X-values.
MUST include only non-negative numbers (but may include
zero values). Can be unsorted.
Y - array[N], values to fit.
N - number of points. If N is less than length of X/Y, only
leading N elements are used.
CnstrLeft- optional equality constraint for model value at the left
boundary (at X=0). Specify NAN (Not-a-Number) if you do
not need constraint on the model value at X=0 (in C++ you
can pass alglib::fp_nan as parameter, in C# it will be
Double.NaN).
See below, section "EQUALITY CONSTRAINTS" for more
information about constraints.
CnstrRight- optional equality constraint for model value at X=infinity.
Specify NAN (Not-a-Number) if you do not need constraint
on the model value (in C++ you can pass alglib::fp_nan as
parameter, in C# it will be Double.NaN).
See below, section "EQUALITY CONSTRAINTS" for more
information about constraints.
Is4PL - whether 4PL or 5PL models are fitted
LambdaV - regularization coefficient, LambdaV>=0.
Set it to zero unless you know what you are doing.
EpsX - stopping condition (step size), EpsX>=0.
Zero value means that small step is automatically chosen.
See notes below for more information.
RsCnt - number of repeated restarts from random points. 4PL/5PL
models are prone to problem of bad local extrema. Utilizing
multiple random restarts allows us to improve algorithm
convergence.
RsCnt>=0.
Zero value means that function automatically choose small
amount of restarts (recommended).
OUTPUT PARAMETERS:
A, B, C, D- parameters of 4PL model
G - parameter of 5PL model; for Is4PL=True, G=1 is returned.
Rep - fitting report. This structure has many fields, but ONLY
ONES LISTED BELOW ARE SET:
* Rep.IterationsCount - number of iterations performed
* Rep.RMSError - root-mean-square error
* Rep.AvgError - average absolute error
* Rep.AvgRelError - average relative error (calculated for
non-zero Y-values)
* Rep.MaxError - maximum absolute error
* Rep.R2 - coefficient of determination, R-squared. This
coefficient is calculated as R2=1-RSS/TSS (in case
of nonlinear regression there are multiple ways to
define R2, each of them giving different results).
NOTE: for better stability B parameter is restricted by [+-1/1000,+-1000]
range, and G is restricted by [1/10,10] range. It prevents algorithm
from making trial steps deep into the area of bad parameters.
NOTE: after you obtained coefficients, you can evaluate model with
LogisticCalc5() function.
NOTE: step is automatically scaled according to scale of parameters being
fitted before we compare its length with EpsX. Thus, this function
can be used to fit data with very small or very large values without
changing EpsX.
EQUALITY CONSTRAINTS ON PARAMETERS
4PL/5PL solver supports equality constraints on model values at the left
boundary (X=0) and right boundary (X=infinity). These constraints are
completely optional and you can specify both of them, only one - or no
constraints at all.
Parameter CnstrLeft contains left constraint (or NAN for unconstrained
fitting), and CnstrRight contains right one. For 4PL, left constraint
ALWAYS corresponds to parameter A, and right one is ALWAYS constraint on
D. That's because 4PL model is normalized in such way that B>=0.
For 5PL model things are different. Unlike 4PL one, 5PL model is NOT
symmetric with respect to change in sign of B. Thus, negative B's are
possible, and left constraint may constrain parameter A (for positive B's)
- or parameter D (for negative B's). Similarly changes meaning of right
constraint.
You do not have to decide what parameter to constrain - algorithm will
automatically determine correct parameters as fitting progresses. However,
question highlighted above is important when you interpret fitting results.
-- ALGLIB PROJECT --
Copyright 14.02.2014 by Bochkanov Sergey
*************************************************************************/
void logisticfit45x(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const double cnstrleft, const double cnstrright, const bool is4pl, const double lambdav, const double epsx, const ae_int_t rscnt, double &a, double &b, double &c, double &d, double &g, lsfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::logisticfit45x(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, cnstrleft, cnstrright, is4pl, lambdav, epsx, rscnt, &a, &b, &c, &d, &g, const_cast<alglib_impl::lsfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Weghted rational least squares fitting using Floater-Hormann rational
functions with optimal D chosen from [0,9], with constraints and
individual weights.
Equidistant grid with M node on [min(x),max(x)] is used to build basis
functions. Different values of D are tried, optimal D (least WEIGHTED root
mean square error) is chosen. Task is linear, so linear least squares
solver is used. Complexity of this computational scheme is O(N*M^2)
(mostly dominated by the least squares solver).
SEE ALSO
* BarycentricFitFloaterHormann(), "lightweight" fitting without invididual
weights and constraints.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
W - weights, array[0..N-1]
Each summand in square sum of approximation deviations from
given values is multiplied by the square of corresponding
weight. Fill it by 1's if you don't want to solve weighted
task.
N - number of points, N>0.
XC - points where function values/derivatives are constrained,
array[0..K-1].
YC - values of constraints, array[0..K-1]
DC - array[0..K-1], types of constraints:
* DC[i]=0 means that S(XC[i])=YC[i]
* DC[i]=1 means that S'(XC[i])=YC[i]
SEE BELOW FOR IMPORTANT INFORMATION ON CONSTRAINTS
K - number of constraints, 0<=K<M.
K=0 means no constraints (XC/YC/DC are not used in such cases)
M - number of basis functions ( = number_of_nodes), M>=2.
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearWC() subroutine.
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
-3 means inconsistent constraints
-1 means another errors in parameters passed
(N<=0, for example)
B - barycentric interpolant.
Rep - report, same format as in LSFitLinearWC() subroutine.
Following fields are set:
* DBest best value of the D parameter
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroutine doesn't calculate task's condition number for K<>0.
SETTING CONSTRAINTS - DANGERS AND OPPORTUNITIES:
Setting constraints can lead to undesired results, like ill-conditioned
behavior, or inconsistency being detected. From the other side, it allows
us to improve quality of the fit. Here we summarize our experience with
constrained barycentric interpolants:
* excessive constraints can be inconsistent. Floater-Hormann basis
functions aren't as flexible as splines (although they are very smooth).
* the more evenly constraints are spread across [min(x),max(x)], the more
chances that they will be consistent
* the greater is M (given fixed constraints), the more chances that
constraints will be consistent
* in the general case, consistency of constraints IS NOT GUARANTEED.
* in the several special cases, however, we CAN guarantee consistency.
* one of this cases is constraints on the function VALUES at the interval
boundaries. Note that consustency of the constraints on the function
DERIVATIVES is NOT guaranteed (you can use in such cases cubic splines
which are more flexible).
* another special case is ONE constraint on the function value (OR, but
not AND, derivative) anywhere in the interval
Our final recommendation is to use constraints WHEN AND ONLY WHEN you
can't solve your task without them. Anything beyond special cases given
above is not guaranteed and may result in inconsistency.
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentricfitfloaterhormannwc(const real_1d_array &x, const real_1d_array &y, const real_1d_array &w, const ae_int_t n, const real_1d_array &xc, const real_1d_array &yc, const integer_1d_array &dc, const ae_int_t k, const ae_int_t m, ae_int_t &info, barycentricinterpolant &b, barycentricfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::barycentricfitfloaterhormannwc(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(xc.c_ptr()), const_cast<alglib_impl::ae_vector*>(yc.c_ptr()), const_cast<alglib_impl::ae_vector*>(dc.c_ptr()), k, m, &info, const_cast<alglib_impl::barycentricinterpolant*>(b.c_ptr()), const_cast<alglib_impl::barycentricfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Rational least squares fitting using Floater-Hormann rational functions
with optimal D chosen from [0,9].
Equidistant grid with M node on [min(x),max(x)] is used to build basis
functions. Different values of D are tried, optimal D (least root mean
square error) is chosen. Task is linear, so linear least squares solver
is used. Complexity of this computational scheme is O(N*M^2) (mostly
dominated by the least squares solver).
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
N - number of points, N>0.
M - number of basis functions ( = number_of_nodes), M>=2.
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearWC() subroutine.
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
-3 means inconsistent constraints
B - barycentric interpolant.
Rep - report, same format as in LSFitLinearWC() subroutine.
Following fields are set:
* DBest best value of the D parameter
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentricfitfloaterhormann(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t m, ae_int_t &info, barycentricinterpolant &b, barycentricfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::barycentricfitfloaterhormann(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, m, &info, const_cast<alglib_impl::barycentricinterpolant*>(b.c_ptr()), const_cast<alglib_impl::barycentricfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Weighted fitting by cubic spline, with constraints on function values or
derivatives.
Equidistant grid with M-2 nodes on [min(x,xc),max(x,xc)] is used to build
basis functions. Basis functions are cubic splines with continuous second
derivatives and non-fixed first derivatives at interval ends. Small
regularizing term is used when solving constrained tasks (to improve
stability).
Task is linear, so linear least squares solver is used. Complexity of this
computational scheme is O(N*M^2), mostly dominated by least squares solver
SEE ALSO
Spline1DFitHermiteWC() - fitting by Hermite splines (more flexible,
less smooth)
Spline1DFitCubic() - "lightweight" fitting by cubic splines,
without invididual weights and constraints
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
W - weights, array[0..N-1]
Each summand in square sum of approximation deviations from
given values is multiplied by the square of corresponding
weight. Fill it by 1's if you don't want to solve weighted
task.
N - number of points (optional):
* N>0
* if given, only first N elements of X/Y/W are processed
* if not given, automatically determined from X/Y/W sizes
XC - points where spline values/derivatives are constrained,
array[0..K-1].
YC - values of constraints, array[0..K-1]
DC - array[0..K-1], types of constraints:
* DC[i]=0 means that S(XC[i])=YC[i]
* DC[i]=1 means that S'(XC[i])=YC[i]
SEE BELOW FOR IMPORTANT INFORMATION ON CONSTRAINTS
K - number of constraints (optional):
* 0<=K<M.
* K=0 means no constraints (XC/YC/DC are not used)
* if given, only first K elements of XC/YC/DC are used
* if not given, automatically determined from XC/YC/DC
M - number of basis functions ( = number_of_nodes+2), M>=4.
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearWC() subroutine.
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
-3 means inconsistent constraints
S - spline interpolant.
Rep - report, same format as in LSFitLinearWC() subroutine.
Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
SETTING CONSTRAINTS - DANGERS AND OPPORTUNITIES:
Setting constraints can lead to undesired results, like ill-conditioned
behavior, or inconsistency being detected. From the other side, it allows
us to improve quality of the fit. Here we summarize our experience with
constrained regression splines:
* excessive constraints can be inconsistent. Splines are piecewise cubic
functions, and it is easy to create an example, where large number of
constraints concentrated in small area will result in inconsistency.
Just because spline is not flexible enough to satisfy all of them. And
same constraints spread across the [min(x),max(x)] will be perfectly
consistent.
* the more evenly constraints are spread across [min(x),max(x)], the more
chances that they will be consistent
* the greater is M (given fixed constraints), the more chances that
constraints will be consistent
* in the general case, consistency of constraints IS NOT GUARANTEED.
* in the several special cases, however, we CAN guarantee consistency.
* one of this cases is constraints on the function values AND/OR its
derivatives at the interval boundaries.
* another special case is ONE constraint on the function value (OR, but
not AND, derivative) anywhere in the interval
Our final recommendation is to use constraints WHEN AND ONLY WHEN you
can't solve your task without them. Anything beyond special cases given
above is not guaranteed and may result in inconsistency.
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
void spline1dfitcubicwc(const real_1d_array &x, const real_1d_array &y, const real_1d_array &w, const ae_int_t n, const real_1d_array &xc, const real_1d_array &yc, const integer_1d_array &dc, const ae_int_t k, const ae_int_t m, ae_int_t &info, spline1dinterpolant &s, spline1dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dfitcubicwc(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(xc.c_ptr()), const_cast<alglib_impl::ae_vector*>(yc.c_ptr()), const_cast<alglib_impl::ae_vector*>(dc.c_ptr()), k, m, &info, const_cast<alglib_impl::spline1dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline1dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Weighted fitting by cubic spline, with constraints on function values or
derivatives.
Equidistant grid with M-2 nodes on [min(x,xc),max(x,xc)] is used to build
basis functions. Basis functions are cubic splines with continuous second
derivatives and non-fixed first derivatives at interval ends. Small
regularizing term is used when solving constrained tasks (to improve
stability).
Task is linear, so linear least squares solver is used. Complexity of this
computational scheme is O(N*M^2), mostly dominated by least squares solver
SEE ALSO
Spline1DFitHermiteWC() - fitting by Hermite splines (more flexible,
less smooth)
Spline1DFitCubic() - "lightweight" fitting by cubic splines,
without invididual weights and constraints
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
W - weights, array[0..N-1]
Each summand in square sum of approximation deviations from
given values is multiplied by the square of corresponding
weight. Fill it by 1's if you don't want to solve weighted
task.
N - number of points (optional):
* N>0
* if given, only first N elements of X/Y/W are processed
* if not given, automatically determined from X/Y/W sizes
XC - points where spline values/derivatives are constrained,
array[0..K-1].
YC - values of constraints, array[0..K-1]
DC - array[0..K-1], types of constraints:
* DC[i]=0 means that S(XC[i])=YC[i]
* DC[i]=1 means that S'(XC[i])=YC[i]
SEE BELOW FOR IMPORTANT INFORMATION ON CONSTRAINTS
K - number of constraints (optional):
* 0<=K<M.
* K=0 means no constraints (XC/YC/DC are not used)
* if given, only first K elements of XC/YC/DC are used
* if not given, automatically determined from XC/YC/DC
M - number of basis functions ( = number_of_nodes+2), M>=4.
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearWC() subroutine.
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
-3 means inconsistent constraints
S - spline interpolant.
Rep - report, same format as in LSFitLinearWC() subroutine.
Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
SETTING CONSTRAINTS - DANGERS AND OPPORTUNITIES:
Setting constraints can lead to undesired results, like ill-conditioned
behavior, or inconsistency being detected. From the other side, it allows
us to improve quality of the fit. Here we summarize our experience with
constrained regression splines:
* excessive constraints can be inconsistent. Splines are piecewise cubic
functions, and it is easy to create an example, where large number of
constraints concentrated in small area will result in inconsistency.
Just because spline is not flexible enough to satisfy all of them. And
same constraints spread across the [min(x),max(x)] will be perfectly
consistent.
* the more evenly constraints are spread across [min(x),max(x)], the more
chances that they will be consistent
* the greater is M (given fixed constraints), the more chances that
constraints will be consistent
* in the general case, consistency of constraints IS NOT GUARANTEED.
* in the several special cases, however, we CAN guarantee consistency.
* one of this cases is constraints on the function values AND/OR its
derivatives at the interval boundaries.
* another special case is ONE constraint on the function value (OR, but
not AND, derivative) anywhere in the interval
Our final recommendation is to use constraints WHEN AND ONLY WHEN you
can't solve your task without them. Anything beyond special cases given
above is not guaranteed and may result in inconsistency.
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dfitcubicwc(const real_1d_array &x, const real_1d_array &y, const real_1d_array &w, const real_1d_array &xc, const real_1d_array &yc, const integer_1d_array &dc, const ae_int_t m, ae_int_t &info, spline1dinterpolant &s, spline1dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t k;
if( (x.length()!=y.length()) || (x.length()!=w.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dfitcubicwc': looks like one of arguments has wrong size");
if( (xc.length()!=yc.length()) || (xc.length()!=dc.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dfitcubicwc': looks like one of arguments has wrong size");
n = x.length();
k = xc.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dfitcubicwc(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(xc.c_ptr()), const_cast<alglib_impl::ae_vector*>(yc.c_ptr()), const_cast<alglib_impl::ae_vector*>(dc.c_ptr()), k, m, &info, const_cast<alglib_impl::spline1dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline1dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Weighted fitting by Hermite spline, with constraints on function values
or first derivatives.
Equidistant grid with M nodes on [min(x,xc),max(x,xc)] is used to build
basis functions. Basis functions are Hermite splines. Small regularizing
term is used when solving constrained tasks (to improve stability).
Task is linear, so linear least squares solver is used. Complexity of this
computational scheme is O(N*M^2), mostly dominated by least squares solver
SEE ALSO
Spline1DFitCubicWC() - fitting by Cubic splines (less flexible,
more smooth)
Spline1DFitHermite() - "lightweight" Hermite fitting, without
invididual weights and constraints
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
W - weights, array[0..N-1]
Each summand in square sum of approximation deviations from
given values is multiplied by the square of corresponding
weight. Fill it by 1's if you don't want to solve weighted
task.
N - number of points (optional):
* N>0
* if given, only first N elements of X/Y/W are processed
* if not given, automatically determined from X/Y/W sizes
XC - points where spline values/derivatives are constrained,
array[0..K-1].
YC - values of constraints, array[0..K-1]
DC - array[0..K-1], types of constraints:
* DC[i]=0 means that S(XC[i])=YC[i]
* DC[i]=1 means that S'(XC[i])=YC[i]
SEE BELOW FOR IMPORTANT INFORMATION ON CONSTRAINTS
K - number of constraints (optional):
* 0<=K<M.
* K=0 means no constraints (XC/YC/DC are not used)
* if given, only first K elements of XC/YC/DC are used
* if not given, automatically determined from XC/YC/DC
M - number of basis functions (= 2 * number of nodes),
M>=4,
M IS EVEN!
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearW() subroutine:
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
-3 means inconsistent constraints
-2 means odd M was passed (which is not supported)
-1 means another errors in parameters passed
(N<=0, for example)
S - spline interpolant.
Rep - report, same format as in LSFitLinearW() subroutine.
Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
IMPORTANT:
this subroitine supports only even M's
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
SETTING CONSTRAINTS - DANGERS AND OPPORTUNITIES:
Setting constraints can lead to undesired results, like ill-conditioned
behavior, or inconsistency being detected. From the other side, it allows
us to improve quality of the fit. Here we summarize our experience with
constrained regression splines:
* excessive constraints can be inconsistent. Splines are piecewise cubic
functions, and it is easy to create an example, where large number of
constraints concentrated in small area will result in inconsistency.
Just because spline is not flexible enough to satisfy all of them. And
same constraints spread across the [min(x),max(x)] will be perfectly
consistent.
* the more evenly constraints are spread across [min(x),max(x)], the more
chances that they will be consistent
* the greater is M (given fixed constraints), the more chances that
constraints will be consistent
* in the general case, consistency of constraints is NOT GUARANTEED.
* in the several special cases, however, we can guarantee consistency.
* one of this cases is M>=4 and constraints on the function value
(AND/OR its derivative) at the interval boundaries.
* another special case is M>=4 and ONE constraint on the function value
(OR, BUT NOT AND, derivative) anywhere in [min(x),max(x)]
Our final recommendation is to use constraints WHEN AND ONLY when you
can't solve your task without them. Anything beyond special cases given
above is not guaranteed and may result in inconsistency.
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
void spline1dfithermitewc(const real_1d_array &x, const real_1d_array &y, const real_1d_array &w, const ae_int_t n, const real_1d_array &xc, const real_1d_array &yc, const integer_1d_array &dc, const ae_int_t k, const ae_int_t m, ae_int_t &info, spline1dinterpolant &s, spline1dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dfithermitewc(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(xc.c_ptr()), const_cast<alglib_impl::ae_vector*>(yc.c_ptr()), const_cast<alglib_impl::ae_vector*>(dc.c_ptr()), k, m, &info, const_cast<alglib_impl::spline1dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline1dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Weighted fitting by Hermite spline, with constraints on function values
or first derivatives.
Equidistant grid with M nodes on [min(x,xc),max(x,xc)] is used to build
basis functions. Basis functions are Hermite splines. Small regularizing
term is used when solving constrained tasks (to improve stability).
Task is linear, so linear least squares solver is used. Complexity of this
computational scheme is O(N*M^2), mostly dominated by least squares solver
SEE ALSO
Spline1DFitCubicWC() - fitting by Cubic splines (less flexible,
more smooth)
Spline1DFitHermite() - "lightweight" Hermite fitting, without
invididual weights and constraints
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
W - weights, array[0..N-1]
Each summand in square sum of approximation deviations from
given values is multiplied by the square of corresponding
weight. Fill it by 1's if you don't want to solve weighted
task.
N - number of points (optional):
* N>0
* if given, only first N elements of X/Y/W are processed
* if not given, automatically determined from X/Y/W sizes
XC - points where spline values/derivatives are constrained,
array[0..K-1].
YC - values of constraints, array[0..K-1]
DC - array[0..K-1], types of constraints:
* DC[i]=0 means that S(XC[i])=YC[i]
* DC[i]=1 means that S'(XC[i])=YC[i]
SEE BELOW FOR IMPORTANT INFORMATION ON CONSTRAINTS
K - number of constraints (optional):
* 0<=K<M.
* K=0 means no constraints (XC/YC/DC are not used)
* if given, only first K elements of XC/YC/DC are used
* if not given, automatically determined from XC/YC/DC
M - number of basis functions (= 2 * number of nodes),
M>=4,
M IS EVEN!
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearW() subroutine:
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
-3 means inconsistent constraints
-2 means odd M was passed (which is not supported)
-1 means another errors in parameters passed
(N<=0, for example)
S - spline interpolant.
Rep - report, same format as in LSFitLinearW() subroutine.
Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
IMPORTANT:
this subroitine supports only even M's
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
SETTING CONSTRAINTS - DANGERS AND OPPORTUNITIES:
Setting constraints can lead to undesired results, like ill-conditioned
behavior, or inconsistency being detected. From the other side, it allows
us to improve quality of the fit. Here we summarize our experience with
constrained regression splines:
* excessive constraints can be inconsistent. Splines are piecewise cubic
functions, and it is easy to create an example, where large number of
constraints concentrated in small area will result in inconsistency.
Just because spline is not flexible enough to satisfy all of them. And
same constraints spread across the [min(x),max(x)] will be perfectly
consistent.
* the more evenly constraints are spread across [min(x),max(x)], the more
chances that they will be consistent
* the greater is M (given fixed constraints), the more chances that
constraints will be consistent
* in the general case, consistency of constraints is NOT GUARANTEED.
* in the several special cases, however, we can guarantee consistency.
* one of this cases is M>=4 and constraints on the function value
(AND/OR its derivative) at the interval boundaries.
* another special case is M>=4 and ONE constraint on the function value
(OR, BUT NOT AND, derivative) anywhere in [min(x),max(x)]
Our final recommendation is to use constraints WHEN AND ONLY when you
can't solve your task without them. Anything beyond special cases given
above is not guaranteed and may result in inconsistency.
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dfithermitewc(const real_1d_array &x, const real_1d_array &y, const real_1d_array &w, const real_1d_array &xc, const real_1d_array &yc, const integer_1d_array &dc, const ae_int_t m, ae_int_t &info, spline1dinterpolant &s, spline1dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t k;
if( (x.length()!=y.length()) || (x.length()!=w.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dfithermitewc': looks like one of arguments has wrong size");
if( (xc.length()!=yc.length()) || (xc.length()!=dc.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dfithermitewc': looks like one of arguments has wrong size");
n = x.length();
k = xc.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dfithermitewc(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(xc.c_ptr()), const_cast<alglib_impl::ae_vector*>(yc.c_ptr()), const_cast<alglib_impl::ae_vector*>(dc.c_ptr()), k, m, &info, const_cast<alglib_impl::spline1dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline1dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Least squares fitting by cubic spline.
This subroutine is "lightweight" alternative for more complex and feature-
rich Spline1DFitCubicWC(). See Spline1DFitCubicWC() for more information
about subroutine parameters (we don't duplicate it here because of length)
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
void spline1dfitcubic(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t m, ae_int_t &info, spline1dinterpolant &s, spline1dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dfitcubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, m, &info, const_cast<alglib_impl::spline1dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline1dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Least squares fitting by cubic spline.
This subroutine is "lightweight" alternative for more complex and feature-
rich Spline1DFitCubicWC(). See Spline1DFitCubicWC() for more information
about subroutine parameters (we don't duplicate it here because of length)
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dfitcubic(const real_1d_array &x, const real_1d_array &y, const ae_int_t m, ae_int_t &info, spline1dinterpolant &s, spline1dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dfitcubic': looks like one of arguments has wrong size");
n = x.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dfitcubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, m, &info, const_cast<alglib_impl::spline1dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline1dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Least squares fitting by Hermite spline.
This subroutine is "lightweight" alternative for more complex and feature-
rich Spline1DFitHermiteWC(). See Spline1DFitHermiteWC() description for
more information about subroutine parameters (we don't duplicate it here
because of length).
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
void spline1dfithermite(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t m, ae_int_t &info, spline1dinterpolant &s, spline1dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dfithermite(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, m, &info, const_cast<alglib_impl::spline1dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline1dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Least squares fitting by Hermite spline.
This subroutine is "lightweight" alternative for more complex and feature-
rich Spline1DFitHermiteWC(). See Spline1DFitHermiteWC() description for
more information about subroutine parameters (we don't duplicate it here
because of length).
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dfithermite(const real_1d_array &x, const real_1d_array &y, const ae_int_t m, ae_int_t &info, spline1dinterpolant &s, spline1dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dfithermite': looks like one of arguments has wrong size");
n = x.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dfithermite(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, m, &info, const_cast<alglib_impl::spline1dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline1dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Weighted linear least squares fitting.
QR decomposition is used to reduce task to MxM, then triangular solver or
SVD-based solver is used depending on condition number of the system. It
allows to maximize speed and retain decent accuracy.
IMPORTANT: if you want to perform polynomial fitting, it may be more
convenient to use PolynomialFit() function. This function gives
best results on polynomial problems and solves numerical
stability issues which arise when you fit high-degree
polynomials to your data.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
Y - array[0..N-1] Function values in N points.
W - array[0..N-1] Weights corresponding to function values.
Each summand in square sum of approximation deviations
from given values is multiplied by the square of
corresponding weight.
FMatrix - a table of basis functions values, array[0..N-1, 0..M-1].
FMatrix[I, J] - value of J-th basis function in I-th point.
N - number of points used. N>=1.
M - number of basis functions, M>=1.
OUTPUT PARAMETERS:
Info - error code:
* -4 internal SVD decomposition subroutine failed (very
rare and for degenerate systems only)
* -1 incorrect N/M were specified
* 1 task is solved
C - decomposition coefficients, array[0..M-1]
Rep - fitting report. Following fields are set:
* Rep.TaskRCond reciprocal of condition number
* R2 non-adjusted coefficient of determination
(non-weighted)
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
ERRORS IN PARAMETERS
This solver also calculates different kinds of errors in parameters and
fills corresponding fields of report:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(F*CovPar*F')),
where F is functions matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
NOTE: covariance matrix is estimated using correction for degrees
of freedom (covariances are divided by N-M instead of dividing
by N).
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitlinearw(const real_1d_array &y, const real_1d_array &w, const real_2d_array &fmatrix, const ae_int_t n, const ae_int_t m, ae_int_t &info, real_1d_array &c, lsfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitlinearw(const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), const_cast<alglib_impl::ae_matrix*>(fmatrix.c_ptr()), n, m, &info, const_cast<alglib_impl::ae_vector*>(c.c_ptr()), const_cast<alglib_impl::lsfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Weighted linear least squares fitting.
QR decomposition is used to reduce task to MxM, then triangular solver or
SVD-based solver is used depending on condition number of the system. It
allows to maximize speed and retain decent accuracy.
IMPORTANT: if you want to perform polynomial fitting, it may be more
convenient to use PolynomialFit() function. This function gives
best results on polynomial problems and solves numerical
stability issues which arise when you fit high-degree
polynomials to your data.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
Y - array[0..N-1] Function values in N points.
W - array[0..N-1] Weights corresponding to function values.
Each summand in square sum of approximation deviations
from given values is multiplied by the square of
corresponding weight.
FMatrix - a table of basis functions values, array[0..N-1, 0..M-1].
FMatrix[I, J] - value of J-th basis function in I-th point.
N - number of points used. N>=1.
M - number of basis functions, M>=1.
OUTPUT PARAMETERS:
Info - error code:
* -4 internal SVD decomposition subroutine failed (very
rare and for degenerate systems only)
* -1 incorrect N/M were specified
* 1 task is solved
C - decomposition coefficients, array[0..M-1]
Rep - fitting report. Following fields are set:
* Rep.TaskRCond reciprocal of condition number
* R2 non-adjusted coefficient of determination
(non-weighted)
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
ERRORS IN PARAMETERS
This solver also calculates different kinds of errors in parameters and
fills corresponding fields of report:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(F*CovPar*F')),
where F is functions matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
NOTE: covariance matrix is estimated using correction for degrees
of freedom (covariances are divided by N-M instead of dividing
by N).
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void lsfitlinearw(const real_1d_array &y, const real_1d_array &w, const real_2d_array &fmatrix, ae_int_t &info, real_1d_array &c, lsfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t m;
if( (y.length()!=w.length()) || (y.length()!=fmatrix.rows()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'lsfitlinearw': looks like one of arguments has wrong size");
n = y.length();
m = fmatrix.cols();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitlinearw(const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), const_cast<alglib_impl::ae_matrix*>(fmatrix.c_ptr()), n, m, &info, const_cast<alglib_impl::ae_vector*>(c.c_ptr()), const_cast<alglib_impl::lsfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Weighted constained linear least squares fitting.
This is variation of LSFitLinearW(), which searchs for min|A*x=b| given
that K additional constaints C*x=bc are satisfied. It reduces original
task to modified one: min|B*y-d| WITHOUT constraints, then LSFitLinearW()
is called.
IMPORTANT: if you want to perform polynomial fitting, it may be more
convenient to use PolynomialFit() function. This function gives
best results on polynomial problems and solves numerical
stability issues which arise when you fit high-degree
polynomials to your data.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
Y - array[0..N-1] Function values in N points.
W - array[0..N-1] Weights corresponding to function values.
Each summand in square sum of approximation deviations
from given values is multiplied by the square of
corresponding weight.
FMatrix - a table of basis functions values, array[0..N-1, 0..M-1].
FMatrix[I,J] - value of J-th basis function in I-th point.
CMatrix - a table of constaints, array[0..K-1,0..M].
I-th row of CMatrix corresponds to I-th linear constraint:
CMatrix[I,0]*C[0] + ... + CMatrix[I,M-1]*C[M-1] = CMatrix[I,M]
N - number of points used. N>=1.
M - number of basis functions, M>=1.
K - number of constraints, 0 <= K < M
K=0 corresponds to absence of constraints.
OUTPUT PARAMETERS:
Info - error code:
* -4 internal SVD decomposition subroutine failed (very
rare and for degenerate systems only)
* -3 either too many constraints (M or more),
degenerate constraints (some constraints are
repetead twice) or inconsistent constraints were
specified.
* 1 task is solved
C - decomposition coefficients, array[0..M-1]
Rep - fitting report. Following fields are set:
* R2 non-adjusted coefficient of determination
(non-weighted)
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
ERRORS IN PARAMETERS
This solver also calculates different kinds of errors in parameters and
fills corresponding fields of report:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(F*CovPar*F')),
where F is functions matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
IMPORTANT: errors in parameters are calculated without taking into
account boundary/linear constraints! Presence of constraints
changes distribution of errors, but there is no easy way to
account for constraints when you calculate covariance matrix.
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
NOTE: covariance matrix is estimated using correction for degrees
of freedom (covariances are divided by N-M instead of dividing
by N).
-- ALGLIB --
Copyright 07.09.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitlinearwc(const real_1d_array &y, const real_1d_array &w, const real_2d_array &fmatrix, const real_2d_array &cmatrix, const ae_int_t n, const ae_int_t m, const ae_int_t k, ae_int_t &info, real_1d_array &c, lsfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitlinearwc(const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), const_cast<alglib_impl::ae_matrix*>(fmatrix.c_ptr()), const_cast<alglib_impl::ae_matrix*>(cmatrix.c_ptr()), n, m, k, &info, const_cast<alglib_impl::ae_vector*>(c.c_ptr()), const_cast<alglib_impl::lsfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Weighted constained linear least squares fitting.
This is variation of LSFitLinearW(), which searchs for min|A*x=b| given
that K additional constaints C*x=bc are satisfied. It reduces original
task to modified one: min|B*y-d| WITHOUT constraints, then LSFitLinearW()
is called.
IMPORTANT: if you want to perform polynomial fitting, it may be more
convenient to use PolynomialFit() function. This function gives
best results on polynomial problems and solves numerical
stability issues which arise when you fit high-degree
polynomials to your data.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
Y - array[0..N-1] Function values in N points.
W - array[0..N-1] Weights corresponding to function values.
Each summand in square sum of approximation deviations
from given values is multiplied by the square of
corresponding weight.
FMatrix - a table of basis functions values, array[0..N-1, 0..M-1].
FMatrix[I,J] - value of J-th basis function in I-th point.
CMatrix - a table of constaints, array[0..K-1,0..M].
I-th row of CMatrix corresponds to I-th linear constraint:
CMatrix[I,0]*C[0] + ... + CMatrix[I,M-1]*C[M-1] = CMatrix[I,M]
N - number of points used. N>=1.
M - number of basis functions, M>=1.
K - number of constraints, 0 <= K < M
K=0 corresponds to absence of constraints.
OUTPUT PARAMETERS:
Info - error code:
* -4 internal SVD decomposition subroutine failed (very
rare and for degenerate systems only)
* -3 either too many constraints (M or more),
degenerate constraints (some constraints are
repetead twice) or inconsistent constraints were
specified.
* 1 task is solved
C - decomposition coefficients, array[0..M-1]
Rep - fitting report. Following fields are set:
* R2 non-adjusted coefficient of determination
(non-weighted)
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
ERRORS IN PARAMETERS
This solver also calculates different kinds of errors in parameters and
fills corresponding fields of report:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(F*CovPar*F')),
where F is functions matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
IMPORTANT: errors in parameters are calculated without taking into
account boundary/linear constraints! Presence of constraints
changes distribution of errors, but there is no easy way to
account for constraints when you calculate covariance matrix.
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
NOTE: covariance matrix is estimated using correction for degrees
of freedom (covariances are divided by N-M instead of dividing
by N).
-- ALGLIB --
Copyright 07.09.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void lsfitlinearwc(const real_1d_array &y, const real_1d_array &w, const real_2d_array &fmatrix, const real_2d_array &cmatrix, ae_int_t &info, real_1d_array &c, lsfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t m;
ae_int_t k;
if( (y.length()!=w.length()) || (y.length()!=fmatrix.rows()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'lsfitlinearwc': looks like one of arguments has wrong size");
if( (fmatrix.cols()!=cmatrix.cols()-1))
_ALGLIB_CPP_EXCEPTION("Error while calling 'lsfitlinearwc': looks like one of arguments has wrong size");
n = y.length();
m = fmatrix.cols();
k = cmatrix.rows();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitlinearwc(const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), const_cast<alglib_impl::ae_matrix*>(fmatrix.c_ptr()), const_cast<alglib_impl::ae_matrix*>(cmatrix.c_ptr()), n, m, k, &info, const_cast<alglib_impl::ae_vector*>(c.c_ptr()), const_cast<alglib_impl::lsfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Linear least squares fitting.
QR decomposition is used to reduce task to MxM, then triangular solver or
SVD-based solver is used depending on condition number of the system. It
allows to maximize speed and retain decent accuracy.
IMPORTANT: if you want to perform polynomial fitting, it may be more
convenient to use PolynomialFit() function. This function gives
best results on polynomial problems and solves numerical
stability issues which arise when you fit high-degree
polynomials to your data.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
Y - array[0..N-1] Function values in N points.
FMatrix - a table of basis functions values, array[0..N-1, 0..M-1].
FMatrix[I, J] - value of J-th basis function in I-th point.
N - number of points used. N>=1.
M - number of basis functions, M>=1.
OUTPUT PARAMETERS:
Info - error code:
* -4 internal SVD decomposition subroutine failed (very
rare and for degenerate systems only)
* 1 task is solved
C - decomposition coefficients, array[0..M-1]
Rep - fitting report. Following fields are set:
* Rep.TaskRCond reciprocal of condition number
* R2 non-adjusted coefficient of determination
(non-weighted)
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
ERRORS IN PARAMETERS
This solver also calculates different kinds of errors in parameters and
fills corresponding fields of report:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(F*CovPar*F')),
where F is functions matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
NOTE: covariance matrix is estimated using correction for degrees
of freedom (covariances are divided by N-M instead of dividing
by N).
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitlinear(const real_1d_array &y, const real_2d_array &fmatrix, const ae_int_t n, const ae_int_t m, ae_int_t &info, real_1d_array &c, lsfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitlinear(const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_matrix*>(fmatrix.c_ptr()), n, m, &info, const_cast<alglib_impl::ae_vector*>(c.c_ptr()), const_cast<alglib_impl::lsfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Linear least squares fitting.
QR decomposition is used to reduce task to MxM, then triangular solver or
SVD-based solver is used depending on condition number of the system. It
allows to maximize speed and retain decent accuracy.
IMPORTANT: if you want to perform polynomial fitting, it may be more
convenient to use PolynomialFit() function. This function gives
best results on polynomial problems and solves numerical
stability issues which arise when you fit high-degree
polynomials to your data.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
Y - array[0..N-1] Function values in N points.
FMatrix - a table of basis functions values, array[0..N-1, 0..M-1].
FMatrix[I, J] - value of J-th basis function in I-th point.
N - number of points used. N>=1.
M - number of basis functions, M>=1.
OUTPUT PARAMETERS:
Info - error code:
* -4 internal SVD decomposition subroutine failed (very
rare and for degenerate systems only)
* 1 task is solved
C - decomposition coefficients, array[0..M-1]
Rep - fitting report. Following fields are set:
* Rep.TaskRCond reciprocal of condition number
* R2 non-adjusted coefficient of determination
(non-weighted)
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
ERRORS IN PARAMETERS
This solver also calculates different kinds of errors in parameters and
fills corresponding fields of report:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(F*CovPar*F')),
where F is functions matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
NOTE: covariance matrix is estimated using correction for degrees
of freedom (covariances are divided by N-M instead of dividing
by N).
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void lsfitlinear(const real_1d_array &y, const real_2d_array &fmatrix, ae_int_t &info, real_1d_array &c, lsfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t m;
if( (y.length()!=fmatrix.rows()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'lsfitlinear': looks like one of arguments has wrong size");
n = y.length();
m = fmatrix.cols();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitlinear(const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_matrix*>(fmatrix.c_ptr()), n, m, &info, const_cast<alglib_impl::ae_vector*>(c.c_ptr()), const_cast<alglib_impl::lsfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Constained linear least squares fitting.
This is variation of LSFitLinear(), which searchs for min|A*x=b| given
that K additional constaints C*x=bc are satisfied. It reduces original
task to modified one: min|B*y-d| WITHOUT constraints, then LSFitLinear()
is called.
IMPORTANT: if you want to perform polynomial fitting, it may be more
convenient to use PolynomialFit() function. This function gives
best results on polynomial problems and solves numerical
stability issues which arise when you fit high-degree
polynomials to your data.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
Y - array[0..N-1] Function values in N points.
FMatrix - a table of basis functions values, array[0..N-1, 0..M-1].
FMatrix[I,J] - value of J-th basis function in I-th point.
CMatrix - a table of constaints, array[0..K-1,0..M].
I-th row of CMatrix corresponds to I-th linear constraint:
CMatrix[I,0]*C[0] + ... + CMatrix[I,M-1]*C[M-1] = CMatrix[I,M]
N - number of points used. N>=1.
M - number of basis functions, M>=1.
K - number of constraints, 0 <= K < M
K=0 corresponds to absence of constraints.
OUTPUT PARAMETERS:
Info - error code:
* -4 internal SVD decomposition subroutine failed (very
rare and for degenerate systems only)
* -3 either too many constraints (M or more),
degenerate constraints (some constraints are
repetead twice) or inconsistent constraints were
specified.
* 1 task is solved
C - decomposition coefficients, array[0..M-1]
Rep - fitting report. Following fields are set:
* R2 non-adjusted coefficient of determination
(non-weighted)
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
ERRORS IN PARAMETERS
This solver also calculates different kinds of errors in parameters and
fills corresponding fields of report:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(F*CovPar*F')),
where F is functions matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
IMPORTANT: errors in parameters are calculated without taking into
account boundary/linear constraints! Presence of constraints
changes distribution of errors, but there is no easy way to
account for constraints when you calculate covariance matrix.
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
NOTE: covariance matrix is estimated using correction for degrees
of freedom (covariances are divided by N-M instead of dividing
by N).
-- ALGLIB --
Copyright 07.09.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitlinearc(const real_1d_array &y, const real_2d_array &fmatrix, const real_2d_array &cmatrix, const ae_int_t n, const ae_int_t m, const ae_int_t k, ae_int_t &info, real_1d_array &c, lsfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitlinearc(const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_matrix*>(fmatrix.c_ptr()), const_cast<alglib_impl::ae_matrix*>(cmatrix.c_ptr()), n, m, k, &info, const_cast<alglib_impl::ae_vector*>(c.c_ptr()), const_cast<alglib_impl::lsfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Constained linear least squares fitting.
This is variation of LSFitLinear(), which searchs for min|A*x=b| given
that K additional constaints C*x=bc are satisfied. It reduces original
task to modified one: min|B*y-d| WITHOUT constraints, then LSFitLinear()
is called.
IMPORTANT: if you want to perform polynomial fitting, it may be more
convenient to use PolynomialFit() function. This function gives
best results on polynomial problems and solves numerical
stability issues which arise when you fit high-degree
polynomials to your data.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
Y - array[0..N-1] Function values in N points.
FMatrix - a table of basis functions values, array[0..N-1, 0..M-1].
FMatrix[I,J] - value of J-th basis function in I-th point.
CMatrix - a table of constaints, array[0..K-1,0..M].
I-th row of CMatrix corresponds to I-th linear constraint:
CMatrix[I,0]*C[0] + ... + CMatrix[I,M-1]*C[M-1] = CMatrix[I,M]
N - number of points used. N>=1.
M - number of basis functions, M>=1.
K - number of constraints, 0 <= K < M
K=0 corresponds to absence of constraints.
OUTPUT PARAMETERS:
Info - error code:
* -4 internal SVD decomposition subroutine failed (very
rare and for degenerate systems only)
* -3 either too many constraints (M or more),
degenerate constraints (some constraints are
repetead twice) or inconsistent constraints were
specified.
* 1 task is solved
C - decomposition coefficients, array[0..M-1]
Rep - fitting report. Following fields are set:
* R2 non-adjusted coefficient of determination
(non-weighted)
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
ERRORS IN PARAMETERS
This solver also calculates different kinds of errors in parameters and
fills corresponding fields of report:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(F*CovPar*F')),
where F is functions matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
IMPORTANT: errors in parameters are calculated without taking into
account boundary/linear constraints! Presence of constraints
changes distribution of errors, but there is no easy way to
account for constraints when you calculate covariance matrix.
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
NOTE: covariance matrix is estimated using correction for degrees
of freedom (covariances are divided by N-M instead of dividing
by N).
-- ALGLIB --
Copyright 07.09.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void lsfitlinearc(const real_1d_array &y, const real_2d_array &fmatrix, const real_2d_array &cmatrix, ae_int_t &info, real_1d_array &c, lsfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t m;
ae_int_t k;
if( (y.length()!=fmatrix.rows()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'lsfitlinearc': looks like one of arguments has wrong size");
if( (fmatrix.cols()!=cmatrix.cols()-1))
_ALGLIB_CPP_EXCEPTION("Error while calling 'lsfitlinearc': looks like one of arguments has wrong size");
n = y.length();
m = fmatrix.cols();
k = cmatrix.rows();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitlinearc(const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_matrix*>(fmatrix.c_ptr()), const_cast<alglib_impl::ae_matrix*>(cmatrix.c_ptr()), n, m, k, &info, const_cast<alglib_impl::ae_vector*>(c.c_ptr()), const_cast<alglib_impl::lsfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Weighted nonlinear least squares fitting using function values only.
Combination of numerical differentiation and secant updates is used to
obtain function Jacobian.
Nonlinear task min(F(c)) is solved, where
F(c) = (w[0]*(f(c,x[0])-y[0]))^2 + ... + (w[n-1]*(f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* w is an N-dimensional vector of weight coefficients,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses only f(c,x[i]).
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
W - weights, array[0..N-1]
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
DiffStep- numerical differentiation step;
should not be very small or large;
large = loss of accuracy
small = growth of round-off errors
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 18.10.2008 by Bochkanov Sergey
*************************************************************************/
void lsfitcreatewf(const real_2d_array &x, const real_1d_array &y, const real_1d_array &w, const real_1d_array &c, const ae_int_t n, const ae_int_t m, const ae_int_t k, const double diffstep, lsfitstate &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitcreatewf(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), const_cast<alglib_impl::ae_vector*>(c.c_ptr()), n, m, k, diffstep, const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Weighted nonlinear least squares fitting using function values only.
Combination of numerical differentiation and secant updates is used to
obtain function Jacobian.
Nonlinear task min(F(c)) is solved, where
F(c) = (w[0]*(f(c,x[0])-y[0]))^2 + ... + (w[n-1]*(f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* w is an N-dimensional vector of weight coefficients,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses only f(c,x[i]).
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
W - weights, array[0..N-1]
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
DiffStep- numerical differentiation step;
should not be very small or large;
large = loss of accuracy
small = growth of round-off errors
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 18.10.2008 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void lsfitcreatewf(const real_2d_array &x, const real_1d_array &y, const real_1d_array &w, const real_1d_array &c, const double diffstep, lsfitstate &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t m;
ae_int_t k;
if( (x.rows()!=y.length()) || (x.rows()!=w.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'lsfitcreatewf': looks like one of arguments has wrong size");
n = x.rows();
m = x.cols();
k = c.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitcreatewf(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), const_cast<alglib_impl::ae_vector*>(c.c_ptr()), n, m, k, diffstep, const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Nonlinear least squares fitting using function values only.
Combination of numerical differentiation and secant updates is used to
obtain function Jacobian.
Nonlinear task min(F(c)) is solved, where
F(c) = (f(c,x[0])-y[0])^2 + ... + (f(c,x[n-1])-y[n-1])^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* w is an N-dimensional vector of weight coefficients,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses only f(c,x[i]).
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
DiffStep- numerical differentiation step;
should not be very small or large;
large = loss of accuracy
small = growth of round-off errors
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 18.10.2008 by Bochkanov Sergey
*************************************************************************/
void lsfitcreatef(const real_2d_array &x, const real_1d_array &y, const real_1d_array &c, const ae_int_t n, const ae_int_t m, const ae_int_t k, const double diffstep, lsfitstate &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitcreatef(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(c.c_ptr()), n, m, k, diffstep, const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Nonlinear least squares fitting using function values only.
Combination of numerical differentiation and secant updates is used to
obtain function Jacobian.
Nonlinear task min(F(c)) is solved, where
F(c) = (f(c,x[0])-y[0])^2 + ... + (f(c,x[n-1])-y[n-1])^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* w is an N-dimensional vector of weight coefficients,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses only f(c,x[i]).
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
DiffStep- numerical differentiation step;
should not be very small or large;
large = loss of accuracy
small = growth of round-off errors
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 18.10.2008 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void lsfitcreatef(const real_2d_array &x, const real_1d_array &y, const real_1d_array &c, const double diffstep, lsfitstate &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t m;
ae_int_t k;
if( (x.rows()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'lsfitcreatef': looks like one of arguments has wrong size");
n = x.rows();
m = x.cols();
k = c.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitcreatef(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(c.c_ptr()), n, m, k, diffstep, const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Weighted nonlinear least squares fitting using gradient only.
Nonlinear task min(F(c)) is solved, where
F(c) = (w[0]*(f(c,x[0])-y[0]))^2 + ... + (w[n-1]*(f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* w is an N-dimensional vector of weight coefficients,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses only f(c,x[i]) and its gradient.
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
W - weights, array[0..N-1]
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
CheapFG - boolean flag, which is:
* True if both function and gradient calculation complexity
are less than O(M^2). An improved algorithm can
be used which corresponds to FGJ scheme from
MINLM unit.
* False otherwise.
Standard Jacibian-bases Levenberg-Marquardt algo
will be used (FJ scheme).
OUTPUT PARAMETERS:
State - structure which stores algorithm state
See also:
LSFitResults
LSFitCreateFG (fitting without weights)
LSFitCreateWFGH (fitting using Hessian)
LSFitCreateFGH (fitting using Hessian, without weights)
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitcreatewfg(const real_2d_array &x, const real_1d_array &y, const real_1d_array &w, const real_1d_array &c, const ae_int_t n, const ae_int_t m, const ae_int_t k, const bool cheapfg, lsfitstate &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitcreatewfg(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), const_cast<alglib_impl::ae_vector*>(c.c_ptr()), n, m, k, cheapfg, const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Weighted nonlinear least squares fitting using gradient only.
Nonlinear task min(F(c)) is solved, where
F(c) = (w[0]*(f(c,x[0])-y[0]))^2 + ... + (w[n-1]*(f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* w is an N-dimensional vector of weight coefficients,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses only f(c,x[i]) and its gradient.
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
W - weights, array[0..N-1]
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
CheapFG - boolean flag, which is:
* True if both function and gradient calculation complexity
are less than O(M^2). An improved algorithm can
be used which corresponds to FGJ scheme from
MINLM unit.
* False otherwise.
Standard Jacibian-bases Levenberg-Marquardt algo
will be used (FJ scheme).
OUTPUT PARAMETERS:
State - structure which stores algorithm state
See also:
LSFitResults
LSFitCreateFG (fitting without weights)
LSFitCreateWFGH (fitting using Hessian)
LSFitCreateFGH (fitting using Hessian, without weights)
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void lsfitcreatewfg(const real_2d_array &x, const real_1d_array &y, const real_1d_array &w, const real_1d_array &c, const bool cheapfg, lsfitstate &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t m;
ae_int_t k;
if( (x.rows()!=y.length()) || (x.rows()!=w.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'lsfitcreatewfg': looks like one of arguments has wrong size");
n = x.rows();
m = x.cols();
k = c.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitcreatewfg(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), const_cast<alglib_impl::ae_vector*>(c.c_ptr()), n, m, k, cheapfg, const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Nonlinear least squares fitting using gradient only, without individual
weights.
Nonlinear task min(F(c)) is solved, where
F(c) = ((f(c,x[0])-y[0]))^2 + ... + ((f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses only f(c,x[i]) and its gradient.
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
CheapFG - boolean flag, which is:
* True if both function and gradient calculation complexity
are less than O(M^2). An improved algorithm can
be used which corresponds to FGJ scheme from
MINLM unit.
* False otherwise.
Standard Jacibian-bases Levenberg-Marquardt algo
will be used (FJ scheme).
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitcreatefg(const real_2d_array &x, const real_1d_array &y, const real_1d_array &c, const ae_int_t n, const ae_int_t m, const ae_int_t k, const bool cheapfg, lsfitstate &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitcreatefg(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(c.c_ptr()), n, m, k, cheapfg, const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Nonlinear least squares fitting using gradient only, without individual
weights.
Nonlinear task min(F(c)) is solved, where
F(c) = ((f(c,x[0])-y[0]))^2 + ... + ((f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses only f(c,x[i]) and its gradient.
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
CheapFG - boolean flag, which is:
* True if both function and gradient calculation complexity
are less than O(M^2). An improved algorithm can
be used which corresponds to FGJ scheme from
MINLM unit.
* False otherwise.
Standard Jacibian-bases Levenberg-Marquardt algo
will be used (FJ scheme).
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void lsfitcreatefg(const real_2d_array &x, const real_1d_array &y, const real_1d_array &c, const bool cheapfg, lsfitstate &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t m;
ae_int_t k;
if( (x.rows()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'lsfitcreatefg': looks like one of arguments has wrong size");
n = x.rows();
m = x.cols();
k = c.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitcreatefg(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(c.c_ptr()), n, m, k, cheapfg, const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Weighted nonlinear least squares fitting using gradient/Hessian.
Nonlinear task min(F(c)) is solved, where
F(c) = (w[0]*(f(c,x[0])-y[0]))^2 + ... + (w[n-1]*(f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* w is an N-dimensional vector of weight coefficients,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses f(c,x[i]), its gradient and its Hessian.
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
W - weights, array[0..N-1]
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitcreatewfgh(const real_2d_array &x, const real_1d_array &y, const real_1d_array &w, const real_1d_array &c, const ae_int_t n, const ae_int_t m, const ae_int_t k, lsfitstate &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitcreatewfgh(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), const_cast<alglib_impl::ae_vector*>(c.c_ptr()), n, m, k, const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Weighted nonlinear least squares fitting using gradient/Hessian.
Nonlinear task min(F(c)) is solved, where
F(c) = (w[0]*(f(c,x[0])-y[0]))^2 + ... + (w[n-1]*(f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* w is an N-dimensional vector of weight coefficients,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses f(c,x[i]), its gradient and its Hessian.
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
W - weights, array[0..N-1]
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void lsfitcreatewfgh(const real_2d_array &x, const real_1d_array &y, const real_1d_array &w, const real_1d_array &c, lsfitstate &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t m;
ae_int_t k;
if( (x.rows()!=y.length()) || (x.rows()!=w.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'lsfitcreatewfgh': looks like one of arguments has wrong size");
n = x.rows();
m = x.cols();
k = c.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitcreatewfgh(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), const_cast<alglib_impl::ae_vector*>(c.c_ptr()), n, m, k, const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Nonlinear least squares fitting using gradient/Hessian, without individial
weights.
Nonlinear task min(F(c)) is solved, where
F(c) = ((f(c,x[0])-y[0]))^2 + ... + ((f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses f(c,x[i]), its gradient and its Hessian.
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitcreatefgh(const real_2d_array &x, const real_1d_array &y, const real_1d_array &c, const ae_int_t n, const ae_int_t m, const ae_int_t k, lsfitstate &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitcreatefgh(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(c.c_ptr()), n, m, k, const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Nonlinear least squares fitting using gradient/Hessian, without individial
weights.
Nonlinear task min(F(c)) is solved, where
F(c) = ((f(c,x[0])-y[0]))^2 + ... + ((f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses f(c,x[i]), its gradient and its Hessian.
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void lsfitcreatefgh(const real_2d_array &x, const real_1d_array &y, const real_1d_array &c, lsfitstate &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
ae_int_t m;
ae_int_t k;
if( (x.rows()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'lsfitcreatefgh': looks like one of arguments has wrong size");
n = x.rows();
m = x.cols();
k = c.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitcreatefgh(const_cast<alglib_impl::ae_matrix*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(c.c_ptr()), n, m, k, const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
Stopping conditions for nonlinear least squares fitting.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsX - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |v|<=EpsX is fulfilled, where:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - ste pvector, dx=X(k+1)-X(k)
* s - scaling coefficients set by LSFitSetScale()
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited. Only Levenberg-Marquardt
iterations are counted (L-BFGS/CG iterations are NOT
counted because their cost is very low compared to that of
LM).
NOTE
Passing EpsX=0 and MaxIts=0 (simultaneously) will lead to automatic
stopping criterion selection (according to the scheme used by MINLM unit).
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitsetcond(const lsfitstate &state, const double epsx, const ae_int_t maxits, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitsetcond(const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), epsx, maxits, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets maximum step length
INPUT PARAMETERS:
State - structure which stores algorithm state
StpMax - maximum step length, >=0. Set StpMax to 0.0, if you don't
want to limit step length.
Use this subroutine when you optimize target function which contains exp()
or other fast growing functions, and optimization algorithm makes too
large steps which leads to overflow. This function allows us to reject
steps that are too large (and therefore expose us to the possible
overflow) without actually calculating function value at the x+stp*d.
NOTE: non-zero StpMax leads to moderate performance degradation because
intermediate step of preconditioned L-BFGS optimization is incompatible
with limits on step size.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void lsfitsetstpmax(const lsfitstate &state, const double stpmax, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitsetstpmax(const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), stpmax, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
When reports are needed, State.C (current parameters) and State.F (current
value of fitting function) are reported.
-- ALGLIB --
Copyright 15.08.2010 by Bochkanov Sergey
*************************************************************************/
void lsfitsetxrep(const lsfitstate &state, const bool needxrep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitsetxrep(const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), needxrep, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets scaling coefficients for underlying optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Generally, scale is NOT considered to be a form of preconditioner. But LM
optimizer is unique in that it uses scaling matrix both in the stopping
condition tests and as Marquardt damping factor.
Proper scaling is very important for the algorithm performance. It is less
important for the quality of results, but still has some influence (it is
easier to converge when variables are properly scaled, so premature
stopping is possible when very badly scalled variables are combined with
relaxed stopping conditions).
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void lsfitsetscale(const lsfitstate &state, const real_1d_array &s, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitsetscale(const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), const_cast<alglib_impl::ae_vector*>(s.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets boundary constraints for underlying optimizer
Boundary constraints are inactive by default (after initial creation).
They are preserved until explicitly turned off with another SetBC() call.
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bounds, array[K].
If some (all) variables are unbounded, you may specify
very small number or -INF (latter is recommended because
it will allow solver to use better algorithm).
BndU - upper bounds, array[K].
If some (all) variables are unbounded, you may specify
very large number or +INF (latter is recommended because
it will allow solver to use better algorithm).
NOTE 1: it is possible to specify BndL[i]=BndU[i]. In this case I-th
variable will be "frozen" at X[i]=BndL[i]=BndU[i].
NOTE 2: unlike other constrained optimization algorithms, this solver has
following useful properties:
* bound constraints are always satisfied exactly
* function is evaluated only INSIDE area specified by bound constraints
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void lsfitsetbc(const lsfitstate &state, const real_1d_array &bndl, const real_1d_array &bndu, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitsetbc(const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), const_cast<alglib_impl::ae_vector*>(bndl.c_ptr()), const_cast<alglib_impl::ae_vector*>(bndu.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets linear constraints for underlying optimizer
Linear constraints are inactive by default (after initial creation).
They are preserved until explicitly turned off with another SetLC() call.
INPUT PARAMETERS:
State - structure stores algorithm state
C - linear constraints, array[K,N+1].
Each row of C represents one constraint, either equality
or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of C (including right part) must be finite.
CT - type of constraints, array[K]:
* if CT[i]>0, then I-th constraint is C[i,*]*x >= C[i,n+1]
* if CT[i]=0, then I-th constraint is C[i,*]*x = C[i,n+1]
* if CT[i]<0, then I-th constraint is C[i,*]*x <= C[i,n+1]
K - number of equality/inequality constraints, K>=0:
* if given, only leading K elements of C/CT are used
* if not given, automatically determined from sizes of C/CT
IMPORTANT: if you have linear constraints, it is strongly recommended to
set scale of variables with lsfitsetscale(). QP solver which is
used to calculate linearly constrained steps heavily relies on
good scaling of input problems.
NOTE: linear (non-box) constraints are satisfied only approximately -
there always exists some violation due to numerical errors and
algorithmic limitations.
NOTE: general linear constraints add significant overhead to solution
process. Although solver performs roughly same amount of iterations
(when compared with similar box-only constrained problem), each
iteration now involves solution of linearly constrained QP
subproblem, which requires ~3-5 times more Cholesky decompositions.
Thus, if you can reformulate your problem in such way this it has
only box constraints, it may be beneficial to do so.
-- ALGLIB --
Copyright 29.04.2017 by Bochkanov Sergey
*************************************************************************/
void lsfitsetlc(const lsfitstate &state, const real_2d_array &c, const integer_1d_array &ct, const ae_int_t k, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitsetlc(const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), const_cast<alglib_impl::ae_matrix*>(c.c_ptr()), const_cast<alglib_impl::ae_vector*>(ct.c_ptr()), k, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets linear constraints for underlying optimizer
Linear constraints are inactive by default (after initial creation).
They are preserved until explicitly turned off with another SetLC() call.
INPUT PARAMETERS:
State - structure stores algorithm state
C - linear constraints, array[K,N+1].
Each row of C represents one constraint, either equality
or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of C (including right part) must be finite.
CT - type of constraints, array[K]:
* if CT[i]>0, then I-th constraint is C[i,*]*x >= C[i,n+1]
* if CT[i]=0, then I-th constraint is C[i,*]*x = C[i,n+1]
* if CT[i]<0, then I-th constraint is C[i,*]*x <= C[i,n+1]
K - number of equality/inequality constraints, K>=0:
* if given, only leading K elements of C/CT are used
* if not given, automatically determined from sizes of C/CT
IMPORTANT: if you have linear constraints, it is strongly recommended to
set scale of variables with lsfitsetscale(). QP solver which is
used to calculate linearly constrained steps heavily relies on
good scaling of input problems.
NOTE: linear (non-box) constraints are satisfied only approximately -
there always exists some violation due to numerical errors and
algorithmic limitations.
NOTE: general linear constraints add significant overhead to solution
process. Although solver performs roughly same amount of iterations
(when compared with similar box-only constrained problem), each
iteration now involves solution of linearly constrained QP
subproblem, which requires ~3-5 times more Cholesky decompositions.
Thus, if you can reformulate your problem in such way this it has
only box constraints, it may be beneficial to do so.
-- ALGLIB --
Copyright 29.04.2017 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void lsfitsetlc(const lsfitstate &state, const real_2d_array &c, const integer_1d_array &ct, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t k;
if( (c.rows()!=ct.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'lsfitsetlc': looks like one of arguments has wrong size");
k = c.rows();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitsetlc(const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), const_cast<alglib_impl::ae_matrix*>(c.c_ptr()), const_cast<alglib_impl::ae_vector*>(ct.c_ptr()), k, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This function provides reverse communication interface
Reverse communication interface is not documented or recommended to use.
See below for functions which provide better documented API
*************************************************************************/
bool lsfititeration(const lsfitstate &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
ae_bool result = alglib_impl::lsfititeration(const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<bool*>(&result));
}
void lsfitfit(lsfitstate &state,
void (*func)(const real_1d_array &c, const real_1d_array &x, double &func, void *ptr),
void (*rep)(const real_1d_array &c, double func, void *ptr),
void *ptr,
const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::ae_assert(func!=NULL, "ALGLIB: error in 'lsfitfit()' (func is NULL)", &_alglib_env_state);
while( alglib_impl::lsfititeration(state.c_ptr(), &_alglib_env_state) )
{
_ALGLIB_CALLBACK_EXCEPTION_GUARD_BEGIN
if( state.needf )
{
func(state.c, state.x, state.f, ptr);
continue;
}
if( state.xupdated )
{
if( rep!=NULL )
rep(state.c, state.f, ptr);
continue;
}
goto lbl_no_callback;
_ALGLIB_CALLBACK_EXCEPTION_GUARD_END
lbl_no_callback:
alglib_impl::ae_assert(ae_false, "ALGLIB: error in 'lsfitfit' (some derivatives were not provided?)", &_alglib_env_state);
}
alglib_impl::ae_state_clear(&_alglib_env_state);
}
void lsfitfit(lsfitstate &state,
void (*func)(const real_1d_array &c, const real_1d_array &x, double &func, void *ptr),
void (*grad)(const real_1d_array &c, const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*rep)(const real_1d_array &c, double func, void *ptr),
void *ptr,
const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::ae_assert(func!=NULL, "ALGLIB: error in 'lsfitfit()' (func is NULL)", &_alglib_env_state);
alglib_impl::ae_assert(grad!=NULL, "ALGLIB: error in 'lsfitfit()' (grad is NULL)", &_alglib_env_state);
while( alglib_impl::lsfititeration(state.c_ptr(), &_alglib_env_state) )
{
_ALGLIB_CALLBACK_EXCEPTION_GUARD_BEGIN
if( state.needf )
{
func(state.c, state.x, state.f, ptr);
continue;
}
if( state.needfg )
{
grad(state.c, state.x, state.f, state.g, ptr);
continue;
}
if( state.xupdated )
{
if( rep!=NULL )
rep(state.c, state.f, ptr);
continue;
}
goto lbl_no_callback;
_ALGLIB_CALLBACK_EXCEPTION_GUARD_END
lbl_no_callback:
alglib_impl::ae_assert(ae_false, "ALGLIB: error in 'lsfitfit' (some derivatives were not provided?)", &_alglib_env_state);
}
alglib_impl::ae_state_clear(&_alglib_env_state);
}
void lsfitfit(lsfitstate &state,
void (*func)(const real_1d_array &c, const real_1d_array &x, double &func, void *ptr),
void (*grad)(const real_1d_array &c, const real_1d_array &x, double &func, real_1d_array &grad, void *ptr),
void (*hess)(const real_1d_array &c, const real_1d_array &x, double &func, real_1d_array &grad, real_2d_array &hess, void *ptr),
void (*rep)(const real_1d_array &c, double func, void *ptr),
void *ptr,
const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::ae_assert(func!=NULL, "ALGLIB: error in 'lsfitfit()' (func is NULL)", &_alglib_env_state);
alglib_impl::ae_assert(grad!=NULL, "ALGLIB: error in 'lsfitfit()' (grad is NULL)", &_alglib_env_state);
alglib_impl::ae_assert(hess!=NULL, "ALGLIB: error in 'lsfitfit()' (hess is NULL)", &_alglib_env_state);
while( alglib_impl::lsfititeration(state.c_ptr(), &_alglib_env_state) )
{
_ALGLIB_CALLBACK_EXCEPTION_GUARD_BEGIN
if( state.needf )
{
func(state.c, state.x, state.f, ptr);
continue;
}
if( state.needfg )
{
grad(state.c, state.x, state.f, state.g, ptr);
continue;
}
if( state.needfgh )
{
hess(state.c, state.x, state.f, state.g, state.h, ptr);
continue;
}
if( state.xupdated )
{
if( rep!=NULL )
rep(state.c, state.f, ptr);
continue;
}
goto lbl_no_callback;
_ALGLIB_CALLBACK_EXCEPTION_GUARD_END
lbl_no_callback:
alglib_impl::ae_assert(ae_false, "ALGLIB: error in 'lsfitfit' (some derivatives were not provided?)", &_alglib_env_state);
}
alglib_impl::ae_state_clear(&_alglib_env_state);
}
/*************************************************************************
Nonlinear least squares fitting results.
Called after return from LSFitFit().
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
Info - completion code:
* -8 optimizer detected NAN/INF in the target
function and/or gradient
* -7 gradient verification failed.
See LSFitSetGradientCheck() for more information.
* -3 inconsistent constraints
* 2 relative step is no more than EpsX.
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible
C - array[0..K-1], solution
Rep - optimization report. On success following fields are set:
* R2 non-adjusted coefficient of determination
(non-weighted)
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
* WRMSError weighted rms error on the (X,Y).
ERRORS IN PARAMETERS
This solver also calculates different kinds of errors in parameters and
fills corresponding fields of report:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(J*CovPar*J')),
where J is Jacobian matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
IMPORTANT: errors in parameters are calculated without taking into
account boundary/linear constraints! Presence of constraints
changes distribution of errors, but there is no easy way to
account for constraints when you calculate covariance matrix.
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
NOTE: covariance matrix is estimated using correction for degrees
of freedom (covariances are divided by N-M instead of dividing
by N).
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitresults(const lsfitstate &state, ae_int_t &info, real_1d_array &c, lsfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitresults(const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), &info, const_cast<alglib_impl::ae_vector*>(c.c_ptr()), const_cast<alglib_impl::lsfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine turns on verification of the user-supplied analytic
gradient:
* user calls this subroutine before fitting begins
* LSFitFit() is called
* prior to actual fitting, for each point in data set X_i and each
component of parameters being fited C_j algorithm performs following
steps:
* two trial steps are made to C_j-TestStep*S[j] and C_j+TestStep*S[j],
where C_j is j-th parameter and S[j] is a scale of j-th parameter
* if needed, steps are bounded with respect to constraints on C[]
* F(X_i|C) is evaluated at these trial points
* we perform one more evaluation in the middle point of the interval
* we build cubic model using function values and derivatives at trial
points and we compare its prediction with actual value in the middle
point
* in case difference between prediction and actual value is higher than
some predetermined threshold, algorithm stops with completion code -7;
Rep.VarIdx is set to index of the parameter with incorrect derivative.
* after verification is over, algorithm proceeds to the actual optimization.
NOTE 1: verification needs N*K (points count * parameters count) gradient
evaluations. It is very costly and you should use it only for low
dimensional problems, when you want to be sure that you've
correctly calculated analytic derivatives. You should not use it
in the production code (unless you want to check derivatives
provided by some third party).
NOTE 2: you should carefully choose TestStep. Value which is too large
(so large that function behaviour is significantly non-cubic) will
lead to false alarms. You may use different step for different
parameters by means of setting scale with LSFitSetScale().
NOTE 3: this function may lead to false positives. In case it reports that
I-th derivative was calculated incorrectly, you may decrease test
step and try one more time - maybe your function changes too
sharply and your step is too large for such rapidly chanding
function.
NOTE 4: this function works only for optimizers created with LSFitCreateWFG()
or LSFitCreateFG() constructors.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step:
* TestStep=0 turns verification off
* TestStep>0 activates verification
-- ALGLIB --
Copyright 15.06.2012 by Bochkanov Sergey
*************************************************************************/
void lsfitsetgradientcheck(const lsfitstate &state, const double teststep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::lsfitsetgradientcheck(const_cast<alglib_impl::lsfitstate*>(state.c_ptr()), teststep, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
#if defined(AE_COMPILE_RBFV2) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_SPLINE2D) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
2-dimensional spline inteprolant
*************************************************************************/
_spline2dinterpolant_owner::_spline2dinterpolant_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_spline2dinterpolant_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::spline2dinterpolant*)alglib_impl::ae_malloc(sizeof(alglib_impl::spline2dinterpolant), &_state);
memset(p_struct, 0, sizeof(alglib_impl::spline2dinterpolant));
alglib_impl::_spline2dinterpolant_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_spline2dinterpolant_owner::_spline2dinterpolant_owner(const _spline2dinterpolant_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_spline2dinterpolant_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: spline2dinterpolant copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::spline2dinterpolant*)alglib_impl::ae_malloc(sizeof(alglib_impl::spline2dinterpolant), &_state);
memset(p_struct, 0, sizeof(alglib_impl::spline2dinterpolant));
alglib_impl::_spline2dinterpolant_init_copy(p_struct, const_cast<alglib_impl::spline2dinterpolant*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_spline2dinterpolant_owner& _spline2dinterpolant_owner::operator=(const _spline2dinterpolant_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: spline2dinterpolant assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: spline2dinterpolant assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_spline2dinterpolant_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::spline2dinterpolant));
alglib_impl::_spline2dinterpolant_init_copy(p_struct, const_cast<alglib_impl::spline2dinterpolant*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_spline2dinterpolant_owner::~_spline2dinterpolant_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_spline2dinterpolant_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::spline2dinterpolant* _spline2dinterpolant_owner::c_ptr()
{
return p_struct;
}
alglib_impl::spline2dinterpolant* _spline2dinterpolant_owner::c_ptr() const
{
return const_cast<alglib_impl::spline2dinterpolant*>(p_struct);
}
spline2dinterpolant::spline2dinterpolant() : _spline2dinterpolant_owner()
{
}
spline2dinterpolant::spline2dinterpolant(const spline2dinterpolant &rhs):_spline2dinterpolant_owner(rhs)
{
}
spline2dinterpolant& spline2dinterpolant::operator=(const spline2dinterpolant &rhs)
{
if( this==&rhs )
return *this;
_spline2dinterpolant_owner::operator=(rhs);
return *this;
}
spline2dinterpolant::~spline2dinterpolant()
{
}
/*************************************************************************
Nonlinear least squares solver used to fit 2D splines to data
*************************************************************************/
_spline2dbuilder_owner::_spline2dbuilder_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_spline2dbuilder_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::spline2dbuilder*)alglib_impl::ae_malloc(sizeof(alglib_impl::spline2dbuilder), &_state);
memset(p_struct, 0, sizeof(alglib_impl::spline2dbuilder));
alglib_impl::_spline2dbuilder_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_spline2dbuilder_owner::_spline2dbuilder_owner(const _spline2dbuilder_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_spline2dbuilder_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: spline2dbuilder copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::spline2dbuilder*)alglib_impl::ae_malloc(sizeof(alglib_impl::spline2dbuilder), &_state);
memset(p_struct, 0, sizeof(alglib_impl::spline2dbuilder));
alglib_impl::_spline2dbuilder_init_copy(p_struct, const_cast<alglib_impl::spline2dbuilder*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_spline2dbuilder_owner& _spline2dbuilder_owner::operator=(const _spline2dbuilder_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: spline2dbuilder assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: spline2dbuilder assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_spline2dbuilder_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::spline2dbuilder));
alglib_impl::_spline2dbuilder_init_copy(p_struct, const_cast<alglib_impl::spline2dbuilder*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_spline2dbuilder_owner::~_spline2dbuilder_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_spline2dbuilder_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::spline2dbuilder* _spline2dbuilder_owner::c_ptr()
{
return p_struct;
}
alglib_impl::spline2dbuilder* _spline2dbuilder_owner::c_ptr() const
{
return const_cast<alglib_impl::spline2dbuilder*>(p_struct);
}
spline2dbuilder::spline2dbuilder() : _spline2dbuilder_owner()
{
}
spline2dbuilder::spline2dbuilder(const spline2dbuilder &rhs):_spline2dbuilder_owner(rhs)
{
}
spline2dbuilder& spline2dbuilder::operator=(const spline2dbuilder &rhs)
{
if( this==&rhs )
return *this;
_spline2dbuilder_owner::operator=(rhs);
return *this;
}
spline2dbuilder::~spline2dbuilder()
{
}
/*************************************************************************
Spline 2D fitting report:
rmserror RMS error
avgerror average error
maxerror maximum error
r2 coefficient of determination, R-squared, 1-RSS/TSS
*************************************************************************/
_spline2dfitreport_owner::_spline2dfitreport_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_spline2dfitreport_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::spline2dfitreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::spline2dfitreport), &_state);
memset(p_struct, 0, sizeof(alglib_impl::spline2dfitreport));
alglib_impl::_spline2dfitreport_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_spline2dfitreport_owner::_spline2dfitreport_owner(const _spline2dfitreport_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_spline2dfitreport_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: spline2dfitreport copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::spline2dfitreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::spline2dfitreport), &_state);
memset(p_struct, 0, sizeof(alglib_impl::spline2dfitreport));
alglib_impl::_spline2dfitreport_init_copy(p_struct, const_cast<alglib_impl::spline2dfitreport*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_spline2dfitreport_owner& _spline2dfitreport_owner::operator=(const _spline2dfitreport_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: spline2dfitreport assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: spline2dfitreport assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_spline2dfitreport_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::spline2dfitreport));
alglib_impl::_spline2dfitreport_init_copy(p_struct, const_cast<alglib_impl::spline2dfitreport*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_spline2dfitreport_owner::~_spline2dfitreport_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_spline2dfitreport_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::spline2dfitreport* _spline2dfitreport_owner::c_ptr()
{
return p_struct;
}
alglib_impl::spline2dfitreport* _spline2dfitreport_owner::c_ptr() const
{
return const_cast<alglib_impl::spline2dfitreport*>(p_struct);
}
spline2dfitreport::spline2dfitreport() : _spline2dfitreport_owner() ,rmserror(p_struct->rmserror),avgerror(p_struct->avgerror),maxerror(p_struct->maxerror),r2(p_struct->r2)
{
}
spline2dfitreport::spline2dfitreport(const spline2dfitreport &rhs):_spline2dfitreport_owner(rhs) ,rmserror(p_struct->rmserror),avgerror(p_struct->avgerror),maxerror(p_struct->maxerror),r2(p_struct->r2)
{
}
spline2dfitreport& spline2dfitreport::operator=(const spline2dfitreport &rhs)
{
if( this==&rhs )
return *this;
_spline2dfitreport_owner::operator=(rhs);
return *this;
}
spline2dfitreport::~spline2dfitreport()
{
}
/*************************************************************************
This function serializes data structure to string.
Important properties of s_out:
* it contains alphanumeric characters, dots, underscores, minus signs
* these symbols are grouped into words, which are separated by spaces
and Windows-style (CR+LF) newlines
* although serializer uses spaces and CR+LF as separators, you can
replace any separator character by arbitrary combination of spaces,
tabs, Windows or Unix newlines. It allows flexible reformatting of
the string in case you want to include it into text or XML file.
But you should not insert separators into the middle of the "words"
nor you should change case of letters.
* s_out can be freely moved between 32-bit and 64-bit systems, little
and big endian machines, and so on. You can serialize structure on
32-bit machine and unserialize it on 64-bit one (or vice versa), or
serialize it on SPARC and unserialize on x86. You can also
serialize it in C++ version of ALGLIB and unserialize in C# one,
and vice versa.
*************************************************************************/
void spline2dserialize(spline2dinterpolant &obj, std::string &s_out)
{
jmp_buf _break_jump;
alglib_impl::ae_state state;
alglib_impl::ae_serializer serializer;
alglib_impl::ae_int_t ssize;
alglib_impl::ae_state_init(&state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&state, &_break_jump);
alglib_impl::ae_serializer_init(&serializer);
alglib_impl::ae_serializer_alloc_start(&serializer);
alglib_impl::spline2dalloc(&serializer, obj.c_ptr(), &state);
ssize = alglib_impl::ae_serializer_get_alloc_size(&serializer);
s_out.clear();
s_out.reserve((size_t)(ssize+1));
alglib_impl::ae_serializer_sstart_str(&serializer, &s_out);
alglib_impl::spline2dserialize(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_stop(&serializer, &state);
alglib_impl::ae_assert( s_out.length()<=(size_t)ssize, "ALGLIB: serialization integrity error", &state);
alglib_impl::ae_serializer_clear(&serializer);
alglib_impl::ae_state_clear(&state);
}
/*************************************************************************
This function unserializes data structure from string.
*************************************************************************/
void spline2dunserialize(const std::string &s_in, spline2dinterpolant &obj)
{
jmp_buf _break_jump;
alglib_impl::ae_state state;
alglib_impl::ae_serializer serializer;
alglib_impl::ae_state_init(&state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&state, &_break_jump);
alglib_impl::ae_serializer_init(&serializer);
alglib_impl::ae_serializer_ustart_str(&serializer, &s_in);
alglib_impl::spline2dunserialize(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_stop(&serializer, &state);
alglib_impl::ae_serializer_clear(&serializer);
alglib_impl::ae_state_clear(&state);
}
/*************************************************************************
This function serializes data structure to C++ stream.
Data stream generated by this function is same as string representation
generated by string version of serializer - alphanumeric characters,
dots, underscores, minus signs, which are grouped into words separated by
spaces and CR+LF.
We recommend you to read comments on string version of serializer to find
out more about serialization of AlGLIB objects.
*************************************************************************/
void spline2dserialize(spline2dinterpolant &obj, std::ostream &s_out)
{
jmp_buf _break_jump;
alglib_impl::ae_state state;
alglib_impl::ae_serializer serializer;
alglib_impl::ae_state_init(&state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&state, &_break_jump);
alglib_impl::ae_serializer_init(&serializer);
alglib_impl::ae_serializer_alloc_start(&serializer);
alglib_impl::spline2dalloc(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_get_alloc_size(&serializer); // not actually needed, but we have to ask
alglib_impl::ae_serializer_sstart_stream(&serializer, &s_out);
alglib_impl::spline2dserialize(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_stop(&serializer, &state);
alglib_impl::ae_serializer_clear(&serializer);
alglib_impl::ae_state_clear(&state);
}
/*************************************************************************
This function unserializes data structure from stream.
*************************************************************************/
void spline2dunserialize(const std::istream &s_in, spline2dinterpolant &obj)
{
jmp_buf _break_jump;
alglib_impl::ae_state state;
alglib_impl::ae_serializer serializer;
alglib_impl::ae_state_init(&state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&state, &_break_jump);
alglib_impl::ae_serializer_init(&serializer);
alglib_impl::ae_serializer_ustart_stream(&serializer, &s_in);
alglib_impl::spline2dunserialize(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_stop(&serializer, &state);
alglib_impl::ae_serializer_clear(&serializer);
alglib_impl::ae_state_clear(&state);
}
/*************************************************************************
This subroutine calculates the value of the bilinear or bicubic spline at
the given point X.
Input parameters:
C - 2D spline object.
Built by spline2dbuildbilinearv or spline2dbuildbicubicv.
X, Y- point
Result:
S(x,y)
-- ALGLIB PROJECT --
Copyright 05.07.2007 by Bochkanov Sergey
*************************************************************************/
double spline2dcalc(const spline2dinterpolant &c, const double x, const double y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::spline2dcalc(const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), x, y, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
This subroutine calculates the value of the bilinear or bicubic spline at
the given point X and its derivatives.
Input parameters:
C - spline interpolant.
X, Y- point
Output parameters:
F - S(x,y)
FX - dS(x,y)/dX
FY - dS(x,y)/dY
FXY - d2S(x,y)/dXdY
-- ALGLIB PROJECT --
Copyright 05.07.2007 by Bochkanov Sergey
*************************************************************************/
void spline2ddiff(const spline2dinterpolant &c, const double x, const double y, double &f, double &fx, double &fy, double &fxy, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2ddiff(const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), x, y, &f, &fx, &fy, &fxy, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine calculates bilinear or bicubic vector-valued spline at the
given point (X,Y).
If you need just some specific component of vector-valued spline, you can
use spline2dcalcvi() function.
INPUT PARAMETERS:
C - spline interpolant.
X, Y- point
F - output buffer, possibly preallocated array. In case array size
is large enough to store result, it is not reallocated. Array
which is too short will be reallocated
OUTPUT PARAMETERS:
F - array[D] (or larger) which stores function values
-- ALGLIB PROJECT --
Copyright 01.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dcalcvbuf(const spline2dinterpolant &c, const double x, const double y, real_1d_array &f, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dcalcvbuf(const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), x, y, const_cast<alglib_impl::ae_vector*>(f.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine calculates specific component of vector-valued bilinear or
bicubic spline at the given point (X,Y).
INPUT PARAMETERS:
C - spline interpolant.
X, Y- point
I - component index, in [0,D). An exception is generated for out
of range values.
RESULT:
value of I-th component
-- ALGLIB PROJECT --
Copyright 01.02.2018 by Bochkanov Sergey
*************************************************************************/
double spline2dcalcvi(const spline2dinterpolant &c, const double x, const double y, const ae_int_t i, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::spline2dcalcvi(const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), x, y, i, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
This subroutine calculates bilinear or bicubic vector-valued spline at the
given point (X,Y).
INPUT PARAMETERS:
C - spline interpolant.
X, Y- point
OUTPUT PARAMETERS:
F - array[D] which stores function values. F is out-parameter and
it is reallocated after call to this function. In case you
want to reuse previously allocated F, you may use
Spline2DCalcVBuf(), which reallocates F only when it is too
small.
-- ALGLIB PROJECT --
Copyright 16.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline2dcalcv(const spline2dinterpolant &c, const double x, const double y, real_1d_array &f, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dcalcv(const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), x, y, const_cast<alglib_impl::ae_vector*>(f.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine calculates value of specific component of bilinear or
bicubic vector-valued spline and its derivatives.
Input parameters:
C - spline interpolant.
X, Y- point
I - component index, in [0,D)
Output parameters:
F - S(x,y)
FX - dS(x,y)/dX
FY - dS(x,y)/dY
FXY - d2S(x,y)/dXdY
-- ALGLIB PROJECT --
Copyright 05.07.2007 by Bochkanov Sergey
*************************************************************************/
void spline2ddiffvi(const spline2dinterpolant &c, const double x, const double y, const ae_int_t i, double &f, double &fx, double &fy, double &fxy, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2ddiffvi(const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), x, y, i, &f, &fx, &fy, &fxy, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine performs linear transformation of the spline argument.
Input parameters:
C - spline interpolant
AX, BX - transformation coefficients: x = A*t + B
AY, BY - transformation coefficients: y = A*u + B
Result:
C - transformed spline
-- ALGLIB PROJECT --
Copyright 30.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline2dlintransxy(const spline2dinterpolant &c, const double ax, const double bx, const double ay, const double by, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dlintransxy(const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), ax, bx, ay, by, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine performs linear transformation of the spline.
Input parameters:
C - spline interpolant.
A, B- transformation coefficients: S2(x,y) = A*S(x,y) + B
Output parameters:
C - transformed spline
-- ALGLIB PROJECT --
Copyright 30.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline2dlintransf(const spline2dinterpolant &c, const double a, const double b, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dlintransf(const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), a, b, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine makes the copy of the spline model.
Input parameters:
C - spline interpolant
Output parameters:
CC - spline copy
-- ALGLIB PROJECT --
Copyright 29.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline2dcopy(const spline2dinterpolant &c, spline2dinterpolant &cc, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dcopy(const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), const_cast<alglib_impl::spline2dinterpolant*>(cc.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Bicubic spline resampling
Input parameters:
A - function values at the old grid,
array[0..OldHeight-1, 0..OldWidth-1]
OldHeight - old grid height, OldHeight>1
OldWidth - old grid width, OldWidth>1
NewHeight - new grid height, NewHeight>1
NewWidth - new grid width, NewWidth>1
Output parameters:
B - function values at the new grid,
array[0..NewHeight-1, 0..NewWidth-1]
-- ALGLIB routine --
15 May, 2007
Copyright by Bochkanov Sergey
*************************************************************************/
void spline2dresamplebicubic(const real_2d_array &a, const ae_int_t oldheight, const ae_int_t oldwidth, real_2d_array &b, const ae_int_t newheight, const ae_int_t newwidth, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dresamplebicubic(const_cast<alglib_impl::ae_matrix*>(a.c_ptr()), oldheight, oldwidth, const_cast<alglib_impl::ae_matrix*>(b.c_ptr()), newheight, newwidth, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
Bilinear spline resampling
Input parameters:
A - function values at the old grid,
array[0..OldHeight-1, 0..OldWidth-1]
OldHeight - old grid height, OldHeight>1
OldWidth - old grid width, OldWidth>1
NewHeight - new grid height, NewHeight>1
NewWidth - new grid width, NewWidth>1
Output parameters:
B - function values at the new grid,
array[0..NewHeight-1, 0..NewWidth-1]
-- ALGLIB routine --
09.07.2007
Copyright by Bochkanov Sergey
*************************************************************************/
void spline2dresamplebilinear(const real_2d_array &a, const ae_int_t oldheight, const ae_int_t oldwidth, real_2d_array &b, const ae_int_t newheight, const ae_int_t newwidth, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dresamplebilinear(const_cast<alglib_impl::ae_matrix*>(a.c_ptr()), oldheight, oldwidth, const_cast<alglib_impl::ae_matrix*>(b.c_ptr()), newheight, newwidth, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine builds bilinear vector-valued spline.
Input parameters:
X - spline abscissas, array[0..N-1]
Y - spline ordinates, array[0..M-1]
F - function values, array[0..M*N*D-1]:
* first D elements store D values at (X[0],Y[0])
* next D elements store D values at (X[1],Y[0])
* general form - D function values at (X[i],Y[j]) are stored
at F[D*(J*N+I)...D*(J*N+I)+D-1].
M,N - grid size, M>=2, N>=2
D - vector dimension, D>=1
Output parameters:
C - spline interpolant
-- ALGLIB PROJECT --
Copyright 16.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildbilinearv(const real_1d_array &x, const ae_int_t n, const real_1d_array &y, const ae_int_t m, const real_1d_array &f, const ae_int_t d, spline2dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildbilinearv(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), m, const_cast<alglib_impl::ae_vector*>(f.c_ptr()), d, const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine builds bicubic vector-valued spline.
Input parameters:
X - spline abscissas, array[0..N-1]
Y - spline ordinates, array[0..M-1]
F - function values, array[0..M*N*D-1]:
* first D elements store D values at (X[0],Y[0])
* next D elements store D values at (X[1],Y[0])
* general form - D function values at (X[i],Y[j]) are stored
at F[D*(J*N+I)...D*(J*N+I)+D-1].
M,N - grid size, M>=2, N>=2
D - vector dimension, D>=1
Output parameters:
C - spline interpolant
-- ALGLIB PROJECT --
Copyright 16.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildbicubicv(const real_1d_array &x, const ae_int_t n, const real_1d_array &y, const ae_int_t m, const real_1d_array &f, const ae_int_t d, spline2dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildbicubicv(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), m, const_cast<alglib_impl::ae_vector*>(f.c_ptr()), d, const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine unpacks two-dimensional spline into the coefficients table
Input parameters:
C - spline interpolant.
Result:
M, N- grid size (x-axis and y-axis)
D - number of components
Tbl - coefficients table, unpacked format,
D - components: [0..(N-1)*(M-1)*D-1, 0..19].
For T=0..D-1 (component index), I = 0...N-2 (x index),
J=0..M-2 (y index):
K := T + I*D + J*D*(N-1)
K-th row stores decomposition for T-th component of the
vector-valued function
Tbl[K,0] = X[i]
Tbl[K,1] = X[i+1]
Tbl[K,2] = Y[j]
Tbl[K,3] = Y[j+1]
Tbl[K,4] = C00
Tbl[K,5] = C01
Tbl[K,6] = C02
Tbl[K,7] = C03
Tbl[K,8] = C10
Tbl[K,9] = C11
...
Tbl[K,19] = C33
On each grid square spline is equals to:
S(x) = SUM(c[i,j]*(t^i)*(u^j), i=0..3, j=0..3)
t = x-x[j]
u = y-y[i]
-- ALGLIB PROJECT --
Copyright 16.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline2dunpackv(const spline2dinterpolant &c, ae_int_t &m, ae_int_t &n, ae_int_t &d, real_2d_array &tbl, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dunpackv(const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), &m, &n, &d, const_cast<alglib_impl::ae_matrix*>(tbl.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine was deprecated in ALGLIB 3.6.0
We recommend you to switch to Spline2DBuildBilinearV(), which is more
flexible and accepts its arguments in more convenient order.
-- ALGLIB PROJECT --
Copyright 05.07.2007 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildbilinear(const real_1d_array &x, const real_1d_array &y, const real_2d_array &f, const ae_int_t m, const ae_int_t n, spline2dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildbilinear(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_matrix*>(f.c_ptr()), m, n, const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine was deprecated in ALGLIB 3.6.0
We recommend you to switch to Spline2DBuildBicubicV(), which is more
flexible and accepts its arguments in more convenient order.
-- ALGLIB PROJECT --
Copyright 05.07.2007 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildbicubic(const real_1d_array &x, const real_1d_array &y, const real_2d_array &f, const ae_int_t m, const ae_int_t n, spline2dinterpolant &c, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildbicubic(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_matrix*>(f.c_ptr()), m, n, const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine was deprecated in ALGLIB 3.6.0
We recommend you to switch to Spline2DUnpackV(), which is more flexible
and accepts its arguments in more convenient order.
-- ALGLIB PROJECT --
Copyright 29.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline2dunpack(const spline2dinterpolant &c, ae_int_t &m, ae_int_t &n, real_2d_array &tbl, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dunpack(const_cast<alglib_impl::spline2dinterpolant*>(c.c_ptr()), &m, &n, const_cast<alglib_impl::ae_matrix*>(tbl.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This subroutine creates least squares solver used to fit 2D splines to
irregularly sampled (scattered) data.
Solver object is used to perform spline fits as follows:
* solver object is created with spline2dbuildercreate() function
* dataset is added with spline2dbuildersetpoints() function
* fit area is chosen:
* spline2dbuildersetarea() - for user-defined area
* spline2dbuildersetareaauto() - for automatically chosen area
* number of grid nodes is chosen with spline2dbuildersetgrid()
* prior term is chosen with one of the following functions:
* spline2dbuildersetlinterm() to set linear prior
* spline2dbuildersetconstterm() to set constant prior
* spline2dbuildersetzeroterm() to set zero prior
* spline2dbuildersetuserterm() to set user-defined constant prior
* solver algorithm is chosen with either:
* spline2dbuildersetalgoblocklls() - BlockLLS algorithm, medium-scale problems
* spline2dbuildersetalgofastddm() - FastDDM algorithm, large-scale problems
* finally, fitting itself is performed with spline2dfit() function.
Most of the steps above can be omitted, solver is configured with good
defaults. The minimum is to call:
* spline2dbuildercreate() to create solver object
* spline2dbuildersetpoints() to specify dataset
* spline2dbuildersetgrid() to tell how many nodes you need
* spline2dfit() to perform fit
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
D - positive number, number of Y-components: D=1 for simple scalar
fit, D>1 for vector-valued spline fitting.
OUTPUT PARAMETERS:
S - solver object
-- ALGLIB PROJECT --
Copyright 29.01.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildercreate(const ae_int_t d, spline2dbuilder &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildercreate(d, const_cast<alglib_impl::spline2dbuilder*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets constant prior term (model is a sum of bicubic spline
and global prior, which can be linear, constant, user-defined constant or
zero).
Constant prior term is determined by least squares fitting.
INPUT PARAMETERS:
S - spline builder
V - value for user-defined prior
-- ALGLIB --
Copyright 01.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetuserterm(const spline2dbuilder &state, const double v, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildersetuserterm(const_cast<alglib_impl::spline2dbuilder*>(state.c_ptr()), v, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets linear prior term (model is a sum of bicubic spline and
global prior, which can be linear, constant, user-defined constant or
zero).
Linear prior term is determined by least squares fitting.
INPUT PARAMETERS:
S - spline builder
-- ALGLIB --
Copyright 01.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetlinterm(const spline2dbuilder &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildersetlinterm(const_cast<alglib_impl::spline2dbuilder*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets constant prior term (model is a sum of bicubic spline
and global prior, which can be linear, constant, user-defined constant or
zero).
Constant prior term is determined by least squares fitting.
INPUT PARAMETERS:
S - spline builder
-- ALGLIB --
Copyright 01.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetconstterm(const spline2dbuilder &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildersetconstterm(const_cast<alglib_impl::spline2dbuilder*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets zero prior term (model is a sum of bicubic spline and
global prior, which can be linear, constant, user-defined constant or
zero).
INPUT PARAMETERS:
S - spline builder
-- ALGLIB --
Copyright 01.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetzeroterm(const spline2dbuilder &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildersetzeroterm(const_cast<alglib_impl::spline2dbuilder*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function adds dataset to the builder object.
This function overrides results of the previous calls, i.e. multiple calls
of this function will result in only the last set being added.
INPUT PARAMETERS:
S - spline 2D builder object
XY - points, array[N,2+D]. One row corresponds to one point
in the dataset. First 2 elements are coordinates, next
D elements are function values. Array may be larger than
specified, in this case only leading [N,NX+NY] elements
will be used.
N - number of points in the dataset
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetpoints(const spline2dbuilder &state, const real_2d_array &xy, const ae_int_t n, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildersetpoints(const_cast<alglib_impl::spline2dbuilder*>(state.c_ptr()), const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), n, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets area where 2D spline interpolant is built. "Auto" means
that area extent is determined automatically from dataset extent.
INPUT PARAMETERS:
S - spline 2D builder object
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetareaauto(const spline2dbuilder &state, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildersetareaauto(const_cast<alglib_impl::spline2dbuilder*>(state.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets area where 2D spline interpolant is built to
user-defined one: [XA,XB]*[YA,YB]
INPUT PARAMETERS:
S - spline 2D builder object
XA,XB - spatial extent in the first (X) dimension, XA<XB
YA,YB - spatial extent in the second (Y) dimension, YA<YB
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetarea(const spline2dbuilder &state, const double xa, const double xb, const double ya, const double yb, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildersetarea(const_cast<alglib_impl::spline2dbuilder*>(state.c_ptr()), xa, xb, ya, yb, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets nodes count for 2D spline interpolant. Fitting is
performed on area defined with one of the "setarea" functions; this one
sets number of nodes placed upon the fitting area.
INPUT PARAMETERS:
S - spline 2D builder object
KX - nodes count for the first (X) dimension; fitting interval
[XA,XB] is separated into KX-1 subintervals, with KX nodes
created at the boundaries.
KY - nodes count for the first (Y) dimension; fitting interval
[YA,YB] is separated into KY-1 subintervals, with KY nodes
created at the boundaries.
NOTE: at least 4 nodes is created in each dimension, so KX and KY are
silently increased if needed.
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetgrid(const spline2dbuilder &state, const ae_int_t kx, const ae_int_t ky, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildersetgrid(const_cast<alglib_impl::spline2dbuilder*>(state.c_ptr()), kx, ky, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function allows you to choose least squares solver used to perform
fitting. This function sets solver algorithm to "FastDDM", which performs
fast parallel fitting by splitting problem into smaller chunks and merging
results together.
This solver is optimized for large-scale problems, starting from 256x256
grids, and up to 10000x10000 grids. Of course, it will work for smaller
grids too.
More detailed description of the algorithm is given below:
* algorithm generates hierarchy of nested grids, ranging from ~16x16
(topmost "layer" of the model) to ~KX*KY one (final layer). Upper layers
model global behavior of the function, lower layers are used to model
fine details. Moving from layer to layer doubles grid density.
* fitting is started from topmost layer, subsequent layers are fitted
using residuals from previous ones.
* user may choose to skip generation of upper layers and generate only a
few bottom ones, which will result in much better performance and
parallelization efficiency, at the cost of algorithm inability to "patch"
large holes in the dataset.
* every layer is regularized using progressively increasing regularization
coefficient; thus, increasing LambdaV penalizes fine details first,
leaving lower frequencies almost intact for a while.
* after fitting is done, all layers are merged together into one bicubic
spline
IMPORTANT: regularization coefficient used by this solver is different
from the one used by BlockLLS. Latter utilizes nonlinearity
penalty, which is global in nature (large regularization
results in global linear trend being extracted); this solver
uses another, localized form of penalty, which is suitable for
parallel processing.
Notes on memory and performance:
* memory requirements: most memory is consumed during modeling of the
higher layers; ~[512*NPoints] bytes is required for a model with full
hierarchy of grids being generated. However, if you skip a few topmost
layers, you will get nearly constant (wrt. points count and grid size)
memory consumption.
* serial running time: O(K*K)+O(NPoints) for a KxK grid
* parallelism potential: good. You may get nearly linear speed-up when
performing fitting with just a few layers. Adding more layers results in
model becoming more global, which somewhat reduces efficiency of the
parallel code.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
S - spline 2D builder object
NLayers - number of layers in the model:
* NLayers>=1 means that up to chosen number of bottom
layers is fitted
* NLayers=0 means that maximum number of layers is chosen
(according to current grid size)
* NLayers<=-1 means that up to |NLayers| topmost layers is
skipped
Recommendations:
* good "default" value is 2 layers
* you may need more layers, if your dataset is very
irregular and you want to "patch" large holes. For a
grid step H (equal to AreaWidth/GridSize) you may expect
that last layer reproduces variations at distance H (and
can patch holes that wide); that higher layers operate
at distances 2*H, 4*H, 8*H and so on.
* good value for "bullletproof" mode is NLayers=0, which
results in complete hierarchy of layers being generated.
LambdaV - regularization coefficient, chosen in such a way that it
penalizes bottom layers (fine details) first.
LambdaV>=0, zero value means that no penalty is applied.
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetalgofastddm(const spline2dbuilder &state, const ae_int_t nlayers, const double lambdav, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildersetalgofastddm(const_cast<alglib_impl::spline2dbuilder*>(state.c_ptr()), nlayers, lambdav, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function allows you to choose least squares solver used to perform
fitting. This function sets solver algorithm to "BlockLLS", which performs
least squares fitting with fast sparse direct solver, with optional
nonsmoothness penalty being applied.
Nonlinearity penalty has the following form:
[ ]
P() ~ Lambda* integral[ (d2S/dx2)^2 + 2*(d2S/dxdy)^2 + (d2S/dy2)^2 ]dxdy
[ ]
here integral is calculated over entire grid, and "~" means "proportional"
because integral is normalized after calcilation. Extremely large values
of Lambda result in linear fit being performed.
NOTE: this algorithm is the most robust and controllable one, but it is
limited by 512x512 grids and (say) up to 1.000.000 points. However,
ALGLIB has one more spline solver: FastDDM algorithm, which is
intended for really large-scale problems (in 10M-100M range). FastDDM
algorithm also has better parallelism properties.
More information on BlockLLS solver:
* memory requirements: ~[32*K^3+256*NPoints] bytes for KxK grid with
NPoints-sized dataset
* serial running time: O(K^4+NPoints)
* parallelism potential: limited. You may get some sublinear gain when
working with large grids (K's in 256..512 range)
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
S - spline 2D builder object
LambdaNS- non-negative value:
* positive value means that some smoothing is applied
* zero value means that no smoothing is applied, and
corresponding entries of design matrix are numerically
zero and dropped from consideration.
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetalgoblocklls(const spline2dbuilder &state, const double lambdans, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildersetalgoblocklls(const_cast<alglib_impl::spline2dbuilder*>(state.c_ptr()), lambdans, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function allows you to choose least squares solver used to perform
fitting. This function sets solver algorithm to "NaiveLLS".
IMPORTANT: NaiveLLS is NOT intended to be used in real life code! This
algorithm solves problem by generated dense (K^2)x(K^2+NPoints)
matrix and solves linear least squares problem with dense
solver.
It is here just to test BlockLLS against reference solver
(and maybe for someone trying to compare well optimized solver
against straightforward approach to the LLS problem).
More information on naive LLS solver:
* memory requirements: ~[8*K^4+256*NPoints] bytes for KxK grid.
* serial running time: O(K^6+NPoints) for KxK grid
* when compared with BlockLLS, NaiveLLS has ~K larger memory demand and
~K^2 larger running time.
INPUT PARAMETERS:
S - spline 2D builder object
LambdaNS- nonsmoothness penalty
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetalgonaivells(const spline2dbuilder &state, const double lambdans, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dbuildersetalgonaivells(const_cast<alglib_impl::spline2dbuilder*>(state.c_ptr()), lambdans, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function fits bicubic spline to current dataset, using current area/
grid and current LLS solver.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
State - spline 2D builder object
OUTPUT PARAMETERS:
S - 2D spline, fit result
Rep - fitting report, which provides some additional info about
errors, R2 coefficient and so on.
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dfit(const spline2dbuilder &state, spline2dinterpolant &s, spline2dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline2dfit(const_cast<alglib_impl::spline2dbuilder*>(state.c_ptr()), const_cast<alglib_impl::spline2dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline2dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
#if defined(AE_COMPILE_RBFV1) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_RBF) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Buffer object which is used to perform nearest neighbor requests in the
multithreaded mode (multiple threads working with same KD-tree object).
This object should be created with KDTreeCreateBuffer().
*************************************************************************/
_rbfcalcbuffer_owner::_rbfcalcbuffer_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_rbfcalcbuffer_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::rbfcalcbuffer*)alglib_impl::ae_malloc(sizeof(alglib_impl::rbfcalcbuffer), &_state);
memset(p_struct, 0, sizeof(alglib_impl::rbfcalcbuffer));
alglib_impl::_rbfcalcbuffer_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_rbfcalcbuffer_owner::_rbfcalcbuffer_owner(const _rbfcalcbuffer_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_rbfcalcbuffer_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: rbfcalcbuffer copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::rbfcalcbuffer*)alglib_impl::ae_malloc(sizeof(alglib_impl::rbfcalcbuffer), &_state);
memset(p_struct, 0, sizeof(alglib_impl::rbfcalcbuffer));
alglib_impl::_rbfcalcbuffer_init_copy(p_struct, const_cast<alglib_impl::rbfcalcbuffer*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_rbfcalcbuffer_owner& _rbfcalcbuffer_owner::operator=(const _rbfcalcbuffer_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: rbfcalcbuffer assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: rbfcalcbuffer assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_rbfcalcbuffer_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::rbfcalcbuffer));
alglib_impl::_rbfcalcbuffer_init_copy(p_struct, const_cast<alglib_impl::rbfcalcbuffer*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_rbfcalcbuffer_owner::~_rbfcalcbuffer_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_rbfcalcbuffer_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::rbfcalcbuffer* _rbfcalcbuffer_owner::c_ptr()
{
return p_struct;
}
alglib_impl::rbfcalcbuffer* _rbfcalcbuffer_owner::c_ptr() const
{
return const_cast<alglib_impl::rbfcalcbuffer*>(p_struct);
}
rbfcalcbuffer::rbfcalcbuffer() : _rbfcalcbuffer_owner()
{
}
rbfcalcbuffer::rbfcalcbuffer(const rbfcalcbuffer &rhs):_rbfcalcbuffer_owner(rhs)
{
}
rbfcalcbuffer& rbfcalcbuffer::operator=(const rbfcalcbuffer &rhs)
{
if( this==&rhs )
return *this;
_rbfcalcbuffer_owner::operator=(rhs);
return *this;
}
rbfcalcbuffer::~rbfcalcbuffer()
{
}
/*************************************************************************
RBF model.
Never try to directly work with fields of this object - always use ALGLIB
functions to use this object.
*************************************************************************/
_rbfmodel_owner::_rbfmodel_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_rbfmodel_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::rbfmodel*)alglib_impl::ae_malloc(sizeof(alglib_impl::rbfmodel), &_state);
memset(p_struct, 0, sizeof(alglib_impl::rbfmodel));
alglib_impl::_rbfmodel_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_rbfmodel_owner::_rbfmodel_owner(const _rbfmodel_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_rbfmodel_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: rbfmodel copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::rbfmodel*)alglib_impl::ae_malloc(sizeof(alglib_impl::rbfmodel), &_state);
memset(p_struct, 0, sizeof(alglib_impl::rbfmodel));
alglib_impl::_rbfmodel_init_copy(p_struct, const_cast<alglib_impl::rbfmodel*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_rbfmodel_owner& _rbfmodel_owner::operator=(const _rbfmodel_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: rbfmodel assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: rbfmodel assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_rbfmodel_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::rbfmodel));
alglib_impl::_rbfmodel_init_copy(p_struct, const_cast<alglib_impl::rbfmodel*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_rbfmodel_owner::~_rbfmodel_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_rbfmodel_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::rbfmodel* _rbfmodel_owner::c_ptr()
{
return p_struct;
}
alglib_impl::rbfmodel* _rbfmodel_owner::c_ptr() const
{
return const_cast<alglib_impl::rbfmodel*>(p_struct);
}
rbfmodel::rbfmodel() : _rbfmodel_owner()
{
}
rbfmodel::rbfmodel(const rbfmodel &rhs):_rbfmodel_owner(rhs)
{
}
rbfmodel& rbfmodel::operator=(const rbfmodel &rhs)
{
if( this==&rhs )
return *this;
_rbfmodel_owner::operator=(rhs);
return *this;
}
rbfmodel::~rbfmodel()
{
}
/*************************************************************************
RBF solution report:
* TerminationType - termination type, positive values - success,
non-positive - failure.
Fields which are set by modern RBF solvers (hierarchical):
* RMSError - root-mean-square error; NAN for old solvers (ML, QNN)
* MaxError - maximum error; NAN for old solvers (ML, QNN)
*************************************************************************/
_rbfreport_owner::_rbfreport_owner()
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_rbfreport_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
p_struct = (alglib_impl::rbfreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::rbfreport), &_state);
memset(p_struct, 0, sizeof(alglib_impl::rbfreport));
alglib_impl::_rbfreport_init(p_struct, &_state, ae_false);
ae_state_clear(&_state);
}
_rbfreport_owner::_rbfreport_owner(const _rbfreport_owner &rhs)
{
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
if( p_struct!=NULL )
{
alglib_impl::_rbfreport_destroy(p_struct);
alglib_impl::ae_free(p_struct);
}
p_struct = NULL;
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
p_struct = NULL;
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: rbfreport copy constructor failure (source is not initialized)", &_state);
p_struct = (alglib_impl::rbfreport*)alglib_impl::ae_malloc(sizeof(alglib_impl::rbfreport), &_state);
memset(p_struct, 0, sizeof(alglib_impl::rbfreport));
alglib_impl::_rbfreport_init_copy(p_struct, const_cast<alglib_impl::rbfreport*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
}
_rbfreport_owner& _rbfreport_owner::operator=(const _rbfreport_owner &rhs)
{
if( this==&rhs )
return *this;
jmp_buf _break_jump;
alglib_impl::ae_state _state;
alglib_impl::ae_state_init(&_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_state.error_msg);
return *this;
#endif
}
alglib_impl::ae_state_set_break_jump(&_state, &_break_jump);
alglib_impl::ae_assert(p_struct!=NULL, "ALGLIB: rbfreport assignment constructor failure (destination is not initialized)", &_state);
alglib_impl::ae_assert(rhs.p_struct!=NULL, "ALGLIB: rbfreport assignment constructor failure (source is not initialized)", &_state);
alglib_impl::_rbfreport_destroy(p_struct);
memset(p_struct, 0, sizeof(alglib_impl::rbfreport));
alglib_impl::_rbfreport_init_copy(p_struct, const_cast<alglib_impl::rbfreport*>(rhs.p_struct), &_state, ae_false);
ae_state_clear(&_state);
return *this;
}
_rbfreport_owner::~_rbfreport_owner()
{
if( p_struct!=NULL )
{
alglib_impl::_rbfreport_destroy(p_struct);
ae_free(p_struct);
}
}
alglib_impl::rbfreport* _rbfreport_owner::c_ptr()
{
return p_struct;
}
alglib_impl::rbfreport* _rbfreport_owner::c_ptr() const
{
return const_cast<alglib_impl::rbfreport*>(p_struct);
}
rbfreport::rbfreport() : _rbfreport_owner() ,rmserror(p_struct->rmserror),maxerror(p_struct->maxerror),arows(p_struct->arows),acols(p_struct->acols),annz(p_struct->annz),iterationscount(p_struct->iterationscount),nmv(p_struct->nmv),terminationtype(p_struct->terminationtype)
{
}
rbfreport::rbfreport(const rbfreport &rhs):_rbfreport_owner(rhs) ,rmserror(p_struct->rmserror),maxerror(p_struct->maxerror),arows(p_struct->arows),acols(p_struct->acols),annz(p_struct->annz),iterationscount(p_struct->iterationscount),nmv(p_struct->nmv),terminationtype(p_struct->terminationtype)
{
}
rbfreport& rbfreport::operator=(const rbfreport &rhs)
{
if( this==&rhs )
return *this;
_rbfreport_owner::operator=(rhs);
return *this;
}
rbfreport::~rbfreport()
{
}
/*************************************************************************
This function serializes data structure to string.
Important properties of s_out:
* it contains alphanumeric characters, dots, underscores, minus signs
* these symbols are grouped into words, which are separated by spaces
and Windows-style (CR+LF) newlines
* although serializer uses spaces and CR+LF as separators, you can
replace any separator character by arbitrary combination of spaces,
tabs, Windows or Unix newlines. It allows flexible reformatting of
the string in case you want to include it into text or XML file.
But you should not insert separators into the middle of the "words"
nor you should change case of letters.
* s_out can be freely moved between 32-bit and 64-bit systems, little
and big endian machines, and so on. You can serialize structure on
32-bit machine and unserialize it on 64-bit one (or vice versa), or
serialize it on SPARC and unserialize on x86. You can also
serialize it in C++ version of ALGLIB and unserialize in C# one,
and vice versa.
*************************************************************************/
void rbfserialize(rbfmodel &obj, std::string &s_out)
{
jmp_buf _break_jump;
alglib_impl::ae_state state;
alglib_impl::ae_serializer serializer;
alglib_impl::ae_int_t ssize;
alglib_impl::ae_state_init(&state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&state, &_break_jump);
alglib_impl::ae_serializer_init(&serializer);
alglib_impl::ae_serializer_alloc_start(&serializer);
alglib_impl::rbfalloc(&serializer, obj.c_ptr(), &state);
ssize = alglib_impl::ae_serializer_get_alloc_size(&serializer);
s_out.clear();
s_out.reserve((size_t)(ssize+1));
alglib_impl::ae_serializer_sstart_str(&serializer, &s_out);
alglib_impl::rbfserialize(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_stop(&serializer, &state);
alglib_impl::ae_assert( s_out.length()<=(size_t)ssize, "ALGLIB: serialization integrity error", &state);
alglib_impl::ae_serializer_clear(&serializer);
alglib_impl::ae_state_clear(&state);
}
/*************************************************************************
This function unserializes data structure from string.
*************************************************************************/
void rbfunserialize(const std::string &s_in, rbfmodel &obj)
{
jmp_buf _break_jump;
alglib_impl::ae_state state;
alglib_impl::ae_serializer serializer;
alglib_impl::ae_state_init(&state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&state, &_break_jump);
alglib_impl::ae_serializer_init(&serializer);
alglib_impl::ae_serializer_ustart_str(&serializer, &s_in);
alglib_impl::rbfunserialize(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_stop(&serializer, &state);
alglib_impl::ae_serializer_clear(&serializer);
alglib_impl::ae_state_clear(&state);
}
/*************************************************************************
This function serializes data structure to C++ stream.
Data stream generated by this function is same as string representation
generated by string version of serializer - alphanumeric characters,
dots, underscores, minus signs, which are grouped into words separated by
spaces and CR+LF.
We recommend you to read comments on string version of serializer to find
out more about serialization of AlGLIB objects.
*************************************************************************/
void rbfserialize(rbfmodel &obj, std::ostream &s_out)
{
jmp_buf _break_jump;
alglib_impl::ae_state state;
alglib_impl::ae_serializer serializer;
alglib_impl::ae_state_init(&state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&state, &_break_jump);
alglib_impl::ae_serializer_init(&serializer);
alglib_impl::ae_serializer_alloc_start(&serializer);
alglib_impl::rbfalloc(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_get_alloc_size(&serializer); // not actually needed, but we have to ask
alglib_impl::ae_serializer_sstart_stream(&serializer, &s_out);
alglib_impl::rbfserialize(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_stop(&serializer, &state);
alglib_impl::ae_serializer_clear(&serializer);
alglib_impl::ae_state_clear(&state);
}
/*************************************************************************
This function unserializes data structure from stream.
*************************************************************************/
void rbfunserialize(const std::istream &s_in, rbfmodel &obj)
{
jmp_buf _break_jump;
alglib_impl::ae_state state;
alglib_impl::ae_serializer serializer;
alglib_impl::ae_state_init(&state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&state, &_break_jump);
alglib_impl::ae_serializer_init(&serializer);
alglib_impl::ae_serializer_ustart_stream(&serializer, &s_in);
alglib_impl::rbfunserialize(&serializer, obj.c_ptr(), &state);
alglib_impl::ae_serializer_stop(&serializer, &state);
alglib_impl::ae_serializer_clear(&serializer);
alglib_impl::ae_state_clear(&state);
}
/*************************************************************************
This function creates RBF model for a scalar (NY=1) or vector (NY>1)
function in a NX-dimensional space (NX>=1).
Newly created model is empty. It can be used for interpolation right after
creation, but it just returns zeros. You have to add points to the model,
tune interpolation settings, and then call model construction function
rbfbuildmodel() which will update model according to your specification.
USAGE:
1. User creates model with rbfcreate()
2. User adds dataset with rbfsetpoints() (points do NOT have to be on a
regular grid) or rbfsetpointsandscales().
3. (OPTIONAL) User chooses polynomial term by calling:
* rbflinterm() to set linear term
* rbfconstterm() to set constant term
* rbfzeroterm() to set zero term
By default, linear term is used.
4. User tweaks algorithm properties with rbfsetalgohierarchical() method
(or chooses one of the legacy algorithms - QNN (rbfsetalgoqnn) or ML
(rbfsetalgomultilayer)).
5. User calls rbfbuildmodel() function which rebuilds model according to
the specification
6. User may call rbfcalc() to calculate model value at the specified point,
rbfgridcalc() to calculate model values at the points of the regular
grid. User may extract model coefficients with rbfunpack() call.
IMPORTANT: we recommend you to use latest model construction algorithm -
hierarchical RBFs, which is activated by rbfsetalgohierarchical()
function. This algorithm is the fastest one, and most memory-
efficient.
However, it is incompatible with older versions of ALGLIB
(pre-3.11). So, if you serialize hierarchical model, you will
be unable to load it in pre-3.11 ALGLIB. Other model types (QNN
and RBF-ML) are still backward-compatible.
INPUT PARAMETERS:
NX - dimension of the space, NX>=1
NY - function dimension, NY>=1
OUTPUT PARAMETERS:
S - RBF model (initially equals to zero)
NOTE 1: memory requirements. RBF models require amount of memory which is
proportional to the number of data points. Some additional memory
is allocated during model construction, but most of this memory is
freed after model coefficients are calculated. Amount of this
additional memory depends on model construction algorithm being
used.
NOTE 2: prior to ALGLIB version 3.11, RBF models supported only NX=2 or
NX=3. Any attempt to create single-dimensional or more than
3-dimensional RBF model resulted in exception.
ALGLIB 3.11 supports any NX>0, but models created with NX!=2 and
NX!=3 are incompatible with (a) older versions of ALGLIB, (b) old
model construction algorithms (QNN or RBF-ML).
So, if you create a model with NX=2 or NX=3, then, depending on
specific model construction algorithm being chosen, you will (QNN
and RBF-ML) or will not (HierarchicalRBF) get backward compatibility
with older versions of ALGLIB. You have a choice here.
However, if you create a model with NX neither 2 nor 3, you have
no backward compatibility from the start, and you are forced to
use hierarchical RBFs and ALGLIB 3.11 or later.
-- ALGLIB --
Copyright 13.12.2011, 20.06.2016 by Bochkanov Sergey
*************************************************************************/
void rbfcreate(const ae_int_t nx, const ae_int_t ny, rbfmodel &s, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfcreate(nx, ny, const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function creates buffer structure which can be used to perform
parallel RBF model evaluations (with one RBF model instance being
used from multiple threads, as long as different threads use different
instances of buffer).
This buffer object can be used with rbftscalcbuf() function (here "ts"
stands for "thread-safe", "buf" is a suffix which denotes function which
reuses previously allocated output space).
How to use it:
* create RBF model structure with rbfcreate()
* load data, tune parameters
* call rbfbuildmodel()
* call rbfcreatecalcbuffer(), once per thread working with RBF model (you
should call this function only AFTER call to rbfbuildmodel(), see below
for more information)
* call rbftscalcbuf() from different threads, with each thread working
with its own copy of buffer object.
INPUT PARAMETERS
S - RBF model
OUTPUT PARAMETERS
Buf - external buffer.
IMPORTANT: buffer object should be used only with RBF model object which
was used to initialize buffer. Any attempt to use buffer with
different object is dangerous - you may get memory violation
error because sizes of internal arrays do not fit to dimensions
of RBF structure.
IMPORTANT: you should call this function only for model which was built
with rbfbuildmodel() function, after successful invocation of
rbfbuildmodel(). Sizes of some internal structures are
determined only after model is built, so buffer object created
before model construction stage will be useless (and any
attempt to use it will result in exception).
-- ALGLIB --
Copyright 02.04.2016 by Sergey Bochkanov
*************************************************************************/
void rbfcreatecalcbuffer(const rbfmodel &s, rbfcalcbuffer &buf, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfcreatecalcbuffer(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), const_cast<alglib_impl::rbfcalcbuffer*>(buf.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function adds dataset.
This function overrides results of the previous calls, i.e. multiple calls
of this function will result in only the last set being added.
IMPORTANT: ALGLIB version 3.11 and later allows you to specify a set of
per-dimension scales. Interpolation radii are multiplied by the
scale vector. It may be useful if you have mixed spatio-temporal
data (say, a set of 3D slices recorded at different times).
You should call rbfsetpointsandscales() function to use this
feature.
INPUT PARAMETERS:
S - RBF model, initialized by rbfcreate() call.
XY - points, array[N,NX+NY]. One row corresponds to one point
in the dataset. First NX elements are coordinates, next
NY elements are function values. Array may be larger than
specified, in this case only leading [N,NX+NY] elements
will be used.
N - number of points in the dataset
After you've added dataset and (optionally) tuned algorithm settings you
should call rbfbuildmodel() in order to build a model for you.
NOTE: dataset added by this function is not saved during model serialization.
MODEL ITSELF is serialized, but data used to build it are not.
So, if you 1) add dataset to empty RBF model, 2) serialize and
unserialize it, then you will get an empty RBF model with no dataset
being attached.
From the other side, if you call rbfbuildmodel() between (1) and (2),
then after (2) you will get your fully constructed RBF model - but
again with no dataset attached, so subsequent calls to rbfbuildmodel()
will produce empty model.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfsetpoints(const rbfmodel &s, const real_2d_array &xy, const ae_int_t n, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetpoints(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), n, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function adds dataset.
This function overrides results of the previous calls, i.e. multiple calls
of this function will result in only the last set being added.
IMPORTANT: ALGLIB version 3.11 and later allows you to specify a set of
per-dimension scales. Interpolation radii are multiplied by the
scale vector. It may be useful if you have mixed spatio-temporal
data (say, a set of 3D slices recorded at different times).
You should call rbfsetpointsandscales() function to use this
feature.
INPUT PARAMETERS:
S - RBF model, initialized by rbfcreate() call.
XY - points, array[N,NX+NY]. One row corresponds to one point
in the dataset. First NX elements are coordinates, next
NY elements are function values. Array may be larger than
specified, in this case only leading [N,NX+NY] elements
will be used.
N - number of points in the dataset
After you've added dataset and (optionally) tuned algorithm settings you
should call rbfbuildmodel() in order to build a model for you.
NOTE: dataset added by this function is not saved during model serialization.
MODEL ITSELF is serialized, but data used to build it are not.
So, if you 1) add dataset to empty RBF model, 2) serialize and
unserialize it, then you will get an empty RBF model with no dataset
being attached.
From the other side, if you call rbfbuildmodel() between (1) and (2),
then after (2) you will get your fully constructed RBF model - but
again with no dataset attached, so subsequent calls to rbfbuildmodel()
will produce empty model.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void rbfsetpoints(const rbfmodel &s, const real_2d_array &xy, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
n = xy.rows();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetpoints(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), n, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This function adds dataset and a vector of per-dimension scales.
It may be useful if you have mixed spatio-temporal data - say, a set of 3D
slices recorded at different times. Such data typically require different
RBF radii for spatial and temporal dimensions. ALGLIB solves this problem
by specifying single RBF radius, which is (optionally) multiplied by the
scale vector.
This function overrides results of the previous calls, i.e. multiple calls
of this function will result in only the last set being added.
IMPORTANT: only HierarchicalRBF algorithm can work with scaled points. So,
using this function results in RBF models which can be used in
ALGLIB 3.11 or later. Previous versions of the library will be
unable to unserialize models produced by HierarchicalRBF algo.
Any attempt to use this function with RBF-ML or QNN algorithms
will result in -3 error code being returned (incorrect
algorithm).
INPUT PARAMETERS:
R - RBF model, initialized by rbfcreate() call.
XY - points, array[N,NX+NY]. One row corresponds to one point
in the dataset. First NX elements are coordinates, next
NY elements are function values. Array may be larger than
specified, in this case only leading [N,NX+NY] elements
will be used.
N - number of points in the dataset
S - array[NX], scale vector, S[i]>0.
After you've added dataset and (optionally) tuned algorithm settings you
should call rbfbuildmodel() in order to build a model for you.
NOTE: dataset added by this function is not saved during model serialization.
MODEL ITSELF is serialized, but data used to build it are not.
So, if you 1) add dataset to empty RBF model, 2) serialize and
unserialize it, then you will get an empty RBF model with no dataset
being attached.
From the other side, if you call rbfbuildmodel() between (1) and (2),
then after (2) you will get your fully constructed RBF model - but
again with no dataset attached, so subsequent calls to rbfbuildmodel()
will produce empty model.
-- ALGLIB --
Copyright 20.06.2016 by Bochkanov Sergey
*************************************************************************/
void rbfsetpointsandscales(const rbfmodel &r, const real_2d_array &xy, const ae_int_t n, const real_1d_array &s, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetpointsandscales(const_cast<alglib_impl::rbfmodel*>(r.c_ptr()), const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(s.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function adds dataset and a vector of per-dimension scales.
It may be useful if you have mixed spatio-temporal data - say, a set of 3D
slices recorded at different times. Such data typically require different
RBF radii for spatial and temporal dimensions. ALGLIB solves this problem
by specifying single RBF radius, which is (optionally) multiplied by the
scale vector.
This function overrides results of the previous calls, i.e. multiple calls
of this function will result in only the last set being added.
IMPORTANT: only HierarchicalRBF algorithm can work with scaled points. So,
using this function results in RBF models which can be used in
ALGLIB 3.11 or later. Previous versions of the library will be
unable to unserialize models produced by HierarchicalRBF algo.
Any attempt to use this function with RBF-ML or QNN algorithms
will result in -3 error code being returned (incorrect
algorithm).
INPUT PARAMETERS:
R - RBF model, initialized by rbfcreate() call.
XY - points, array[N,NX+NY]. One row corresponds to one point
in the dataset. First NX elements are coordinates, next
NY elements are function values. Array may be larger than
specified, in this case only leading [N,NX+NY] elements
will be used.
N - number of points in the dataset
S - array[NX], scale vector, S[i]>0.
After you've added dataset and (optionally) tuned algorithm settings you
should call rbfbuildmodel() in order to build a model for you.
NOTE: dataset added by this function is not saved during model serialization.
MODEL ITSELF is serialized, but data used to build it are not.
So, if you 1) add dataset to empty RBF model, 2) serialize and
unserialize it, then you will get an empty RBF model with no dataset
being attached.
From the other side, if you call rbfbuildmodel() between (1) and (2),
then after (2) you will get your fully constructed RBF model - but
again with no dataset attached, so subsequent calls to rbfbuildmodel()
will produce empty model.
-- ALGLIB --
Copyright 20.06.2016 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void rbfsetpointsandscales(const rbfmodel &r, const real_2d_array &xy, const real_1d_array &s, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
n = xy.rows();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetpointsandscales(const_cast<alglib_impl::rbfmodel*>(r.c_ptr()), const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), n, const_cast<alglib_impl::ae_vector*>(s.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
DEPRECATED:since version 3.11 ALGLIB includes new RBF model construction
algorithm, Hierarchical RBF. This algorithm is faster and
requires less memory than QNN and RBF-ML. It is especially good
for large-scale interpolation problems. So, we recommend you to
consider Hierarchical RBF as default option.
==========================================================================
This function sets RBF interpolation algorithm. ALGLIB supports several
RBF algorithms with different properties.
This algorithm is called RBF-QNN and it is good for point sets with
following properties:
a) all points are distinct
b) all points are well separated.
c) points distribution is approximately uniform. There is no "contour
lines", clusters of points, or other small-scale structures.
Algorithm description:
1) interpolation centers are allocated to data points
2) interpolation radii are calculated as distances to the nearest centers
times Q coefficient (where Q is a value from [0.75,1.50]).
3) after performing (2) radii are transformed in order to avoid situation
when single outlier has very large radius and influences many points
across all dataset. Transformation has following form:
new_r[i] = min(r[i],Z*median(r[]))
where r[i] is I-th radius, median() is a median radius across entire
dataset, Z is user-specified value which controls amount of deviation
from median radius.
When (a) is violated, we will be unable to build RBF model. When (b) or
(c) are violated, model will be built, but interpolation quality will be
low. See http://www.alglib.net/interpolation/ for more information on this
subject.
This algorithm is used by default.
Additional Q parameter controls smoothness properties of the RBF basis:
* Q<0.75 will give perfectly conditioned basis, but terrible smoothness
properties (RBF interpolant will have sharp peaks around function values)
* Q around 1.0 gives good balance between smoothness and condition number
* Q>1.5 will lead to badly conditioned systems and slow convergence of the
underlying linear solver (although smoothness will be very good)
* Q>2.0 will effectively make optimizer useless because it won't converge
within reasonable amount of iterations. It is possible to set such large
Q, but it is advised not to do so.
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
Q - Q parameter, Q>0, recommended value - 1.0
Z - Z parameter, Z>0, recommended value - 5.0
NOTE: this function has some serialization-related subtleties. We
recommend you to study serialization examples from ALGLIB Reference
Manual if you want to perform serialization of your models.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfsetalgoqnn(const rbfmodel &s, const double q, const double z, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetalgoqnn(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), q, z, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
DEPRECATED:since version 3.11 ALGLIB includes new RBF model construction
algorithm, Hierarchical RBF. This algorithm is faster and
requires less memory than QNN and RBF-ML. It is especially good
for large-scale interpolation problems. So, we recommend you to
consider Hierarchical RBF as default option.
==========================================================================
This function sets RBF interpolation algorithm. ALGLIB supports several
RBF algorithms with different properties.
This algorithm is called RBF-QNN and it is good for point sets with
following properties:
a) all points are distinct
b) all points are well separated.
c) points distribution is approximately uniform. There is no "contour
lines", clusters of points, or other small-scale structures.
Algorithm description:
1) interpolation centers are allocated to data points
2) interpolation radii are calculated as distances to the nearest centers
times Q coefficient (where Q is a value from [0.75,1.50]).
3) after performing (2) radii are transformed in order to avoid situation
when single outlier has very large radius and influences many points
across all dataset. Transformation has following form:
new_r[i] = min(r[i],Z*median(r[]))
where r[i] is I-th radius, median() is a median radius across entire
dataset, Z is user-specified value which controls amount of deviation
from median radius.
When (a) is violated, we will be unable to build RBF model. When (b) or
(c) are violated, model will be built, but interpolation quality will be
low. See http://www.alglib.net/interpolation/ for more information on this
subject.
This algorithm is used by default.
Additional Q parameter controls smoothness properties of the RBF basis:
* Q<0.75 will give perfectly conditioned basis, but terrible smoothness
properties (RBF interpolant will have sharp peaks around function values)
* Q around 1.0 gives good balance between smoothness and condition number
* Q>1.5 will lead to badly conditioned systems and slow convergence of the
underlying linear solver (although smoothness will be very good)
* Q>2.0 will effectively make optimizer useless because it won't converge
within reasonable amount of iterations. It is possible to set such large
Q, but it is advised not to do so.
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
Q - Q parameter, Q>0, recommended value - 1.0
Z - Z parameter, Z>0, recommended value - 5.0
NOTE: this function has some serialization-related subtleties. We
recommend you to study serialization examples from ALGLIB Reference
Manual if you want to perform serialization of your models.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void rbfsetalgoqnn(const rbfmodel &s, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
double q;
double z;
q = 1.0;
z = 5.0;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetalgoqnn(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), q, z, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
DEPRECATED:since version 3.11 ALGLIB includes new RBF model construction
algorithm, Hierarchical RBF. This algorithm is faster and
requires less memory than QNN and RBF-ML. It is especially good
for large-scale interpolation problems. So, we recommend you to
consider Hierarchical RBF as default option.
==========================================================================
This function sets RBF interpolation algorithm. ALGLIB supports several
RBF algorithms with different properties.
This algorithm is called RBF-ML. It builds multilayer RBF model, i.e.
model with subsequently decreasing radii, which allows us to combine
smoothness (due to large radii of the first layers) with exactness (due
to small radii of the last layers) and fast convergence.
Internally RBF-ML uses many different means of acceleration, from sparse
matrices to KD-trees, which results in algorithm whose working time is
roughly proportional to N*log(N)*Density*RBase^2*NLayers, where N is a
number of points, Density is an average density if points per unit of the
interpolation space, RBase is an initial radius, NLayers is a number of
layers.
RBF-ML is good for following kinds of interpolation problems:
1. "exact" problems (perfect fit) with well separated points
2. least squares problems with arbitrary distribution of points (algorithm
gives perfect fit where it is possible, and resorts to least squares
fit in the hard areas).
3. noisy problems where we want to apply some controlled amount of
smoothing.
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
RBase - RBase parameter, RBase>0
NLayers - NLayers parameter, NLayers>0, recommended value to start
with - about 5.
LambdaV - regularization value, can be useful when solving problem
in the least squares sense. Optimal lambda is problem-
dependent and require trial and error. In our experience,
good lambda can be as large as 0.1, and you can use 0.001
as initial guess.
Default value - 0.01, which is used when LambdaV is not
given. You can specify zero value, but it is not
recommended to do so.
TUNING ALGORITHM
In order to use this algorithm you have to choose three parameters:
* initial radius RBase
* number of layers in the model NLayers
* regularization coefficient LambdaV
Initial radius is easy to choose - you can pick any number several times
larger than the average distance between points. Algorithm won't break
down if you choose radius which is too large (model construction time will
increase, but model will be built correctly).
Choose such number of layers that RLast=RBase/2^(NLayers-1) (radius used
by the last layer) will be smaller than the typical distance between
points. In case model error is too large, you can increase number of
layers. Having more layers will make model construction and evaluation
proportionally slower, but it will allow you to have model which precisely
fits your data. From the other side, if you want to suppress noise, you
can DECREASE number of layers to make your model less flexible.
Regularization coefficient LambdaV controls smoothness of the individual
models built for each layer. We recommend you to use default value in case
you don't want to tune this parameter, because having non-zero LambdaV
accelerates and stabilizes internal iterative algorithm. In case you want
to suppress noise you can use LambdaV as additional parameter (larger
value = more smoothness) to tune.
TYPICAL ERRORS
1. Using initial radius which is too large. Memory requirements of the
RBF-ML are roughly proportional to N*Density*RBase^2 (where Density is
an average density of points per unit of the interpolation space). In
the extreme case of the very large RBase we will need O(N^2) units of
memory - and many layers in order to decrease radius to some reasonably
small value.
2. Using too small number of layers - RBF models with large radius are not
flexible enough to reproduce small variations in the target function.
You need many layers with different radii, from large to small, in
order to have good model.
3. Using initial radius which is too small. You will get model with
"holes" in the areas which are too far away from interpolation centers.
However, algorithm will work correctly (and quickly) in this case.
4. Using too many layers - you will get too large and too slow model. This
model will perfectly reproduce your function, but maybe you will be
able to achieve similar results with less layers (and less memory).
-- ALGLIB --
Copyright 02.03.2012 by Bochkanov Sergey
*************************************************************************/
void rbfsetalgomultilayer(const rbfmodel &s, const double rbase, const ae_int_t nlayers, const double lambdav, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetalgomultilayer(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), rbase, nlayers, lambdav, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
DEPRECATED:since version 3.11 ALGLIB includes new RBF model construction
algorithm, Hierarchical RBF. This algorithm is faster and
requires less memory than QNN and RBF-ML. It is especially good
for large-scale interpolation problems. So, we recommend you to
consider Hierarchical RBF as default option.
==========================================================================
This function sets RBF interpolation algorithm. ALGLIB supports several
RBF algorithms with different properties.
This algorithm is called RBF-ML. It builds multilayer RBF model, i.e.
model with subsequently decreasing radii, which allows us to combine
smoothness (due to large radii of the first layers) with exactness (due
to small radii of the last layers) and fast convergence.
Internally RBF-ML uses many different means of acceleration, from sparse
matrices to KD-trees, which results in algorithm whose working time is
roughly proportional to N*log(N)*Density*RBase^2*NLayers, where N is a
number of points, Density is an average density if points per unit of the
interpolation space, RBase is an initial radius, NLayers is a number of
layers.
RBF-ML is good for following kinds of interpolation problems:
1. "exact" problems (perfect fit) with well separated points
2. least squares problems with arbitrary distribution of points (algorithm
gives perfect fit where it is possible, and resorts to least squares
fit in the hard areas).
3. noisy problems where we want to apply some controlled amount of
smoothing.
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
RBase - RBase parameter, RBase>0
NLayers - NLayers parameter, NLayers>0, recommended value to start
with - about 5.
LambdaV - regularization value, can be useful when solving problem
in the least squares sense. Optimal lambda is problem-
dependent and require trial and error. In our experience,
good lambda can be as large as 0.1, and you can use 0.001
as initial guess.
Default value - 0.01, which is used when LambdaV is not
given. You can specify zero value, but it is not
recommended to do so.
TUNING ALGORITHM
In order to use this algorithm you have to choose three parameters:
* initial radius RBase
* number of layers in the model NLayers
* regularization coefficient LambdaV
Initial radius is easy to choose - you can pick any number several times
larger than the average distance between points. Algorithm won't break
down if you choose radius which is too large (model construction time will
increase, but model will be built correctly).
Choose such number of layers that RLast=RBase/2^(NLayers-1) (radius used
by the last layer) will be smaller than the typical distance between
points. In case model error is too large, you can increase number of
layers. Having more layers will make model construction and evaluation
proportionally slower, but it will allow you to have model which precisely
fits your data. From the other side, if you want to suppress noise, you
can DECREASE number of layers to make your model less flexible.
Regularization coefficient LambdaV controls smoothness of the individual
models built for each layer. We recommend you to use default value in case
you don't want to tune this parameter, because having non-zero LambdaV
accelerates and stabilizes internal iterative algorithm. In case you want
to suppress noise you can use LambdaV as additional parameter (larger
value = more smoothness) to tune.
TYPICAL ERRORS
1. Using initial radius which is too large. Memory requirements of the
RBF-ML are roughly proportional to N*Density*RBase^2 (where Density is
an average density of points per unit of the interpolation space). In
the extreme case of the very large RBase we will need O(N^2) units of
memory - and many layers in order to decrease radius to some reasonably
small value.
2. Using too small number of layers - RBF models with large radius are not
flexible enough to reproduce small variations in the target function.
You need many layers with different radii, from large to small, in
order to have good model.
3. Using initial radius which is too small. You will get model with
"holes" in the areas which are too far away from interpolation centers.
However, algorithm will work correctly (and quickly) in this case.
4. Using too many layers - you will get too large and too slow model. This
model will perfectly reproduce your function, but maybe you will be
able to achieve similar results with less layers (and less memory).
-- ALGLIB --
Copyright 02.03.2012 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void rbfsetalgomultilayer(const rbfmodel &s, const double rbase, const ae_int_t nlayers, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
double lambdav;
lambdav = 0.01;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetalgomultilayer(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), rbase, nlayers, lambdav, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This function sets RBF interpolation algorithm. ALGLIB supports several
RBF algorithms with different properties.
This algorithm is called Hierarchical RBF. It similar to its previous
incarnation, RBF-ML, i.e. it also builds a sequence of models with
decreasing radii. However, it uses more economical way of building upper
layers (ones with large radii), which results in faster model construction
and evaluation, as well as smaller memory footprint during construction.
This algorithm has following important features:
* ability to handle millions of points
* controllable smoothing via nonlinearity penalization
* support for NX-dimensional models with NX=1 or NX>3 (unlike QNN or RBF-ML)
* support for specification of per-dimensional radii via scale vector,
which is set by means of rbfsetpointsandscales() function. This feature
is useful if you solve spatio-temporal interpolation problems, where
different radii are required for spatial and temporal dimensions.
Running times are roughly proportional to:
* N*log(N)*NLayers - for model construction
* N*NLayers - for model evaluation
You may see that running time does not depend on search radius or points
density, just on number of layers in the hierarchy.
IMPORTANT: this model construction algorithm was introduced in ALGLIB 3.11
and produces models which are INCOMPATIBLE with previous
versions of ALGLIB. You can not unserialize models produced
with this function in ALGLIB 3.10 or earlier.
INPUT PARAMETERS:
S - RBF model, initialized by rbfcreate() call
RBase - RBase parameter, RBase>0
NLayers - NLayers parameter, NLayers>0, recommended value to start
with - about 5.
LambdaNS- >=0, nonlinearity penalty coefficient, negative values are
not allowed. This parameter adds controllable smoothing to
the problem, which may reduce noise. Specification of non-
zero lambda means that in addition to fitting error solver
will also minimize LambdaNS*|S''(x)|^2 (appropriately
generalized to multiple dimensions.
Specification of exactly zero value means that no penalty
is added (we do not even evaluate matrix of second
derivatives which is necessary for smoothing).
Calculation of nonlinearity penalty is costly - it results
in several-fold increase of model construction time.
Evaluation time remains the same.
Optimal lambda is problem-dependent and requires trial
and error. Good value to start from is 1e-5...1e-6,
which corresponds to slightly noticeable smoothing of the
function. Value 1e-2 usually means that quite heavy
smoothing is applied.
TUNING ALGORITHM
In order to use this algorithm you have to choose three parameters:
* initial radius RBase
* number of layers in the model NLayers
* penalty coefficient LambdaNS
Initial radius is easy to choose - you can pick any number several times
larger than the average distance between points. Algorithm won't break
down if you choose radius which is too large (model construction time will
increase, but model will be built correctly).
Choose such number of layers that RLast=RBase/2^(NLayers-1) (radius used
by the last layer) will be smaller than the typical distance between
points. In case model error is too large, you can increase number of
layers. Having more layers will make model construction and evaluation
proportionally slower, but it will allow you to have model which precisely
fits your data. From the other side, if you want to suppress noise, you
can DECREASE number of layers to make your model less flexible (or specify
non-zero LambdaNS).
TYPICAL ERRORS
1. Using too small number of layers - RBF models with large radius are not
flexible enough to reproduce small variations in the target function.
You need many layers with different radii, from large to small, in
order to have good model.
2. Using initial radius which is too small. You will get model with
"holes" in the areas which are too far away from interpolation centers.
However, algorithm will work correctly (and quickly) in this case.
-- ALGLIB --
Copyright 20.06.2016 by Bochkanov Sergey
*************************************************************************/
void rbfsetalgohierarchical(const rbfmodel &s, const double rbase, const ae_int_t nlayers, const double lambdans, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetalgohierarchical(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), rbase, nlayers, lambdans, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets linear term (model is a sum of radial basis functions
plus linear polynomial). This function won't have effect until next call
to RBFBuildModel().
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
NOTE: this function has some serialization-related subtleties. We
recommend you to study serialization examples from ALGLIB Reference
Manual if you want to perform serialization of your models.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfsetlinterm(const rbfmodel &s, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetlinterm(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets constant term (model is a sum of radial basis functions
plus constant). This function won't have effect until next call to
RBFBuildModel().
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
NOTE: this function has some serialization-related subtleties. We
recommend you to study serialization examples from ALGLIB Reference
Manual if you want to perform serialization of your models.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfsetconstterm(const rbfmodel &s, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetconstterm(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets zero term (model is a sum of radial basis functions
without polynomial term). This function won't have effect until next call
to RBFBuildModel().
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
NOTE: this function has some serialization-related subtleties. We
recommend you to study serialization examples from ALGLIB Reference
Manual if you want to perform serialization of your models.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfsetzeroterm(const rbfmodel &s, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetzeroterm(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets basis function type, which can be:
* 0 for classic Gaussian
* 1 for fast and compact bell-like basis function, which becomes exactly
zero at distance equal to 3*R (default option).
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
BF - basis function type:
* 0 - classic Gaussian
* 1 - fast and compact one
-- ALGLIB --
Copyright 01.02.2017 by Bochkanov Sergey
*************************************************************************/
void rbfsetv2bf(const rbfmodel &s, const ae_int_t bf, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetv2bf(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), bf, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets stopping criteria of the underlying linear solver for
hierarchical (version 2) RBF constructor.
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
MaxIts - this criterion will stop algorithm after MaxIts iterations.
Typically a few hundreds iterations is required, with 400
being a good default value to start experimentation.
Zero value means that default value will be selected.
-- ALGLIB --
Copyright 01.02.2017 by Bochkanov Sergey
*************************************************************************/
void rbfsetv2its(const rbfmodel &s, const ae_int_t maxits, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetv2its(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), maxits, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function sets support radius parameter of hierarchical (version 2)
RBF constructor.
Hierarchical RBF model achieves great speed-up by removing from the model
excessive (too dense) nodes. Say, if you have RBF radius equal to 1 meter,
and two nodes are just 1 millimeter apart, you may remove one of them
without reducing model quality.
Support radius parameter is used to justify which points need removal, and
which do not. If two points are less than SUPPORT_R*CUR_RADIUS units of
distance apart, one of them is removed from the model. The larger support
radius is, the faster model construction AND evaluation are. However,
too large values result in "bumpy" models.
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
R - support radius coefficient, >=0.
Recommended values are [0.1,0.4] range, with 0.1 being
default value.
-- ALGLIB --
Copyright 01.02.2017 by Bochkanov Sergey
*************************************************************************/
void rbfsetv2supportr(const rbfmodel &s, const double r, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfsetv2supportr(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), r, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function builds RBF model and returns report (contains some
information which can be used for evaluation of the algorithm properties).
Call to this function modifies RBF model by calculating its centers/radii/
weights and saving them into RBFModel structure. Initially RBFModel
contain zero coefficients, but after call to this function we will have
coefficients which were calculated in order to fit our dataset.
After you called this function you can call RBFCalc(), RBFGridCalc() and
other model calculation functions.
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
Rep - report:
* Rep.TerminationType:
* -5 - non-distinct basis function centers were detected,
interpolation aborted; only QNN returns this
error code, other algorithms can handle non-
distinct nodes.
* -4 - nonconvergence of the internal SVD solver
* -3 incorrect model construction algorithm was chosen:
QNN or RBF-ML, combined with one of the incompatible
features - NX=1 or NX>3; points with per-dimension
scales.
* 1 - successful termination
* 8 - a termination request was submitted via
rbfrequesttermination() function.
Fields which are set only by modern RBF solvers (hierarchical
or nonnegative; older solvers like QNN and ML initialize these
fields by NANs):
* rep.rmserror - root-mean-square error at nodes
* rep.maxerror - maximum error at nodes
Fields are used for debugging purposes:
* Rep.IterationsCount - iterations count of the LSQR solver
* Rep.NMV - number of matrix-vector products
* Rep.ARows - rows count for the system matrix
* Rep.ACols - columns count for the system matrix
* Rep.ANNZ - number of significantly non-zero elements
(elements above some algorithm-determined threshold)
NOTE: failure to build model will leave current state of the structure
unchanged.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfbuildmodel(const rbfmodel &s, rbfreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfbuildmodel(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), const_cast<alglib_impl::rbfreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates values of the RBF model in the given point.
IMPORTANT: this function works only with modern (hierarchical) RBFs. It
can not be used with legacy (version 1) RBFs because older RBF
code does not support 1-dimensional models.
This function should be used when we have NY=1 (scalar function) and NX=1
(1-dimensional space). If you have 3-dimensional space, use rbfcalc3(). If
you have 2-dimensional space, use rbfcalc3(). If you have general
situation (NX-dimensional space, NY-dimensional function) you should use
generic rbfcalc().
If you want to perform parallel model evaluation from multiple threads,
use rbftscalcbuf() with per-thread buffer object.
This function returns 0.0 when:
* model is not initialized
* NX<>1
* NY<>1
INPUT PARAMETERS:
S - RBF model
X0 - X-coordinate, finite number
RESULT:
value of the model or 0.0 (as defined above)
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
double rbfcalc1(const rbfmodel &s, const double x0, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::rbfcalc1(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), x0, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
This function calculates values of the RBF model in the given point.
This function should be used when we have NY=1 (scalar function) and NX=2
(2-dimensional space). If you have 3-dimensional space, use rbfcalc3(). If
you have general situation (NX-dimensional space, NY-dimensional function)
you should use generic rbfcalc().
If you want to calculate function values many times, consider using
rbfgridcalc2v(), which is far more efficient than many subsequent calls to
rbfcalc2().
If you want to perform parallel model evaluation from multiple threads,
use rbftscalcbuf() with per-thread buffer object.
This function returns 0.0 when:
* model is not initialized
* NX<>2
*NY<>1
INPUT PARAMETERS:
S - RBF model
X0 - first coordinate, finite number
X1 - second coordinate, finite number
RESULT:
value of the model or 0.0 (as defined above)
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
double rbfcalc2(const rbfmodel &s, const double x0, const double x1, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::rbfcalc2(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), x0, x1, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
This function calculates value of the RBF model in the given point.
This function should be used when we have NY=1 (scalar function) and NX=3
(3-dimensional space). If you have 2-dimensional space, use rbfcalc2(). If
you have general situation (NX-dimensional space, NY-dimensional function)
you should use generic rbfcalc().
If you want to calculate function values many times, consider using
rbfgridcalc3v(), which is far more efficient than many subsequent calls to
rbfcalc3().
If you want to perform parallel model evaluation from multiple threads,
use rbftscalcbuf() with per-thread buffer object.
This function returns 0.0 when:
* model is not initialized
* NX<>3
*NY<>1
INPUT PARAMETERS:
S - RBF model
X0 - first coordinate, finite number
X1 - second coordinate, finite number
X2 - third coordinate, finite number
RESULT:
value of the model or 0.0 (as defined above)
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
double rbfcalc3(const rbfmodel &s, const double x0, const double x1, const double x2, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::rbfcalc3(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), x0, x1, x2, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
This function calculates values of the RBF model at the given point.
This is general function which can be used for arbitrary NX (dimension of
the space of arguments) and NY (dimension of the function itself). However
when you have NY=1 you may find more convenient to use rbfcalc2() or
rbfcalc3().
If you want to perform parallel model evaluation from multiple threads,
use rbftscalcbuf() with per-thread buffer object.
This function returns 0.0 when model is not initialized.
INPUT PARAMETERS:
S - RBF model
X - coordinates, array[NX].
X may have more than NX elements, in this case only
leading NX will be used.
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is out-parameter and
reallocated after call to this function. In case you want
to reuse previously allocated Y, you may use RBFCalcBuf(),
which reallocates Y only when it is too small.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfcalc(const rbfmodel &s, const real_1d_array &x, real_1d_array &y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfcalc(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates values of the RBF model at the given point.
Same as rbfcalc(), but does not reallocate Y when in is large enough to
store function values.
If you want to perform parallel model evaluation from multiple threads,
use rbftscalcbuf() with per-thread buffer object.
INPUT PARAMETERS:
S - RBF model
X - coordinates, array[NX].
X may have more than NX elements, in this case only
leading NX will be used.
Y - possibly preallocated array
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is not reallocated when it
is larger than NY.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfcalcbuf(const rbfmodel &s, const real_1d_array &x, real_1d_array &y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfcalcbuf(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates values of the RBF model at the given point, using
external buffer object (internal temporaries of RBF model are not
modified).
This function allows to use same RBF model object in different threads,
assuming that different threads use different instances of buffer
structure.
INPUT PARAMETERS:
S - RBF model, may be shared between different threads
Buf - buffer object created for this particular instance of RBF
model with rbfcreatecalcbuffer().
X - coordinates, array[NX].
X may have more than NX elements, in this case only
leading NX will be used.
Y - possibly preallocated array
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is not reallocated when it
is larger than NY.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbftscalcbuf(const rbfmodel &s, const rbfcalcbuffer &buf, const real_1d_array &x, real_1d_array &y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbftscalcbuf(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), const_cast<alglib_impl::rbfcalcbuffer*>(buf.c_ptr()), const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This is legacy function for gridded calculation of RBF model.
It is superseded by rbfgridcalc2v() and rbfgridcalc2vsubset() functions.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfgridcalc2(const rbfmodel &s, const real_1d_array &x0, const ae_int_t n0, const real_1d_array &x1, const ae_int_t n1, real_2d_array &y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfgridcalc2(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), const_cast<alglib_impl::ae_vector*>(x0.c_ptr()), n0, const_cast<alglib_impl::ae_vector*>(x1.c_ptr()), n1, const_cast<alglib_impl::ae_matrix*>(y.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates values of the RBF model at the regular grid,
which has N0*N1 points, with Point[I,J] = (X0[I], X1[J]). Vector-valued
RBF models are supported.
This function returns 0.0 when:
* model is not initialized
* NX<>2
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
NOTE: Parallel processing is implemented only for modern (hierarchical)
RBFs. Legacy version 1 RBFs (created by QNN or RBF-ML) are still
processed serially.
INPUT PARAMETERS:
S - RBF model, used in read-only mode, can be shared between
multiple invocations of this function from multiple
threads.
X0 - array of grid nodes, first coordinates, array[N0].
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N0 - grid size (number of nodes) in the first dimension
X1 - array of grid nodes, second coordinates, array[N1]
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N1 - grid size (number of nodes) in the second dimension
OUTPUT PARAMETERS:
Y - function values, array[NY*N0*N1], where NY is a number of
"output" vector values (this function supports vector-
valued RBF models). Y is out-variable and is reallocated
by this function.
Y[K+NY*(I0+I1*N0)]=F_k(X0[I0],X1[I1]), for:
* K=0...NY-1
* I0=0...N0-1
* I1=0...N1-1
NOTE: this function supports weakly ordered grid nodes, i.e. you may have
X[i]=X[i+1] for some i. It does not provide you any performance
benefits due to duplication of points, just convenience and
flexibility.
NOTE: this function is re-entrant, i.e. you may use same rbfmodel
structure in multiple threads calling this function for different
grids.
NOTE: if you need function values on some subset of regular grid, which
may be described as "several compact and dense islands", you may
use rbfgridcalc2vsubset().
-- ALGLIB --
Copyright 27.01.2017 by Bochkanov Sergey
*************************************************************************/
void rbfgridcalc2v(const rbfmodel &s, const real_1d_array &x0, const ae_int_t n0, const real_1d_array &x1, const ae_int_t n1, real_1d_array &y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfgridcalc2v(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), const_cast<alglib_impl::ae_vector*>(x0.c_ptr()), n0, const_cast<alglib_impl::ae_vector*>(x1.c_ptr()), n1, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates values of the RBF model at some subset of regular
grid:
* grid has N0*N1 points, with Point[I,J] = (X0[I], X1[J])
* only values at some subset of this grid are required
Vector-valued RBF models are supported.
This function returns 0.0 when:
* model is not initialized
* NX<>2
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
NOTE: Parallel processing is implemented only for modern (hierarchical)
RBFs. Legacy version 1 RBFs (created by QNN or RBF-ML) are still
processed serially.
INPUT PARAMETERS:
S - RBF model, used in read-only mode, can be shared between
multiple invocations of this function from multiple
threads.
X0 - array of grid nodes, first coordinates, array[N0].
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N0 - grid size (number of nodes) in the first dimension
X1 - array of grid nodes, second coordinates, array[N1]
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N1 - grid size (number of nodes) in the second dimension
FlagY - array[N0*N1]:
* Y[I0+I1*N0] corresponds to node (X0[I0],X1[I1])
* it is a "bitmap" array which contains False for nodes
which are NOT calculated, and True for nodes which are
required.
OUTPUT PARAMETERS:
Y - function values, array[NY*N0*N1*N2], where NY is a number
of "output" vector values (this function supports vector-
valued RBF models):
* Y[K+NY*(I0+I1*N0)]=F_k(X0[I0],X1[I1]),
for K=0...NY-1, I0=0...N0-1, I1=0...N1-1.
* elements of Y[] which correspond to FlagY[]=True are
loaded by model values (which may be exactly zero for
some nodes).
* elements of Y[] which correspond to FlagY[]=False MAY be
initialized by zeros OR may be calculated. This function
processes grid as a hierarchy of nested blocks and
micro-rows. If just one element of micro-row is required,
entire micro-row (up to 8 nodes in the current version,
but no promises) is calculated.
NOTE: this function supports weakly ordered grid nodes, i.e. you may have
X[i]=X[i+1] for some i. It does not provide you any performance
benefits due to duplication of points, just convenience and
flexibility.
NOTE: this function is re-entrant, i.e. you may use same rbfmodel
structure in multiple threads calling this function for different
grids.
-- ALGLIB --
Copyright 04.03.2016 by Bochkanov Sergey
*************************************************************************/
void rbfgridcalc2vsubset(const rbfmodel &s, const real_1d_array &x0, const ae_int_t n0, const real_1d_array &x1, const ae_int_t n1, const boolean_1d_array &flagy, real_1d_array &y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfgridcalc2vsubset(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), const_cast<alglib_impl::ae_vector*>(x0.c_ptr()), n0, const_cast<alglib_impl::ae_vector*>(x1.c_ptr()), n1, const_cast<alglib_impl::ae_vector*>(flagy.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates values of the RBF model at the regular grid,
which has N0*N1*N2 points, with Point[I,J,K] = (X0[I], X1[J], X2[K]).
Vector-valued RBF models are supported.
This function returns 0.0 when:
* model is not initialized
* NX<>3
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
NOTE: Parallel processing is implemented only for modern (hierarchical)
RBFs. Legacy version 1 RBFs (created by QNN or RBF-ML) are still
processed serially.
INPUT PARAMETERS:
S - RBF model, used in read-only mode, can be shared between
multiple invocations of this function from multiple
threads.
X0 - array of grid nodes, first coordinates, array[N0].
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N0 - grid size (number of nodes) in the first dimension
X1 - array of grid nodes, second coordinates, array[N1]
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N1 - grid size (number of nodes) in the second dimension
X2 - array of grid nodes, third coordinates, array[N2]
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N2 - grid size (number of nodes) in the third dimension
OUTPUT PARAMETERS:
Y - function values, array[NY*N0*N1*N2], where NY is a number
of "output" vector values (this function supports vector-
valued RBF models). Y is out-variable and is reallocated
by this function.
Y[K+NY*(I0+I1*N0+I2*N0*N1)]=F_k(X0[I0],X1[I1],X2[I2]), for:
* K=0...NY-1
* I0=0...N0-1
* I1=0...N1-1
* I2=0...N2-1
NOTE: this function supports weakly ordered grid nodes, i.e. you may have
X[i]=X[i+1] for some i. It does not provide you any performance
benefits due to duplication of points, just convenience and
flexibility.
NOTE: this function is re-entrant, i.e. you may use same rbfmodel
structure in multiple threads calling this function for different
grids.
NOTE: if you need function values on some subset of regular grid, which
may be described as "several compact and dense islands", you may
use rbfgridcalc3vsubset().
-- ALGLIB --
Copyright 04.03.2016 by Bochkanov Sergey
*************************************************************************/
void rbfgridcalc3v(const rbfmodel &s, const real_1d_array &x0, const ae_int_t n0, const real_1d_array &x1, const ae_int_t n1, const real_1d_array &x2, const ae_int_t n2, real_1d_array &y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfgridcalc3v(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), const_cast<alglib_impl::ae_vector*>(x0.c_ptr()), n0, const_cast<alglib_impl::ae_vector*>(x1.c_ptr()), n1, const_cast<alglib_impl::ae_vector*>(x2.c_ptr()), n2, const_cast<alglib_impl::ae_vector*>(y.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function calculates values of the RBF model at some subset of regular
grid:
* grid has N0*N1*N2 points, with Point[I,J,K] = (X0[I], X1[J], X2[K])
* only values at some subset of this grid are required
Vector-valued RBF models are supported.
This function returns 0.0 when:
* model is not initialized
* NX<>3
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
NOTE: Parallel processing is implemented only for modern (hierarchical)
RBFs. Legacy version 1 RBFs (created by QNN or RBF-ML) are still
processed serially.
INPUT PARAMETERS:
S - RBF model, used in read-only mode, can be shared between
multiple invocations of this function from multiple
threads.
X0 - array of grid nodes, first coordinates, array[N0].
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N0 - grid size (number of nodes) in the first dimension
X1 - array of grid nodes, second coordinates, array[N1]
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N1 - grid size (number of nodes) in the second dimension
X2 - array of grid nodes, third coordinates, array[N2]
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N2 - grid size (number of nodes) in the third dimension
FlagY - array[N0*N1*N2]:
* Y[I0+I1*N0+I2*N0*N1] corresponds to node (X0[I0],X1[I1],X2[I2])
* it is a "bitmap" array which contains False for nodes
which are NOT calculated, and True for nodes which are
required.
OUTPUT PARAMETERS:
Y - function values, array[NY*N0*N1*N2], where NY is a number
of "output" vector values (this function supports vector-
valued RBF models):
* Y[K+NY*(I0+I1*N0+I2*N0*N1)]=F_k(X0[I0],X1[I1],X2[I2]),
for K=0...NY-1, I0=0...N0-1, I1=0...N1-1, I2=0...N2-1.
* elements of Y[] which correspond to FlagY[]=True are
loaded by model values (which may be exactly zero for
some nodes).
* elements of Y[] which correspond to FlagY[]=False MAY be
initialized by zeros OR may be calculated. This function
processes grid as a hierarchy of nested blocks and
micro-rows. If just one element of micro-row is required,
entire micro-row (up to 8 nodes in the current version,
but no promises) is calculated.
NOTE: this function supports weakly ordered grid nodes, i.e. you may have
X[i]=X[i+1] for some i. It does not provide you any performance
benefits due to duplication of points, just convenience and
flexibility.
NOTE: this function is re-entrant, i.e. you may use same rbfmodel
structure in multiple threads calling this function for different
grids.
-- ALGLIB --
Copyright 04.03.2016 by Bochkanov Sergey
*************************************************************************/
void rbfgridcalc3vsubset(const rbfmodel &s, const real_1d_array &x0, const ae_int_t n0, const real_1d_array &x1, const ae_int_t n1, const real_1d_array &x2, const ae_int_t n2, const boolean_1d_array &flagy, real_1d_array &y, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfgridcalc3vsubset(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), const_cast<alglib_impl::ae_vector*>(x0.c_ptr()), n0, const_cast<alglib_impl::ae_vector*>(x1.c_ptr()), n1, const_cast<alglib_impl::ae_vector*>(x2.c_ptr()), n2, const_cast<alglib_impl::ae_vector*>(flagy.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function "unpacks" RBF model by extracting its coefficients.
INPUT PARAMETERS:
S - RBF model
OUTPUT PARAMETERS:
NX - dimensionality of argument
NY - dimensionality of the target function
XWR - model information, array[NC,NX+NY+1].
One row of the array corresponds to one basis function:
* first NX columns - coordinates of the center
* next NY columns - weights, one per dimension of the
function being modelled
For ModelVersion=1:
* last column - radius, same for all dimensions of
the function being modelled
For ModelVersion=2:
* last NX columns - radii, one per dimension
NC - number of the centers
V - polynomial term , array[NY,NX+1]. One row per one
dimension of the function being modelled. First NX
elements are linear coefficients, V[NX] is equal to the
constant part.
ModelVersion-version of the RBF model:
* 1 - for models created by QNN and RBF-ML algorithms,
compatible with ALGLIB 3.10 or earlier.
* 2 - for models created by HierarchicalRBF, requires
ALGLIB 3.11 or later
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfunpack(const rbfmodel &s, ae_int_t &nx, ae_int_t &ny, real_2d_array &xwr, ae_int_t &nc, real_2d_array &v, ae_int_t &modelversion, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfunpack(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), &nx, &ny, const_cast<alglib_impl::ae_matrix*>(xwr.c_ptr()), &nc, const_cast<alglib_impl::ae_matrix*>(v.c_ptr()), &modelversion, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function returns model version.
INPUT PARAMETERS:
S - RBF model
RESULT:
* 1 - for models created by QNN and RBF-ML algorithms,
compatible with ALGLIB 3.10 or earlier.
* 2 - for models created by HierarchicalRBF, requires
ALGLIB 3.11 or later
-- ALGLIB --
Copyright 06.07.2016 by Bochkanov Sergey
*************************************************************************/
ae_int_t rbfgetmodelversion(const rbfmodel &s, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::ae_int_t result = alglib_impl::rbfgetmodelversion(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<ae_int_t*>(&result));
}
/*************************************************************************
This function is used to peek into hierarchical RBF construction process
from some other thread and get current progress indicator. It returns
value in [0,1].
IMPORTANT: only HRBFs (hierarchical RBFs) support peeking into progress
indicator. Legacy RBF-ML and RBF-QNN do not support it. You
will always get 0 value.
INPUT PARAMETERS:
S - RBF model object
RESULT:
progress value, in [0,1]
-- ALGLIB --
Copyright 17.11.2018 by Bochkanov Sergey
*************************************************************************/
double rbfpeekprogress(const rbfmodel &s, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return 0;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
double result = alglib_impl::rbfpeekprogress(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return *(reinterpret_cast<double*>(&result));
}
/*************************************************************************
This function is used to submit a request for termination of the
hierarchical RBF construction process from some other thread. As result,
RBF construction is terminated smoothly (with proper deallocation of all
necessary resources) and resultant model is filled by zeros.
A rep.terminationtype=8 will be returned upon receiving such request.
IMPORTANT: only HRBFs (hierarchical RBFs) support termination requests.
Legacy RBF-ML and RBF-QNN do not support it. An attempt to
terminate their construction will be ignored.
IMPORTANT: termination request flag is cleared when the model construction
starts. Thus, any pre-construction termination requests will be
silently ignored - only ones submitted AFTER construction has
actually began will be handled.
INPUT PARAMETERS:
S - RBF model object
-- ALGLIB --
Copyright 17.11.2018 by Bochkanov Sergey
*************************************************************************/
void rbfrequesttermination(const rbfmodel &s, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::rbfrequesttermination(const_cast<alglib_impl::rbfmodel*>(s.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
#if defined(AE_COMPILE_INTCOMP) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This function is left for backward compatibility.
Use fitspheremc() instead.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void nsfitspheremcc(const real_2d_array &xy, const ae_int_t npoints, const ae_int_t nx, real_1d_array &cx, double &rhi, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::nsfitspheremcc(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), npoints, nx, const_cast<alglib_impl::ae_vector*>(cx.c_ptr()), &rhi, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function is left for backward compatibility.
Use fitspheremi() instead.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void nsfitspheremic(const real_2d_array &xy, const ae_int_t npoints, const ae_int_t nx, real_1d_array &cx, double &rlo, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::nsfitspheremic(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), npoints, nx, const_cast<alglib_impl::ae_vector*>(cx.c_ptr()), &rlo, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function is left for backward compatibility.
Use fitspheremz() instead.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void nsfitspheremzc(const real_2d_array &xy, const ae_int_t npoints, const ae_int_t nx, real_1d_array &cx, double &rlo, double &rhi, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::nsfitspheremzc(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), npoints, nx, const_cast<alglib_impl::ae_vector*>(cx.c_ptr()), &rlo, &rhi, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function is left for backward compatibility.
Use fitspherex() instead.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void nsfitspherex(const real_2d_array &xy, const ae_int_t npoints, const ae_int_t nx, const ae_int_t problemtype, const double epsx, const ae_int_t aulits, const double penalty, real_1d_array &cx, double &rlo, double &rhi, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::nsfitspherex(const_cast<alglib_impl::ae_matrix*>(xy.c_ptr()), npoints, nx, problemtype, epsx, aulits, penalty, const_cast<alglib_impl::ae_vector*>(cx.c_ptr()), &rlo, &rhi, &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function is an obsolete and deprecated version of fitting by
penalized cubic spline.
It was superseded by spline1dfit(), which is an orders of magnitude faster
and more memory-efficient implementation.
Do NOT use this function in the new code!
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
void spline1dfitpenalized(const real_1d_array &x, const real_1d_array &y, const ae_int_t n, const ae_int_t m, const double rho, ae_int_t &info, spline1dinterpolant &s, spline1dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dfitpenalized(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, m, rho, &info, const_cast<alglib_impl::spline1dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline1dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function is an obsolete and deprecated version of fitting by
penalized cubic spline.
It was superseded by spline1dfit(), which is an orders of magnitude faster
and more memory-efficient implementation.
Do NOT use this function in the new code!
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dfitpenalized(const real_1d_array &x, const real_1d_array &y, const ae_int_t m, const double rho, ae_int_t &info, spline1dinterpolant &s, spline1dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
if( (x.length()!=y.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dfitpenalized': looks like one of arguments has wrong size");
n = x.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dfitpenalized(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), n, m, rho, &info, const_cast<alglib_impl::spline1dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline1dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
/*************************************************************************
This function is an obsolete and deprecated version of fitting by
penalized cubic spline.
It was superseded by spline1dfit(), which is an orders of magnitude faster
and more memory-efficient implementation.
Do NOT use this function in the new code!
-- ALGLIB PROJECT --
Copyright 19.10.2010 by Bochkanov Sergey
*************************************************************************/
void spline1dfitpenalizedw(const real_1d_array &x, const real_1d_array &y, const real_1d_array &w, const ae_int_t n, const ae_int_t m, const double rho, ae_int_t &info, spline1dinterpolant &s, spline1dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
{
#if !defined(AE_NO_EXCEPTIONS)
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
#else
_ALGLIB_SET_ERROR_FLAG(_alglib_env_state.error_msg);
return;
#endif
}
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dfitpenalizedw(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), n, m, rho, &info, const_cast<alglib_impl::spline1dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline1dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
/*************************************************************************
This function is an obsolete and deprecated version of fitting by
penalized cubic spline.
It was superseded by spline1dfit(), which is an orders of magnitude faster
and more memory-efficient implementation.
Do NOT use this function in the new code!
-- ALGLIB PROJECT --
Copyright 19.10.2010 by Bochkanov Sergey
*************************************************************************/
#if !defined(AE_NO_EXCEPTIONS)
void spline1dfitpenalizedw(const real_1d_array &x, const real_1d_array &y, const real_1d_array &w, const ae_int_t m, const double rho, ae_int_t &info, spline1dinterpolant &s, spline1dfitreport &rep, const xparams _xparams)
{
jmp_buf _break_jump;
alglib_impl::ae_state _alglib_env_state;
ae_int_t n;
if( (x.length()!=y.length()) || (x.length()!=w.length()))
_ALGLIB_CPP_EXCEPTION("Error while calling 'spline1dfitpenalizedw': looks like one of arguments has wrong size");
n = x.length();
alglib_impl::ae_state_init(&_alglib_env_state);
if( setjmp(_break_jump) )
_ALGLIB_CPP_EXCEPTION(_alglib_env_state.error_msg);
ae_state_set_break_jump(&_alglib_env_state, &_break_jump);
if( _xparams.flags!=0x0 )
ae_state_set_flags(&_alglib_env_state, _xparams.flags);
alglib_impl::spline1dfitpenalizedw(const_cast<alglib_impl::ae_vector*>(x.c_ptr()), const_cast<alglib_impl::ae_vector*>(y.c_ptr()), const_cast<alglib_impl::ae_vector*>(w.c_ptr()), n, m, rho, &info, const_cast<alglib_impl::spline1dinterpolant*>(s.c_ptr()), const_cast<alglib_impl::spline1dfitreport*>(rep.c_ptr()), &_alglib_env_state);
alglib_impl::ae_state_clear(&_alglib_env_state);
return;
}
#endif
#endif
}
/////////////////////////////////////////////////////////////////////////
//
// THIS SECTION CONTAINS IMPLEMENTATION OF COMPUTATIONAL CORE
//
/////////////////////////////////////////////////////////////////////////
namespace alglib_impl
{
#if defined(AE_COMPILE_IDW) || !defined(AE_PARTIAL_BUILD)
static double idw_w0 = 1.0;
static double idw_meps = 1.0E-50;
static ae_int_t idw_defaultnlayers = 16;
static double idw_defaultlambda0 = 0.3333;
static void idw_errormetricsviacalc(idwbuilder* state,
idwmodel* model,
idwreport* rep,
ae_state *_state);
#endif
#if defined(AE_COMPILE_RATINT) || !defined(AE_PARTIAL_BUILD)
static void ratint_barycentricnormalize(barycentricinterpolant* b,
ae_state *_state);
#endif
#if defined(AE_COMPILE_FITSPHERE) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_INTFITSERV) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_SPLINE1D) || !defined(AE_PARTIAL_BUILD)
static double spline1d_lambdareg = 1.0e-9;
static double spline1d_cholreg = 1.0e-12;
static void spline1d_spline1dgriddiffcubicinternal(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t boundltype,
double boundl,
ae_int_t boundrtype,
double boundr,
/* Real */ ae_vector* d,
/* Real */ ae_vector* a1,
/* Real */ ae_vector* a2,
/* Real */ ae_vector* a3,
/* Real */ ae_vector* b,
/* Real */ ae_vector* dt,
ae_state *_state);
static void spline1d_heapsortpoints(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_state *_state);
static void spline1d_heapsortppoints(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Integer */ ae_vector* p,
ae_int_t n,
ae_state *_state);
static void spline1d_solvetridiagonal(/* Real */ ae_vector* a,
/* Real */ ae_vector* b,
/* Real */ ae_vector* c,
/* Real */ ae_vector* d,
ae_int_t n,
/* Real */ ae_vector* x,
ae_state *_state);
static void spline1d_solvecyclictridiagonal(/* Real */ ae_vector* a,
/* Real */ ae_vector* b,
/* Real */ ae_vector* c,
/* Real */ ae_vector* d,
ae_int_t n,
/* Real */ ae_vector* x,
ae_state *_state);
static double spline1d_diffthreepoint(double t,
double x0,
double f0,
double x1,
double f1,
double x2,
double f2,
ae_state *_state);
static void spline1d_hermitecalc(double p0,
double m0,
double p1,
double m1,
double t,
double* s,
double* ds,
ae_state *_state);
static double spline1d_rescaleval(double a0,
double b0,
double a1,
double b1,
double t,
ae_state *_state);
#endif
#if defined(AE_COMPILE_PARAMETRIC) || !defined(AE_PARTIAL_BUILD)
static void parametric_pspline2par(/* Real */ ae_matrix* xy,
ae_int_t n,
ae_int_t pt,
/* Real */ ae_vector* p,
ae_state *_state);
static void parametric_pspline3par(/* Real */ ae_matrix* xy,
ae_int_t n,
ae_int_t pt,
/* Real */ ae_vector* p,
ae_state *_state);
static void parametric_rdpanalyzesectionpar(/* Real */ ae_matrix* xy,
ae_int_t i0,
ae_int_t i1,
ae_int_t d,
ae_int_t* worstidx,
double* worsterror,
ae_state *_state);
#endif
#if defined(AE_COMPILE_SPLINE3D) || !defined(AE_PARTIAL_BUILD)
static void spline3d_spline3ddiff(spline3dinterpolant* c,
double x,
double y,
double z,
double* f,
double* fx,
double* fy,
double* fxy,
ae_state *_state);
#endif
#if defined(AE_COMPILE_POLINT) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_LSFIT) || !defined(AE_PARTIAL_BUILD)
static void lsfit_rdpanalyzesection(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t i0,
ae_int_t i1,
ae_int_t* worstidx,
double* worsterror,
ae_state *_state);
static void lsfit_rdprecursive(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t i0,
ae_int_t i1,
double eps,
/* Real */ ae_vector* xout,
/* Real */ ae_vector* yout,
ae_int_t* nout,
ae_state *_state);
static void lsfit_logisticfitinternal(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_bool is4pl,
double lambdav,
minlmstate* state,
minlmreport* replm,
/* Real */ ae_vector* p1,
double* flast,
ae_state *_state);
static void lsfit_logisticfit45errors(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
double a,
double b,
double c,
double d,
double g,
lsfitreport* rep,
ae_state *_state);
static void lsfit_spline1dfitinternal(ae_int_t st,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
ae_int_t n,
/* Real */ ae_vector* xc,
/* Real */ ae_vector* yc,
/* Integer */ ae_vector* dc,
ae_int_t k,
ae_int_t m,
ae_int_t* info,
spline1dinterpolant* s,
spline1dfitreport* rep,
ae_state *_state);
static void lsfit_lsfitlinearinternal(/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
/* Real */ ae_matrix* fmatrix,
ae_int_t n,
ae_int_t m,
ae_int_t* info,
/* Real */ ae_vector* c,
lsfitreport* rep,
ae_state *_state);
static void lsfit_lsfitclearrequestfields(lsfitstate* state,
ae_state *_state);
static void lsfit_barycentriccalcbasis(barycentricinterpolant* b,
double t,
/* Real */ ae_vector* y,
ae_state *_state);
static void lsfit_internalchebyshevfit(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
ae_int_t n,
/* Real */ ae_vector* xc,
/* Real */ ae_vector* yc,
/* Integer */ ae_vector* dc,
ae_int_t k,
ae_int_t m,
ae_int_t* info,
/* Real */ ae_vector* c,
lsfitreport* rep,
ae_state *_state);
static void lsfit_barycentricfitwcfixedd(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
ae_int_t n,
/* Real */ ae_vector* xc,
/* Real */ ae_vector* yc,
/* Integer */ ae_vector* dc,
ae_int_t k,
ae_int_t m,
ae_int_t d,
ae_int_t* info,
barycentricinterpolant* b,
barycentricfitreport* rep,
ae_state *_state);
static void lsfit_clearreport(lsfitreport* rep, ae_state *_state);
static void lsfit_estimateerrors(/* Real */ ae_matrix* f1,
/* Real */ ae_vector* f0,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
/* Real */ ae_vector* x,
/* Real */ ae_vector* s,
ae_int_t n,
ae_int_t k,
lsfitreport* rep,
/* Real */ ae_matrix* z,
ae_int_t zkind,
ae_state *_state);
#endif
#if defined(AE_COMPILE_RBFV2) || !defined(AE_PARTIAL_BUILD)
static double rbfv2_defaultlambdareg = 1.0E-6;
static double rbfv2_defaultsupportr = 0.10;
static ae_int_t rbfv2_defaultmaxits = 400;
static ae_int_t rbfv2_defaultbf = 1;
static ae_int_t rbfv2_maxnodesize = 6;
static double rbfv2_complexitymultiplier = 100.0;
static ae_bool rbfv2_rbfv2buildlinearmodel(/* Real */ ae_matrix* x,
/* Real */ ae_matrix* y,
ae_int_t n,
ae_int_t nx,
ae_int_t ny,
ae_int_t modeltype,
/* Real */ ae_matrix* v,
ae_state *_state);
static void rbfv2_allocatecalcbuffer(rbfv2model* s,
rbfv2calcbuffer* buf,
ae_state *_state);
static void rbfv2_convertandappendtree(kdtree* curtree,
ae_int_t n,
ae_int_t nx,
ae_int_t ny,
/* Integer */ ae_vector* kdnodes,
/* Real */ ae_vector* kdsplits,
/* Real */ ae_vector* cw,
ae_state *_state);
static void rbfv2_converttreerec(kdtree* curtree,
ae_int_t n,
ae_int_t nx,
ae_int_t ny,
ae_int_t nodeoffset,
ae_int_t nodesbase,
ae_int_t splitsbase,
ae_int_t cwbase,
/* Integer */ ae_vector* localnodes,
ae_int_t* localnodessize,
/* Real */ ae_vector* localsplits,
ae_int_t* localsplitssize,
/* Real */ ae_vector* localcw,
ae_int_t* localcwsize,
/* Real */ ae_matrix* xybuf,
ae_state *_state);
static void rbfv2_partialcalcrec(rbfv2model* s,
rbfv2calcbuffer* buf,
ae_int_t rootidx,
double invr2,
double queryr2,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state);
static void rbfv2_partialrowcalcrec(rbfv2model* s,
rbfv2calcbuffer* buf,
ae_int_t rootidx,
double invr2,
double rquery2,
double rfar2,
/* Real */ ae_vector* cx,
/* Real */ ae_vector* rx,
/* Boolean */ ae_vector* rf,
ae_int_t rowsize,
/* Real */ ae_vector* ry,
ae_state *_state);
static void rbfv2_preparepartialquery(/* Real */ ae_vector* x,
/* Real */ ae_vector* kdboxmin,
/* Real */ ae_vector* kdboxmax,
ae_int_t nx,
rbfv2calcbuffer* buf,
ae_int_t* cnt,
ae_state *_state);
static void rbfv2_partialqueryrec(/* Integer */ ae_vector* kdnodes,
/* Real */ ae_vector* kdsplits,
/* Real */ ae_vector* cw,
ae_int_t nx,
ae_int_t ny,
rbfv2calcbuffer* buf,
ae_int_t rootidx,
double queryr2,
/* Real */ ae_vector* x,
/* Real */ ae_vector* r2,
/* Integer */ ae_vector* offs,
ae_int_t* k,
ae_state *_state);
static ae_int_t rbfv2_partialcountrec(/* Integer */ ae_vector* kdnodes,
/* Real */ ae_vector* kdsplits,
/* Real */ ae_vector* cw,
ae_int_t nx,
ae_int_t ny,
rbfv2calcbuffer* buf,
ae_int_t rootidx,
double queryr2,
/* Real */ ae_vector* x,
ae_state *_state);
static void rbfv2_partialunpackrec(/* Integer */ ae_vector* kdnodes,
/* Real */ ae_vector* kdsplits,
/* Real */ ae_vector* cw,
/* Real */ ae_vector* s,
ae_int_t nx,
ae_int_t ny,
ae_int_t rootidx,
double r,
/* Real */ ae_matrix* xwr,
ae_int_t* k,
ae_state *_state);
static ae_int_t rbfv2_designmatrixrowsize(/* Integer */ ae_vector* kdnodes,
/* Real */ ae_vector* kdsplits,
/* Real */ ae_vector* cw,
/* Real */ ae_vector* ri,
/* Integer */ ae_vector* kdroots,
/* Real */ ae_vector* kdboxmin,
/* Real */ ae_vector* kdboxmax,
ae_int_t nx,
ae_int_t ny,
ae_int_t nh,
ae_int_t level,
double rcoeff,
/* Real */ ae_vector* x0,
rbfv2calcbuffer* calcbuf,
ae_state *_state);
static void rbfv2_designmatrixgeneraterow(/* Integer */ ae_vector* kdnodes,
/* Real */ ae_vector* kdsplits,
/* Real */ ae_vector* cw,
/* Real */ ae_vector* ri,
/* Integer */ ae_vector* kdroots,
/* Real */ ae_vector* kdboxmin,
/* Real */ ae_vector* kdboxmax,
/* Integer */ ae_vector* cwrange,
ae_int_t nx,
ae_int_t ny,
ae_int_t nh,
ae_int_t level,
ae_int_t bf,
double rcoeff,
ae_int_t rowsperpoint,
double penalty,
/* Real */ ae_vector* x0,
rbfv2calcbuffer* calcbuf,
/* Real */ ae_vector* tmpr2,
/* Integer */ ae_vector* tmpoffs,
/* Integer */ ae_vector* rowidx,
/* Real */ ae_vector* rowval,
ae_int_t* rowsize,
ae_state *_state);
static void rbfv2_zerofill(rbfv2model* s,
ae_int_t nx,
ae_int_t ny,
ae_int_t bf,
ae_state *_state);
#endif
#if defined(AE_COMPILE_SPLINE2D) || !defined(AE_PARTIAL_BUILD)
static double spline2d_cholreg = 1.0E-12;
static double spline2d_lambdaregblocklls = 1.0E-6;
static double spline2d_lambdaregfastddm = 1.0E-4;
static double spline2d_lambdadecay = 0.5;
static void spline2d_bicubiccalcderivatives(/* Real */ ae_matrix* a,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t m,
ae_int_t n,
/* Real */ ae_matrix* dx,
/* Real */ ae_matrix* dy,
/* Real */ ae_matrix* dxy,
ae_state *_state);
static void spline2d_generatedesignmatrix(/* Real */ ae_vector* xy,
ae_int_t npoints,
ae_int_t d,
ae_int_t kx,
ae_int_t ky,
double smoothing,
double lambdareg,
spline1dinterpolant* basis1,
sparsematrix* av,
sparsematrix* ah,
ae_int_t* arows,
ae_state *_state);
static void spline2d_updatesplinetable(/* Real */ ae_vector* z,
ae_int_t kx,
ae_int_t ky,
ae_int_t d,
spline1dinterpolant* basis1,
ae_int_t bfrad,
/* Real */ ae_vector* ftbl,
ae_int_t m,
ae_int_t n,
ae_int_t scalexy,
ae_state *_state);
static void spline2d_fastddmfit(/* Real */ ae_vector* xy,
ae_int_t npoints,
ae_int_t d,
ae_int_t kx,
ae_int_t ky,
ae_int_t basecasex,
ae_int_t basecasey,
ae_int_t maxcoresize,
ae_int_t interfacesize,
ae_int_t nlayers,
double smoothing,
ae_int_t lsqrcnt,
spline1dinterpolant* basis1,
spline2dinterpolant* spline,
spline2dfitreport* rep,
double tss,
ae_state *_state);
static void spline2d_fastddmfitlayer(/* Real */ ae_vector* xy,
ae_int_t d,
ae_int_t scalexy,
/* Integer */ ae_vector* xyindex,
ae_int_t basecasex,
ae_int_t tilex0,
ae_int_t tilex1,
ae_int_t tilescountx,
ae_int_t basecasey,
ae_int_t tiley0,
ae_int_t tiley1,
ae_int_t tilescounty,
ae_int_t maxcoresize,
ae_int_t interfacesize,
ae_int_t lsqrcnt,
double lambdareg,
spline1dinterpolant* basis1,
ae_shared_pool* pool,
spline2dinterpolant* spline,
ae_state *_state);
ae_bool _trypexec_spline2d_fastddmfitlayer(/* Real */ ae_vector* xy,
ae_int_t d,
ae_int_t scalexy,
/* Integer */ ae_vector* xyindex,
ae_int_t basecasex,
ae_int_t tilex0,
ae_int_t tilex1,
ae_int_t tilescountx,
ae_int_t basecasey,
ae_int_t tiley0,
ae_int_t tiley1,
ae_int_t tilescounty,
ae_int_t maxcoresize,
ae_int_t interfacesize,
ae_int_t lsqrcnt,
double lambdareg,
spline1dinterpolant* basis1,
ae_shared_pool* pool,
spline2dinterpolant* spline, ae_state *_state);
static void spline2d_blockllsfit(spline2dxdesignmatrix* xdesign,
ae_int_t lsqrcnt,
/* Real */ ae_vector* z,
spline2dfitreport* rep,
double tss,
spline2dblockllsbuf* buf,
ae_state *_state);
static void spline2d_naivellsfit(sparsematrix* av,
sparsematrix* ah,
ae_int_t arows,
/* Real */ ae_vector* xy,
ae_int_t kx,
ae_int_t ky,
ae_int_t npoints,
ae_int_t d,
ae_int_t lsqrcnt,
/* Real */ ae_vector* z,
spline2dfitreport* rep,
double tss,
ae_state *_state);
static ae_int_t spline2d_getcelloffset(ae_int_t kx,
ae_int_t ky,
ae_int_t blockbandwidth,
ae_int_t i,
ae_int_t j,
ae_state *_state);
static void spline2d_copycellto(ae_int_t kx,
ae_int_t ky,
ae_int_t blockbandwidth,
/* Real */ ae_matrix* blockata,
ae_int_t i,
ae_int_t j,
/* Real */ ae_matrix* dst,
ae_int_t dst0,
ae_int_t dst1,
ae_state *_state);
static void spline2d_flushtozerocell(ae_int_t kx,
ae_int_t ky,
ae_int_t blockbandwidth,
/* Real */ ae_matrix* blockata,
ae_int_t i,
ae_int_t j,
double eps,
ae_state *_state);
static void spline2d_blockllsgenerateata(sparsematrix* ah,
ae_int_t ky0,
ae_int_t ky1,
ae_int_t kx,
ae_int_t ky,
/* Real */ ae_matrix* blockata,
sreal* mxata,
ae_state *_state);
ae_bool _trypexec_spline2d_blockllsgenerateata(sparsematrix* ah,
ae_int_t ky0,
ae_int_t ky1,
ae_int_t kx,
ae_int_t ky,
/* Real */ ae_matrix* blockata,
sreal* mxata, ae_state *_state);
static ae_bool spline2d_blockllscholesky(/* Real */ ae_matrix* blockata,
ae_int_t kx,
ae_int_t ky,
/* Real */ ae_matrix* trsmbuf2,
/* Real */ ae_matrix* cholbuf2,
/* Real */ ae_vector* cholbuf1,
ae_state *_state);
static void spline2d_blockllstrsv(/* Real */ ae_matrix* blockata,
ae_int_t kx,
ae_int_t ky,
ae_bool transu,
/* Real */ ae_vector* b,
ae_state *_state);
static void spline2d_computeresidualsfromscratch(/* Real */ ae_vector* xy,
/* Real */ ae_vector* yraw,
ae_int_t npoints,
ae_int_t d,
ae_int_t scalexy,
spline2dinterpolant* spline,
ae_state *_state);
ae_bool _trypexec_spline2d_computeresidualsfromscratch(/* Real */ ae_vector* xy,
/* Real */ ae_vector* yraw,
ae_int_t npoints,
ae_int_t d,
ae_int_t scalexy,
spline2dinterpolant* spline, ae_state *_state);
static void spline2d_computeresidualsfromscratchrec(/* Real */ ae_vector* xy,
/* Real */ ae_vector* yraw,
ae_int_t pt0,
ae_int_t pt1,
ae_int_t chunksize,
ae_int_t d,
ae_int_t scalexy,
spline2dinterpolant* spline,
ae_shared_pool* pool,
ae_state *_state);
ae_bool _trypexec_spline2d_computeresidualsfromscratchrec(/* Real */ ae_vector* xy,
/* Real */ ae_vector* yraw,
ae_int_t pt0,
ae_int_t pt1,
ae_int_t chunksize,
ae_int_t d,
ae_int_t scalexy,
spline2dinterpolant* spline,
ae_shared_pool* pool, ae_state *_state);
static void spline2d_reorderdatasetandbuildindex(/* Real */ ae_vector* xy,
ae_int_t npoints,
ae_int_t d,
/* Real */ ae_vector* shadow,
ae_int_t ns,
ae_int_t kx,
ae_int_t ky,
/* Integer */ ae_vector* xyindex,
/* Integer */ ae_vector* bufi,
ae_state *_state);
static void spline2d_rescaledatasetandrefineindex(/* Real */ ae_vector* xy,
ae_int_t npoints,
ae_int_t d,
/* Real */ ae_vector* shadow,
ae_int_t ns,
ae_int_t kx,
ae_int_t ky,
/* Integer */ ae_vector* xyindex,
/* Integer */ ae_vector* bufi,
ae_state *_state);
static void spline2d_expandindexrows(/* Real */ ae_vector* xy,
ae_int_t d,
/* Real */ ae_vector* shadow,
ae_int_t ns,
/* Integer */ ae_vector* cidx,
ae_int_t pt0,
ae_int_t pt1,
/* Integer */ ae_vector* xyindexprev,
ae_int_t row0,
ae_int_t row1,
/* Integer */ ae_vector* xyindexnew,
ae_int_t kxnew,
ae_int_t kynew,
ae_bool rootcall,
ae_state *_state);
ae_bool _trypexec_spline2d_expandindexrows(/* Real */ ae_vector* xy,
ae_int_t d,
/* Real */ ae_vector* shadow,
ae_int_t ns,
/* Integer */ ae_vector* cidx,
ae_int_t pt0,
ae_int_t pt1,
/* Integer */ ae_vector* xyindexprev,
ae_int_t row0,
ae_int_t row1,
/* Integer */ ae_vector* xyindexnew,
ae_int_t kxnew,
ae_int_t kynew,
ae_bool rootcall, ae_state *_state);
static void spline2d_reorderdatasetandbuildindexrec(/* Real */ ae_vector* xy,
ae_int_t d,
/* Real */ ae_vector* shadow,
ae_int_t ns,
/* Integer */ ae_vector* cidx,
ae_int_t pt0,
ae_int_t pt1,
/* Integer */ ae_vector* xyindex,
ae_int_t idx0,
ae_int_t idx1,
ae_bool rootcall,
ae_state *_state);
ae_bool _trypexec_spline2d_reorderdatasetandbuildindexrec(/* Real */ ae_vector* xy,
ae_int_t d,
/* Real */ ae_vector* shadow,
ae_int_t ns,
/* Integer */ ae_vector* cidx,
ae_int_t pt0,
ae_int_t pt1,
/* Integer */ ae_vector* xyindex,
ae_int_t idx0,
ae_int_t idx1,
ae_bool rootcall, ae_state *_state);
static void spline2d_xdesigngenerate(/* Real */ ae_vector* xy,
/* Integer */ ae_vector* xyindex,
ae_int_t kx0,
ae_int_t kx1,
ae_int_t kxtotal,
ae_int_t ky0,
ae_int_t ky1,
ae_int_t kytotal,
ae_int_t d,
double lambdareg,
double lambdans,
spline1dinterpolant* basis1,
spline2dxdesignmatrix* a,
ae_state *_state);
static void spline2d_xdesignmv(spline2dxdesignmatrix* a,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state);
static void spline2d_xdesignmtv(spline2dxdesignmatrix* a,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state);
static void spline2d_xdesignblockata(spline2dxdesignmatrix* a,
/* Real */ ae_matrix* blockata,
double* mxata,
ae_state *_state);
#endif
#if defined(AE_COMPILE_RBFV1) || !defined(AE_PARTIAL_BUILD)
static ae_int_t rbfv1_mxnx = 3;
static double rbfv1_rbffarradius = 6;
static double rbfv1_rbfnearradius = 2.1;
static double rbfv1_rbfmlradius = 3;
static double rbfv1_minbasecasecost = 100000;
static ae_bool rbfv1_rbfv1buildlinearmodel(/* Real */ ae_matrix* x,
/* Real */ ae_matrix* y,
ae_int_t n,
ae_int_t ny,
ae_int_t modeltype,
/* Real */ ae_matrix* v,
ae_state *_state);
static void rbfv1_buildrbfmodellsqr(/* Real */ ae_matrix* x,
/* Real */ ae_matrix* y,
/* Real */ ae_matrix* xc,
/* Real */ ae_vector* r,
ae_int_t n,
ae_int_t nc,
ae_int_t ny,
kdtree* pointstree,
kdtree* centerstree,
double epsort,
double epserr,
ae_int_t maxits,
ae_int_t* gnnz,
ae_int_t* snnz,
/* Real */ ae_matrix* w,
ae_int_t* info,
ae_int_t* iterationscount,
ae_int_t* nmv,
ae_state *_state);
static void rbfv1_buildrbfmlayersmodellsqr(/* Real */ ae_matrix* x,
/* Real */ ae_matrix* y,
/* Real */ ae_matrix* xc,
double rval,
/* Real */ ae_vector* r,
ae_int_t n,
ae_int_t* nc,
ae_int_t ny,
ae_int_t nlayers,
kdtree* centerstree,
double epsort,
double epserr,
ae_int_t maxits,
double lambdav,
ae_int_t* annz,
/* Real */ ae_matrix* w,
ae_int_t* info,
ae_int_t* iterationscount,
ae_int_t* nmv,
ae_state *_state);
#endif
#if defined(AE_COMPILE_RBF) || !defined(AE_PARTIAL_BUILD)
static double rbf_eps = 1.0E-6;
static double rbf_rbffarradius = 6;
static ae_int_t rbf_rbffirstversion = 0;
static ae_int_t rbf_rbfversion2 = 2;
static void rbf_rbfpreparenonserializablefields(rbfmodel* s,
ae_state *_state);
static void rbf_initializev1(ae_int_t nx,
ae_int_t ny,
rbfv1model* s,
ae_state *_state);
static void rbf_initializev2(ae_int_t nx,
ae_int_t ny,
rbfv2model* s,
ae_state *_state);
static void rbf_clearreportfields(rbfreport* rep, ae_state *_state);
#endif
#if defined(AE_COMPILE_INTCOMP) || !defined(AE_PARTIAL_BUILD)
#endif
#if defined(AE_COMPILE_IDW) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This function creates buffer structure which can be used to perform
parallel IDW model evaluations (with one IDW model instance being
used from multiple threads, as long as different threads use different
instances of buffer).
This buffer object can be used with idwtscalcbuf() function (here "ts"
stands for "thread-safe", "buf" is a suffix which denotes function which
reuses previously allocated output space).
How to use it:
* create IDW model structure or load it from file
* call idwcreatecalcbuffer(), once per thread working with IDW model (you
should call this function only AFTER model initialization, see below for
more information)
* call idwtscalcbuf() from different threads, with each thread working
with its own copy of buffer object.
INPUT PARAMETERS
S - IDW model
OUTPUT PARAMETERS
Buf - external buffer.
IMPORTANT: buffer object should be used only with IDW model object which
was used to initialize buffer. Any attempt to use buffer with
different object is dangerous - you may get memory violation
error because sizes of internal arrays do not fit to dimensions
of the IDW structure.
IMPORTANT: you should call this function only for model which was built
with model builder (or unserialized from file). Sizes of some
internal structures are determined only after model is built,
so buffer object created before model construction stage will
be useless (and any attempt to use it will result in exception).
-- ALGLIB --
Copyright 22.10.2018 by Sergey Bochkanov
*************************************************************************/
void idwcreatecalcbuffer(idwmodel* s,
idwcalcbuffer* buf,
ae_state *_state)
{
_idwcalcbuffer_clear(buf);
ae_assert(s->nx>=1, "IDWCreateCalcBuffer: integrity check failed", _state);
ae_assert(s->ny>=1, "IDWCreateCalcBuffer: integrity check failed", _state);
ae_assert(s->nlayers>=0, "IDWCreateCalcBuffer: integrity check failed", _state);
ae_assert(s->algotype>=0, "IDWCreateCalcBuffer: integrity check failed", _state);
if( s->nlayers>=1&&s->algotype!=0 )
{
kdtreecreaterequestbuffer(&s->tree, &buf->requestbuffer, _state);
}
rvectorsetlengthatleast(&buf->x, s->nx, _state);
rvectorsetlengthatleast(&buf->y, s->ny, _state);
rvectorsetlengthatleast(&buf->tsyw, s->ny*ae_maxint(s->nlayers, 1, _state), _state);
rvectorsetlengthatleast(&buf->tsw, ae_maxint(s->nlayers, 1, _state), _state);
}
/*************************************************************************
This subroutine creates builder object used to generate IDW model from
irregularly sampled (scattered) dataset. Multidimensional scalar/vector-
-valued are supported.
Builder object is used to fit model to data as follows:
* builder object is created with idwbuildercreate() function
* dataset is added with idwbuildersetpoints() function
* one of the modern IDW algorithms is chosen with either:
* idwbuildersetalgomstab() - Multilayer STABilized algorithm (interpolation)
Alternatively, one of the textbook algorithms can be chosen (not recommended):
* idwbuildersetalgotextbookshepard() - textbook Shepard algorithm
* idwbuildersetalgotextbookmodshepard()-textbook modified Shepard algorithm
* finally, model construction is performed with idwfit() function.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
NX - dimensionality of the argument, NX>=1
NY - dimensionality of the function being modeled, NY>=1;
NY=1 corresponds to classic scalar function, NY>=1 corresponds
to vector-valued function.
OUTPUT PARAMETERS:
State- builder object
-- ALGLIB PROJECT --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildercreate(ae_int_t nx,
ae_int_t ny,
idwbuilder* state,
ae_state *_state)
{
_idwbuilder_clear(state);
ae_assert(nx>=1, "IDWBuilderCreate: NX<=0", _state);
ae_assert(ny>=1, "IDWBuilderCreate: NY<=0", _state);
/*
* We choose reasonable defaults for the algorithm:
* * MSTAB algorithm
* * 12 layers
* * default radius
* * default Lambda0
*/
state->algotype = 2;
state->priortermtype = 2;
rvectorsetlengthatleast(&state->priortermval, ny, _state);
state->nlayers = idw_defaultnlayers;
state->r0 = (double)(0);
state->rdecay = 0.5;
state->lambda0 = idw_defaultlambda0;
state->lambdalast = (double)(0);
state->lambdadecay = 1.0;
/*
* Other parameters, not used but initialized
*/
state->shepardp = (double)(0);
/*
* Initial dataset is empty
*/
state->npoints = 0;
state->nx = nx;
state->ny = ny;
}
/*************************************************************************
This function changes number of layers used by IDW-MSTAB algorithm.
The more layers you have, the finer details can be reproduced with IDW
model. The less layers you have, the less memory and CPU time is consumed
by the model.
Memory consumption grows linearly with layers count, running time grows
sub-linearly.
The default number of layers is 16, which allows you to reproduce details
at distance down to SRad/65536. You will rarely need to change it.
INPUT PARAMETERS:
State - builder object
NLayers - NLayers>=1, the number of layers used by the model.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetnlayers(idwbuilder* state,
ae_int_t nlayers,
ae_state *_state)
{
ae_assert(nlayers>=1, "IDWBuilderSetNLayers: N<1", _state);
state->nlayers = nlayers;
}
/*************************************************************************
This function adds dataset to the builder object.
This function overrides results of the previous calls, i.e. multiple calls
of this function will result in only the last set being added.
INPUT PARAMETERS:
State - builder object
XY - points, array[N,NX+NY]. One row corresponds to one point
in the dataset. First NX elements are coordinates, next
NY elements are function values. Array may be larger than
specified, in this case only leading [N,NX+NY] elements
will be used.
N - number of points in the dataset, N>=0.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetpoints(idwbuilder* state,
/* Real */ ae_matrix* xy,
ae_int_t n,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
ae_int_t ew;
ae_assert(n>=0, "IDWBuilderSetPoints: N<0", _state);
ae_assert(xy->rows>=n, "IDWBuilderSetPoints: Rows(XY)<N", _state);
ae_assert(n==0||xy->cols>=state->nx+state->ny, "IDWBuilderSetPoints: Cols(XY)<NX+NY", _state);
ae_assert(apservisfinitematrix(xy, n, state->nx+state->ny, _state), "IDWBuilderSetPoints: XY contains infinite or NaN values!", _state);
state->npoints = n;
ew = state->nx+state->ny;
rvectorsetlengthatleast(&state->xy, n*ew, _state);
for(i=0; i<=n-1; i++)
{
for(j=0; j<=ew-1; j++)
{
state->xy.ptr.p_double[i*ew+j] = xy->ptr.pp_double[i][j];
}
}
}
/*************************************************************************
This function sets IDW model construction algorithm to the Multilayer
Stabilized IDW method (IDW-MSTAB), a latest incarnation of the inverse
distance weighting interpolation which fixes shortcomings of the original
and modified Shepard's variants.
The distinctive features of IDW-MSTAB are:
1) exact interpolation is pursued (as opposed to fitting and noise
suppression)
2) improved robustness when compared with that of other algorithms:
* MSTAB shows almost no strange fitting artifacts like ripples and
sharp spikes (unlike N-dimensional splines and HRBFs)
* MSTAB does not return function values far from the interval spanned
by the dataset; say, if all your points have |f|<=1, you can be sure
that model value won't deviate too much from [-1,+1]
3) good model construction time competing with that of HRBFs and bicubic
splines
4) ability to work with any number of dimensions, starting from NX=1
The drawbacks of IDW-MSTAB (and all IDW algorithms in general) are:
1) dependence of the model evaluation time on the search radius
2) bad extrapolation properties, models built by this method are usually
conservative in their predictions
Thus, IDW-MSTAB is a good "default" option if you want to perform
scattered multidimensional interpolation. Although it has its drawbacks,
it is easy to use and robust, which makes it a good first step.
INPUT PARAMETERS:
State - builder object
SRad - initial search radius, SRad>0 is required. A model value
is obtained by "smart" averaging of the dataset points
within search radius.
NOTE 1: IDW interpolation can correctly handle ANY dataset, including
datasets with non-distinct points. In case non-distinct points are
found, an average value for this point will be calculated.
NOTE 2: the memory requirements for model storage are O(NPoints*NLayers).
The model construction needs twice as much memory as model storage.
NOTE 3: by default 16 IDW layers are built which is enough for most cases.
You can change this parameter with idwbuildersetnlayers() method.
Larger values may be necessary if you need to reproduce extrafine
details at distances smaller than SRad/65536. Smaller value may
be necessary if you have to save memory and computing time, and
ready to sacrifice some model quality.
ALGORITHM DESCRIPTION
ALGLIB implementation of IDW is somewhat similar to the modified Shepard's
method (one with search radius R) but overcomes several of its drawbacks,
namely:
1) a tendency to show stepwise behavior for uniform datasets
2) a tendency to show terrible interpolation properties for highly
nonuniform datasets which often arise in geospatial tasks
(function values are densely sampled across multiple separated
"tracks")
IDW-MSTAB method performs several passes over dataset and builds a sequence
of progressively refined IDW models (layers), which starts from one with
largest search radius SRad and continues to smaller search radii until
required number of layers is built. Highest layers reproduce global
behavior of the target function at larger distances whilst lower layers
reproduce fine details at smaller distances.
Each layer is an IDW model built with following modifications:
* weights go to zero when distance approach to the current search radius
* an additional regularizing term is added to the distance: w=1/(d^2+lambda)
* an additional fictional term with unit weight and zero function value is
added in order to promote continuity properties at the isolated and
boundary points
By default, 16 layers is built, which is enough for most cases. You can
change this parameter with idwbuildersetnlayers() method.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetalgomstab(idwbuilder* state,
double srad,
ae_state *_state)
{
ae_assert(ae_isfinite(srad, _state), "IDWBuilderSetAlgoMSTAB: SRad is not finite", _state);
ae_assert(ae_fp_greater(srad,(double)(0)), "IDWBuilderSetAlgoMSTAB: SRad<=0", _state);
/*
* Set algorithm
*/
state->algotype = 2;
/*
* Set options
*/
state->r0 = srad;
state->rdecay = 0.5;
state->lambda0 = idw_defaultlambda0;
state->lambdalast = (double)(0);
state->lambdadecay = 1.0;
}
/*************************************************************************
This function sets IDW model construction algorithm to the textbook
Shepard's algorithm with custom (user-specified) power parameter.
IMPORTANT: we do NOT recommend using textbook IDW algorithms because they
have terrible interpolation properties. Use MSTAB in all cases.
INPUT PARAMETERS:
State - builder object
P - power parameter, P>0; good value to start with is 2.0
NOTE 1: IDW interpolation can correctly handle ANY dataset, including
datasets with non-distinct points. In case non-distinct points are
found, an average value for this point will be calculated.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetalgotextbookshepard(idwbuilder* state,
double p,
ae_state *_state)
{
ae_assert(ae_isfinite(p, _state), "IDWBuilderSetAlgoShepard: P is not finite", _state);
ae_assert(ae_fp_greater(p,(double)(0)), "IDWBuilderSetAlgoShepard: P<=0", _state);
/*
* Set algorithm and options
*/
state->algotype = 0;
state->shepardp = p;
}
/*************************************************************************
This function sets IDW model construction algorithm to the 'textbook'
modified Shepard's algorithm with user-specified search radius.
IMPORTANT: we do NOT recommend using textbook IDW algorithms because they
have terrible interpolation properties. Use MSTAB in all cases.
INPUT PARAMETERS:
State - builder object
R - search radius
NOTE 1: IDW interpolation can correctly handle ANY dataset, including
datasets with non-distinct points. In case non-distinct points are
found, an average value for this point will be calculated.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetalgotextbookmodshepard(idwbuilder* state,
double r,
ae_state *_state)
{
ae_assert(ae_isfinite(r, _state), "IDWBuilderSetAlgoModShepard: R is not finite", _state);
ae_assert(ae_fp_greater(r,(double)(0)), "IDWBuilderSetAlgoModShepard: R<=0", _state);
/*
* Set algorithm and options
*/
state->algotype = 1;
state->r0 = r;
}
/*************************************************************************
This function sets prior term (model value at infinity) as user-specified
value.
INPUT PARAMETERS:
S - spline builder
V - value for user-defined prior
NOTE: for vector-valued models all components of the prior are set to same
user-specified value
-- ALGLIB --
Copyright 29.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetuserterm(idwbuilder* state, double v, ae_state *_state)
{
ae_int_t j;
ae_assert(ae_isfinite(v, _state), "IDWBuilderSetUserTerm: infinite/NAN value passed", _state);
state->priortermtype = 0;
for(j=0; j<=state->ny-1; j++)
{
state->priortermval.ptr.p_double[j] = v;
}
}
/*************************************************************************
This function sets constant prior term (model value at infinity).
Constant prior term is determined as mean value over dataset.
INPUT PARAMETERS:
S - spline builder
-- ALGLIB --
Copyright 29.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetconstterm(idwbuilder* state, ae_state *_state)
{
state->priortermtype = 2;
}
/*************************************************************************
This function sets zero prior term (model value at infinity).
INPUT PARAMETERS:
S - spline builder
-- ALGLIB --
Copyright 29.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwbuildersetzeroterm(idwbuilder* state, ae_state *_state)
{
state->priortermtype = 3;
}
/*************************************************************************
IDW interpolation: scalar target, 1-dimensional argument
NOTE: this function modifies internal temporaries of the IDW model, thus
IT IS NOT THREAD-SAFE! If you want to perform parallel model
evaluation from the multiple threads, use idwtscalcbuf() with per-
thread buffer object.
INPUT PARAMETERS:
S - IDW interpolant built with IDW builder
X0 - argument value
Result:
IDW interpolant S(X0)
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
double idwcalc1(idwmodel* s, double x0, ae_state *_state)
{
double result;
ae_assert(s->nx==1, "IDWCalc1: S.NX<>1", _state);
ae_assert(s->ny==1, "IDWCalc1: S.NY<>1", _state);
ae_assert(ae_isfinite(x0, _state), "IDWCalc1: X0 is INF or NAN", _state);
s->buffer.x.ptr.p_double[0] = x0;
idwtscalcbuf(s, &s->buffer, &s->buffer.x, &s->buffer.y, _state);
result = s->buffer.y.ptr.p_double[0];
return result;
}
/*************************************************************************
IDW interpolation: scalar target, 2-dimensional argument
NOTE: this function modifies internal temporaries of the IDW model, thus
IT IS NOT THREAD-SAFE! If you want to perform parallel model
evaluation from the multiple threads, use idwtscalcbuf() with per-
thread buffer object.
INPUT PARAMETERS:
S - IDW interpolant built with IDW builder
X0, X1 - argument value
Result:
IDW interpolant S(X0,X1)
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
double idwcalc2(idwmodel* s, double x0, double x1, ae_state *_state)
{
double result;
ae_assert(s->nx==2, "IDWCalc2: S.NX<>2", _state);
ae_assert(s->ny==1, "IDWCalc2: S.NY<>1", _state);
ae_assert(ae_isfinite(x0, _state), "IDWCalc2: X0 is INF or NAN", _state);
ae_assert(ae_isfinite(x1, _state), "IDWCalc2: X1 is INF or NAN", _state);
s->buffer.x.ptr.p_double[0] = x0;
s->buffer.x.ptr.p_double[1] = x1;
idwtscalcbuf(s, &s->buffer, &s->buffer.x, &s->buffer.y, _state);
result = s->buffer.y.ptr.p_double[0];
return result;
}
/*************************************************************************
IDW interpolation: scalar target, 3-dimensional argument
NOTE: this function modifies internal temporaries of the IDW model, thus
IT IS NOT THREAD-SAFE! If you want to perform parallel model
evaluation from the multiple threads, use idwtscalcbuf() with per-
thread buffer object.
INPUT PARAMETERS:
S - IDW interpolant built with IDW builder
X0,X1,X2- argument value
Result:
IDW interpolant S(X0,X1,X2)
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
double idwcalc3(idwmodel* s,
double x0,
double x1,
double x2,
ae_state *_state)
{
double result;
ae_assert(s->nx==3, "IDWCalc3: S.NX<>3", _state);
ae_assert(s->ny==1, "IDWCalc3: S.NY<>1", _state);
ae_assert(ae_isfinite(x0, _state), "IDWCalc3: X0 is INF or NAN", _state);
ae_assert(ae_isfinite(x1, _state), "IDWCalc3: X1 is INF or NAN", _state);
ae_assert(ae_isfinite(x2, _state), "IDWCalc3: X2 is INF or NAN", _state);
s->buffer.x.ptr.p_double[0] = x0;
s->buffer.x.ptr.p_double[1] = x1;
s->buffer.x.ptr.p_double[2] = x2;
idwtscalcbuf(s, &s->buffer, &s->buffer.x, &s->buffer.y, _state);
result = s->buffer.y.ptr.p_double[0];
return result;
}
/*************************************************************************
This function calculates values of the IDW model at the given point.
This is general function which can be used for arbitrary NX (dimension of
the space of arguments) and NY (dimension of the function itself). However
when you have NY=1 you may find more convenient to use idwcalc1(),
idwcalc2() or idwcalc3().
NOTE: this function modifies internal temporaries of the IDW model, thus
IT IS NOT THREAD-SAFE! If you want to perform parallel model
evaluation from the multiple threads, use idwtscalcbuf() with per-
thread buffer object.
INPUT PARAMETERS:
S - IDW model
X - coordinates, array[NX]. X may have more than NX elements,
in this case only leading NX will be used.
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is out-parameter and will be
reallocated after call to this function. In case you want
to reuse previously allocated Y, you may use idwcalcbuf(),
which reallocates Y only when it is too small.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwcalc(idwmodel* s,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_vector_clear(y);
idwtscalcbuf(s, &s->buffer, x, y, _state);
}
/*************************************************************************
This function calculates values of the IDW model at the given point.
Same as idwcalc(), but does not reallocate Y when in is large enough to
store function values.
NOTE: this function modifies internal temporaries of the IDW model, thus
IT IS NOT THREAD-SAFE! If you want to perform parallel model
evaluation from the multiple threads, use idwtscalcbuf() with per-
thread buffer object.
INPUT PARAMETERS:
S - IDW model
X - coordinates, array[NX]. X may have more than NX elements,
in this case only leading NX will be used.
Y - possibly preallocated array
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is not reallocated when it
is larger than NY.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwcalcbuf(idwmodel* s,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state)
{
idwtscalcbuf(s, &s->buffer, x, y, _state);
}
/*************************************************************************
This function calculates values of the IDW model at the given point, using
external buffer object (internal temporaries of IDW model are not
modified).
This function allows to use same IDW model object in different threads,
assuming that different threads use different instances of the buffer
structure.
INPUT PARAMETERS:
S - IDW model, may be shared between different threads
Buf - buffer object created for this particular instance of IDW
model with idwcreatecalcbuffer().
X - coordinates, array[NX]. X may have more than NX elements,
in this case only leading NX will be used.
Y - possibly preallocated array
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is not reallocated when it
is larger than NY.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void idwtscalcbuf(idwmodel* s,
idwcalcbuffer* buf,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
ae_int_t ew;
ae_int_t k;
ae_int_t layeridx;
ae_int_t nx;
ae_int_t ny;
ae_int_t npoints;
double v;
double vv;
double f;
double p;
double r;
double eps;
double lambdacur;
double lambdadecay;
double invrdecay;
double invr;
ae_bool fastcalcpossible;
double wf0;
double ws0;
double wf1;
double ws1;
nx = s->nx;
ny = s->ny;
ae_assert(x->cnt>=nx, "IDWTsCalcBuf: Length(X)<NX", _state);
ae_assert(isfinitevector(x, nx, _state), "IDWTsCalcBuf: X contains infinite or NaN values", _state);
/*
* Avoid spurious compiler warnings
*/
wf0 = (double)(0);
ws0 = (double)(0);
wf1 = (double)(0);
ws1 = (double)(0);
/*
* Allocate output
*/
if( y->cnt<ny )
{
ae_vector_set_length(y, ny, _state);
}
/*
* Quick exit for NLayers=0 (no dataset)
*/
if( s->nlayers==0 )
{
for(j=0; j<=ny-1; j++)
{
y->ptr.p_double[j] = s->globalprior.ptr.p_double[j];
}
return;
}
/*
* Textbook Shepard's method
*/
if( s->algotype==0 )
{
npoints = s->npoints;
ae_assert(npoints>0, "IDWTsCalcBuf: integrity check failed", _state);
eps = 1.0E-50;
ew = nx+ny;
p = s->shepardp;
for(j=0; j<=ny-1; j++)
{
y->ptr.p_double[j] = (double)(0);
buf->tsyw.ptr.p_double[j] = eps;
}
for(i=0; i<=npoints-1; i++)
{
/*
* Compute squared distance
*/
v = (double)(0);
for(j=0; j<=nx-1; j++)
{
vv = s->shepardxy.ptr.p_double[i*ew+j]-x->ptr.p_double[j];
v = v+vv*vv;
}
/*
* Compute weight (with small regularizing addition)
*/
v = ae_pow(v, p*0.5, _state);
v = 1/(eps+v);
/*
* Accumulate
*/
for(j=0; j<=ny-1; j++)
{
y->ptr.p_double[j] = y->ptr.p_double[j]+v*s->shepardxy.ptr.p_double[i*ew+nx+j];
buf->tsyw.ptr.p_double[j] = buf->tsyw.ptr.p_double[j]+v;
}
}
for(j=0; j<=ny-1; j++)
{
y->ptr.p_double[j] = y->ptr.p_double[j]/buf->tsyw.ptr.p_double[j]+s->globalprior.ptr.p_double[j];
}
return;
}
/*
* Textbook modified Shepard's method
*/
if( s->algotype==1 )
{
eps = 1.0E-50;
r = s->r0;
for(j=0; j<=ny-1; j++)
{
y->ptr.p_double[j] = (double)(0);
buf->tsyw.ptr.p_double[j] = eps;
}
k = kdtreetsqueryrnn(&s->tree, &buf->requestbuffer, x, r, ae_true, _state);
kdtreetsqueryresultsxy(&s->tree, &buf->requestbuffer, &buf->tsxy, _state);
kdtreetsqueryresultsdistances(&s->tree, &buf->requestbuffer, &buf->tsdist, _state);
for(i=0; i<=k-1; i++)
{
v = buf->tsdist.ptr.p_double[i];
v = (r-v)/(r*v+eps);
v = v*v;
for(j=0; j<=ny-1; j++)
{
y->ptr.p_double[j] = y->ptr.p_double[j]+v*buf->tsxy.ptr.pp_double[i][nx+j];
buf->tsyw.ptr.p_double[j] = buf->tsyw.ptr.p_double[j]+v;
}
}
for(j=0; j<=ny-1; j++)
{
y->ptr.p_double[j] = y->ptr.p_double[j]/buf->tsyw.ptr.p_double[j]+s->globalprior.ptr.p_double[j];
}
return;
}
/*
* MSTAB
*/
if( s->algotype==2 )
{
ae_assert(ae_fp_eq(idw_w0,(double)(1)), "IDWTsCalcBuf: unexpected W0, integrity check failed", _state);
invrdecay = 1/s->rdecay;
invr = 1/s->r0;
lambdadecay = s->lambdadecay;
fastcalcpossible = (ny==1&&s->nlayers>=3)&&ae_fp_eq(lambdadecay,(double)(1));
if( fastcalcpossible )
{
/*
* Important special case, NY=1, no lambda-decay,
* we can perform optimized fast evaluation
*/
wf0 = (double)(0);
ws0 = idw_w0;
wf1 = (double)(0);
ws1 = idw_w0;
for(j=0; j<=s->nlayers-1; j++)
{
buf->tsyw.ptr.p_double[j] = (double)(0);
buf->tsw.ptr.p_double[j] = idw_w0;
}
}
else
{
/*
* Setup variables for generic evaluation path
*/
for(j=0; j<=ny*s->nlayers-1; j++)
{
buf->tsyw.ptr.p_double[j] = (double)(0);
}
for(j=0; j<=s->nlayers-1; j++)
{
buf->tsw.ptr.p_double[j] = idw_w0;
}
}
k = kdtreetsqueryrnnu(&s->tree, &buf->requestbuffer, x, s->r0, ae_true, _state);
kdtreetsqueryresultsxy(&s->tree, &buf->requestbuffer, &buf->tsxy, _state);
kdtreetsqueryresultsdistances(&s->tree, &buf->requestbuffer, &buf->tsdist, _state);
for(i=0; i<=k-1; i++)
{
lambdacur = s->lambda0;
vv = buf->tsdist.ptr.p_double[i]*invr;
if( fastcalcpossible )
{
/*
* Important special case, fast evaluation possible
*/
v = vv*vv;
v = (1-v)*(1-v)/(v+lambdacur);
f = buf->tsxy.ptr.pp_double[i][nx+0];
wf0 = wf0+v*f;
ws0 = ws0+v;
vv = vv*invrdecay;
if( vv>=1.0 )
{
continue;
}
v = vv*vv;
v = (1-v)*(1-v)/(v+lambdacur);
f = buf->tsxy.ptr.pp_double[i][nx+1];
wf1 = wf1+v*f;
ws1 = ws1+v;
vv = vv*invrdecay;
if( vv>=1.0 )
{
continue;
}
for(layeridx=2; layeridx<=s->nlayers-1; layeridx++)
{
if( layeridx==s->nlayers-1 )
{
lambdacur = s->lambdalast;
}
v = vv*vv;
v = (1-v)*(1-v)/(v+lambdacur);
f = buf->tsxy.ptr.pp_double[i][nx+layeridx];
buf->tsyw.ptr.p_double[layeridx] = buf->tsyw.ptr.p_double[layeridx]+v*f;
buf->tsw.ptr.p_double[layeridx] = buf->tsw.ptr.p_double[layeridx]+v;
vv = vv*invrdecay;
if( vv>=1.0 )
{
break;
}
}
}
else
{
/*
* General case
*/
for(layeridx=0; layeridx<=s->nlayers-1; layeridx++)
{
if( layeridx==s->nlayers-1 )
{
lambdacur = s->lambdalast;
}
if( vv>=1.0 )
{
break;
}
v = vv*vv;
v = (1-v)*(1-v)/(v+lambdacur);
for(j=0; j<=ny-1; j++)
{
f = buf->tsxy.ptr.pp_double[i][nx+layeridx*ny+j];
buf->tsyw.ptr.p_double[layeridx*ny+j] = buf->tsyw.ptr.p_double[layeridx*ny+j]+v*f;
}
buf->tsw.ptr.p_double[layeridx] = buf->tsw.ptr.p_double[layeridx]+v;
lambdacur = lambdacur*lambdadecay;
vv = vv*invrdecay;
}
}
}
if( fastcalcpossible )
{
/*
* Important special case, finalize evaluations
*/
buf->tsyw.ptr.p_double[0] = wf0;
buf->tsw.ptr.p_double[0] = ws0;
buf->tsyw.ptr.p_double[1] = wf1;
buf->tsw.ptr.p_double[1] = ws1;
}
for(j=0; j<=ny-1; j++)
{
y->ptr.p_double[j] = s->globalprior.ptr.p_double[j];
}
for(layeridx=0; layeridx<=s->nlayers-1; layeridx++)
{
for(j=0; j<=ny-1; j++)
{
y->ptr.p_double[j] = y->ptr.p_double[j]+buf->tsyw.ptr.p_double[layeridx*ny+j]/buf->tsw.ptr.p_double[layeridx];
}
}
return;
}
/*
*
*/
ae_assert(ae_false, "IDWTsCalcBuf: unexpected AlgoType", _state);
}
/*************************************************************************
This function fits IDW model to the dataset using current IDW construction
algorithm. A model being built and fitting report are returned.
INPUT PARAMETERS:
State - builder object
OUTPUT PARAMETERS:
Model - an IDW model built with current algorithm
Rep - model fitting report, fields of this structure contain
information about average fitting errors.
NOTE: although IDW-MSTAB algorithm is an interpolation method, i.e. it
tries to fit the model exactly, it can handle datasets with non-
distinct points which can not be fit exactly; in such cases least-
squares fitting is performed.
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
void idwfit(idwbuilder* state,
idwmodel* model,
idwreport* rep,
ae_state *_state)
{
ae_int_t i;
ae_int_t i0;
ae_int_t j;
ae_int_t k;
ae_int_t layeridx;
ae_int_t srcidx;
double v;
double vv;
ae_int_t npoints;
ae_int_t nx;
ae_int_t ny;
double rcur;
double lambdacur;
double rss;
double tss;
_idwmodel_clear(model);
_idwreport_clear(rep);
nx = state->nx;
ny = state->ny;
npoints = state->npoints;
/*
* Clear report fields
*/
rep->rmserror = (double)(0);
rep->avgerror = (double)(0);
rep->maxerror = (double)(0);
rep->r2 = 1.0;
/*
* Quick exit for empty dataset
*/
if( state->npoints==0 )
{
model->nx = nx;
model->ny = ny;
ae_vector_set_length(&model->globalprior, ny, _state);
for(i=0; i<=ny-1; i++)
{
model->globalprior.ptr.p_double[i] = (double)(0);
}
model->algotype = 0;
model->nlayers = 0;
model->r0 = (double)(1);
model->rdecay = 0.5;
model->lambda0 = (double)(0);
model->lambdalast = (double)(0);
model->lambdadecay = (double)(1);
model->shepardp = (double)(2);
model->npoints = 0;
idwcreatecalcbuffer(model, &model->buffer, _state);
return;
}
/*
* Compute temporaries which will be required later:
* * global mean
*/
ae_assert(state->npoints>0, "IDWFit: integrity check failed", _state);
rvectorsetlengthatleast(&state->tmpmean, ny, _state);
for(j=0; j<=ny-1; j++)
{
state->tmpmean.ptr.p_double[j] = (double)(0);
}
for(i=0; i<=npoints-1; i++)
{
for(j=0; j<=ny-1; j++)
{
state->tmpmean.ptr.p_double[j] = state->tmpmean.ptr.p_double[j]+state->xy.ptr.p_double[i*(nx+ny)+nx+j];
}
}
for(j=0; j<=ny-1; j++)
{
state->tmpmean.ptr.p_double[j] = state->tmpmean.ptr.p_double[j]/npoints;
}
/*
* Compute global prior
*
* NOTE: for original Shepard's method it is always mean value
*/
rvectorsetlengthatleast(&model->globalprior, ny, _state);
for(j=0; j<=ny-1; j++)
{
model->globalprior.ptr.p_double[j] = state->tmpmean.ptr.p_double[j];
}
if( state->algotype!=0 )
{
/*
* Algorithm is set to one of the "advanced" versions with search
* radius which can handle non-mean prior term
*/
if( state->priortermtype==0 )
{
/*
* User-specified prior
*/
for(j=0; j<=ny-1; j++)
{
model->globalprior.ptr.p_double[j] = state->priortermval.ptr.p_double[j];
}
}
if( state->priortermtype==3 )
{
/*
* Zero prior
*/
for(j=0; j<=ny-1; j++)
{
model->globalprior.ptr.p_double[j] = (double)(0);
}
}
}
/*
* Textbook Shepard
*/
if( state->algotype==0 )
{
/*
* Initialize model
*/
model->algotype = 0;
model->nx = nx;
model->ny = ny;
model->nlayers = 1;
model->r0 = (double)(1);
model->rdecay = 0.5;
model->lambda0 = (double)(0);
model->lambdalast = (double)(0);
model->lambdadecay = (double)(1);
model->shepardp = state->shepardp;
/*
* Copy dataset
*/
rvectorsetlengthatleast(&model->shepardxy, npoints*(nx+ny), _state);
for(i=0; i<=npoints-1; i++)
{
for(j=0; j<=nx-1; j++)
{
model->shepardxy.ptr.p_double[i*(nx+ny)+j] = state->xy.ptr.p_double[i*(nx+ny)+j];
}
for(j=0; j<=ny-1; j++)
{
model->shepardxy.ptr.p_double[i*(nx+ny)+nx+j] = state->xy.ptr.p_double[i*(nx+ny)+nx+j]-model->globalprior.ptr.p_double[j];
}
}
model->npoints = npoints;
/*
* Prepare internal buffer
* Evaluate report fields
*/
idwcreatecalcbuffer(model, &model->buffer, _state);
idw_errormetricsviacalc(state, model, rep, _state);
return;
}
/*
* Textbook modified Shepard's method
*/
if( state->algotype==1 )
{
/*
* Initialize model
*/
model->algotype = 1;
model->nx = nx;
model->ny = ny;
model->nlayers = 1;
model->r0 = state->r0;
model->rdecay = (double)(1);
model->lambda0 = (double)(0);
model->lambdalast = (double)(0);
model->lambdadecay = (double)(1);
model->shepardp = (double)(0);
/*
* Build kd-tree search structure
*/
rmatrixsetlengthatleast(&state->tmpxy, npoints, nx+ny, _state);
for(i=0; i<=npoints-1; i++)
{
for(j=0; j<=nx-1; j++)
{
state->tmpxy.ptr.pp_double[i][j] = state->xy.ptr.p_double[i*(nx+ny)+j];
}
for(j=0; j<=ny-1; j++)
{
state->tmpxy.ptr.pp_double[i][nx+j] = state->xy.ptr.p_double[i*(nx+ny)+nx+j]-model->globalprior.ptr.p_double[j];
}
}
kdtreebuild(&state->tmpxy, npoints, nx, ny, 2, &model->tree, _state);
/*
* Prepare internal buffer
* Evaluate report fields
*/
idwcreatecalcbuffer(model, &model->buffer, _state);
idw_errormetricsviacalc(state, model, rep, _state);
return;
}
/*
* MSTAB algorithm
*/
if( state->algotype==2 )
{
ae_assert(state->nlayers>=1, "IDWFit: integrity check failed", _state);
/*
* Initialize model
*/
model->algotype = 2;
model->nx = nx;
model->ny = ny;
model->nlayers = state->nlayers;
model->r0 = state->r0;
model->rdecay = 0.5;
model->lambda0 = state->lambda0;
model->lambdadecay = 1.0;
model->lambdalast = idw_meps;
model->shepardp = (double)(0);
/*
* Build kd-tree search structure,
* prepare input residuals for the first layer of the model
*/
rmatrixsetlengthatleast(&state->tmpxy, npoints, nx, _state);
rmatrixsetlengthatleast(&state->tmplayers, npoints, nx+ny*(state->nlayers+1), _state);
ivectorsetlengthatleast(&state->tmptags, npoints, _state);
for(i=0; i<=npoints-1; i++)
{
for(j=0; j<=nx-1; j++)
{
v = state->xy.ptr.p_double[i*(nx+ny)+j];
state->tmpxy.ptr.pp_double[i][j] = v;
state->tmplayers.ptr.pp_double[i][j] = v;
}
state->tmptags.ptr.p_int[i] = i;
for(j=0; j<=ny-1; j++)
{
state->tmplayers.ptr.pp_double[i][nx+j] = state->xy.ptr.p_double[i*(nx+ny)+nx+j]-model->globalprior.ptr.p_double[j];
}
}
kdtreebuildtagged(&state->tmpxy, &state->tmptags, npoints, nx, 0, 2, &state->tmptree, _state);
/*
* Iteratively build layer by layer
*/
rvectorsetlengthatleast(&state->tmpx, nx, _state);
rvectorsetlengthatleast(&state->tmpwy, ny, _state);
rvectorsetlengthatleast(&state->tmpw, ny, _state);
for(layeridx=0; layeridx<=state->nlayers-1; layeridx++)
{
/*
* Determine layer metrics
*/
rcur = model->r0*ae_pow(model->rdecay, (double)(layeridx), _state);
lambdacur = model->lambda0*ae_pow(model->lambdadecay, (double)(layeridx), _state);
if( layeridx==state->nlayers-1 )
{
lambdacur = model->lambdalast;
}
/*
* For each point compute residual from fitting with current layer
*/
for(i=0; i<=npoints-1; i++)
{
for(j=0; j<=nx-1; j++)
{
state->tmpx.ptr.p_double[j] = state->tmplayers.ptr.pp_double[i][j];
}
k = kdtreequeryrnn(&state->tmptree, &state->tmpx, rcur, ae_true, _state);
kdtreequeryresultstags(&state->tmptree, &state->tmptags, _state);
kdtreequeryresultsdistances(&state->tmptree, &state->tmpdist, _state);
for(j=0; j<=ny-1; j++)
{
state->tmpwy.ptr.p_double[j] = (double)(0);
state->tmpw.ptr.p_double[j] = idw_w0;
}
for(i0=0; i0<=k-1; i0++)
{
vv = state->tmpdist.ptr.p_double[i0]/rcur;
vv = vv*vv;
v = (1-vv)*(1-vv)/(vv+lambdacur);
srcidx = state->tmptags.ptr.p_int[i0];
for(j=0; j<=ny-1; j++)
{
state->tmpwy.ptr.p_double[j] = state->tmpwy.ptr.p_double[j]+v*state->tmplayers.ptr.pp_double[srcidx][nx+layeridx*ny+j];
state->tmpw.ptr.p_double[j] = state->tmpw.ptr.p_double[j]+v;
}
}
for(j=0; j<=ny-1; j++)
{
v = state->tmplayers.ptr.pp_double[i][nx+layeridx*ny+j];
state->tmplayers.ptr.pp_double[i][nx+(layeridx+1)*ny+j] = v-state->tmpwy.ptr.p_double[j]/state->tmpw.ptr.p_double[j];
}
}
}
kdtreebuild(&state->tmplayers, npoints, nx, ny*state->nlayers, 2, &model->tree, _state);
/*
* Evaluate report fields
*/
rep->rmserror = (double)(0);
rep->avgerror = (double)(0);
rep->maxerror = (double)(0);
rss = (double)(0);
tss = (double)(0);
for(i=0; i<=npoints-1; i++)
{
for(j=0; j<=ny-1; j++)
{
v = ae_fabs(state->tmplayers.ptr.pp_double[i][nx+state->nlayers*ny+j], _state);
rep->rmserror = rep->rmserror+v*v;
rep->avgerror = rep->avgerror+v;
rep->maxerror = ae_maxreal(rep->maxerror, ae_fabs(v, _state), _state);
rss = rss+v*v;
tss = tss+ae_sqr(state->xy.ptr.p_double[i*(nx+ny)+nx+j]-state->tmpmean.ptr.p_double[j], _state);
}
}
rep->rmserror = ae_sqrt(rep->rmserror/(npoints*ny), _state);
rep->avgerror = rep->avgerror/(npoints*ny);
rep->r2 = 1.0-rss/coalesce(tss, 1.0, _state);
/*
* Prepare internal buffer
*/
idwcreatecalcbuffer(model, &model->buffer, _state);
return;
}
/*
* Unknown algorithm
*/
ae_assert(ae_false, "IDWFit: integrity check failed, unexpected algorithm", _state);
}
/*************************************************************************
Serializer: allocation
-- ALGLIB --
Copyright 28.02.2018 by Bochkanov Sergey
*************************************************************************/
void idwalloc(ae_serializer* s, idwmodel* model, ae_state *_state)
{
ae_bool processed;
/*
* Header
*/
ae_serializer_alloc_entry(s);
/*
* Algorithm type and fields which are set for all algorithms
*/
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
allocrealarray(s, &model->globalprior, -1, _state);
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
/*
* Algorithm-specific fields
*/
processed = ae_false;
if( model->algotype==0 )
{
ae_serializer_alloc_entry(s);
allocrealarray(s, &model->shepardxy, -1, _state);
processed = ae_true;
}
if( model->algotype>0 )
{
kdtreealloc(s, &model->tree, _state);
processed = ae_true;
}
ae_assert(processed, "IDW: integrity check failed during serialization", _state);
}
/*************************************************************************
Serializer: serialization
-- ALGLIB --
Copyright 28.02.2018 by Bochkanov Sergey
*************************************************************************/
void idwserialize(ae_serializer* s, idwmodel* model, ae_state *_state)
{
ae_bool processed;
/*
* Header
*/
ae_serializer_serialize_int(s, getidwserializationcode(_state), _state);
/*
* Algorithm type and fields which are set for all algorithms
*/
ae_serializer_serialize_int(s, model->algotype, _state);
ae_serializer_serialize_int(s, model->nx, _state);
ae_serializer_serialize_int(s, model->ny, _state);
serializerealarray(s, &model->globalprior, -1, _state);
ae_serializer_serialize_int(s, model->nlayers, _state);
ae_serializer_serialize_double(s, model->r0, _state);
ae_serializer_serialize_double(s, model->rdecay, _state);
ae_serializer_serialize_double(s, model->lambda0, _state);
ae_serializer_serialize_double(s, model->lambdalast, _state);
ae_serializer_serialize_double(s, model->lambdadecay, _state);
ae_serializer_serialize_double(s, model->shepardp, _state);
/*
* Algorithm-specific fields
*/
processed = ae_false;
if( model->algotype==0 )
{
ae_serializer_serialize_int(s, model->npoints, _state);
serializerealarray(s, &model->shepardxy, -1, _state);
processed = ae_true;
}
if( model->algotype>0 )
{
kdtreeserialize(s, &model->tree, _state);
processed = ae_true;
}
ae_assert(processed, "IDW: integrity check failed during serialization", _state);
}
/*************************************************************************
Serializer: unserialization
-- ALGLIB --
Copyright 28.02.2018 by Bochkanov Sergey
*************************************************************************/
void idwunserialize(ae_serializer* s, idwmodel* model, ae_state *_state)
{
ae_bool processed;
ae_int_t scode;
_idwmodel_clear(model);
/*
* Header
*/
ae_serializer_unserialize_int(s, &scode, _state);
ae_assert(scode==getidwserializationcode(_state), "IDWUnserialize: stream header corrupted", _state);
/*
* Algorithm type and fields which are set for all algorithms
*/
ae_serializer_unserialize_int(s, &model->algotype, _state);
ae_serializer_unserialize_int(s, &model->nx, _state);
ae_serializer_unserialize_int(s, &model->ny, _state);
unserializerealarray(s, &model->globalprior, _state);
ae_serializer_unserialize_int(s, &model->nlayers, _state);
ae_serializer_unserialize_double(s, &model->r0, _state);
ae_serializer_unserialize_double(s, &model->rdecay, _state);
ae_serializer_unserialize_double(s, &model->lambda0, _state);
ae_serializer_unserialize_double(s, &model->lambdalast, _state);
ae_serializer_unserialize_double(s, &model->lambdadecay, _state);
ae_serializer_unserialize_double(s, &model->shepardp, _state);
/*
* Algorithm-specific fields
*/
processed = ae_false;
if( model->algotype==0 )
{
ae_serializer_unserialize_int(s, &model->npoints, _state);
unserializerealarray(s, &model->shepardxy, _state);
processed = ae_true;
}
if( model->algotype>0 )
{
kdtreeunserialize(s, &model->tree, _state);
processed = ae_true;
}
ae_assert(processed, "IDW: integrity check failed during serialization", _state);
/*
* Temporary buffers
*/
idwcreatecalcbuffer(model, &model->buffer, _state);
}
/*************************************************************************
This function evaluates error metrics for the model using IDWTsCalcBuf()
to calculate model at each point.
NOTE: modern IDW algorithms (MSTAB, MSMOOTH) can generate residuals during
model construction, so they do not need this function in order to
evaluate error metrics.
Following fields of Rep are filled:
* rep.rmserror
* rep.avgerror
* rep.maxerror
* rep.r2
-- ALGLIB --
Copyright 22.10.2018 by Bochkanov Sergey
*************************************************************************/
static void idw_errormetricsviacalc(idwbuilder* state,
idwmodel* model,
idwreport* rep,
ae_state *_state)
{
ae_int_t npoints;
ae_int_t nx;
ae_int_t ny;
ae_int_t i;
ae_int_t j;
double v;
double vv;
double rss;
double tss;
npoints = state->npoints;
nx = state->nx;
ny = state->ny;
if( npoints==0 )
{
rep->rmserror = (double)(0);
rep->avgerror = (double)(0);
rep->maxerror = (double)(0);
rep->r2 = (double)(1);
return;
}
rep->rmserror = (double)(0);
rep->avgerror = (double)(0);
rep->maxerror = (double)(0);
rss = (double)(0);
tss = (double)(0);
for(i=0; i<=npoints-1; i++)
{
for(j=0; j<=nx-1; j++)
{
model->buffer.x.ptr.p_double[j] = state->xy.ptr.p_double[i*(nx+ny)+j];
}
idwtscalcbuf(model, &model->buffer, &model->buffer.x, &model->buffer.y, _state);
for(j=0; j<=ny-1; j++)
{
vv = state->xy.ptr.p_double[i*(nx+ny)+nx+j];
v = ae_fabs(vv-model->buffer.y.ptr.p_double[j], _state);
rep->rmserror = rep->rmserror+v*v;
rep->avgerror = rep->avgerror+v;
rep->maxerror = ae_maxreal(rep->maxerror, v, _state);
rss = rss+v*v;
tss = tss+ae_sqr(vv-state->tmpmean.ptr.p_double[j], _state);
}
}
rep->rmserror = ae_sqrt(rep->rmserror/(npoints*ny), _state);
rep->avgerror = rep->avgerror/(npoints*ny);
rep->r2 = 1.0-rss/coalesce(tss, 1.0, _state);
}
void _idwcalcbuffer_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
idwcalcbuffer *p = (idwcalcbuffer*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->x, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->y, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tsyw, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tsw, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->tsxy, 0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tsdist, 0, DT_REAL, _state, make_automatic);
_kdtreerequestbuffer_init(&p->requestbuffer, _state, make_automatic);
}
void _idwcalcbuffer_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
idwcalcbuffer *dst = (idwcalcbuffer*)_dst;
idwcalcbuffer *src = (idwcalcbuffer*)_src;
ae_vector_init_copy(&dst->x, &src->x, _state, make_automatic);
ae_vector_init_copy(&dst->y, &src->y, _state, make_automatic);
ae_vector_init_copy(&dst->tsyw, &src->tsyw, _state, make_automatic);
ae_vector_init_copy(&dst->tsw, &src->tsw, _state, make_automatic);
ae_matrix_init_copy(&dst->tsxy, &src->tsxy, _state, make_automatic);
ae_vector_init_copy(&dst->tsdist, &src->tsdist, _state, make_automatic);
_kdtreerequestbuffer_init_copy(&dst->requestbuffer, &src->requestbuffer, _state, make_automatic);
}
void _idwcalcbuffer_clear(void* _p)
{
idwcalcbuffer *p = (idwcalcbuffer*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->x);
ae_vector_clear(&p->y);
ae_vector_clear(&p->tsyw);
ae_vector_clear(&p->tsw);
ae_matrix_clear(&p->tsxy);
ae_vector_clear(&p->tsdist);
_kdtreerequestbuffer_clear(&p->requestbuffer);
}
void _idwcalcbuffer_destroy(void* _p)
{
idwcalcbuffer *p = (idwcalcbuffer*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->x);
ae_vector_destroy(&p->y);
ae_vector_destroy(&p->tsyw);
ae_vector_destroy(&p->tsw);
ae_matrix_destroy(&p->tsxy);
ae_vector_destroy(&p->tsdist);
_kdtreerequestbuffer_destroy(&p->requestbuffer);
}
void _idwmodel_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
idwmodel *p = (idwmodel*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->globalprior, 0, DT_REAL, _state, make_automatic);
_kdtree_init(&p->tree, _state, make_automatic);
ae_vector_init(&p->shepardxy, 0, DT_REAL, _state, make_automatic);
_idwcalcbuffer_init(&p->buffer, _state, make_automatic);
}
void _idwmodel_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
idwmodel *dst = (idwmodel*)_dst;
idwmodel *src = (idwmodel*)_src;
dst->nx = src->nx;
dst->ny = src->ny;
ae_vector_init_copy(&dst->globalprior, &src->globalprior, _state, make_automatic);
dst->algotype = src->algotype;
dst->nlayers = src->nlayers;
dst->r0 = src->r0;
dst->rdecay = src->rdecay;
dst->lambda0 = src->lambda0;
dst->lambdalast = src->lambdalast;
dst->lambdadecay = src->lambdadecay;
dst->shepardp = src->shepardp;
_kdtree_init_copy(&dst->tree, &src->tree, _state, make_automatic);
dst->npoints = src->npoints;
ae_vector_init_copy(&dst->shepardxy, &src->shepardxy, _state, make_automatic);
_idwcalcbuffer_init_copy(&dst->buffer, &src->buffer, _state, make_automatic);
}
void _idwmodel_clear(void* _p)
{
idwmodel *p = (idwmodel*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->globalprior);
_kdtree_clear(&p->tree);
ae_vector_clear(&p->shepardxy);
_idwcalcbuffer_clear(&p->buffer);
}
void _idwmodel_destroy(void* _p)
{
idwmodel *p = (idwmodel*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->globalprior);
_kdtree_destroy(&p->tree);
ae_vector_destroy(&p->shepardxy);
_idwcalcbuffer_destroy(&p->buffer);
}
void _idwbuilder_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
idwbuilder *p = (idwbuilder*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->priortermval, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->xy, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->tmpxy, 0, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->tmplayers, 0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tmptags, 0, DT_INT, _state, make_automatic);
ae_vector_init(&p->tmpdist, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tmpx, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tmpwy, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tmpw, 0, DT_REAL, _state, make_automatic);
_kdtree_init(&p->tmptree, _state, make_automatic);
ae_vector_init(&p->tmpmean, 0, DT_REAL, _state, make_automatic);
}
void _idwbuilder_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
idwbuilder *dst = (idwbuilder*)_dst;
idwbuilder *src = (idwbuilder*)_src;
dst->priortermtype = src->priortermtype;
ae_vector_init_copy(&dst->priortermval, &src->priortermval, _state, make_automatic);
dst->algotype = src->algotype;
dst->nlayers = src->nlayers;
dst->r0 = src->r0;
dst->rdecay = src->rdecay;
dst->lambda0 = src->lambda0;
dst->lambdalast = src->lambdalast;
dst->lambdadecay = src->lambdadecay;
dst->shepardp = src->shepardp;
ae_vector_init_copy(&dst->xy, &src->xy, _state, make_automatic);
dst->npoints = src->npoints;
dst->nx = src->nx;
dst->ny = src->ny;
ae_matrix_init_copy(&dst->tmpxy, &src->tmpxy, _state, make_automatic);
ae_matrix_init_copy(&dst->tmplayers, &src->tmplayers, _state, make_automatic);
ae_vector_init_copy(&dst->tmptags, &src->tmptags, _state, make_automatic);
ae_vector_init_copy(&dst->tmpdist, &src->tmpdist, _state, make_automatic);
ae_vector_init_copy(&dst->tmpx, &src->tmpx, _state, make_automatic);
ae_vector_init_copy(&dst->tmpwy, &src->tmpwy, _state, make_automatic);
ae_vector_init_copy(&dst->tmpw, &src->tmpw, _state, make_automatic);
_kdtree_init_copy(&dst->tmptree, &src->tmptree, _state, make_automatic);
ae_vector_init_copy(&dst->tmpmean, &src->tmpmean, _state, make_automatic);
}
void _idwbuilder_clear(void* _p)
{
idwbuilder *p = (idwbuilder*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->priortermval);
ae_vector_clear(&p->xy);
ae_matrix_clear(&p->tmpxy);
ae_matrix_clear(&p->tmplayers);
ae_vector_clear(&p->tmptags);
ae_vector_clear(&p->tmpdist);
ae_vector_clear(&p->tmpx);
ae_vector_clear(&p->tmpwy);
ae_vector_clear(&p->tmpw);
_kdtree_clear(&p->tmptree);
ae_vector_clear(&p->tmpmean);
}
void _idwbuilder_destroy(void* _p)
{
idwbuilder *p = (idwbuilder*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->priortermval);
ae_vector_destroy(&p->xy);
ae_matrix_destroy(&p->tmpxy);
ae_matrix_destroy(&p->tmplayers);
ae_vector_destroy(&p->tmptags);
ae_vector_destroy(&p->tmpdist);
ae_vector_destroy(&p->tmpx);
ae_vector_destroy(&p->tmpwy);
ae_vector_destroy(&p->tmpw);
_kdtree_destroy(&p->tmptree);
ae_vector_destroy(&p->tmpmean);
}
void _idwreport_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
idwreport *p = (idwreport*)_p;
ae_touch_ptr((void*)p);
}
void _idwreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
idwreport *dst = (idwreport*)_dst;
idwreport *src = (idwreport*)_src;
dst->rmserror = src->rmserror;
dst->avgerror = src->avgerror;
dst->maxerror = src->maxerror;
dst->r2 = src->r2;
}
void _idwreport_clear(void* _p)
{
idwreport *p = (idwreport*)_p;
ae_touch_ptr((void*)p);
}
void _idwreport_destroy(void* _p)
{
idwreport *p = (idwreport*)_p;
ae_touch_ptr((void*)p);
}
#endif
#if defined(AE_COMPILE_RATINT) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Rational interpolation using barycentric formula
F(t) = SUM(i=0,n-1,w[i]*f[i]/(t-x[i])) / SUM(i=0,n-1,w[i]/(t-x[i]))
Input parameters:
B - barycentric interpolant built with one of model building
subroutines.
T - interpolation point
Result:
barycentric interpolant F(t)
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
double barycentriccalc(barycentricinterpolant* b,
double t,
ae_state *_state)
{
double s1;
double s2;
double s;
double v;
ae_int_t i;
double result;
ae_assert(!ae_isinf(t, _state), "BarycentricCalc: infinite T!", _state);
/*
* special case: NaN
*/
if( ae_isnan(t, _state) )
{
result = _state->v_nan;
return result;
}
/*
* special case: N=1
*/
if( b->n==1 )
{
result = b->sy*b->y.ptr.p_double[0];
return result;
}
/*
* Here we assume that task is normalized, i.e.:
* 1. abs(Y[i])<=1
* 2. abs(W[i])<=1
* 3. X[] is ordered
*/
s = ae_fabs(t-b->x.ptr.p_double[0], _state);
for(i=0; i<=b->n-1; i++)
{
v = b->x.ptr.p_double[i];
if( ae_fp_eq(v,t) )
{
result = b->sy*b->y.ptr.p_double[i];
return result;
}
v = ae_fabs(t-v, _state);
if( ae_fp_less(v,s) )
{
s = v;
}
}
s1 = (double)(0);
s2 = (double)(0);
for(i=0; i<=b->n-1; i++)
{
v = s/(t-b->x.ptr.p_double[i]);
v = v*b->w.ptr.p_double[i];
s1 = s1+v*b->y.ptr.p_double[i];
s2 = s2+v;
}
result = b->sy*s1/s2;
return result;
}
/*************************************************************************
Differentiation of barycentric interpolant: first derivative.
Algorithm used in this subroutine is very robust and should not fail until
provided with values too close to MaxRealNumber (usually MaxRealNumber/N
or greater will overflow).
INPUT PARAMETERS:
B - barycentric interpolant built with one of model building
subroutines.
T - interpolation point
OUTPUT PARAMETERS:
F - barycentric interpolant at T
DF - first derivative
NOTE
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentricdiff1(barycentricinterpolant* b,
double t,
double* f,
double* df,
ae_state *_state)
{
double v;
double vv;
ae_int_t i;
ae_int_t k;
double n0;
double n1;
double d0;
double d1;
double s0;
double s1;
double xk;
double xi;
double xmin;
double xmax;
double xscale1;
double xoffs1;
double xscale2;
double xoffs2;
double xprev;
*f = 0;
*df = 0;
ae_assert(!ae_isinf(t, _state), "BarycentricDiff1: infinite T!", _state);
/*
* special case: NaN
*/
if( ae_isnan(t, _state) )
{
*f = _state->v_nan;
*df = _state->v_nan;
return;
}
/*
* special case: N=1
*/
if( b->n==1 )
{
*f = b->sy*b->y.ptr.p_double[0];
*df = (double)(0);
return;
}
if( ae_fp_eq(b->sy,(double)(0)) )
{
*f = (double)(0);
*df = (double)(0);
return;
}
ae_assert(ae_fp_greater(b->sy,(double)(0)), "BarycentricDiff1: internal error", _state);
/*
* We assume than N>1 and B.SY>0. Find:
* 1. pivot point (X[i] closest to T)
* 2. width of interval containing X[i]
*/
v = ae_fabs(b->x.ptr.p_double[0]-t, _state);
k = 0;
xmin = b->x.ptr.p_double[0];
xmax = b->x.ptr.p_double[0];
for(i=1; i<=b->n-1; i++)
{
vv = b->x.ptr.p_double[i];
if( ae_fp_less(ae_fabs(vv-t, _state),v) )
{
v = ae_fabs(vv-t, _state);
k = i;
}
xmin = ae_minreal(xmin, vv, _state);
xmax = ae_maxreal(xmax, vv, _state);
}
/*
* pivot point found, calculate dNumerator and dDenominator
*/
xscale1 = 1/(xmax-xmin);
xoffs1 = -xmin/(xmax-xmin)+1;
xscale2 = (double)(2);
xoffs2 = (double)(-3);
t = t*xscale1+xoffs1;
t = t*xscale2+xoffs2;
xk = b->x.ptr.p_double[k];
xk = xk*xscale1+xoffs1;
xk = xk*xscale2+xoffs2;
v = t-xk;
n0 = (double)(0);
n1 = (double)(0);
d0 = (double)(0);
d1 = (double)(0);
xprev = (double)(-2);
for(i=0; i<=b->n-1; i++)
{
xi = b->x.ptr.p_double[i];
xi = xi*xscale1+xoffs1;
xi = xi*xscale2+xoffs2;
ae_assert(ae_fp_greater(xi,xprev), "BarycentricDiff1: points are too close!", _state);
xprev = xi;
if( i!=k )
{
vv = ae_sqr(t-xi, _state);
s0 = (t-xk)/(t-xi);
s1 = (xk-xi)/vv;
}
else
{
s0 = (double)(1);
s1 = (double)(0);
}
vv = b->w.ptr.p_double[i]*b->y.ptr.p_double[i];
n0 = n0+s0*vv;
n1 = n1+s1*vv;
vv = b->w.ptr.p_double[i];
d0 = d0+s0*vv;
d1 = d1+s1*vv;
}
*f = b->sy*n0/d0;
*df = (n1*d0-n0*d1)/ae_sqr(d0, _state);
if( ae_fp_neq(*df,(double)(0)) )
{
*df = ae_sign(*df, _state)*ae_exp(ae_log(ae_fabs(*df, _state), _state)+ae_log(b->sy, _state)+ae_log(xscale1, _state)+ae_log(xscale2, _state), _state);
}
}
/*************************************************************************
Differentiation of barycentric interpolant: first/second derivatives.
INPUT PARAMETERS:
B - barycentric interpolant built with one of model building
subroutines.
T - interpolation point
OUTPUT PARAMETERS:
F - barycentric interpolant at T
DF - first derivative
D2F - second derivative
NOTE: this algorithm may fail due to overflow/underflor if used on data
whose values are close to MaxRealNumber or MinRealNumber. Use more robust
BarycentricDiff1() subroutine in such cases.
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentricdiff2(barycentricinterpolant* b,
double t,
double* f,
double* df,
double* d2f,
ae_state *_state)
{
double v;
double vv;
ae_int_t i;
ae_int_t k;
double n0;
double n1;
double n2;
double d0;
double d1;
double d2;
double s0;
double s1;
double s2;
double xk;
double xi;
*f = 0;
*df = 0;
*d2f = 0;
ae_assert(!ae_isinf(t, _state), "BarycentricDiff1: infinite T!", _state);
/*
* special case: NaN
*/
if( ae_isnan(t, _state) )
{
*f = _state->v_nan;
*df = _state->v_nan;
*d2f = _state->v_nan;
return;
}
/*
* special case: N=1
*/
if( b->n==1 )
{
*f = b->sy*b->y.ptr.p_double[0];
*df = (double)(0);
*d2f = (double)(0);
return;
}
if( ae_fp_eq(b->sy,(double)(0)) )
{
*f = (double)(0);
*df = (double)(0);
*d2f = (double)(0);
return;
}
/*
* We assume than N>1 and B.SY>0. Find:
* 1. pivot point (X[i] closest to T)
* 2. width of interval containing X[i]
*/
ae_assert(ae_fp_greater(b->sy,(double)(0)), "BarycentricDiff: internal error", _state);
*f = (double)(0);
*df = (double)(0);
*d2f = (double)(0);
v = ae_fabs(b->x.ptr.p_double[0]-t, _state);
k = 0;
for(i=1; i<=b->n-1; i++)
{
vv = b->x.ptr.p_double[i];
if( ae_fp_less(ae_fabs(vv-t, _state),v) )
{
v = ae_fabs(vv-t, _state);
k = i;
}
}
/*
* pivot point found, calculate dNumerator and dDenominator
*/
xk = b->x.ptr.p_double[k];
v = t-xk;
n0 = (double)(0);
n1 = (double)(0);
n2 = (double)(0);
d0 = (double)(0);
d1 = (double)(0);
d2 = (double)(0);
for(i=0; i<=b->n-1; i++)
{
if( i!=k )
{
xi = b->x.ptr.p_double[i];
vv = ae_sqr(t-xi, _state);
s0 = (t-xk)/(t-xi);
s1 = (xk-xi)/vv;
s2 = -2*(xk-xi)/(vv*(t-xi));
}
else
{
s0 = (double)(1);
s1 = (double)(0);
s2 = (double)(0);
}
vv = b->w.ptr.p_double[i]*b->y.ptr.p_double[i];
n0 = n0+s0*vv;
n1 = n1+s1*vv;
n2 = n2+s2*vv;
vv = b->w.ptr.p_double[i];
d0 = d0+s0*vv;
d1 = d1+s1*vv;
d2 = d2+s2*vv;
}
*f = b->sy*n0/d0;
*df = b->sy*(n1*d0-n0*d1)/ae_sqr(d0, _state);
*d2f = b->sy*((n2*d0-n0*d2)*ae_sqr(d0, _state)-(n1*d0-n0*d1)*2*d0*d1)/ae_sqr(ae_sqr(d0, _state), _state);
}
/*************************************************************************
This subroutine performs linear transformation of the argument.
INPUT PARAMETERS:
B - rational interpolant in barycentric form
CA, CB - transformation coefficients: x = CA*t + CB
OUTPUT PARAMETERS:
B - transformed interpolant with X replaced by T
-- ALGLIB PROJECT --
Copyright 19.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentriclintransx(barycentricinterpolant* b,
double ca,
double cb,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
double v;
/*
* special case, replace by constant F(CB)
*/
if( ae_fp_eq(ca,(double)(0)) )
{
b->sy = barycentriccalc(b, cb, _state);
v = (double)(1);
for(i=0; i<=b->n-1; i++)
{
b->y.ptr.p_double[i] = (double)(1);
b->w.ptr.p_double[i] = v;
v = -v;
}
return;
}
/*
* general case: CA<>0
*/
for(i=0; i<=b->n-1; i++)
{
b->x.ptr.p_double[i] = (b->x.ptr.p_double[i]-cb)/ca;
}
if( ae_fp_less(ca,(double)(0)) )
{
for(i=0; i<=b->n-1; i++)
{
if( i<b->n-1-i )
{
j = b->n-1-i;
v = b->x.ptr.p_double[i];
b->x.ptr.p_double[i] = b->x.ptr.p_double[j];
b->x.ptr.p_double[j] = v;
v = b->y.ptr.p_double[i];
b->y.ptr.p_double[i] = b->y.ptr.p_double[j];
b->y.ptr.p_double[j] = v;
v = b->w.ptr.p_double[i];
b->w.ptr.p_double[i] = b->w.ptr.p_double[j];
b->w.ptr.p_double[j] = v;
}
else
{
break;
}
}
}
}
/*************************************************************************
This subroutine performs linear transformation of the barycentric
interpolant.
INPUT PARAMETERS:
B - rational interpolant in barycentric form
CA, CB - transformation coefficients: B2(x) = CA*B(x) + CB
OUTPUT PARAMETERS:
B - transformed interpolant
-- ALGLIB PROJECT --
Copyright 19.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentriclintransy(barycentricinterpolant* b,
double ca,
double cb,
ae_state *_state)
{
ae_int_t i;
double v;
for(i=0; i<=b->n-1; i++)
{
b->y.ptr.p_double[i] = ca*b->sy*b->y.ptr.p_double[i]+cb;
}
b->sy = (double)(0);
for(i=0; i<=b->n-1; i++)
{
b->sy = ae_maxreal(b->sy, ae_fabs(b->y.ptr.p_double[i], _state), _state);
}
if( ae_fp_greater(b->sy,(double)(0)) )
{
v = 1/b->sy;
ae_v_muld(&b->y.ptr.p_double[0], 1, ae_v_len(0,b->n-1), v);
}
}
/*************************************************************************
Extracts X/Y/W arrays from rational interpolant
INPUT PARAMETERS:
B - barycentric interpolant
OUTPUT PARAMETERS:
N - nodes count, N>0
X - interpolation nodes, array[0..N-1]
F - function values, array[0..N-1]
W - barycentric weights, array[0..N-1]
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentricunpack(barycentricinterpolant* b,
ae_int_t* n,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
ae_state *_state)
{
double v;
*n = 0;
ae_vector_clear(x);
ae_vector_clear(y);
ae_vector_clear(w);
*n = b->n;
ae_vector_set_length(x, *n, _state);
ae_vector_set_length(y, *n, _state);
ae_vector_set_length(w, *n, _state);
v = b->sy;
ae_v_move(&x->ptr.p_double[0], 1, &b->x.ptr.p_double[0], 1, ae_v_len(0,*n-1));
ae_v_moved(&y->ptr.p_double[0], 1, &b->y.ptr.p_double[0], 1, ae_v_len(0,*n-1), v);
ae_v_move(&w->ptr.p_double[0], 1, &b->w.ptr.p_double[0], 1, ae_v_len(0,*n-1));
}
/*************************************************************************
Rational interpolant from X/Y/W arrays
F(t) = SUM(i=0,n-1,w[i]*f[i]/(t-x[i])) / SUM(i=0,n-1,w[i]/(t-x[i]))
INPUT PARAMETERS:
X - interpolation nodes, array[0..N-1]
F - function values, array[0..N-1]
W - barycentric weights, array[0..N-1]
N - nodes count, N>0
OUTPUT PARAMETERS:
B - barycentric interpolant built from (X, Y, W)
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentricbuildxyw(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
ae_int_t n,
barycentricinterpolant* b,
ae_state *_state)
{
_barycentricinterpolant_clear(b);
ae_assert(n>0, "BarycentricBuildXYW: incorrect N!", _state);
/*
* fill X/Y/W
*/
ae_vector_set_length(&b->x, n, _state);
ae_vector_set_length(&b->y, n, _state);
ae_vector_set_length(&b->w, n, _state);
ae_v_move(&b->x.ptr.p_double[0], 1, &x->ptr.p_double[0], 1, ae_v_len(0,n-1));
ae_v_move(&b->y.ptr.p_double[0], 1, &y->ptr.p_double[0], 1, ae_v_len(0,n-1));
ae_v_move(&b->w.ptr.p_double[0], 1, &w->ptr.p_double[0], 1, ae_v_len(0,n-1));
b->n = n;
/*
* Normalize
*/
ratint_barycentricnormalize(b, _state);
}
/*************************************************************************
Rational interpolant without poles
The subroutine constructs the rational interpolating function without real
poles (see 'Barycentric rational interpolation with no poles and high
rates of approximation', Michael S. Floater. and Kai Hormann, for more
information on this subject).
Input parameters:
X - interpolation nodes, array[0..N-1].
Y - function values, array[0..N-1].
N - number of nodes, N>0.
D - order of the interpolation scheme, 0 <= D <= N-1.
D<0 will cause an error.
D>=N it will be replaced with D=N-1.
if you don't know what D to choose, use small value about 3-5.
Output parameters:
B - barycentric interpolant.
Note:
this algorithm always succeeds and calculates the weights with close
to machine precision.
-- ALGLIB PROJECT --
Copyright 17.06.2007 by Bochkanov Sergey
*************************************************************************/
void barycentricbuildfloaterhormann(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t d,
barycentricinterpolant* b,
ae_state *_state)
{
ae_frame _frame_block;
double s0;
double s;
double v;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_vector perm;
ae_vector wtemp;
ae_vector sortrbuf;
ae_vector sortrbuf2;
ae_frame_make(_state, &_frame_block);
memset(&perm, 0, sizeof(perm));
memset(&wtemp, 0, sizeof(wtemp));
memset(&sortrbuf, 0, sizeof(sortrbuf));
memset(&sortrbuf2, 0, sizeof(sortrbuf2));
_barycentricinterpolant_clear(b);
ae_vector_init(&perm, 0, DT_INT, _state, ae_true);
ae_vector_init(&wtemp, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sortrbuf, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sortrbuf2, 0, DT_REAL, _state, ae_true);
ae_assert(n>0, "BarycentricFloaterHormann: N<=0!", _state);
ae_assert(d>=0, "BarycentricFloaterHormann: incorrect D!", _state);
/*
* Prepare
*/
if( d>n-1 )
{
d = n-1;
}
b->n = n;
/*
* special case: N=1
*/
if( n==1 )
{
ae_vector_set_length(&b->x, n, _state);
ae_vector_set_length(&b->y, n, _state);
ae_vector_set_length(&b->w, n, _state);
b->x.ptr.p_double[0] = x->ptr.p_double[0];
b->y.ptr.p_double[0] = y->ptr.p_double[0];
b->w.ptr.p_double[0] = (double)(1);
ratint_barycentricnormalize(b, _state);
ae_frame_leave(_state);
return;
}
/*
* Fill X/Y
*/
ae_vector_set_length(&b->x, n, _state);
ae_vector_set_length(&b->y, n, _state);
ae_v_move(&b->x.ptr.p_double[0], 1, &x->ptr.p_double[0], 1, ae_v_len(0,n-1));
ae_v_move(&b->y.ptr.p_double[0], 1, &y->ptr.p_double[0], 1, ae_v_len(0,n-1));
tagsortfastr(&b->x, &b->y, &sortrbuf, &sortrbuf2, n, _state);
/*
* Calculate Wk
*/
ae_vector_set_length(&b->w, n, _state);
s0 = (double)(1);
for(k=1; k<=d; k++)
{
s0 = -s0;
}
for(k=0; k<=n-1; k++)
{
/*
* Wk
*/
s = (double)(0);
for(i=ae_maxint(k-d, 0, _state); i<=ae_minint(k, n-1-d, _state); i++)
{
v = (double)(1);
for(j=i; j<=i+d; j++)
{
if( j!=k )
{
v = v/ae_fabs(b->x.ptr.p_double[k]-b->x.ptr.p_double[j], _state);
}
}
s = s+v;
}
b->w.ptr.p_double[k] = s0*s;
/*
* Next S0
*/
s0 = -s0;
}
/*
* Normalize
*/
ratint_barycentricnormalize(b, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Copying of the barycentric interpolant (for internal use only)
INPUT PARAMETERS:
B - barycentric interpolant
OUTPUT PARAMETERS:
B2 - copy(B1)
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentriccopy(barycentricinterpolant* b,
barycentricinterpolant* b2,
ae_state *_state)
{
_barycentricinterpolant_clear(b2);
b2->n = b->n;
b2->sy = b->sy;
ae_vector_set_length(&b2->x, b2->n, _state);
ae_vector_set_length(&b2->y, b2->n, _state);
ae_vector_set_length(&b2->w, b2->n, _state);
ae_v_move(&b2->x.ptr.p_double[0], 1, &b->x.ptr.p_double[0], 1, ae_v_len(0,b2->n-1));
ae_v_move(&b2->y.ptr.p_double[0], 1, &b->y.ptr.p_double[0], 1, ae_v_len(0,b2->n-1));
ae_v_move(&b2->w.ptr.p_double[0], 1, &b->w.ptr.p_double[0], 1, ae_v_len(0,b2->n-1));
}
/*************************************************************************
Normalization of barycentric interpolant:
* B.N, B.X, B.Y and B.W are initialized
* B.SY is NOT initialized
* Y[] is normalized, scaling coefficient is stored in B.SY
* W[] is normalized, no scaling coefficient is stored
* X[] is sorted
Internal subroutine.
*************************************************************************/
static void ratint_barycentricnormalize(barycentricinterpolant* b,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector p1;
ae_vector p2;
ae_int_t i;
ae_int_t j;
ae_int_t j2;
double v;
ae_frame_make(_state, &_frame_block);
memset(&p1, 0, sizeof(p1));
memset(&p2, 0, sizeof(p2));
ae_vector_init(&p1, 0, DT_INT, _state, ae_true);
ae_vector_init(&p2, 0, DT_INT, _state, ae_true);
/*
* Normalize task: |Y|<=1, |W|<=1, sort X[]
*/
b->sy = (double)(0);
for(i=0; i<=b->n-1; i++)
{
b->sy = ae_maxreal(b->sy, ae_fabs(b->y.ptr.p_double[i], _state), _state);
}
if( ae_fp_greater(b->sy,(double)(0))&&ae_fp_greater(ae_fabs(b->sy-1, _state),10*ae_machineepsilon) )
{
v = 1/b->sy;
ae_v_muld(&b->y.ptr.p_double[0], 1, ae_v_len(0,b->n-1), v);
}
v = (double)(0);
for(i=0; i<=b->n-1; i++)
{
v = ae_maxreal(v, ae_fabs(b->w.ptr.p_double[i], _state), _state);
}
if( ae_fp_greater(v,(double)(0))&&ae_fp_greater(ae_fabs(v-1, _state),10*ae_machineepsilon) )
{
v = 1/v;
ae_v_muld(&b->w.ptr.p_double[0], 1, ae_v_len(0,b->n-1), v);
}
for(i=0; i<=b->n-2; i++)
{
if( ae_fp_less(b->x.ptr.p_double[i+1],b->x.ptr.p_double[i]) )
{
tagsort(&b->x, b->n, &p1, &p2, _state);
for(j=0; j<=b->n-1; j++)
{
j2 = p2.ptr.p_int[j];
v = b->y.ptr.p_double[j];
b->y.ptr.p_double[j] = b->y.ptr.p_double[j2];
b->y.ptr.p_double[j2] = v;
v = b->w.ptr.p_double[j];
b->w.ptr.p_double[j] = b->w.ptr.p_double[j2];
b->w.ptr.p_double[j2] = v;
}
break;
}
}
ae_frame_leave(_state);
}
void _barycentricinterpolant_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
barycentricinterpolant *p = (barycentricinterpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->x, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->y, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->w, 0, DT_REAL, _state, make_automatic);
}
void _barycentricinterpolant_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
barycentricinterpolant *dst = (barycentricinterpolant*)_dst;
barycentricinterpolant *src = (barycentricinterpolant*)_src;
dst->n = src->n;
dst->sy = src->sy;
ae_vector_init_copy(&dst->x, &src->x, _state, make_automatic);
ae_vector_init_copy(&dst->y, &src->y, _state, make_automatic);
ae_vector_init_copy(&dst->w, &src->w, _state, make_automatic);
}
void _barycentricinterpolant_clear(void* _p)
{
barycentricinterpolant *p = (barycentricinterpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->x);
ae_vector_clear(&p->y);
ae_vector_clear(&p->w);
}
void _barycentricinterpolant_destroy(void* _p)
{
barycentricinterpolant *p = (barycentricinterpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->x);
ae_vector_destroy(&p->y);
ae_vector_destroy(&p->w);
}
#endif
#if defined(AE_COMPILE_FITSPHERE) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Fits least squares (LS) circle (or NX-dimensional sphere) to data (a set
of points in NX-dimensional space).
Least squares circle minimizes sum of squared deviations between distances
from points to the center and some "candidate" radius, which is also
fitted to the data.
INPUT PARAMETERS:
XY - array[NPoints,NX] (or larger), contains dataset.
One row = one point in NX-dimensional space.
NPoints - dataset size, NPoints>0
NX - space dimensionality, NX>0 (1, 2, 3, 4, 5 and so on)
OUTPUT PARAMETERS:
CX - central point for a sphere
R - radius
-- ALGLIB --
Copyright 07.05.2018 by Bochkanov Sergey
*************************************************************************/
void fitspherels(/* Real */ ae_matrix* xy,
ae_int_t npoints,
ae_int_t nx,
/* Real */ ae_vector* cx,
double* r,
ae_state *_state)
{
double dummy;
ae_vector_clear(cx);
*r = 0;
fitspherex(xy, npoints, nx, 0, 0.0, 0, 0.0, cx, &dummy, r, _state);
}
/*************************************************************************
Fits minimum circumscribed (MC) circle (or NX-dimensional sphere) to data
(a set of points in NX-dimensional space).
INPUT PARAMETERS:
XY - array[NPoints,NX] (or larger), contains dataset.
One row = one point in NX-dimensional space.
NPoints - dataset size, NPoints>0
NX - space dimensionality, NX>0 (1, 2, 3, 4, 5 and so on)
OUTPUT PARAMETERS:
CX - central point for a sphere
RHi - radius
NOTE: this function is an easy-to-use wrapper around more powerful "expert"
function fitspherex().
This wrapper is optimized for ease of use and stability - at the
cost of somewhat lower performance (we have to use very tight
stopping criteria for inner optimizer because we want to make sure
that it will converge on any dataset).
If you are ready to experiment with settings of "expert" function,
you can achieve ~2-4x speedup over standard "bulletproof" settings.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void fitspheremc(/* Real */ ae_matrix* xy,
ae_int_t npoints,
ae_int_t nx,
/* Real */ ae_vector* cx,
double* rhi,
ae_state *_state)
{
double dummy;
ae_vector_clear(cx);
*rhi = 0;
fitspherex(xy, npoints, nx, 1, 0.0, 0, 0.0, cx, &dummy, rhi, _state);
}
/*************************************************************************
Fits maximum inscribed circle (or NX-dimensional sphere) to data (a set of
points in NX-dimensional space).
INPUT PARAMETERS:
XY - array[NPoints,NX] (or larger), contains dataset.
One row = one point in NX-dimensional space.
NPoints - dataset size, NPoints>0
NX - space dimensionality, NX>0 (1, 2, 3, 4, 5 and so on)
OUTPUT PARAMETERS:
CX - central point for a sphere
RLo - radius
NOTE: this function is an easy-to-use wrapper around more powerful "expert"
function fitspherex().
This wrapper is optimized for ease of use and stability - at the
cost of somewhat lower performance (we have to use very tight
stopping criteria for inner optimizer because we want to make sure
that it will converge on any dataset).
If you are ready to experiment with settings of "expert" function,
you can achieve ~2-4x speedup over standard "bulletproof" settings.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void fitspheremi(/* Real */ ae_matrix* xy,
ae_int_t npoints,
ae_int_t nx,
/* Real */ ae_vector* cx,
double* rlo,
ae_state *_state)
{
double dummy;
ae_vector_clear(cx);
*rlo = 0;
fitspherex(xy, npoints, nx, 2, 0.0, 0, 0.0, cx, rlo, &dummy, _state);
}
/*************************************************************************
Fits minimum zone circle (or NX-dimensional sphere) to data (a set of
points in NX-dimensional space).
INPUT PARAMETERS:
XY - array[NPoints,NX] (or larger), contains dataset.
One row = one point in NX-dimensional space.
NPoints - dataset size, NPoints>0
NX - space dimensionality, NX>0 (1, 2, 3, 4, 5 and so on)
OUTPUT PARAMETERS:
CX - central point for a sphere
RLo - radius of inscribed circle
RHo - radius of circumscribed circle
NOTE: this function is an easy-to-use wrapper around more powerful "expert"
function fitspherex().
This wrapper is optimized for ease of use and stability - at the
cost of somewhat lower performance (we have to use very tight
stopping criteria for inner optimizer because we want to make sure
that it will converge on any dataset).
If you are ready to experiment with settings of "expert" function,
you can achieve ~2-4x speedup over standard "bulletproof" settings.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void fitspheremz(/* Real */ ae_matrix* xy,
ae_int_t npoints,
ae_int_t nx,
/* Real */ ae_vector* cx,
double* rlo,
double* rhi,
ae_state *_state)
{
ae_vector_clear(cx);
*rlo = 0;
*rhi = 0;
fitspherex(xy, npoints, nx, 3, 0.0, 0, 0.0, cx, rlo, rhi, _state);
}
/*************************************************************************
Fitting minimum circumscribed, maximum inscribed or minimum zone circles
(or NX-dimensional spheres) to data (a set of points in NX-dimensional
space).
This is expert function which allows to tweak many parameters of
underlying nonlinear solver:
* stopping criteria for inner iterations
* number of outer iterations
* penalty coefficient used to handle nonlinear constraints (we convert
unconstrained nonsmooth optimization problem ivolving max() and/or min()
operations to quadratically constrained smooth one).
You may tweak all these parameters or only some of them, leaving other
ones at their default state - just specify zero value, and solver will
fill it with appropriate default one.
These comments also include some discussion of approach used to handle
such unusual fitting problem, its stability, drawbacks of alternative
methods, and convergence properties.
INPUT PARAMETERS:
XY - array[NPoints,NX] (or larger), contains dataset.
One row = one point in NX-dimensional space.
NPoints - dataset size, NPoints>0
NX - space dimensionality, NX>0 (1, 2, 3, 4, 5 and so on)
ProblemType-used to encode problem type:
* 0 for least squares circle
* 1 for minimum circumscribed circle/sphere fitting (MC)
* 2 for maximum inscribed circle/sphere fitting (MI)
* 3 for minimum zone circle fitting (difference between
Rhi and Rlo is minimized), denoted as MZ
EpsX - stopping condition for NLC optimizer:
* must be non-negative
* use 0 to choose default value (1.0E-12 is used by default)
* you may specify larger values, up to 1.0E-6, if you want
to speed-up solver; NLC solver performs several
preconditioned outer iterations, so final result
typically has precision much better than EpsX.
AULIts - number of outer iterations performed by NLC optimizer:
* must be non-negative
* use 0 to choose default value (20 is used by default)
* you may specify values smaller than 20 if you want to
speed up solver; 10 often results in good combination of
precision and speed; sometimes you may get good results
with just 6 outer iterations.
Ignored for ProblemType=0.
Penalty - penalty coefficient for NLC optimizer:
* must be non-negative
* use 0 to choose default value (1.0E6 in current version)
* it should be really large, 1.0E6...1.0E7 is a good value
to start from;
* generally, default value is good enough
Ignored for ProblemType=0.
OUTPUT PARAMETERS:
CX - central point for a sphere
RLo - radius:
* for ProblemType=2,3, radius of the inscribed sphere
* for ProblemType=0 - radius of the least squares sphere
* for ProblemType=1 - zero
RHo - radius:
* for ProblemType=1,3, radius of the circumscribed sphere
* for ProblemType=0 - radius of the least squares sphere
* for ProblemType=2 - zero
NOTE: ON THE UNIQUENESS OF SOLUTIONS
ALGLIB provides solution to several related circle fitting problems: MC
(minimum circumscribed), MI (maximum inscribed) and MZ (minimum zone)
fitting, LS (least squares) fitting.
It is important to note that among these problems only MC and LS are
convex and have unique solution independently from starting point.
As for MI, it may (or may not, depending on dataset properties) have
multiple solutions, and it always has one degenerate solution C=infinity
which corresponds to infinitely large radius. Thus, there are no guarantees
that solution to MI returned by this solver will be the best one (and no
one can provide you with such guarantee because problem is NP-hard). The
only guarantee you have is that this solution is locally optimal, i.e. it
can not be improved by infinitesimally small tweaks in the parameters.
It is also possible to "run away" to infinity when started from bad
initial point located outside of point cloud (or when point cloud does not
span entire circumference/surface of the sphere).
Finally, MZ (minimum zone circle) stands somewhere between MC and MI in
stability. It is somewhat regularized by "circumscribed" term of the merit
function; however, solutions to MZ may be non-unique, and in some unlucky
cases it is also possible to "run away to infinity".
NOTE: ON THE NONLINEARLY CONSTRAINED PROGRAMMING APPROACH
The problem formulation for MC (minimum circumscribed circle; for the
sake of simplicity we omit MZ and MI here) is:
[ [ ]2 ]
min [ max [ XY[i]-C ] ]
C [ i [ ] ]
i.e. it is unconstrained nonsmooth optimization problem of finding "best"
central point, with radius R being unambiguously determined from C. In
order to move away from non-smoothness we use following reformulation:
[ ] [ ]2
min [ R ] subject to R>=0, [ XY[i]-C ] <= R^2
C,R [ ] [ ]
i.e. it becomes smooth quadratically constrained optimization problem with
linear target function. Such problem statement is 100% equivalent to the
original nonsmooth one, but much easier to approach. We solve it with
MinNLC solver provided by ALGLIB.
NOTE: ON INSTABILITY OF SEQUENTIAL LINEARIZATION APPROACH
ALGLIB has nonlinearly constrained solver which proved to be stable on
such problems. However, some authors proposed to linearize constraints in
the vicinity of current approximation (Ci,Ri) and to get next approximate
solution (Ci+1,Ri+1) as solution to linear programming problem. Obviously,
LP problems are easier than nonlinearly constrained ones.
Indeed, such approach to MC/MI/MZ resulted in ~10-20x increase in
performance (when compared with NLC solver). However, it turned out that
in some cases linearized model fails to predict correct direction for next
step and tells us that we converged to solution even when we are still 2-4
digits of precision away from it.
It is important that it is not failure of LP solver - it is failure of the
linear model; even when solved exactly, it fails to handle subtle
nonlinearities which arise near the solution. We validated it by comparing
results returned by ALGLIB linear solver with that of MATLAB.
In our experiments with linearization:
* MC failed most often, at both realistic and synthetic datasets
* MI sometimes failed, but sometimes succeeded
* MZ often succeeded; our guess is that presence of two independent sets
of constraints (one set for Rlo and another one for Rhi) and two terms
in the target function (Rlo and Rhi) regularizes task, so when linear
model fails to handle nonlinearities from Rlo, it uses Rhi as a hint
(and vice versa).
Because linearization approach failed to achieve stable results, we do not
include it in ALGLIB.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void fitspherex(/* Real */ ae_matrix* xy,
ae_int_t npoints,
ae_int_t nx,
ae_int_t problemtype,
double epsx,
ae_int_t aulits,
double penalty,
/* Real */ ae_vector* cx,
double* rlo,
double* rhi,
ae_state *_state)
{
ae_frame _frame_block;
fitsphereinternalreport rep;
ae_frame_make(_state, &_frame_block);
memset(&rep, 0, sizeof(rep));
ae_vector_clear(cx);
*rlo = 0;
*rhi = 0;
_fitsphereinternalreport_init(&rep, _state, ae_true);
ae_assert(ae_isfinite(penalty, _state)&&ae_fp_greater_eq(penalty,(double)(0)), "FitSphereX: Penalty<0 or is not finite", _state);
ae_assert(ae_isfinite(epsx, _state)&&ae_fp_greater_eq(epsx,(double)(0)), "FitSphereX: EpsX<0 or is not finite", _state);
ae_assert(aulits>=0, "FitSphereX: AULIts<0", _state);
fitsphereinternal(xy, npoints, nx, problemtype, 0, epsx, aulits, penalty, cx, rlo, rhi, &rep, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Fitting minimum circumscribed, maximum inscribed or minimum zone circles
(or NX-dimensional spheres) to data (a set of points in NX-dimensional
space).
Internal computational function.
INPUT PARAMETERS:
XY - array[NPoints,NX] (or larger), contains dataset.
One row = one point in NX-dimensional space.
NPoints - dataset size, NPoints>0
NX - space dimensionality, NX>0 (1, 2, 3, 4, 5 and so on)
ProblemType-used to encode problem type:
* 0 for least squares circle
* 1 for minimum circumscribed circle/sphere fitting (MC)
* 2 for maximum inscribed circle/sphere fitting (MI)
* 3 for minimum zone circle fitting (difference between
Rhi and Rlo is minimized), denoted as MZ
SolverType- solver to use:
* 0 use best solver available (1 in current version)
* 1 use nonlinearly constrained optimization approach, AUL
(it is roughly 10-20 times slower than SPC-LIN, but
much more stable)
* 2 use special fast IMPRECISE solver, SPC-LIN sequential
linearization approach; SPC-LIN is fast, but sometimes
fails to converge with more than 3 digits of precision;
see comments below.
NOT RECOMMENDED UNLESS YOU REALLY NEED HIGH PERFORMANCE
AT THE COST OF SOME PRECISION.
* 3 use nonlinearly constrained optimization approach, SLP
(most robust one, but somewhat slower than AUL)
Ignored for ProblemType=0.
EpsX - stopping criteria for SLP and NLC optimizers:
* must be non-negative
* use 0 to choose default value (1.0E-12 is used by default)
* if you use SLP solver, you should use default values
* if you use NLC solver, you may specify larger values, up
to 1.0E-6, if you want to speed-up solver; NLC solver
performs several preconditioned outer iterations, so final
result typically has precision much better than EpsX.
AULIts - number of iterations performed by NLC optimizer:
* must be non-negative
* use 0 to choose default value (20 is used by default)
* you may specify values smaller than 20 if you want to
speed up solver; 10 often results in good combination of
precision and speed
Ignored for ProblemType=0.
Penalty - penalty coefficient for NLC optimizer (ignored for SLP):
* must be non-negative
* use 0 to choose default value (1.0E6 in current version)
* it should be really large, 1.0E6...1.0E7 is a good value
to start from;
* generally, default value is good enough
* ignored by SLP optimizer
Ignored for ProblemType=0.
OUTPUT PARAMETERS:
CX - central point for a sphere
RLo - radius:
* for ProblemType=2,3, radius of the inscribed sphere
* for ProblemType=0 - radius of the least squares sphere
* for ProblemType=1 - zero
RHo - radius:
* for ProblemType=1,3, radius of the circumscribed sphere
* for ProblemType=0 - radius of the least squares sphere
* for ProblemType=2 - zero
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void fitsphereinternal(/* Real */ ae_matrix* xy,
ae_int_t npoints,
ae_int_t nx,
ae_int_t problemtype,
ae_int_t solvertype,
double epsx,
ae_int_t aulits,
double penalty,
/* Real */ ae_vector* cx,
double* rlo,
double* rhi,
fitsphereinternalreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_int_t j;
double v;
double vv;
ae_int_t cpr;
ae_bool userlo;
ae_bool userhi;
double vlo;
double vhi;
ae_vector vmin;
ae_vector vmax;
double spread;
ae_vector pcr;
ae_vector scr;
ae_vector bl;
ae_vector bu;
ae_int_t suboffset;
ae_int_t dstrow;
minnlcstate nlcstate;
minnlcreport nlcrep;
ae_matrix cmatrix;
ae_vector ct;
ae_int_t outeridx;
ae_int_t maxouterits;
ae_int_t maxits;
double safeguard;
double bi;
minbleicstate blcstate;
minbleicreport blcrep;
ae_vector prevc;
minlmstate lmstate;
minlmreport lmrep;
ae_frame_make(_state, &_frame_block);
memset(&vmin, 0, sizeof(vmin));
memset(&vmax, 0, sizeof(vmax));
memset(&pcr, 0, sizeof(pcr));
memset(&scr, 0, sizeof(scr));
memset(&bl, 0, sizeof(bl));
memset(&bu, 0, sizeof(bu));
memset(&nlcstate, 0, sizeof(nlcstate));
memset(&nlcrep, 0, sizeof(nlcrep));
memset(&cmatrix, 0, sizeof(cmatrix));
memset(&ct, 0, sizeof(ct));
memset(&blcstate, 0, sizeof(blcstate));
memset(&blcrep, 0, sizeof(blcrep));
memset(&prevc, 0, sizeof(prevc));
memset(&lmstate, 0, sizeof(lmstate));
memset(&lmrep, 0, sizeof(lmrep));
ae_vector_clear(cx);
*rlo = 0;
*rhi = 0;
_fitsphereinternalreport_clear(rep);
ae_vector_init(&vmin, 0, DT_REAL, _state, ae_true);
ae_vector_init(&vmax, 0, DT_REAL, _state, ae_true);
ae_vector_init(&pcr, 0, DT_REAL, _state, ae_true);
ae_vector_init(&scr, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bl, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bu, 0, DT_REAL, _state, ae_true);
_minnlcstate_init(&nlcstate, _state, ae_true);
_minnlcreport_init(&nlcrep, _state, ae_true);
ae_matrix_init(&cmatrix, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&ct, 0, DT_INT, _state, ae_true);
_minbleicstate_init(&blcstate, _state, ae_true);
_minbleicreport_init(&blcrep, _state, ae_true);
ae_vector_init(&prevc, 0, DT_REAL, _state, ae_true);
_minlmstate_init(&lmstate, _state, ae_true);
_minlmreport_init(&lmrep, _state, ae_true);
/*
* Check input parameters
*/
ae_assert(npoints>0, "FitSphereX: NPoints<=0", _state);
ae_assert(nx>0, "FitSphereX: NX<=0", _state);
ae_assert(apservisfinitematrix(xy, npoints, nx, _state), "FitSphereX: XY contains infinite or NAN values", _state);
ae_assert(problemtype>=0&&problemtype<=3, "FitSphereX: ProblemType is neither 0, 1, 2 or 3", _state);
ae_assert(solvertype>=0&&solvertype<=3, "FitSphereX: ProblemType is neither 1, 2 or 3", _state);
ae_assert(ae_isfinite(penalty, _state)&&ae_fp_greater_eq(penalty,(double)(0)), "FitSphereX: Penalty<0 or is not finite", _state);
ae_assert(ae_isfinite(epsx, _state)&&ae_fp_greater_eq(epsx,(double)(0)), "FitSphereX: EpsX<0 or is not finite", _state);
ae_assert(aulits>=0, "FitSphereX: AULIts<0", _state);
if( solvertype==0 )
{
solvertype = 1;
}
if( ae_fp_eq(penalty,(double)(0)) )
{
penalty = 1.0E6;
}
if( ae_fp_eq(epsx,(double)(0)) )
{
epsx = 1.0E-12;
}
if( aulits==0 )
{
aulits = 20;
}
safeguard = (double)(10);
maxouterits = 10;
maxits = 10000;
rep->nfev = 0;
rep->iterationscount = 0;
/*
* Determine initial values, initial estimates and spread of the points
*/
ae_vector_set_length(&vmin, nx, _state);
ae_vector_set_length(&vmax, nx, _state);
ae_vector_set_length(cx, nx, _state);
for(j=0; j<=nx-1; j++)
{
vmin.ptr.p_double[j] = xy->ptr.pp_double[0][j];
vmax.ptr.p_double[j] = xy->ptr.pp_double[0][j];
cx->ptr.p_double[j] = (double)(0);
}
for(i=0; i<=npoints-1; i++)
{
for(j=0; j<=nx-1; j++)
{
cx->ptr.p_double[j] = cx->ptr.p_double[j]+xy->ptr.pp_double[i][j];
vmin.ptr.p_double[j] = ae_minreal(vmin.ptr.p_double[j], xy->ptr.pp_double[i][j], _state);
vmax.ptr.p_double[j] = ae_maxreal(vmax.ptr.p_double[j], xy->ptr.pp_double[i][j], _state);
}
}
spread = (double)(0);
for(j=0; j<=nx-1; j++)
{
cx->ptr.p_double[j] = cx->ptr.p_double[j]/npoints;
spread = ae_maxreal(spread, vmax.ptr.p_double[j]-vmin.ptr.p_double[j], _state);
}
*rlo = ae_maxrealnumber;
*rhi = (double)(0);
for(i=0; i<=npoints-1; i++)
{
v = (double)(0);
for(j=0; j<=nx-1; j++)
{
v = v+ae_sqr(xy->ptr.pp_double[i][j]-cx->ptr.p_double[j], _state);
}
v = ae_sqrt(v, _state);
*rhi = ae_maxreal(*rhi, v, _state);
*rlo = ae_minreal(*rlo, v, _state);
}
/*
* Handle degenerate case of zero spread
*/
if( ae_fp_eq(spread,(double)(0)) )
{
for(j=0; j<=nx-1; j++)
{
cx->ptr.p_double[j] = vmin.ptr.p_double[j];
}
*rhi = (double)(0);
*rlo = (double)(0);
ae_frame_leave(_state);
return;
}
/*
* Prepare initial point for optimizer, scale vector and box constraints
*/
ae_vector_set_length(&pcr, nx+2, _state);
ae_vector_set_length(&scr, nx+2, _state);
ae_vector_set_length(&bl, nx+2, _state);
ae_vector_set_length(&bu, nx+2, _state);
for(j=0; j<=nx-1; j++)
{
pcr.ptr.p_double[j] = cx->ptr.p_double[j];
scr.ptr.p_double[j] = 0.1*spread;
bl.ptr.p_double[j] = cx->ptr.p_double[j]-safeguard*spread;
bu.ptr.p_double[j] = cx->ptr.p_double[j]+safeguard*spread;
}
pcr.ptr.p_double[nx+0] = *rlo;
pcr.ptr.p_double[nx+1] = *rhi;
scr.ptr.p_double[nx+0] = 0.5*spread;
scr.ptr.p_double[nx+1] = 0.5*spread;
bl.ptr.p_double[nx+0] = (double)(0);
bl.ptr.p_double[nx+1] = (double)(0);
bu.ptr.p_double[nx+0] = safeguard*(*rhi);
bu.ptr.p_double[nx+1] = safeguard*(*rhi);
/*
* First branch: least squares fitting vs MI/MC/MZ fitting
*/
if( problemtype==0 )
{
/*
* Solve problem with Levenberg-Marquardt algorithm
*/
pcr.ptr.p_double[nx] = *rhi;
minlmcreatevj(nx+1, npoints, &pcr, &lmstate, _state);
minlmsetscale(&lmstate, &scr, _state);
minlmsetbc(&lmstate, &bl, &bu, _state);
minlmsetcond(&lmstate, epsx, maxits, _state);
while(minlmiteration(&lmstate, _state))
{
if( lmstate.needfij||lmstate.needfi )
{
inc(&rep->nfev, _state);
for(i=0; i<=npoints-1; i++)
{
v = (double)(0);
for(j=0; j<=nx-1; j++)
{
v = v+ae_sqr(lmstate.x.ptr.p_double[j]-xy->ptr.pp_double[i][j], _state);
}
lmstate.fi.ptr.p_double[i] = ae_sqrt(v, _state)-lmstate.x.ptr.p_double[nx];
if( lmstate.needfij )
{
for(j=0; j<=nx-1; j++)
{
lmstate.j.ptr.pp_double[i][j] = 0.5/(1.0E-9*spread+ae_sqrt(v, _state))*2*(lmstate.x.ptr.p_double[j]-xy->ptr.pp_double[i][j]);
}
lmstate.j.ptr.pp_double[i][nx] = (double)(-1);
}
}
continue;
}
ae_assert(ae_false, "Assertion failed", _state);
}
minlmresults(&lmstate, &pcr, &lmrep, _state);
ae_assert(lmrep.terminationtype>0, "FitSphereX: unexpected failure of LM solver", _state);
rep->iterationscount = rep->iterationscount+lmrep.iterationscount;
/*
* Offload center coordinates from PCR to CX,
* re-calculate exact value of RLo/RHi using CX.
*/
for(j=0; j<=nx-1; j++)
{
cx->ptr.p_double[j] = pcr.ptr.p_double[j];
}
vv = (double)(0);
for(i=0; i<=npoints-1; i++)
{
v = (double)(0);
for(j=0; j<=nx-1; j++)
{
v = v+ae_sqr(xy->ptr.pp_double[i][j]-cx->ptr.p_double[j], _state);
}
v = ae_sqrt(v, _state);
vv = vv+v/npoints;
}
*rlo = vv;
*rhi = vv;
}
else
{
/*
* MI, MC, MZ fitting.
* Prepare problem metrics
*/
userlo = problemtype==2||problemtype==3;
userhi = problemtype==1||problemtype==3;
if( userlo&&userhi )
{
cpr = 2;
}
else
{
cpr = 1;
}
if( userlo )
{
vlo = (double)(1);
}
else
{
vlo = (double)(0);
}
if( userhi )
{
vhi = (double)(1);
}
else
{
vhi = (double)(0);
}
/*
* Solve with NLC solver; problem is treated as general nonlinearly constrained
* programming, with augmented Lagrangian solver or SLP being used.
*/
if( solvertype==1||solvertype==3 )
{
minnlccreate(nx+2, &pcr, &nlcstate, _state);
minnlcsetscale(&nlcstate, &scr, _state);
minnlcsetbc(&nlcstate, &bl, &bu, _state);
minnlcsetnlc(&nlcstate, 0, cpr*npoints, _state);
minnlcsetcond(&nlcstate, epsx, maxits, _state);
minnlcsetprecexactrobust(&nlcstate, 5, _state);
minnlcsetstpmax(&nlcstate, 0.1, _state);
if( solvertype==1 )
{
minnlcsetalgoaul(&nlcstate, penalty, aulits, _state);
}
else
{
minnlcsetalgoslp(&nlcstate, _state);
}
minnlcrestartfrom(&nlcstate, &pcr, _state);
while(minnlciteration(&nlcstate, _state))
{
if( nlcstate.needfij )
{
inc(&rep->nfev, _state);
nlcstate.fi.ptr.p_double[0] = vhi*nlcstate.x.ptr.p_double[nx+1]-vlo*nlcstate.x.ptr.p_double[nx+0];
for(j=0; j<=nx-1; j++)
{
nlcstate.j.ptr.pp_double[0][j] = (double)(0);
}
nlcstate.j.ptr.pp_double[0][nx+0] = -1*vlo;
nlcstate.j.ptr.pp_double[0][nx+1] = 1*vhi;
for(i=0; i<=npoints-1; i++)
{
suboffset = 0;
if( userhi )
{
dstrow = 1+cpr*i+suboffset;
v = (double)(0);
for(j=0; j<=nx-1; j++)
{
vv = nlcstate.x.ptr.p_double[j]-xy->ptr.pp_double[i][j];
v = v+vv*vv;
nlcstate.j.ptr.pp_double[dstrow][j] = 2*vv;
}
vv = nlcstate.x.ptr.p_double[nx+1];
v = v-vv*vv;
nlcstate.j.ptr.pp_double[dstrow][nx+0] = (double)(0);
nlcstate.j.ptr.pp_double[dstrow][nx+1] = -2*vv;
nlcstate.fi.ptr.p_double[dstrow] = v;
inc(&suboffset, _state);
}
if( userlo )
{
dstrow = 1+cpr*i+suboffset;
v = (double)(0);
for(j=0; j<=nx-1; j++)
{
vv = nlcstate.x.ptr.p_double[j]-xy->ptr.pp_double[i][j];
v = v-vv*vv;
nlcstate.j.ptr.pp_double[dstrow][j] = -2*vv;
}
vv = nlcstate.x.ptr.p_double[nx+0];
v = v+vv*vv;
nlcstate.j.ptr.pp_double[dstrow][nx+0] = 2*vv;
nlcstate.j.ptr.pp_double[dstrow][nx+1] = (double)(0);
nlcstate.fi.ptr.p_double[dstrow] = v;
inc(&suboffset, _state);
}
ae_assert(suboffset==cpr, "Assertion failed", _state);
}
continue;
}
ae_assert(ae_false, "Assertion failed", _state);
}
minnlcresults(&nlcstate, &pcr, &nlcrep, _state);
ae_assert(nlcrep.terminationtype>0, "FitSphereX: unexpected failure of NLC solver", _state);
rep->iterationscount = rep->iterationscount+nlcrep.iterationscount;
/*
* Offload center coordinates from PCR to CX,
* re-calculate exact value of RLo/RHi using CX.
*/
for(j=0; j<=nx-1; j++)
{
cx->ptr.p_double[j] = pcr.ptr.p_double[j];
}
*rlo = ae_maxrealnumber;
*rhi = (double)(0);
for(i=0; i<=npoints-1; i++)
{
v = (double)(0);
for(j=0; j<=nx-1; j++)
{
v = v+ae_sqr(xy->ptr.pp_double[i][j]-cx->ptr.p_double[j], _state);
}
v = ae_sqrt(v, _state);
*rhi = ae_maxreal(*rhi, v, _state);
*rlo = ae_minreal(*rlo, v, _state);
}
if( !userlo )
{
*rlo = (double)(0);
}
if( !userhi )
{
*rhi = (double)(0);
}
ae_frame_leave(_state);
return;
}
/*
* Solve problem with SLP (sequential LP) approach; this approach
* is much faster than NLP, but often fails for MI and MC (for MZ
* it performs well enough).
*
* REFERENCE: "On a sequential linear programming approach to finding
* the smallest circumscribed, largest inscribed, and minimum
* zone circle or sphere", Helmuth Spath and G.A.Watson
*/
if( solvertype==2 )
{
ae_matrix_set_length(&cmatrix, cpr*npoints, nx+3, _state);
ae_vector_set_length(&ct, cpr*npoints, _state);
ae_vector_set_length(&prevc, nx, _state);
minbleiccreate(nx+2, &pcr, &blcstate, _state);
minbleicsetscale(&blcstate, &scr, _state);
minbleicsetbc(&blcstate, &bl, &bu, _state);
minbleicsetcond(&blcstate, (double)(0), (double)(0), epsx, maxits, _state);
for(outeridx=0; outeridx<=maxouterits-1; outeridx++)
{
/*
* Prepare initial point for algorithm; center coordinates at
* PCR are used to calculate RLo/RHi and update PCR with them.
*/
*rlo = ae_maxrealnumber;
*rhi = (double)(0);
for(i=0; i<=npoints-1; i++)
{
v = (double)(0);
for(j=0; j<=nx-1; j++)
{
v = v+ae_sqr(xy->ptr.pp_double[i][j]-pcr.ptr.p_double[j], _state);
}
v = ae_sqrt(v, _state);
*rhi = ae_maxreal(*rhi, v, _state);
*rlo = ae_minreal(*rlo, v, _state);
}
pcr.ptr.p_double[nx+0] = *rlo*0.99999;
pcr.ptr.p_double[nx+1] = *rhi/0.99999;
/*
* Generate matrix of linear constraints
*/
for(i=0; i<=npoints-1; i++)
{
v = (double)(0);
for(j=0; j<=nx-1; j++)
{
v = v+ae_sqr(xy->ptr.pp_double[i][j], _state);
}
bi = -v/2;
suboffset = 0;
if( userhi )
{
dstrow = cpr*i+suboffset;
for(j=0; j<=nx-1; j++)
{
cmatrix.ptr.pp_double[dstrow][j] = pcr.ptr.p_double[j]/2-xy->ptr.pp_double[i][j];
}
cmatrix.ptr.pp_double[dstrow][nx+0] = (double)(0);
cmatrix.ptr.pp_double[dstrow][nx+1] = -*rhi/2;
cmatrix.ptr.pp_double[dstrow][nx+2] = bi;
ct.ptr.p_int[dstrow] = -1;
inc(&suboffset, _state);
}
if( userlo )
{
dstrow = cpr*i+suboffset;
for(j=0; j<=nx-1; j++)
{
cmatrix.ptr.pp_double[dstrow][j] = -(pcr.ptr.p_double[j]/2-xy->ptr.pp_double[i][j]);
}
cmatrix.ptr.pp_double[dstrow][nx+0] = *rlo/2;
cmatrix.ptr.pp_double[dstrow][nx+1] = (double)(0);
cmatrix.ptr.pp_double[dstrow][nx+2] = -bi;
ct.ptr.p_int[dstrow] = -1;
inc(&suboffset, _state);
}
ae_assert(suboffset==cpr, "Assertion failed", _state);
}
/*
* Solve LP subproblem with MinBLEIC
*/
for(j=0; j<=nx-1; j++)
{
prevc.ptr.p_double[j] = pcr.ptr.p_double[j];
}
minbleicsetlc(&blcstate, &cmatrix, &ct, cpr*npoints, _state);
minbleicrestartfrom(&blcstate, &pcr, _state);
while(minbleiciteration(&blcstate, _state))
{
if( blcstate.needfg )
{
inc(&rep->nfev, _state);
blcstate.f = vhi*blcstate.x.ptr.p_double[nx+1]-vlo*blcstate.x.ptr.p_double[nx+0];
for(j=0; j<=nx-1; j++)
{
blcstate.g.ptr.p_double[j] = (double)(0);
}
blcstate.g.ptr.p_double[nx+0] = -1*vlo;
blcstate.g.ptr.p_double[nx+1] = 1*vhi;
continue;
}
}
minbleicresults(&blcstate, &pcr, &blcrep, _state);
ae_assert(blcrep.terminationtype>0, "FitSphereX: unexpected failure of BLEIC solver", _state);
rep->iterationscount = rep->iterationscount+blcrep.iterationscount;
/*
* Terminate iterations early if we converged
*/
v = (double)(0);
for(j=0; j<=nx-1; j++)
{
v = v+ae_sqr(prevc.ptr.p_double[j]-pcr.ptr.p_double[j], _state);
}
v = ae_sqrt(v, _state);
if( ae_fp_less_eq(v,epsx) )
{
break;
}
}
/*
* Offload center coordinates from PCR to CX,
* re-calculate exact value of RLo/RHi using CX.
*/
for(j=0; j<=nx-1; j++)
{
cx->ptr.p_double[j] = pcr.ptr.p_double[j];
}
*rlo = ae_maxrealnumber;
*rhi = (double)(0);
for(i=0; i<=npoints-1; i++)
{
v = (double)(0);
for(j=0; j<=nx-1; j++)
{
v = v+ae_sqr(xy->ptr.pp_double[i][j]-cx->ptr.p_double[j], _state);
}
v = ae_sqrt(v, _state);
*rhi = ae_maxreal(*rhi, v, _state);
*rlo = ae_minreal(*rlo, v, _state);
}
if( !userlo )
{
*rlo = (double)(0);
}
if( !userhi )
{
*rhi = (double)(0);
}
ae_frame_leave(_state);
return;
}
/*
* Oooops...!
*/
ae_assert(ae_false, "FitSphereX: integrity check failed", _state);
}
ae_frame_leave(_state);
}
void _fitsphereinternalreport_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
fitsphereinternalreport *p = (fitsphereinternalreport*)_p;
ae_touch_ptr((void*)p);
}
void _fitsphereinternalreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
fitsphereinternalreport *dst = (fitsphereinternalreport*)_dst;
fitsphereinternalreport *src = (fitsphereinternalreport*)_src;
dst->nfev = src->nfev;
dst->iterationscount = src->iterationscount;
}
void _fitsphereinternalreport_clear(void* _p)
{
fitsphereinternalreport *p = (fitsphereinternalreport*)_p;
ae_touch_ptr((void*)p);
}
void _fitsphereinternalreport_destroy(void* _p)
{
fitsphereinternalreport *p = (fitsphereinternalreport*)_p;
ae_touch_ptr((void*)p);
}
#endif
#if defined(AE_COMPILE_INTFITSERV) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Internal subroutine: automatic scaling for LLS tasks.
NEVER CALL IT DIRECTLY!
Maps abscissas to [-1,1], standartizes ordinates and correspondingly scales
constraints. It also scales weights so that max(W[i])=1
Transformations performed:
* X, XC [XA,XB] => [-1,+1]
transformation makes min(X)=-1, max(X)=+1
* Y [SA,SB] => [0,1]
transformation makes mean(Y)=0, stddev(Y)=1
* YC transformed accordingly to SA, SB, DC[I]
-- ALGLIB PROJECT --
Copyright 08.09.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitscalexy(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
ae_int_t n,
/* Real */ ae_vector* xc,
/* Real */ ae_vector* yc,
/* Integer */ ae_vector* dc,
ae_int_t k,
double* xa,
double* xb,
double* sa,
double* sb,
/* Real */ ae_vector* xoriginal,
/* Real */ ae_vector* yoriginal,
ae_state *_state)
{
double xmin;
double xmax;
ae_int_t i;
double mx;
*xa = 0;
*xb = 0;
*sa = 0;
*sb = 0;
ae_vector_clear(xoriginal);
ae_vector_clear(yoriginal);
ae_assert(n>=1, "LSFitScaleXY: incorrect N", _state);
ae_assert(k>=0, "LSFitScaleXY: incorrect K", _state);
xmin = x->ptr.p_double[0];
xmax = x->ptr.p_double[0];
for(i=1; i<=n-1; i++)
{
xmin = ae_minreal(xmin, x->ptr.p_double[i], _state);
xmax = ae_maxreal(xmax, x->ptr.p_double[i], _state);
}
for(i=0; i<=k-1; i++)
{
xmin = ae_minreal(xmin, xc->ptr.p_double[i], _state);
xmax = ae_maxreal(xmax, xc->ptr.p_double[i], _state);
}
if( ae_fp_eq(xmin,xmax) )
{
if( ae_fp_eq(xmin,(double)(0)) )
{
xmin = (double)(-1);
xmax = (double)(1);
}
else
{
if( ae_fp_greater(xmin,(double)(0)) )
{
xmin = 0.5*xmin;
}
else
{
xmax = 0.5*xmax;
}
}
}
ae_vector_set_length(xoriginal, n, _state);
ae_v_move(&xoriginal->ptr.p_double[0], 1, &x->ptr.p_double[0], 1, ae_v_len(0,n-1));
*xa = xmin;
*xb = xmax;
for(i=0; i<=n-1; i++)
{
x->ptr.p_double[i] = 2*(x->ptr.p_double[i]-0.5*(*xa+(*xb)))/(*xb-(*xa));
}
for(i=0; i<=k-1; i++)
{
ae_assert(dc->ptr.p_int[i]>=0, "LSFitScaleXY: internal error!", _state);
xc->ptr.p_double[i] = 2*(xc->ptr.p_double[i]-0.5*(*xa+(*xb)))/(*xb-(*xa));
yc->ptr.p_double[i] = yc->ptr.p_double[i]*ae_pow(0.5*(*xb-(*xa)), (double)(dc->ptr.p_int[i]), _state);
}
ae_vector_set_length(yoriginal, n, _state);
ae_v_move(&yoriginal->ptr.p_double[0], 1, &y->ptr.p_double[0], 1, ae_v_len(0,n-1));
*sa = (double)(0);
for(i=0; i<=n-1; i++)
{
*sa = *sa+y->ptr.p_double[i];
}
*sa = *sa/n;
*sb = (double)(0);
for(i=0; i<=n-1; i++)
{
*sb = *sb+ae_sqr(y->ptr.p_double[i]-(*sa), _state);
}
*sb = ae_sqrt(*sb/n, _state)+(*sa);
if( ae_fp_eq(*sb,*sa) )
{
*sb = 2*(*sa);
}
if( ae_fp_eq(*sb,*sa) )
{
*sb = *sa+1;
}
for(i=0; i<=n-1; i++)
{
y->ptr.p_double[i] = (y->ptr.p_double[i]-(*sa))/(*sb-(*sa));
}
for(i=0; i<=k-1; i++)
{
if( dc->ptr.p_int[i]==0 )
{
yc->ptr.p_double[i] = (yc->ptr.p_double[i]-(*sa))/(*sb-(*sa));
}
else
{
yc->ptr.p_double[i] = yc->ptr.p_double[i]/(*sb-(*sa));
}
}
mx = (double)(0);
for(i=0; i<=n-1; i++)
{
mx = ae_maxreal(mx, ae_fabs(w->ptr.p_double[i], _state), _state);
}
if( ae_fp_neq(mx,(double)(0)) )
{
for(i=0; i<=n-1; i++)
{
w->ptr.p_double[i] = w->ptr.p_double[i]/mx;
}
}
}
void buildpriorterm(/* Real */ ae_matrix* xy,
ae_int_t n,
ae_int_t nx,
ae_int_t ny,
ae_int_t modeltype,
double priorval,
/* Real */ ae_matrix* v,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_int_t j;
ae_int_t j0;
ae_int_t j1;
double rj;
ae_matrix araw;
ae_matrix amod;
ae_matrix braw;
ae_vector tmp0;
double lambdareg;
ae_int_t rfsits;
ae_frame_make(_state, &_frame_block);
memset(&araw, 0, sizeof(araw));
memset(&amod, 0, sizeof(amod));
memset(&braw, 0, sizeof(braw));
memset(&tmp0, 0, sizeof(tmp0));
ae_matrix_clear(v);
ae_matrix_init(&araw, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&amod, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&braw, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp0, 0, DT_REAL, _state, ae_true);
ae_assert(n>=0, "BuildPriorTerm: N<0", _state);
ae_assert(nx>0, "BuildPriorTerm: NX<=0", _state);
ae_assert(ny>0, "BuildPriorTerm: NY<=0", _state);
ae_matrix_set_length(v, ny, nx+1, _state);
for(i=0; i<=v->rows-1; i++)
{
for(j=0; j<=v->cols-1; j++)
{
v->ptr.pp_double[i][j] = (double)(0);
}
}
if( n==0 )
{
if( modeltype==0 )
{
for(i=0; i<=ny-1; i++)
{
v->ptr.pp_double[i][nx] = priorval;
}
ae_frame_leave(_state);
return;
}
if( modeltype==1 )
{
ae_frame_leave(_state);
return;
}
if( modeltype==2 )
{
ae_frame_leave(_state);
return;
}
if( modeltype==3 )
{
ae_frame_leave(_state);
return;
}
ae_assert(ae_false, "BuildPriorTerm: unexpected model type", _state);
}
if( modeltype==0 )
{
for(i=0; i<=ny-1; i++)
{
v->ptr.pp_double[i][nx] = priorval;
}
for(i=0; i<=n-1; i++)
{
for(j=0; j<=ny-1; j++)
{
xy->ptr.pp_double[i][nx+j] = xy->ptr.pp_double[i][nx+j]-priorval;
}
}
ae_frame_leave(_state);
return;
}
if( modeltype==2 )
{
for(i=0; i<=n-1; i++)
{
for(j=0; j<=ny-1; j++)
{
v->ptr.pp_double[j][nx] = v->ptr.pp_double[j][nx]+xy->ptr.pp_double[i][nx+j];
}
}
for(j=0; j<=ny-1; j++)
{
v->ptr.pp_double[j][nx] = v->ptr.pp_double[j][nx]/coalesce((double)(n), (double)(1), _state);
}
for(i=0; i<=n-1; i++)
{
for(j=0; j<=ny-1; j++)
{
xy->ptr.pp_double[i][nx+j] = xy->ptr.pp_double[i][nx+j]-v->ptr.pp_double[j][nx];
}
}
ae_frame_leave(_state);
return;
}
if( modeltype==3 )
{
ae_frame_leave(_state);
return;
}
ae_assert(modeltype==1, "BuildPriorTerm: unexpected model type", _state);
lambdareg = 0.0;
ae_matrix_set_length(&araw, nx+1, nx+1, _state);
ae_matrix_set_length(&braw, nx+1, ny, _state);
ae_vector_set_length(&tmp0, nx+1, _state);
ae_matrix_set_length(&amod, nx+1, nx+1, _state);
for(i=0; i<=nx; i++)
{
for(j=0; j<=nx; j++)
{
araw.ptr.pp_double[i][j] = (double)(0);
}
}
for(i=0; i<=n-1; i++)
{
for(j=0; j<=nx-1; j++)
{
tmp0.ptr.p_double[j] = xy->ptr.pp_double[i][j];
}
tmp0.ptr.p_double[nx] = 1.0;
for(j0=0; j0<=nx; j0++)
{
for(j1=0; j1<=nx; j1++)
{
araw.ptr.pp_double[j0][j1] = araw.ptr.pp_double[j0][j1]+tmp0.ptr.p_double[j0]*tmp0.ptr.p_double[j1];
}
}
}
for(rfsits=1; rfsits<=3; rfsits++)
{
for(i=0; i<=nx; i++)
{
for(j=0; j<=ny-1; j++)
{
braw.ptr.pp_double[i][j] = (double)(0);
}
}
for(i=0; i<=n-1; i++)
{
for(j=0; j<=nx-1; j++)
{
tmp0.ptr.p_double[j] = xy->ptr.pp_double[i][j];
}
tmp0.ptr.p_double[nx] = 1.0;
for(j=0; j<=ny-1; j++)
{
rj = xy->ptr.pp_double[i][nx+j];
for(j0=0; j0<=nx; j0++)
{
rj = rj-tmp0.ptr.p_double[j0]*v->ptr.pp_double[j][j0];
}
for(j0=0; j0<=nx; j0++)
{
braw.ptr.pp_double[j0][j] = braw.ptr.pp_double[j0][j]+rj*tmp0.ptr.p_double[j0];
}
}
}
for(;;)
{
for(i=0; i<=nx; i++)
{
for(j=0; j<=nx; j++)
{
amod.ptr.pp_double[i][j] = araw.ptr.pp_double[i][j];
}
amod.ptr.pp_double[i][i] = amod.ptr.pp_double[i][i]+lambdareg*coalesce(amod.ptr.pp_double[i][i], (double)(1), _state);
}
if( spdmatrixcholesky(&amod, nx+1, ae_true, _state) )
{
break;
}
lambdareg = coalesce(10*lambdareg, 1.0E-12, _state);
}
rmatrixlefttrsm(nx+1, ny, &amod, 0, 0, ae_true, ae_false, 1, &braw, 0, 0, _state);
rmatrixlefttrsm(nx+1, ny, &amod, 0, 0, ae_true, ae_false, 0, &braw, 0, 0, _state);
for(i=0; i<=nx; i++)
{
for(j=0; j<=ny-1; j++)
{
v->ptr.pp_double[j][i] = v->ptr.pp_double[j][i]+braw.ptr.pp_double[i][j];
}
}
}
for(i=0; i<=n-1; i++)
{
for(j=0; j<=nx-1; j++)
{
tmp0.ptr.p_double[j] = xy->ptr.pp_double[i][j];
}
tmp0.ptr.p_double[nx] = 1.0;
for(j=0; j<=ny-1; j++)
{
rj = 0.0;
for(j0=0; j0<=nx; j0++)
{
rj = rj+tmp0.ptr.p_double[j0]*v->ptr.pp_double[j][j0];
}
xy->ptr.pp_double[i][nx+j] = xy->ptr.pp_double[i][nx+j]-rj;
}
}
ae_frame_leave(_state);
}
void buildpriorterm1(/* Real */ ae_vector* xy1,
ae_int_t n,
ae_int_t nx,
ae_int_t ny,
ae_int_t modeltype,
double priorval,
/* Real */ ae_matrix* v,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_int_t j;
ae_int_t j0;
ae_int_t j1;
ae_int_t ew;
double rj;
ae_matrix araw;
ae_matrix amod;
ae_matrix braw;
ae_vector tmp0;
double lambdareg;
ae_int_t rfsits;
ae_frame_make(_state, &_frame_block);
memset(&araw, 0, sizeof(araw));
memset(&amod, 0, sizeof(amod));
memset(&braw, 0, sizeof(braw));
memset(&tmp0, 0, sizeof(tmp0));
ae_matrix_clear(v);
ae_matrix_init(&araw, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&amod, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&braw, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp0, 0, DT_REAL, _state, ae_true);
ae_assert(n>=0, "BuildPriorTerm: N<0", _state);
ae_assert(nx>0, "BuildPriorTerm: NX<=0", _state);
ae_assert(ny>0, "BuildPriorTerm: NY<=0", _state);
ew = nx+ny;
ae_matrix_set_length(v, ny, nx+1, _state);
for(i=0; i<=v->rows-1; i++)
{
for(j=0; j<=v->cols-1; j++)
{
v->ptr.pp_double[i][j] = (double)(0);
}
}
if( n==0 )
{
if( modeltype==0 )
{
for(i=0; i<=ny-1; i++)
{
v->ptr.pp_double[i][nx] = priorval;
}
ae_frame_leave(_state);
return;
}
if( modeltype==1 )
{
ae_frame_leave(_state);
return;
}
if( modeltype==2 )
{
ae_frame_leave(_state);
return;
}
if( modeltype==3 )
{
ae_frame_leave(_state);
return;
}
ae_assert(ae_false, "BuildPriorTerm: unexpected model type", _state);
}
if( modeltype==0 )
{
for(i=0; i<=ny-1; i++)
{
v->ptr.pp_double[i][nx] = priorval;
}
for(i=0; i<=n-1; i++)
{
for(j=0; j<=ny-1; j++)
{
xy1->ptr.p_double[i*ew+nx+j] = xy1->ptr.p_double[i*ew+nx+j]-priorval;
}
}
ae_frame_leave(_state);
return;
}
if( modeltype==2 )
{
for(i=0; i<=n-1; i++)
{
for(j=0; j<=ny-1; j++)
{
v->ptr.pp_double[j][nx] = v->ptr.pp_double[j][nx]+xy1->ptr.p_double[i*ew+nx+j];
}
}
for(j=0; j<=ny-1; j++)
{
v->ptr.pp_double[j][nx] = v->ptr.pp_double[j][nx]/coalesce((double)(n), (double)(1), _state);
}
for(i=0; i<=n-1; i++)
{
for(j=0; j<=ny-1; j++)
{
xy1->ptr.p_double[i*ew+nx+j] = xy1->ptr.p_double[i*ew+nx+j]-v->ptr.pp_double[j][nx];
}
}
ae_frame_leave(_state);
return;
}
if( modeltype==3 )
{
ae_frame_leave(_state);
return;
}
ae_assert(modeltype==1, "BuildPriorTerm: unexpected model type", _state);
lambdareg = 0.0;
ae_matrix_set_length(&araw, nx+1, nx+1, _state);
ae_matrix_set_length(&braw, nx+1, ny, _state);
ae_vector_set_length(&tmp0, nx+1, _state);
ae_matrix_set_length(&amod, nx+1, nx+1, _state);
for(i=0; i<=nx; i++)
{
for(j=0; j<=nx; j++)
{
araw.ptr.pp_double[i][j] = (double)(0);
}
}
for(i=0; i<=n-1; i++)
{
for(j=0; j<=nx-1; j++)
{
tmp0.ptr.p_double[j] = xy1->ptr.p_double[i*ew+j];
}
tmp0.ptr.p_double[nx] = 1.0;
for(j0=0; j0<=nx; j0++)
{
for(j1=0; j1<=nx; j1++)
{
araw.ptr.pp_double[j0][j1] = araw.ptr.pp_double[j0][j1]+tmp0.ptr.p_double[j0]*tmp0.ptr.p_double[j1];
}
}
}
for(rfsits=1; rfsits<=3; rfsits++)
{
for(i=0; i<=nx; i++)
{
for(j=0; j<=ny-1; j++)
{
braw.ptr.pp_double[i][j] = (double)(0);
}
}
for(i=0; i<=n-1; i++)
{
for(j=0; j<=nx-1; j++)
{
tmp0.ptr.p_double[j] = xy1->ptr.p_double[i*ew+j];
}
tmp0.ptr.p_double[nx] = 1.0;
for(j=0; j<=ny-1; j++)
{
rj = xy1->ptr.p_double[i*ew+nx+j];
for(j0=0; j0<=nx; j0++)
{
rj = rj-tmp0.ptr.p_double[j0]*v->ptr.pp_double[j][j0];
}
for(j0=0; j0<=nx; j0++)
{
braw.ptr.pp_double[j0][j] = braw.ptr.pp_double[j0][j]+rj*tmp0.ptr.p_double[j0];
}
}
}
for(;;)
{
for(i=0; i<=nx; i++)
{
for(j=0; j<=nx; j++)
{
amod.ptr.pp_double[i][j] = araw.ptr.pp_double[i][j];
}
amod.ptr.pp_double[i][i] = amod.ptr.pp_double[i][i]+lambdareg*coalesce(amod.ptr.pp_double[i][i], (double)(1), _state);
}
if( spdmatrixcholesky(&amod, nx+1, ae_true, _state) )
{
break;
}
lambdareg = coalesce(10*lambdareg, 1.0E-12, _state);
}
rmatrixlefttrsm(nx+1, ny, &amod, 0, 0, ae_true, ae_false, 1, &braw, 0, 0, _state);
rmatrixlefttrsm(nx+1, ny, &amod, 0, 0, ae_true, ae_false, 0, &braw, 0, 0, _state);
for(i=0; i<=nx; i++)
{
for(j=0; j<=ny-1; j++)
{
v->ptr.pp_double[j][i] = v->ptr.pp_double[j][i]+braw.ptr.pp_double[i][j];
}
}
}
for(i=0; i<=n-1; i++)
{
for(j=0; j<=nx-1; j++)
{
tmp0.ptr.p_double[j] = xy1->ptr.p_double[i*ew+j];
}
tmp0.ptr.p_double[nx] = 1.0;
for(j=0; j<=ny-1; j++)
{
rj = 0.0;
for(j0=0; j0<=nx; j0++)
{
rj = rj+tmp0.ptr.p_double[j0]*v->ptr.pp_double[j][j0];
}
xy1->ptr.p_double[i*ew+nx+j] = xy1->ptr.p_double[i*ew+nx+j]-rj;
}
}
ae_frame_leave(_state);
}
#endif
#if defined(AE_COMPILE_SPLINE1D) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This subroutine builds linear spline interpolant
INPUT PARAMETERS:
X - spline nodes, array[0..N-1]
Y - function values, array[0..N-1]
N - points count (optional):
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
OUTPUT PARAMETERS:
C - spline interpolant
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
-- ALGLIB PROJECT --
Copyright 24.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dbuildlinear(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
spline1dinterpolant* c,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_int_t i;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
_spline1dinterpolant_clear(c);
ae_assert(n>1, "Spline1DBuildLinear: N<2!", _state);
ae_assert(x->cnt>=n, "Spline1DBuildLinear: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DBuildLinear: Length(Y)<N!", _state);
/*
* check and sort points
*/
ae_assert(isfinitevector(x, n, _state), "Spline1DBuildLinear: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, n, _state), "Spline1DBuildLinear: Y contains infinite or NAN values!", _state);
spline1d_heapsortpoints(x, y, n, _state);
ae_assert(aredistinct(x, n, _state), "Spline1DBuildLinear: at least two consequent points are too close!", _state);
/*
* Build
*/
c->periodic = ae_false;
c->n = n;
c->k = 3;
c->continuity = 0;
ae_vector_set_length(&c->x, n, _state);
ae_vector_set_length(&c->c, 4*(n-1)+2, _state);
for(i=0; i<=n-1; i++)
{
c->x.ptr.p_double[i] = x->ptr.p_double[i];
}
for(i=0; i<=n-2; i++)
{
c->c.ptr.p_double[4*i+0] = y->ptr.p_double[i];
c->c.ptr.p_double[4*i+1] = (y->ptr.p_double[i+1]-y->ptr.p_double[i])/(x->ptr.p_double[i+1]-x->ptr.p_double[i]);
c->c.ptr.p_double[4*i+2] = (double)(0);
c->c.ptr.p_double[4*i+3] = (double)(0);
}
c->c.ptr.p_double[4*(n-1)+0] = y->ptr.p_double[n-1];
c->c.ptr.p_double[4*(n-1)+1] = c->c.ptr.p_double[4*(n-2)+1];
ae_frame_leave(_state);
}
/*************************************************************************
This subroutine builds cubic spline interpolant.
INPUT PARAMETERS:
X - spline nodes, array[0..N-1].
Y - function values, array[0..N-1].
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
OUTPUT PARAMETERS:
C - spline interpolant
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dbuildcubic(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t boundltype,
double boundl,
ae_int_t boundrtype,
double boundr,
spline1dinterpolant* c,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_vector a1;
ae_vector a2;
ae_vector a3;
ae_vector b;
ae_vector dt;
ae_vector d;
ae_vector p;
ae_int_t ylen;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&a1, 0, sizeof(a1));
memset(&a2, 0, sizeof(a2));
memset(&a3, 0, sizeof(a3));
memset(&b, 0, sizeof(b));
memset(&dt, 0, sizeof(dt));
memset(&d, 0, sizeof(d));
memset(&p, 0, sizeof(p));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
_spline1dinterpolant_clear(c);
ae_vector_init(&a1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&a2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&a3, 0, DT_REAL, _state, ae_true);
ae_vector_init(&b, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dt, 0, DT_REAL, _state, ae_true);
ae_vector_init(&d, 0, DT_REAL, _state, ae_true);
ae_vector_init(&p, 0, DT_INT, _state, ae_true);
/*
* check correctness of boundary conditions
*/
ae_assert(((boundltype==-1||boundltype==0)||boundltype==1)||boundltype==2, "Spline1DBuildCubic: incorrect BoundLType!", _state);
ae_assert(((boundrtype==-1||boundrtype==0)||boundrtype==1)||boundrtype==2, "Spline1DBuildCubic: incorrect BoundRType!", _state);
ae_assert((boundrtype==-1&&boundltype==-1)||(boundrtype!=-1&&boundltype!=-1), "Spline1DBuildCubic: incorrect BoundLType/BoundRType!", _state);
if( boundltype==1||boundltype==2 )
{
ae_assert(ae_isfinite(boundl, _state), "Spline1DBuildCubic: BoundL is infinite or NAN!", _state);
}
if( boundrtype==1||boundrtype==2 )
{
ae_assert(ae_isfinite(boundr, _state), "Spline1DBuildCubic: BoundR is infinite or NAN!", _state);
}
/*
* check lengths of arguments
*/
ae_assert(n>=2, "Spline1DBuildCubic: N<2!", _state);
ae_assert(x->cnt>=n, "Spline1DBuildCubic: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DBuildCubic: Length(Y)<N!", _state);
/*
* check and sort points
*/
ylen = n;
if( boundltype==-1 )
{
ylen = n-1;
}
ae_assert(isfinitevector(x, n, _state), "Spline1DBuildCubic: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, ylen, _state), "Spline1DBuildCubic: Y contains infinite or NAN values!", _state);
spline1d_heapsortppoints(x, y, &p, n, _state);
ae_assert(aredistinct(x, n, _state), "Spline1DBuildCubic: at least two consequent points are too close!", _state);
/*
* Now we've checked and preordered everything,
* so we can call internal function to calculate derivatives,
* and then build Hermite spline using these derivatives
*/
if( boundltype==-1||boundrtype==-1 )
{
y->ptr.p_double[n-1] = y->ptr.p_double[0];
}
spline1d_spline1dgriddiffcubicinternal(x, y, n, boundltype, boundl, boundrtype, boundr, &d, &a1, &a2, &a3, &b, &dt, _state);
spline1dbuildhermite(x, y, &d, n, c, _state);
c->periodic = boundltype==-1||boundrtype==-1;
c->continuity = 2;
ae_frame_leave(_state);
}
/*************************************************************************
This function solves following problem: given table y[] of function values
at nodes x[], it calculates and returns table of function derivatives d[]
(calculated at the same nodes x[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - spline nodes
Y - function values
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
OUTPUT PARAMETERS:
D - derivative values at X[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Derivative values are correctly reordered on return, so D[I] is always
equal to S'(X[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
void spline1dgriddiffcubic(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t boundltype,
double boundl,
ae_int_t boundrtype,
double boundr,
/* Real */ ae_vector* d,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_vector a1;
ae_vector a2;
ae_vector a3;
ae_vector b;
ae_vector dt;
ae_vector p;
ae_int_t i;
ae_int_t ylen;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&a1, 0, sizeof(a1));
memset(&a2, 0, sizeof(a2));
memset(&a3, 0, sizeof(a3));
memset(&b, 0, sizeof(b));
memset(&dt, 0, sizeof(dt));
memset(&p, 0, sizeof(p));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
ae_vector_clear(d);
ae_vector_init(&a1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&a2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&a3, 0, DT_REAL, _state, ae_true);
ae_vector_init(&b, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dt, 0, DT_REAL, _state, ae_true);
ae_vector_init(&p, 0, DT_INT, _state, ae_true);
/*
* check correctness of boundary conditions
*/
ae_assert(((boundltype==-1||boundltype==0)||boundltype==1)||boundltype==2, "Spline1DGridDiffCubic: incorrect BoundLType!", _state);
ae_assert(((boundrtype==-1||boundrtype==0)||boundrtype==1)||boundrtype==2, "Spline1DGridDiffCubic: incorrect BoundRType!", _state);
ae_assert((boundrtype==-1&&boundltype==-1)||(boundrtype!=-1&&boundltype!=-1), "Spline1DGridDiffCubic: incorrect BoundLType/BoundRType!", _state);
if( boundltype==1||boundltype==2 )
{
ae_assert(ae_isfinite(boundl, _state), "Spline1DGridDiffCubic: BoundL is infinite or NAN!", _state);
}
if( boundrtype==1||boundrtype==2 )
{
ae_assert(ae_isfinite(boundr, _state), "Spline1DGridDiffCubic: BoundR is infinite or NAN!", _state);
}
/*
* check lengths of arguments
*/
ae_assert(n>=2, "Spline1DGridDiffCubic: N<2!", _state);
ae_assert(x->cnt>=n, "Spline1DGridDiffCubic: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DGridDiffCubic: Length(Y)<N!", _state);
/*
* check and sort points
*/
ylen = n;
if( boundltype==-1 )
{
ylen = n-1;
}
ae_assert(isfinitevector(x, n, _state), "Spline1DGridDiffCubic: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, ylen, _state), "Spline1DGridDiffCubic: Y contains infinite or NAN values!", _state);
spline1d_heapsortppoints(x, y, &p, n, _state);
ae_assert(aredistinct(x, n, _state), "Spline1DGridDiffCubic: at least two consequent points are too close!", _state);
/*
* Now we've checked and preordered everything,
* so we can call internal function.
*/
spline1d_spline1dgriddiffcubicinternal(x, y, n, boundltype, boundl, boundrtype, boundr, d, &a1, &a2, &a3, &b, &dt, _state);
/*
* Remember that HeapSortPPoints() call?
* Now we have to reorder them back.
*/
if( dt.cnt<n )
{
ae_vector_set_length(&dt, n, _state);
}
for(i=0; i<=n-1; i++)
{
dt.ptr.p_double[p.ptr.p_int[i]] = d->ptr.p_double[i];
}
ae_v_move(&d->ptr.p_double[0], 1, &dt.ptr.p_double[0], 1, ae_v_len(0,n-1));
ae_frame_leave(_state);
}
/*************************************************************************
This function solves following problem: given table y[] of function values
at nodes x[], it calculates and returns tables of first and second
function derivatives d1[] and d2[] (calculated at the same nodes x[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - spline nodes
Y - function values
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
OUTPUT PARAMETERS:
D1 - S' values at X[]
D2 - S'' values at X[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Derivative values are correctly reordered on return, so D[I] is always
equal to S'(X[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
void spline1dgriddiff2cubic(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t boundltype,
double boundl,
ae_int_t boundrtype,
double boundr,
/* Real */ ae_vector* d1,
/* Real */ ae_vector* d2,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_vector a1;
ae_vector a2;
ae_vector a3;
ae_vector b;
ae_vector dt;
ae_vector p;
ae_int_t i;
ae_int_t ylen;
double delta;
double delta2;
double delta3;
double s2;
double s3;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&a1, 0, sizeof(a1));
memset(&a2, 0, sizeof(a2));
memset(&a3, 0, sizeof(a3));
memset(&b, 0, sizeof(b));
memset(&dt, 0, sizeof(dt));
memset(&p, 0, sizeof(p));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
ae_vector_clear(d1);
ae_vector_clear(d2);
ae_vector_init(&a1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&a2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&a3, 0, DT_REAL, _state, ae_true);
ae_vector_init(&b, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dt, 0, DT_REAL, _state, ae_true);
ae_vector_init(&p, 0, DT_INT, _state, ae_true);
/*
* check correctness of boundary conditions
*/
ae_assert(((boundltype==-1||boundltype==0)||boundltype==1)||boundltype==2, "Spline1DGridDiff2Cubic: incorrect BoundLType!", _state);
ae_assert(((boundrtype==-1||boundrtype==0)||boundrtype==1)||boundrtype==2, "Spline1DGridDiff2Cubic: incorrect BoundRType!", _state);
ae_assert((boundrtype==-1&&boundltype==-1)||(boundrtype!=-1&&boundltype!=-1), "Spline1DGridDiff2Cubic: incorrect BoundLType/BoundRType!", _state);
if( boundltype==1||boundltype==2 )
{
ae_assert(ae_isfinite(boundl, _state), "Spline1DGridDiff2Cubic: BoundL is infinite or NAN!", _state);
}
if( boundrtype==1||boundrtype==2 )
{
ae_assert(ae_isfinite(boundr, _state), "Spline1DGridDiff2Cubic: BoundR is infinite or NAN!", _state);
}
/*
* check lengths of arguments
*/
ae_assert(n>=2, "Spline1DGridDiff2Cubic: N<2!", _state);
ae_assert(x->cnt>=n, "Spline1DGridDiff2Cubic: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DGridDiff2Cubic: Length(Y)<N!", _state);
/*
* check and sort points
*/
ylen = n;
if( boundltype==-1 )
{
ylen = n-1;
}
ae_assert(isfinitevector(x, n, _state), "Spline1DGridDiff2Cubic: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, ylen, _state), "Spline1DGridDiff2Cubic: Y contains infinite or NAN values!", _state);
spline1d_heapsortppoints(x, y, &p, n, _state);
ae_assert(aredistinct(x, n, _state), "Spline1DGridDiff2Cubic: at least two consequent points are too close!", _state);
/*
* Now we've checked and preordered everything,
* so we can call internal function.
*
* After this call we will calculate second derivatives
* (manually, by converting to the power basis)
*/
spline1d_spline1dgriddiffcubicinternal(x, y, n, boundltype, boundl, boundrtype, boundr, d1, &a1, &a2, &a3, &b, &dt, _state);
ae_vector_set_length(d2, n, _state);
delta = (double)(0);
s2 = (double)(0);
s3 = (double)(0);
for(i=0; i<=n-2; i++)
{
/*
* We convert from Hermite basis to the power basis.
* Si is coefficient before x^i.
*
* Inside this cycle we need just S2,
* because we calculate S'' exactly at spline node,
* (only x^2 matters at x=0), but after iterations
* will be over, we will need other coefficients
* to calculate spline value at the last node.
*/
delta = x->ptr.p_double[i+1]-x->ptr.p_double[i];
delta2 = ae_sqr(delta, _state);
delta3 = delta*delta2;
s2 = (3*(y->ptr.p_double[i+1]-y->ptr.p_double[i])-2*d1->ptr.p_double[i]*delta-d1->ptr.p_double[i+1]*delta)/delta2;
s3 = (2*(y->ptr.p_double[i]-y->ptr.p_double[i+1])+d1->ptr.p_double[i]*delta+d1->ptr.p_double[i+1]*delta)/delta3;
d2->ptr.p_double[i] = 2*s2;
}
d2->ptr.p_double[n-1] = 2*s2+6*s3*delta;
/*
* Remember that HeapSortPPoints() call?
* Now we have to reorder them back.
*/
if( dt.cnt<n )
{
ae_vector_set_length(&dt, n, _state);
}
for(i=0; i<=n-1; i++)
{
dt.ptr.p_double[p.ptr.p_int[i]] = d1->ptr.p_double[i];
}
ae_v_move(&d1->ptr.p_double[0], 1, &dt.ptr.p_double[0], 1, ae_v_len(0,n-1));
for(i=0; i<=n-1; i++)
{
dt.ptr.p_double[p.ptr.p_int[i]] = d2->ptr.p_double[i];
}
ae_v_move(&d2->ptr.p_double[0], 1, &dt.ptr.p_double[0], 1, ae_v_len(0,n-1));
ae_frame_leave(_state);
}
/*************************************************************************
This function solves following problem: given table y[] of function values
at old nodes x[] and new nodes x2[], it calculates and returns table of
function values y2[] (calculated at x2[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - old spline nodes
Y - function values
X2 - new spline nodes
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points from X/Y are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
N2 - new points count:
* N2>=2
* if given, only first N2 points from X2 are used
* if not given, automatically detected from X2 size
OUTPUT PARAMETERS:
F2 - function values at X2[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Function values are correctly reordered on return, so F2[I] is always
equal to S(X2[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
void spline1dconvcubic(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t boundltype,
double boundl,
ae_int_t boundrtype,
double boundr,
/* Real */ ae_vector* x2,
ae_int_t n2,
/* Real */ ae_vector* y2,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_vector _x2;
ae_vector a1;
ae_vector a2;
ae_vector a3;
ae_vector b;
ae_vector d;
ae_vector dt;
ae_vector d1;
ae_vector d2;
ae_vector p;
ae_vector p2;
ae_int_t i;
ae_int_t ylen;
double t;
double t2;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&_x2, 0, sizeof(_x2));
memset(&a1, 0, sizeof(a1));
memset(&a2, 0, sizeof(a2));
memset(&a3, 0, sizeof(a3));
memset(&b, 0, sizeof(b));
memset(&d, 0, sizeof(d));
memset(&dt, 0, sizeof(dt));
memset(&d1, 0, sizeof(d1));
memset(&d2, 0, sizeof(d2));
memset(&p, 0, sizeof(p));
memset(&p2, 0, sizeof(p2));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
ae_vector_init_copy(&_x2, x2, _state, ae_true);
x2 = &_x2;
ae_vector_clear(y2);
ae_vector_init(&a1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&a2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&a3, 0, DT_REAL, _state, ae_true);
ae_vector_init(&b, 0, DT_REAL, _state, ae_true);
ae_vector_init(&d, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dt, 0, DT_REAL, _state, ae_true);
ae_vector_init(&d1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&d2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&p, 0, DT_INT, _state, ae_true);
ae_vector_init(&p2, 0, DT_INT, _state, ae_true);
/*
* check correctness of boundary conditions
*/
ae_assert(((boundltype==-1||boundltype==0)||boundltype==1)||boundltype==2, "Spline1DConvCubic: incorrect BoundLType!", _state);
ae_assert(((boundrtype==-1||boundrtype==0)||boundrtype==1)||boundrtype==2, "Spline1DConvCubic: incorrect BoundRType!", _state);
ae_assert((boundrtype==-1&&boundltype==-1)||(boundrtype!=-1&&boundltype!=-1), "Spline1DConvCubic: incorrect BoundLType/BoundRType!", _state);
if( boundltype==1||boundltype==2 )
{
ae_assert(ae_isfinite(boundl, _state), "Spline1DConvCubic: BoundL is infinite or NAN!", _state);
}
if( boundrtype==1||boundrtype==2 )
{
ae_assert(ae_isfinite(boundr, _state), "Spline1DConvCubic: BoundR is infinite or NAN!", _state);
}
/*
* check lengths of arguments
*/
ae_assert(n>=2, "Spline1DConvCubic: N<2!", _state);
ae_assert(x->cnt>=n, "Spline1DConvCubic: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DConvCubic: Length(Y)<N!", _state);
ae_assert(n2>=2, "Spline1DConvCubic: N2<2!", _state);
ae_assert(x2->cnt>=n2, "Spline1DConvCubic: Length(X2)<N2!", _state);
/*
* check and sort X/Y
*/
ylen = n;
if( boundltype==-1 )
{
ylen = n-1;
}
ae_assert(isfinitevector(x, n, _state), "Spline1DConvCubic: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, ylen, _state), "Spline1DConvCubic: Y contains infinite or NAN values!", _state);
ae_assert(isfinitevector(x2, n2, _state), "Spline1DConvCubic: X2 contains infinite or NAN values!", _state);
spline1d_heapsortppoints(x, y, &p, n, _state);
ae_assert(aredistinct(x, n, _state), "Spline1DConvCubic: at least two consequent points are too close!", _state);
/*
* set up DT (we will need it below)
*/
ae_vector_set_length(&dt, ae_maxint(n, n2, _state), _state);
/*
* sort X2:
* * use fake array DT because HeapSortPPoints() needs both integer AND real arrays
* * if we have periodic problem, wrap points
* * sort them, store permutation at P2
*/
if( boundrtype==-1&&boundltype==-1 )
{
for(i=0; i<=n2-1; i++)
{
t = x2->ptr.p_double[i];
apperiodicmap(&t, x->ptr.p_double[0], x->ptr.p_double[n-1], &t2, _state);
x2->ptr.p_double[i] = t;
}
}
spline1d_heapsortppoints(x2, &dt, &p2, n2, _state);
/*
* Now we've checked and preordered everything, so we:
* * call internal GridDiff() function to get Hermite form of spline
* * convert using internal Conv() function
* * convert Y2 back to original order
*/
spline1d_spline1dgriddiffcubicinternal(x, y, n, boundltype, boundl, boundrtype, boundr, &d, &a1, &a2, &a3, &b, &dt, _state);
spline1dconvdiffinternal(x, y, &d, n, x2, n2, y2, ae_true, &d1, ae_false, &d2, ae_false, _state);
ae_assert(dt.cnt>=n2, "Spline1DConvCubic: internal error!", _state);
for(i=0; i<=n2-1; i++)
{
dt.ptr.p_double[p2.ptr.p_int[i]] = y2->ptr.p_double[i];
}
ae_v_move(&y2->ptr.p_double[0], 1, &dt.ptr.p_double[0], 1, ae_v_len(0,n2-1));
ae_frame_leave(_state);
}
/*************************************************************************
This function solves following problem: given table y[] of function values
at old nodes x[] and new nodes x2[], it calculates and returns table of
function values y2[] and derivatives d2[] (calculated at x2[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - old spline nodes
Y - function values
X2 - new spline nodes
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points from X/Y are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
N2 - new points count:
* N2>=2
* if given, only first N2 points from X2 are used
* if not given, automatically detected from X2 size
OUTPUT PARAMETERS:
F2 - function values at X2[]
D2 - first derivatives at X2[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Function values are correctly reordered on return, so F2[I] is always
equal to S(X2[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
void spline1dconvdiffcubic(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t boundltype,
double boundl,
ae_int_t boundrtype,
double boundr,
/* Real */ ae_vector* x2,
ae_int_t n2,
/* Real */ ae_vector* y2,
/* Real */ ae_vector* d2,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_vector _x2;
ae_vector a1;
ae_vector a2;
ae_vector a3;
ae_vector b;
ae_vector d;
ae_vector dt;
ae_vector rt1;
ae_vector p;
ae_vector p2;
ae_int_t i;
ae_int_t ylen;
double t;
double t2;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&_x2, 0, sizeof(_x2));
memset(&a1, 0, sizeof(a1));
memset(&a2, 0, sizeof(a2));
memset(&a3, 0, sizeof(a3));
memset(&b, 0, sizeof(b));
memset(&d, 0, sizeof(d));
memset(&dt, 0, sizeof(dt));
memset(&rt1, 0, sizeof(rt1));
memset(&p, 0, sizeof(p));
memset(&p2, 0, sizeof(p2));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
ae_vector_init_copy(&_x2, x2, _state, ae_true);
x2 = &_x2;
ae_vector_clear(y2);
ae_vector_clear(d2);
ae_vector_init(&a1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&a2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&a3, 0, DT_REAL, _state, ae_true);
ae_vector_init(&b, 0, DT_REAL, _state, ae_true);
ae_vector_init(&d, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dt, 0, DT_REAL, _state, ae_true);
ae_vector_init(&rt1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&p, 0, DT_INT, _state, ae_true);
ae_vector_init(&p2, 0, DT_INT, _state, ae_true);
/*
* check correctness of boundary conditions
*/
ae_assert(((boundltype==-1||boundltype==0)||boundltype==1)||boundltype==2, "Spline1DConvDiffCubic: incorrect BoundLType!", _state);
ae_assert(((boundrtype==-1||boundrtype==0)||boundrtype==1)||boundrtype==2, "Spline1DConvDiffCubic: incorrect BoundRType!", _state);
ae_assert((boundrtype==-1&&boundltype==-1)||(boundrtype!=-1&&boundltype!=-1), "Spline1DConvDiffCubic: incorrect BoundLType/BoundRType!", _state);
if( boundltype==1||boundltype==2 )
{
ae_assert(ae_isfinite(boundl, _state), "Spline1DConvDiffCubic: BoundL is infinite or NAN!", _state);
}
if( boundrtype==1||boundrtype==2 )
{
ae_assert(ae_isfinite(boundr, _state), "Spline1DConvDiffCubic: BoundR is infinite or NAN!", _state);
}
/*
* check lengths of arguments
*/
ae_assert(n>=2, "Spline1DConvDiffCubic: N<2!", _state);
ae_assert(x->cnt>=n, "Spline1DConvDiffCubic: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DConvDiffCubic: Length(Y)<N!", _state);
ae_assert(n2>=2, "Spline1DConvDiffCubic: N2<2!", _state);
ae_assert(x2->cnt>=n2, "Spline1DConvDiffCubic: Length(X2)<N2!", _state);
/*
* check and sort X/Y
*/
ylen = n;
if( boundltype==-1 )
{
ylen = n-1;
}
ae_assert(isfinitevector(x, n, _state), "Spline1DConvDiffCubic: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, ylen, _state), "Spline1DConvDiffCubic: Y contains infinite or NAN values!", _state);
ae_assert(isfinitevector(x2, n2, _state), "Spline1DConvDiffCubic: X2 contains infinite or NAN values!", _state);
spline1d_heapsortppoints(x, y, &p, n, _state);
ae_assert(aredistinct(x, n, _state), "Spline1DConvDiffCubic: at least two consequent points are too close!", _state);
/*
* set up DT (we will need it below)
*/
ae_vector_set_length(&dt, ae_maxint(n, n2, _state), _state);
/*
* sort X2:
* * use fake array DT because HeapSortPPoints() needs both integer AND real arrays
* * if we have periodic problem, wrap points
* * sort them, store permutation at P2
*/
if( boundrtype==-1&&boundltype==-1 )
{
for(i=0; i<=n2-1; i++)
{
t = x2->ptr.p_double[i];
apperiodicmap(&t, x->ptr.p_double[0], x->ptr.p_double[n-1], &t2, _state);
x2->ptr.p_double[i] = t;
}
}
spline1d_heapsortppoints(x2, &dt, &p2, n2, _state);
/*
* Now we've checked and preordered everything, so we:
* * call internal GridDiff() function to get Hermite form of spline
* * convert using internal Conv() function
* * convert Y2 back to original order
*/
spline1d_spline1dgriddiffcubicinternal(x, y, n, boundltype, boundl, boundrtype, boundr, &d, &a1, &a2, &a3, &b, &dt, _state);
spline1dconvdiffinternal(x, y, &d, n, x2, n2, y2, ae_true, d2, ae_true, &rt1, ae_false, _state);
ae_assert(dt.cnt>=n2, "Spline1DConvDiffCubic: internal error!", _state);
for(i=0; i<=n2-1; i++)
{
dt.ptr.p_double[p2.ptr.p_int[i]] = y2->ptr.p_double[i];
}
ae_v_move(&y2->ptr.p_double[0], 1, &dt.ptr.p_double[0], 1, ae_v_len(0,n2-1));
for(i=0; i<=n2-1; i++)
{
dt.ptr.p_double[p2.ptr.p_int[i]] = d2->ptr.p_double[i];
}
ae_v_move(&d2->ptr.p_double[0], 1, &dt.ptr.p_double[0], 1, ae_v_len(0,n2-1));
ae_frame_leave(_state);
}
/*************************************************************************
This function solves following problem: given table y[] of function values
at old nodes x[] and new nodes x2[], it calculates and returns table of
function values y2[], first and second derivatives d2[] and dd2[]
(calculated at x2[]).
This function yields same result as Spline1DBuildCubic() call followed by
sequence of Spline1DDiff() calls, but it can be several times faster when
called for ordered X[] and X2[].
INPUT PARAMETERS:
X - old spline nodes
Y - function values
X2 - new spline nodes
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points from X/Y are used
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundLType - boundary condition type for the left boundary
BoundL - left boundary condition (first or second derivative,
depending on the BoundLType)
BoundRType - boundary condition type for the right boundary
BoundR - right boundary condition (first or second derivative,
depending on the BoundRType)
N2 - new points count:
* N2>=2
* if given, only first N2 points from X2 are used
* if not given, automatically detected from X2 size
OUTPUT PARAMETERS:
F2 - function values at X2[]
D2 - first derivatives at X2[]
DD2 - second derivatives at X2[]
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
Function values are correctly reordered on return, so F2[I] is always
equal to S(X2[I]) independently of points order.
SETTING BOUNDARY VALUES:
The BoundLType/BoundRType parameters can have the following values:
* -1, which corresonds to the periodic (cyclic) boundary conditions.
In this case:
* both BoundLType and BoundRType must be equal to -1.
* BoundL/BoundR are ignored
* Y[last] is ignored (it is assumed to be equal to Y[first]).
* 0, which corresponds to the parabolically terminated spline
(BoundL and/or BoundR are ignored).
* 1, which corresponds to the first derivative boundary condition
* 2, which corresponds to the second derivative boundary condition
* by default, BoundType=0 is used
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
void spline1dconvdiff2cubic(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t boundltype,
double boundl,
ae_int_t boundrtype,
double boundr,
/* Real */ ae_vector* x2,
ae_int_t n2,
/* Real */ ae_vector* y2,
/* Real */ ae_vector* d2,
/* Real */ ae_vector* dd2,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_vector _x2;
ae_vector a1;
ae_vector a2;
ae_vector a3;
ae_vector b;
ae_vector d;
ae_vector dt;
ae_vector p;
ae_vector p2;
ae_int_t i;
ae_int_t ylen;
double t;
double t2;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&_x2, 0, sizeof(_x2));
memset(&a1, 0, sizeof(a1));
memset(&a2, 0, sizeof(a2));
memset(&a3, 0, sizeof(a3));
memset(&b, 0, sizeof(b));
memset(&d, 0, sizeof(d));
memset(&dt, 0, sizeof(dt));
memset(&p, 0, sizeof(p));
memset(&p2, 0, sizeof(p2));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
ae_vector_init_copy(&_x2, x2, _state, ae_true);
x2 = &_x2;
ae_vector_clear(y2);
ae_vector_clear(d2);
ae_vector_clear(dd2);
ae_vector_init(&a1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&a2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&a3, 0, DT_REAL, _state, ae_true);
ae_vector_init(&b, 0, DT_REAL, _state, ae_true);
ae_vector_init(&d, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dt, 0, DT_REAL, _state, ae_true);
ae_vector_init(&p, 0, DT_INT, _state, ae_true);
ae_vector_init(&p2, 0, DT_INT, _state, ae_true);
/*
* check correctness of boundary conditions
*/
ae_assert(((boundltype==-1||boundltype==0)||boundltype==1)||boundltype==2, "Spline1DConvDiff2Cubic: incorrect BoundLType!", _state);
ae_assert(((boundrtype==-1||boundrtype==0)||boundrtype==1)||boundrtype==2, "Spline1DConvDiff2Cubic: incorrect BoundRType!", _state);
ae_assert((boundrtype==-1&&boundltype==-1)||(boundrtype!=-1&&boundltype!=-1), "Spline1DConvDiff2Cubic: incorrect BoundLType/BoundRType!", _state);
if( boundltype==1||boundltype==2 )
{
ae_assert(ae_isfinite(boundl, _state), "Spline1DConvDiff2Cubic: BoundL is infinite or NAN!", _state);
}
if( boundrtype==1||boundrtype==2 )
{
ae_assert(ae_isfinite(boundr, _state), "Spline1DConvDiff2Cubic: BoundR is infinite or NAN!", _state);
}
/*
* check lengths of arguments
*/
ae_assert(n>=2, "Spline1DConvDiff2Cubic: N<2!", _state);
ae_assert(x->cnt>=n, "Spline1DConvDiff2Cubic: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DConvDiff2Cubic: Length(Y)<N!", _state);
ae_assert(n2>=2, "Spline1DConvDiff2Cubic: N2<2!", _state);
ae_assert(x2->cnt>=n2, "Spline1DConvDiff2Cubic: Length(X2)<N2!", _state);
/*
* check and sort X/Y
*/
ylen = n;
if( boundltype==-1 )
{
ylen = n-1;
}
ae_assert(isfinitevector(x, n, _state), "Spline1DConvDiff2Cubic: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, ylen, _state), "Spline1DConvDiff2Cubic: Y contains infinite or NAN values!", _state);
ae_assert(isfinitevector(x2, n2, _state), "Spline1DConvDiff2Cubic: X2 contains infinite or NAN values!", _state);
spline1d_heapsortppoints(x, y, &p, n, _state);
ae_assert(aredistinct(x, n, _state), "Spline1DConvDiff2Cubic: at least two consequent points are too close!", _state);
/*
* set up DT (we will need it below)
*/
ae_vector_set_length(&dt, ae_maxint(n, n2, _state), _state);
/*
* sort X2:
* * use fake array DT because HeapSortPPoints() needs both integer AND real arrays
* * if we have periodic problem, wrap points
* * sort them, store permutation at P2
*/
if( boundrtype==-1&&boundltype==-1 )
{
for(i=0; i<=n2-1; i++)
{
t = x2->ptr.p_double[i];
apperiodicmap(&t, x->ptr.p_double[0], x->ptr.p_double[n-1], &t2, _state);
x2->ptr.p_double[i] = t;
}
}
spline1d_heapsortppoints(x2, &dt, &p2, n2, _state);
/*
* Now we've checked and preordered everything, so we:
* * call internal GridDiff() function to get Hermite form of spline
* * convert using internal Conv() function
* * convert Y2 back to original order
*/
spline1d_spline1dgriddiffcubicinternal(x, y, n, boundltype, boundl, boundrtype, boundr, &d, &a1, &a2, &a3, &b, &dt, _state);
spline1dconvdiffinternal(x, y, &d, n, x2, n2, y2, ae_true, d2, ae_true, dd2, ae_true, _state);
ae_assert(dt.cnt>=n2, "Spline1DConvDiff2Cubic: internal error!", _state);
for(i=0; i<=n2-1; i++)
{
dt.ptr.p_double[p2.ptr.p_int[i]] = y2->ptr.p_double[i];
}
ae_v_move(&y2->ptr.p_double[0], 1, &dt.ptr.p_double[0], 1, ae_v_len(0,n2-1));
for(i=0; i<=n2-1; i++)
{
dt.ptr.p_double[p2.ptr.p_int[i]] = d2->ptr.p_double[i];
}
ae_v_move(&d2->ptr.p_double[0], 1, &dt.ptr.p_double[0], 1, ae_v_len(0,n2-1));
for(i=0; i<=n2-1; i++)
{
dt.ptr.p_double[p2.ptr.p_int[i]] = dd2->ptr.p_double[i];
}
ae_v_move(&dd2->ptr.p_double[0], 1, &dt.ptr.p_double[0], 1, ae_v_len(0,n2-1));
ae_frame_leave(_state);
}
/*************************************************************************
This subroutine builds Catmull-Rom spline interpolant.
INPUT PARAMETERS:
X - spline nodes, array[0..N-1].
Y - function values, array[0..N-1].
OPTIONAL PARAMETERS:
N - points count:
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
BoundType - boundary condition type:
* -1 for periodic boundary condition
* 0 for parabolically terminated spline (default)
Tension - tension parameter:
* tension=0 corresponds to classic Catmull-Rom spline (default)
* 0<tension<1 corresponds to more general form - cardinal spline
OUTPUT PARAMETERS:
C - spline interpolant
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS:
Problems with periodic boundary conditions have Y[first_point]=Y[last_point].
However, this subroutine doesn't require you to specify equal values for
the first and last points - it automatically forces them to be equal by
copying Y[first_point] (corresponds to the leftmost, minimal X[]) to
Y[last_point]. However it is recommended to pass consistent values of Y[],
i.e. to make Y[first_point]=Y[last_point].
-- ALGLIB PROJECT --
Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dbuildcatmullrom(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t boundtype,
double tension,
spline1dinterpolant* c,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_vector d;
ae_int_t i;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&d, 0, sizeof(d));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
_spline1dinterpolant_clear(c);
ae_vector_init(&d, 0, DT_REAL, _state, ae_true);
ae_assert(n>=2, "Spline1DBuildCatmullRom: N<2!", _state);
ae_assert(boundtype==-1||boundtype==0, "Spline1DBuildCatmullRom: incorrect BoundType!", _state);
ae_assert(ae_fp_greater_eq(tension,(double)(0)), "Spline1DBuildCatmullRom: Tension<0!", _state);
ae_assert(ae_fp_less_eq(tension,(double)(1)), "Spline1DBuildCatmullRom: Tension>1!", _state);
ae_assert(x->cnt>=n, "Spline1DBuildCatmullRom: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DBuildCatmullRom: Length(Y)<N!", _state);
/*
* check and sort points
*/
ae_assert(isfinitevector(x, n, _state), "Spline1DBuildCatmullRom: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, n, _state), "Spline1DBuildCatmullRom: Y contains infinite or NAN values!", _state);
spline1d_heapsortpoints(x, y, n, _state);
ae_assert(aredistinct(x, n, _state), "Spline1DBuildCatmullRom: at least two consequent points are too close!", _state);
/*
* Special cases:
* * N=2, parabolic terminated boundary condition on both ends
* * N=2, periodic boundary condition
*/
if( n==2&&boundtype==0 )
{
/*
* Just linear spline
*/
spline1dbuildlinear(x, y, n, c, _state);
ae_frame_leave(_state);
return;
}
if( n==2&&boundtype==-1 )
{
/*
* Same as cubic spline with periodic conditions
*/
spline1dbuildcubic(x, y, n, -1, 0.0, -1, 0.0, c, _state);
ae_frame_leave(_state);
return;
}
/*
* Periodic or non-periodic boundary conditions
*/
if( boundtype==-1 )
{
/*
* Periodic boundary conditions
*/
y->ptr.p_double[n-1] = y->ptr.p_double[0];
ae_vector_set_length(&d, n, _state);
d.ptr.p_double[0] = (y->ptr.p_double[1]-y->ptr.p_double[n-2])/(2*(x->ptr.p_double[1]-x->ptr.p_double[0]+x->ptr.p_double[n-1]-x->ptr.p_double[n-2]));
for(i=1; i<=n-2; i++)
{
d.ptr.p_double[i] = (1-tension)*(y->ptr.p_double[i+1]-y->ptr.p_double[i-1])/(x->ptr.p_double[i+1]-x->ptr.p_double[i-1]);
}
d.ptr.p_double[n-1] = d.ptr.p_double[0];
/*
* Now problem is reduced to the cubic Hermite spline
*/
spline1dbuildhermite(x, y, &d, n, c, _state);
c->periodic = ae_true;
}
else
{
/*
* Non-periodic boundary conditions
*/
ae_vector_set_length(&d, n, _state);
for(i=1; i<=n-2; i++)
{
d.ptr.p_double[i] = (1-tension)*(y->ptr.p_double[i+1]-y->ptr.p_double[i-1])/(x->ptr.p_double[i+1]-x->ptr.p_double[i-1]);
}
d.ptr.p_double[0] = 2*(y->ptr.p_double[1]-y->ptr.p_double[0])/(x->ptr.p_double[1]-x->ptr.p_double[0])-d.ptr.p_double[1];
d.ptr.p_double[n-1] = 2*(y->ptr.p_double[n-1]-y->ptr.p_double[n-2])/(x->ptr.p_double[n-1]-x->ptr.p_double[n-2])-d.ptr.p_double[n-2];
/*
* Now problem is reduced to the cubic Hermite spline
*/
spline1dbuildhermite(x, y, &d, n, c, _state);
}
ae_frame_leave(_state);
}
/*************************************************************************
This subroutine builds Hermite spline interpolant.
INPUT PARAMETERS:
X - spline nodes, array[0..N-1]
Y - function values, array[0..N-1]
D - derivatives, array[0..N-1]
N - points count (optional):
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
OUTPUT PARAMETERS:
C - spline interpolant.
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
-- ALGLIB PROJECT --
Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dbuildhermite(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* d,
ae_int_t n,
spline1dinterpolant* c,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_vector _d;
ae_int_t i;
double delta;
double delta2;
double delta3;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&_d, 0, sizeof(_d));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
ae_vector_init_copy(&_d, d, _state, ae_true);
d = &_d;
_spline1dinterpolant_clear(c);
ae_assert(n>=2, "Spline1DBuildHermite: N<2!", _state);
ae_assert(x->cnt>=n, "Spline1DBuildHermite: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DBuildHermite: Length(Y)<N!", _state);
ae_assert(d->cnt>=n, "Spline1DBuildHermite: Length(D)<N!", _state);
/*
* check and sort points
*/
ae_assert(isfinitevector(x, n, _state), "Spline1DBuildHermite: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, n, _state), "Spline1DBuildHermite: Y contains infinite or NAN values!", _state);
ae_assert(isfinitevector(d, n, _state), "Spline1DBuildHermite: D contains infinite or NAN values!", _state);
heapsortdpoints(x, y, d, n, _state);
ae_assert(aredistinct(x, n, _state), "Spline1DBuildHermite: at least two consequent points are too close!", _state);
/*
* Build
*/
ae_vector_set_length(&c->x, n, _state);
ae_vector_set_length(&c->c, 4*(n-1)+2, _state);
c->periodic = ae_false;
c->k = 3;
c->n = n;
c->continuity = 1;
for(i=0; i<=n-1; i++)
{
c->x.ptr.p_double[i] = x->ptr.p_double[i];
}
for(i=0; i<=n-2; i++)
{
delta = x->ptr.p_double[i+1]-x->ptr.p_double[i];
delta2 = ae_sqr(delta, _state);
delta3 = delta*delta2;
c->c.ptr.p_double[4*i+0] = y->ptr.p_double[i];
c->c.ptr.p_double[4*i+1] = d->ptr.p_double[i];
c->c.ptr.p_double[4*i+2] = (3*(y->ptr.p_double[i+1]-y->ptr.p_double[i])-2*d->ptr.p_double[i]*delta-d->ptr.p_double[i+1]*delta)/delta2;
c->c.ptr.p_double[4*i+3] = (2*(y->ptr.p_double[i]-y->ptr.p_double[i+1])+d->ptr.p_double[i]*delta+d->ptr.p_double[i+1]*delta)/delta3;
}
c->c.ptr.p_double[4*(n-1)+0] = y->ptr.p_double[n-1];
c->c.ptr.p_double[4*(n-1)+1] = d->ptr.p_double[n-1];
ae_frame_leave(_state);
}
/*************************************************************************
This subroutine builds Akima spline interpolant
INPUT PARAMETERS:
X - spline nodes, array[0..N-1]
Y - function values, array[0..N-1]
N - points count (optional):
* N>=2
* if given, only first N points are used to build spline
* if not given, automatically detected from X/Y sizes
(len(X) must be equal to len(Y))
OUTPUT PARAMETERS:
C - spline interpolant
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
-- ALGLIB PROJECT --
Copyright 24.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dbuildakima(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
spline1dinterpolant* c,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_int_t i;
ae_vector d;
ae_vector w;
ae_vector diff;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&d, 0, sizeof(d));
memset(&w, 0, sizeof(w));
memset(&diff, 0, sizeof(diff));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
_spline1dinterpolant_clear(c);
ae_vector_init(&d, 0, DT_REAL, _state, ae_true);
ae_vector_init(&w, 0, DT_REAL, _state, ae_true);
ae_vector_init(&diff, 0, DT_REAL, _state, ae_true);
ae_assert(n>=2, "Spline1DBuildAkima: N<2!", _state);
ae_assert(x->cnt>=n, "Spline1DBuildAkima: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DBuildAkima: Length(Y)<N!", _state);
/*
* check and sort points
*/
ae_assert(isfinitevector(x, n, _state), "Spline1DBuildAkima: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, n, _state), "Spline1DBuildAkima: Y contains infinite or NAN values!", _state);
spline1d_heapsortpoints(x, y, n, _state);
ae_assert(aredistinct(x, n, _state), "Spline1DBuildAkima: at least two consequent points are too close!", _state);
/*
* Handle special cases: N=2, N=3, N=4
*/
if( n<=4 )
{
spline1dbuildcubic(x, y, n, 0, 0.0, 0, 0.0, c, _state);
ae_frame_leave(_state);
return;
}
/*
* Prepare W (weights), Diff (divided differences)
*/
ae_vector_set_length(&w, n-1, _state);
ae_vector_set_length(&diff, n-1, _state);
for(i=0; i<=n-2; i++)
{
diff.ptr.p_double[i] = (y->ptr.p_double[i+1]-y->ptr.p_double[i])/(x->ptr.p_double[i+1]-x->ptr.p_double[i]);
}
for(i=1; i<=n-2; i++)
{
w.ptr.p_double[i] = ae_fabs(diff.ptr.p_double[i]-diff.ptr.p_double[i-1], _state);
}
/*
* Prepare Hermite interpolation scheme
*/
ae_vector_set_length(&d, n, _state);
for(i=2; i<=n-3; i++)
{
if( ae_fp_neq(ae_fabs(w.ptr.p_double[i-1], _state)+ae_fabs(w.ptr.p_double[i+1], _state),(double)(0)) )
{
d.ptr.p_double[i] = (w.ptr.p_double[i+1]*diff.ptr.p_double[i-1]+w.ptr.p_double[i-1]*diff.ptr.p_double[i])/(w.ptr.p_double[i+1]+w.ptr.p_double[i-1]);
}
else
{
d.ptr.p_double[i] = ((x->ptr.p_double[i+1]-x->ptr.p_double[i])*diff.ptr.p_double[i-1]+(x->ptr.p_double[i]-x->ptr.p_double[i-1])*diff.ptr.p_double[i])/(x->ptr.p_double[i+1]-x->ptr.p_double[i-1]);
}
}
d.ptr.p_double[0] = spline1d_diffthreepoint(x->ptr.p_double[0], x->ptr.p_double[0], y->ptr.p_double[0], x->ptr.p_double[1], y->ptr.p_double[1], x->ptr.p_double[2], y->ptr.p_double[2], _state);
d.ptr.p_double[1] = spline1d_diffthreepoint(x->ptr.p_double[1], x->ptr.p_double[0], y->ptr.p_double[0], x->ptr.p_double[1], y->ptr.p_double[1], x->ptr.p_double[2], y->ptr.p_double[2], _state);
d.ptr.p_double[n-2] = spline1d_diffthreepoint(x->ptr.p_double[n-2], x->ptr.p_double[n-3], y->ptr.p_double[n-3], x->ptr.p_double[n-2], y->ptr.p_double[n-2], x->ptr.p_double[n-1], y->ptr.p_double[n-1], _state);
d.ptr.p_double[n-1] = spline1d_diffthreepoint(x->ptr.p_double[n-1], x->ptr.p_double[n-3], y->ptr.p_double[n-3], x->ptr.p_double[n-2], y->ptr.p_double[n-2], x->ptr.p_double[n-1], y->ptr.p_double[n-1], _state);
/*
* Build Akima spline using Hermite interpolation scheme
*/
spline1dbuildhermite(x, y, &d, n, c, _state);
ae_frame_leave(_state);
}
/*************************************************************************
This subroutine calculates the value of the spline at the given point X.
INPUT PARAMETERS:
C - spline interpolant
X - point
Result:
S(x)
-- ALGLIB PROJECT --
Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
double spline1dcalc(spline1dinterpolant* c, double x, ae_state *_state)
{
ae_int_t l;
ae_int_t r;
ae_int_t m;
double t;
double result;
ae_assert(c->k==3, "Spline1DCalc: internal error", _state);
ae_assert(!ae_isinf(x, _state), "Spline1DCalc: infinite X!", _state);
/*
* special case: NaN
*/
if( ae_isnan(x, _state) )
{
result = _state->v_nan;
return result;
}
/*
* correct if periodic
*/
if( c->periodic )
{
apperiodicmap(&x, c->x.ptr.p_double[0], c->x.ptr.p_double[c->n-1], &t, _state);
}
/*
* Binary search in the [ x[0], ..., x[n-2] ] (x[n-1] is not included)
*/
l = 0;
r = c->n-2+1;
while(l!=r-1)
{
m = (l+r)/2;
if( c->x.ptr.p_double[m]>=x )
{
r = m;
}
else
{
l = m;
}
}
/*
* Interpolation
*/
x = x-c->x.ptr.p_double[l];
m = 4*l;
result = c->c.ptr.p_double[m]+x*(c->c.ptr.p_double[m+1]+x*(c->c.ptr.p_double[m+2]+x*c->c.ptr.p_double[m+3]));
return result;
}
/*************************************************************************
This subroutine differentiates the spline.
INPUT PARAMETERS:
C - spline interpolant.
X - point
Result:
S - S(x)
DS - S'(x)
D2S - S''(x)
-- ALGLIB PROJECT --
Copyright 24.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1ddiff(spline1dinterpolant* c,
double x,
double* s,
double* ds,
double* d2s,
ae_state *_state)
{
ae_int_t l;
ae_int_t r;
ae_int_t m;
double t;
*s = 0;
*ds = 0;
*d2s = 0;
ae_assert(c->k==3, "Spline1DDiff: internal error", _state);
ae_assert(!ae_isinf(x, _state), "Spline1DDiff: infinite X!", _state);
/*
* special case: NaN
*/
if( ae_isnan(x, _state) )
{
*s = _state->v_nan;
*ds = _state->v_nan;
*d2s = _state->v_nan;
return;
}
/*
* correct if periodic
*/
if( c->periodic )
{
apperiodicmap(&x, c->x.ptr.p_double[0], c->x.ptr.p_double[c->n-1], &t, _state);
}
/*
* Binary search
*/
l = 0;
r = c->n-2+1;
while(l!=r-1)
{
m = (l+r)/2;
if( c->x.ptr.p_double[m]>=x )
{
r = m;
}
else
{
l = m;
}
}
/*
* Differentiation
*/
x = x-c->x.ptr.p_double[l];
m = 4*l;
*s = c->c.ptr.p_double[m]+x*(c->c.ptr.p_double[m+1]+x*(c->c.ptr.p_double[m+2]+x*c->c.ptr.p_double[m+3]));
*ds = c->c.ptr.p_double[m+1]+2*x*c->c.ptr.p_double[m+2]+3*ae_sqr(x, _state)*c->c.ptr.p_double[m+3];
*d2s = 2*c->c.ptr.p_double[m+2]+6*x*c->c.ptr.p_double[m+3];
}
/*************************************************************************
This subroutine makes the copy of the spline.
INPUT PARAMETERS:
C - spline interpolant.
Result:
CC - spline copy
-- ALGLIB PROJECT --
Copyright 29.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dcopy(spline1dinterpolant* c,
spline1dinterpolant* cc,
ae_state *_state)
{
ae_int_t s;
_spline1dinterpolant_clear(cc);
cc->periodic = c->periodic;
cc->n = c->n;
cc->k = c->k;
cc->continuity = c->continuity;
ae_vector_set_length(&cc->x, cc->n, _state);
ae_v_move(&cc->x.ptr.p_double[0], 1, &c->x.ptr.p_double[0], 1, ae_v_len(0,cc->n-1));
s = c->c.cnt;
ae_vector_set_length(&cc->c, s, _state);
ae_v_move(&cc->c.ptr.p_double[0], 1, &c->c.ptr.p_double[0], 1, ae_v_len(0,s-1));
}
/*************************************************************************
This subroutine unpacks the spline into the coefficients table.
INPUT PARAMETERS:
C - spline interpolant.
X - point
OUTPUT PARAMETERS:
Tbl - coefficients table, unpacked format, array[0..N-2, 0..5].
For I = 0...N-2:
Tbl[I,0] = X[i]
Tbl[I,1] = X[i+1]
Tbl[I,2] = C0
Tbl[I,3] = C1
Tbl[I,4] = C2
Tbl[I,5] = C3
On [x[i], x[i+1]] spline is equals to:
S(x) = C0 + C1*t + C2*t^2 + C3*t^3
t = x-x[i]
NOTE:
You can rebuild spline with Spline1DBuildHermite() function, which
accepts as inputs function values and derivatives at nodes, which are
easy to calculate when you have coefficients.
-- ALGLIB PROJECT --
Copyright 29.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dunpack(spline1dinterpolant* c,
ae_int_t* n,
/* Real */ ae_matrix* tbl,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
*n = 0;
ae_matrix_clear(tbl);
ae_matrix_set_length(tbl, c->n-2+1, 2+c->k+1, _state);
*n = c->n;
/*
* Fill
*/
for(i=0; i<=*n-2; i++)
{
tbl->ptr.pp_double[i][0] = c->x.ptr.p_double[i];
tbl->ptr.pp_double[i][1] = c->x.ptr.p_double[i+1];
for(j=0; j<=c->k; j++)
{
tbl->ptr.pp_double[i][2+j] = c->c.ptr.p_double[(c->k+1)*i+j];
}
}
}
/*************************************************************************
This subroutine performs linear transformation of the spline argument.
INPUT PARAMETERS:
C - spline interpolant.
A, B- transformation coefficients: x = A*t + B
Result:
C - transformed spline
-- ALGLIB PROJECT --
Copyright 30.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dlintransx(spline1dinterpolant* c,
double a,
double b,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_int_t n;
double v;
double dv;
double d2v;
ae_vector x;
ae_vector y;
ae_vector d;
ae_bool isperiodic;
ae_int_t contval;
ae_frame_make(_state, &_frame_block);
memset(&x, 0, sizeof(x));
memset(&y, 0, sizeof(y));
memset(&d, 0, sizeof(d));
ae_vector_init(&x, 0, DT_REAL, _state, ae_true);
ae_vector_init(&y, 0, DT_REAL, _state, ae_true);
ae_vector_init(&d, 0, DT_REAL, _state, ae_true);
ae_assert(c->k==3, "Spline1DLinTransX: internal error", _state);
n = c->n;
ae_vector_set_length(&x, n, _state);
ae_vector_set_length(&y, n, _state);
ae_vector_set_length(&d, n, _state);
/*
* Unpack, X, Y, dY/dX.
* Scale and pack with Spline1DBuildHermite again.
*/
if( ae_fp_eq(a,(double)(0)) )
{
/*
* Special case: A=0
*/
v = spline1dcalc(c, b, _state);
for(i=0; i<=n-1; i++)
{
x.ptr.p_double[i] = c->x.ptr.p_double[i];
y.ptr.p_double[i] = v;
d.ptr.p_double[i] = 0.0;
}
}
else
{
/*
* General case, A<>0
*/
for(i=0; i<=n-1; i++)
{
x.ptr.p_double[i] = c->x.ptr.p_double[i];
spline1ddiff(c, x.ptr.p_double[i], &v, &dv, &d2v, _state);
x.ptr.p_double[i] = (x.ptr.p_double[i]-b)/a;
y.ptr.p_double[i] = v;
d.ptr.p_double[i] = a*dv;
}
}
isperiodic = c->periodic;
contval = c->continuity;
if( contval>0 )
{
spline1dbuildhermite(&x, &y, &d, n, c, _state);
}
else
{
spline1dbuildlinear(&x, &y, n, c, _state);
}
c->periodic = isperiodic;
c->continuity = contval;
ae_frame_leave(_state);
}
/*************************************************************************
This subroutine performs linear transformation of the spline.
INPUT PARAMETERS:
C - spline interpolant.
A, B- transformation coefficients: S2(x) = A*S(x) + B
Result:
C - transformed spline
-- ALGLIB PROJECT --
Copyright 30.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline1dlintransy(spline1dinterpolant* c,
double a,
double b,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
ae_int_t n;
ae_assert(c->k==3, "Spline1DLinTransX: internal error", _state);
n = c->n;
for(i=0; i<=n-2; i++)
{
c->c.ptr.p_double[4*i] = a*c->c.ptr.p_double[4*i]+b;
for(j=1; j<=3; j++)
{
c->c.ptr.p_double[4*i+j] = a*c->c.ptr.p_double[4*i+j];
}
}
c->c.ptr.p_double[4*(n-1)+0] = a*c->c.ptr.p_double[4*(n-1)+0]+b;
c->c.ptr.p_double[4*(n-1)+1] = a*c->c.ptr.p_double[4*(n-1)+1];
}
/*************************************************************************
This subroutine integrates the spline.
INPUT PARAMETERS:
C - spline interpolant.
X - right bound of the integration interval [a, x],
here 'a' denotes min(x[])
Result:
integral(S(t)dt,a,x)
-- ALGLIB PROJECT --
Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
double spline1dintegrate(spline1dinterpolant* c,
double x,
ae_state *_state)
{
ae_int_t n;
ae_int_t i;
ae_int_t j;
ae_int_t l;
ae_int_t r;
ae_int_t m;
double w;
double v;
double t;
double intab;
double additionalterm;
double result;
n = c->n;
/*
* Periodic splines require special treatment. We make
* following transformation:
*
* integral(S(t)dt,A,X) = integral(S(t)dt,A,Z)+AdditionalTerm
*
* here X may lie outside of [A,B], Z lies strictly in [A,B],
* AdditionalTerm is equals to integral(S(t)dt,A,B) times some
* integer number (may be zero).
*/
if( c->periodic&&(ae_fp_less(x,c->x.ptr.p_double[0])||ae_fp_greater(x,c->x.ptr.p_double[c->n-1])) )
{
/*
* compute integral(S(x)dx,A,B)
*/
intab = (double)(0);
for(i=0; i<=c->n-2; i++)
{
w = c->x.ptr.p_double[i+1]-c->x.ptr.p_double[i];
m = (c->k+1)*i;
intab = intab+c->c.ptr.p_double[m]*w;
v = w;
for(j=1; j<=c->k; j++)
{
v = v*w;
intab = intab+c->c.ptr.p_double[m+j]*v/(j+1);
}
}
/*
* map X into [A,B]
*/
apperiodicmap(&x, c->x.ptr.p_double[0], c->x.ptr.p_double[c->n-1], &t, _state);
additionalterm = t*intab;
}
else
{
additionalterm = (double)(0);
}
/*
* Binary search in the [ x[0], ..., x[n-2] ] (x[n-1] is not included)
*/
l = 0;
r = n-2+1;
while(l!=r-1)
{
m = (l+r)/2;
if( ae_fp_greater_eq(c->x.ptr.p_double[m],x) )
{
r = m;
}
else
{
l = m;
}
}
/*
* Integration
*/
result = (double)(0);
for(i=0; i<=l-1; i++)
{
w = c->x.ptr.p_double[i+1]-c->x.ptr.p_double[i];
m = (c->k+1)*i;
result = result+c->c.ptr.p_double[m]*w;
v = w;
for(j=1; j<=c->k; j++)
{
v = v*w;
result = result+c->c.ptr.p_double[m+j]*v/(j+1);
}
}
w = x-c->x.ptr.p_double[l];
m = (c->k+1)*l;
v = w;
result = result+c->c.ptr.p_double[m]*w;
for(j=1; j<=c->k; j++)
{
v = v*w;
result = result+c->c.ptr.p_double[m+j]*v/(j+1);
}
result = result+additionalterm;
return result;
}
/*************************************************************************
Fitting by smoothing (penalized) cubic spline.
This function approximates N scattered points (some of X[] may be equal to
each other) by cubic spline with M nodes at equidistant grid spanning
interval [min(x,xc),max(x,xc)].
The problem is regularized by adding nonlinearity penalty to usual least
squares penalty function:
MERIT_FUNC = F_LS + F_NL
where F_LS is a least squares error term, and F_NL is a nonlinearity
penalty which is roughly proportional to LambdaNS*integral{ S''(x)^2*dx }.
Algorithm applies automatic renormalization of F_NL which makes penalty
term roughly invariant to scaling of X[] and changes in M.
This function is a new edition of penalized regression spline fitting,
a fast and compact one which needs much less resources that its previous
version: just O(maxMN) memory and O(maxMN*log(maxMN)) time.
NOTE: it is OK to run this function with both M<<N and M>>N; say, it is
possible to process 100 points with 1000-node spline.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
N - number of points (optional):
* N>0
* if given, only first N elements of X/Y are processed
* if not given, automatically determined from lengths
M - number of basis functions ( = number_of_nodes), M>=4.
LambdaNS - LambdaNS>=0, regularization constant passed by user.
It penalizes nonlinearity in the regression spline.
Possible values to start from are 0.00001, 0.1, 1
OUTPUT PARAMETERS:
S - spline interpolant.
Rep - Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
-- ALGLIB PROJECT --
Copyright 27.08.2019 by Bochkanov Sergey
*************************************************************************/
void spline1dfit(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t m,
double lambdans,
spline1dinterpolant* s,
spline1dfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_int_t bfrad;
double xa;
double xb;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t k0;
ae_int_t k1;
double v;
double dv;
double d2v;
ae_int_t gridexpansion;
ae_vector xywork;
ae_matrix vterm;
ae_vector sx;
ae_vector sy;
ae_vector sdy;
ae_vector tmpx;
ae_vector tmpy;
spline1dinterpolant basis1;
sparsematrix av;
sparsematrix ah;
sparsematrix ata;
ae_vector targets;
double meany;
ae_int_t lsqrcnt;
ae_int_t nrel;
double rss;
double tss;
ae_int_t arows;
ae_vector tmp0;
ae_vector tmp1;
linlsqrstate solver;
linlsqrreport srep;
double creg;
double mxata;
ae_int_t bw;
ae_vector nzidx;
ae_vector nzval;
ae_int_t nzcnt;
double scaletargetsby;
double scalepenaltyby;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&xywork, 0, sizeof(xywork));
memset(&vterm, 0, sizeof(vterm));
memset(&sx, 0, sizeof(sx));
memset(&sy, 0, sizeof(sy));
memset(&sdy, 0, sizeof(sdy));
memset(&tmpx, 0, sizeof(tmpx));
memset(&tmpy, 0, sizeof(tmpy));
memset(&basis1, 0, sizeof(basis1));
memset(&av, 0, sizeof(av));
memset(&ah, 0, sizeof(ah));
memset(&ata, 0, sizeof(ata));
memset(&targets, 0, sizeof(targets));
memset(&tmp0, 0, sizeof(tmp0));
memset(&tmp1, 0, sizeof(tmp1));
memset(&solver, 0, sizeof(solver));
memset(&srep, 0, sizeof(srep));
memset(&nzidx, 0, sizeof(nzidx));
memset(&nzval, 0, sizeof(nzval));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
_spline1dinterpolant_clear(s);
_spline1dfitreport_clear(rep);
ae_vector_init(&xywork, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&vterm, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sy, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sdy, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmpx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmpy, 0, DT_REAL, _state, ae_true);
_spline1dinterpolant_init(&basis1, _state, ae_true);
_sparsematrix_init(&av, _state, ae_true);
_sparsematrix_init(&ah, _state, ae_true);
_sparsematrix_init(&ata, _state, ae_true);
ae_vector_init(&targets, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp1, 0, DT_REAL, _state, ae_true);
_linlsqrstate_init(&solver, _state, ae_true);
_linlsqrreport_init(&srep, _state, ae_true);
ae_vector_init(&nzidx, 0, DT_INT, _state, ae_true);
ae_vector_init(&nzval, 0, DT_REAL, _state, ae_true);
ae_assert(n>=1, "Spline1DFit: N<1!", _state);
ae_assert(m>=1, "Spline1DFit: M<1!", _state);
ae_assert(x->cnt>=n, "Spline1DFit: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DFit: Length(Y)<N!", _state);
ae_assert(isfinitevector(x, n, _state), "Spline1DFit: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, n, _state), "Spline1DFit: Y contains infinite or NAN values!", _state);
ae_assert(ae_isfinite(lambdans, _state), "Spline1DFit: LambdaNS is infinite!", _state);
ae_assert(ae_fp_greater_eq(lambdans,(double)(0)), "Spline1DFit: LambdaNS<0!", _state);
bfrad = 2;
lsqrcnt = 10;
/*
* Sort points.
* Determine actual area size, make sure that XA<XB
*/
tagsortfastr(x, y, &tmpx, &tmpy, n, _state);
xa = x->ptr.p_double[0];
xb = x->ptr.p_double[n-1];
if( ae_fp_eq(xa,xb) )
{
v = xa;
if( ae_fp_greater_eq(v,(double)(0)) )
{
xa = v/2-1;
xb = v*2+1;
}
else
{
xa = v*2-1;
xb = v/2+1;
}
}
ae_assert(ae_fp_less(xa,xb), "Spline1DFit: integrity error", _state);
/*
* Perform a grid correction according to current grid expansion size.
*/
m = ae_maxint(m, 4, _state);
gridexpansion = 1;
v = (xb-xa)/m;
xa = xa-v*gridexpansion;
xb = xb+v*gridexpansion;
m = m+2*gridexpansion;
/*
* Convert X/Y to work representation, remove linear trend (in
* order to improve condition number).
*
* Compute total-sum-of-squares (needed later for R2 coefficient).
*/
ae_vector_set_length(&xywork, 2*n, _state);
for(i=0; i<=n-1; i++)
{
xywork.ptr.p_double[2*i+0] = (x->ptr.p_double[i]-xa)/(xb-xa);
xywork.ptr.p_double[2*i+1] = y->ptr.p_double[i];
}
buildpriorterm1(&xywork, n, 1, 1, 1, 0.0, &vterm, _state);
meany = (double)(0);
for(i=0; i<=n-1; i++)
{
meany = meany+y->ptr.p_double[i];
}
meany = meany/n;
tss = (double)(0);
for(i=0; i<=n-1; i++)
{
tss = tss+ae_sqr(y->ptr.p_double[i]-meany, _state);
}
/*
* Build 1D compact basis function
* Generate design matrix AV ("vertical") and its transpose AH ("horizontal").
*/
ae_vector_set_length(&tmpx, 7, _state);
ae_vector_set_length(&tmpy, 7, _state);
tmpx.ptr.p_double[0] = -(double)3/(double)(m-1);
tmpx.ptr.p_double[1] = -(double)2/(double)(m-1);
tmpx.ptr.p_double[2] = -(double)1/(double)(m-1);
tmpx.ptr.p_double[3] = (double)0/(double)(m-1);
tmpx.ptr.p_double[4] = (double)1/(double)(m-1);
tmpx.ptr.p_double[5] = (double)2/(double)(m-1);
tmpx.ptr.p_double[6] = (double)3/(double)(m-1);
tmpy.ptr.p_double[0] = (double)(0);
tmpy.ptr.p_double[1] = (double)(0);
tmpy.ptr.p_double[2] = (double)1/(double)12;
tmpy.ptr.p_double[3] = (double)2/(double)6;
tmpy.ptr.p_double[4] = (double)1/(double)12;
tmpy.ptr.p_double[5] = (double)(0);
tmpy.ptr.p_double[6] = (double)(0);
spline1dbuildcubic(&tmpx, &tmpy, tmpx.cnt, 2, 0.0, 2, 0.0, &basis1, _state);
arows = n+2*m;
sparsecreate(arows, m, 0, &av, _state);
setlengthzero(&targets, arows, _state);
scaletargetsby = 1/ae_sqrt((double)(n), _state);
scalepenaltyby = 1/ae_sqrt((double)(m), _state);
for(i=0; i<=n-1; i++)
{
/*
* Generate design matrix row #I which corresponds to I-th dataset point
*/
k = ae_ifloor(boundval(xywork.ptr.p_double[2*i+0]*(m-1), (double)(0), (double)(m-1), _state), _state);
k0 = ae_maxint(k-(bfrad-1), 0, _state);
k1 = ae_minint(k+bfrad, m-1, _state);
for(j=k0; j<=k1; j++)
{
sparseset(&av, i, j, spline1dcalc(&basis1, xywork.ptr.p_double[2*i+0]-(double)j/(double)(m-1), _state)*scaletargetsby, _state);
}
targets.ptr.p_double[i] = xywork.ptr.p_double[2*i+1]*scaletargetsby;
}
for(i=0; i<=m-1; i++)
{
/*
* Generate design matrix row #(I+N) which corresponds to nonlinearity penalty at I-th node
*/
k0 = ae_maxint(i-(bfrad-1), 0, _state);
k1 = ae_minint(i+(bfrad-1), m-1, _state);
for(j=k0; j<=k1; j++)
{
spline1ddiff(&basis1, (double)i/(double)(m-1)-(double)j/(double)(m-1), &v, &dv, &d2v, _state);
sparseset(&av, n+i, j, lambdans*d2v*scalepenaltyby, _state);
}
}
for(i=0; i<=m-1; i++)
{
/*
* Generate design matrix row #(I+N+M) which corresponds to regularization for I-th coefficient
*/
sparseset(&av, n+m+i, i, spline1d_lambdareg, _state);
}
sparseconverttocrs(&av, _state);
sparsecopytransposecrs(&av, &ah, _state);
/*
* Build 7-diagonal (bandwidth=3) normal equations matrix and perform Cholesky
* decomposition (to be used later as preconditioner for LSQR iterations).
*/
bw = 3;
sparsecreatesksband(m, m, bw, &ata, _state);
mxata = (double)(0);
for(i=0; i<=m-1; i++)
{
for(j=i; j<=ae_minint(i+bw, m-1, _state); j++)
{
/*
* Get pattern of nonzeros in one of the rows (let it be I-th one)
* and compute dot product only for nonzero entries.
*/
sparsegetcompressedrow(&ah, i, &nzidx, &nzval, &nzcnt, _state);
v = (double)(0);
for(k=0; k<=nzcnt-1; k++)
{
v = v+sparseget(&ah, i, nzidx.ptr.p_int[k], _state)*sparseget(&ah, j, nzidx.ptr.p_int[k], _state);
}
/*
* Update ATA and max(ATA)
*/
sparseset(&ata, i, j, v, _state);
if( i==j )
{
mxata = ae_maxreal(mxata, ae_fabs(v, _state), _state);
}
}
}
mxata = coalesce(mxata, 1.0, _state);
creg = spline1d_cholreg;
for(;;)
{
/*
* Regularization
*/
for(i=0; i<=m-1; i++)
{
sparseset(&ata, i, i, sparseget(&ata, i, i, _state)+mxata*creg, _state);
}
/*
* Try Cholesky factorization.
*/
if( !sparsecholeskyskyline(&ata, m, ae_true, _state) )
{
/*
* Factorization failed, increase regularizer and repeat
*/
creg = coalesce(10*creg, 1.0E-12, _state);
continue;
}
break;
}
/*
* Solve with preconditioned LSQR:
*
* use Cholesky factor U of squared design matrix A'*A to
* transform min|A*x-b| to min|[A*inv(U)]*y-b| with y=U*x.
*
* Preconditioned problem is solved with LSQR solver, which
* gives superior results to normal equations approach. Due
* to Cholesky preconditioner being utilized we can solve
* problem in just a few iterations.
*/
rvectorsetlengthatleast(&tmp0, arows, _state);
rvectorsetlengthatleast(&tmp1, m, _state);
linlsqrcreatebuf(arows, m, &solver, _state);
linlsqrsetb(&solver, &targets, _state);
linlsqrsetcond(&solver, 1.0E-14, 1.0E-14, lsqrcnt, _state);
while(linlsqriteration(&solver, _state))
{
if( solver.needmv )
{
for(i=0; i<=m-1; i++)
{
tmp1.ptr.p_double[i] = solver.x.ptr.p_double[i];
}
/*
* Use Cholesky factorization of the system matrix
* as preconditioner: solve TRSV(U,Solver.X)
*/
sparsetrsv(&ata, ae_true, ae_false, 0, &tmp1, _state);
/*
* After preconditioning is done, multiply by A
*/
sparsemv(&av, &tmp1, &solver.mv, _state);
}
if( solver.needmtv )
{
/*
* Multiply by design matrix A
*/
sparsemtv(&av, &solver.x, &solver.mtv, _state);
/*
* Multiply by preconditioner: solve TRSV(U',A*Solver.X)
*/
sparsetrsv(&ata, ae_true, ae_false, 1, &solver.mtv, _state);
}
}
linlsqrresults(&solver, &tmp1, &srep, _state);
sparsetrsv(&ata, ae_true, ae_false, 0, &tmp1, _state);
/*
* Generate output spline as a table of spline valued and first
* derivatives at nodes (used to build Hermite spline)
*/
ae_vector_set_length(&sx, m, _state);
ae_vector_set_length(&sy, m, _state);
ae_vector_set_length(&sdy, m, _state);
for(i=0; i<=m-1; i++)
{
sx.ptr.p_double[i] = (double)i/(double)(m-1);
sy.ptr.p_double[i] = (double)(0);
sdy.ptr.p_double[i] = (double)(0);
}
for(i=0; i<=m-1; i++)
{
k0 = ae_maxint(i-(bfrad-1), 0, _state);
k1 = ae_minint(i+bfrad, m-1, _state);
for(j=k0; j<=k1; j++)
{
spline1ddiff(&basis1, (double)j/(double)(m-1)-(double)i/(double)(m-1), &v, &dv, &d2v, _state);
sy.ptr.p_double[j] = sy.ptr.p_double[j]+tmp1.ptr.p_double[i]*v;
sdy.ptr.p_double[j] = sdy.ptr.p_double[j]+tmp1.ptr.p_double[i]*dv;
}
}
/*
* Calculate model values
*/
sparsemv(&av, &tmp1, &tmp0, _state);
for(i=0; i<=n-1; i++)
{
tmp0.ptr.p_double[i] = tmp0.ptr.p_double[i]/scaletargetsby;
}
rss = 0.0;
nrel = 0;
rep->rmserror = (double)(0);
rep->maxerror = (double)(0);
rep->avgerror = (double)(0);
rep->avgrelerror = (double)(0);
for(i=0; i<=n-1; i++)
{
v = xywork.ptr.p_double[2*i+1]-tmp0.ptr.p_double[i];
rss = rss+v*v;
rep->rmserror = rep->rmserror+ae_sqr(v, _state);
rep->avgerror = rep->avgerror+ae_fabs(v, _state);
rep->maxerror = ae_maxreal(rep->maxerror, ae_fabs(v, _state), _state);
if( ae_fp_neq(y->ptr.p_double[i],(double)(0)) )
{
rep->avgrelerror = rep->avgrelerror+ae_fabs(v/y->ptr.p_double[i], _state);
nrel = nrel+1;
}
}
rep->rmserror = ae_sqrt(rep->rmserror/n, _state);
rep->avgerror = rep->avgerror/n;
rep->avgrelerror = rep->avgrelerror/coalesce((double)(nrel), 1.0, _state);
/*
* Append prior term.
* Transform spline to original coordinates.
* Output.
*/
for(i=0; i<=m-1; i++)
{
sy.ptr.p_double[i] = sy.ptr.p_double[i]+vterm.ptr.pp_double[0][0]*sx.ptr.p_double[i]+vterm.ptr.pp_double[0][1];
sdy.ptr.p_double[i] = sdy.ptr.p_double[i]+vterm.ptr.pp_double[0][0];
}
for(i=0; i<=m-1; i++)
{
sx.ptr.p_double[i] = sx.ptr.p_double[i]*(xb-xa)+xa;
sdy.ptr.p_double[i] = sdy.ptr.p_double[i]/(xb-xa);
}
spline1dbuildhermite(&sx, &sy, &sdy, m, s, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Internal version of Spline1DConvDiff
Converts from Hermite spline given by grid XOld to new grid X2
INPUT PARAMETERS:
XOld - old grid
YOld - values at old grid
DOld - first derivative at old grid
N - grid size
X2 - new grid
N2 - new grid size
Y - possibly preallocated output array
(reallocate if too small)
NeedY - do we need Y?
D1 - possibly preallocated output array
(reallocate if too small)
NeedD1 - do we need D1?
D2 - possibly preallocated output array
(reallocate if too small)
NeedD2 - do we need D1?
OUTPUT ARRAYS:
Y - values, if needed
D1 - first derivative, if needed
D2 - second derivative, if needed
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
void spline1dconvdiffinternal(/* Real */ ae_vector* xold,
/* Real */ ae_vector* yold,
/* Real */ ae_vector* dold,
ae_int_t n,
/* Real */ ae_vector* x2,
ae_int_t n2,
/* Real */ ae_vector* y,
ae_bool needy,
/* Real */ ae_vector* d1,
ae_bool needd1,
/* Real */ ae_vector* d2,
ae_bool needd2,
ae_state *_state)
{
ae_int_t intervalindex;
ae_int_t pointindex;
ae_bool havetoadvance;
double c0;
double c1;
double c2;
double c3;
double a;
double b;
double w;
double w2;
double w3;
double fa;
double fb;
double da;
double db;
double t;
/*
* Prepare space
*/
if( needy&&y->cnt<n2 )
{
ae_vector_set_length(y, n2, _state);
}
if( needd1&&d1->cnt<n2 )
{
ae_vector_set_length(d1, n2, _state);
}
if( needd2&&d2->cnt<n2 )
{
ae_vector_set_length(d2, n2, _state);
}
/*
* These assignments aren't actually needed
* (variables are initialized in the loop below),
* but without them compiler will complain about uninitialized locals
*/
c0 = (double)(0);
c1 = (double)(0);
c2 = (double)(0);
c3 = (double)(0);
a = (double)(0);
b = (double)(0);
/*
* Cycle
*/
intervalindex = -1;
pointindex = 0;
for(;;)
{
/*
* are we ready to exit?
*/
if( pointindex>=n2 )
{
break;
}
t = x2->ptr.p_double[pointindex];
/*
* do we need to advance interval?
*/
havetoadvance = ae_false;
if( intervalindex==-1 )
{
havetoadvance = ae_true;
}
else
{
if( intervalindex<n-2 )
{
havetoadvance = ae_fp_greater_eq(t,b);
}
}
if( havetoadvance )
{
intervalindex = intervalindex+1;
a = xold->ptr.p_double[intervalindex];
b = xold->ptr.p_double[intervalindex+1];
w = b-a;
w2 = w*w;
w3 = w*w2;
fa = yold->ptr.p_double[intervalindex];
fb = yold->ptr.p_double[intervalindex+1];
da = dold->ptr.p_double[intervalindex];
db = dold->ptr.p_double[intervalindex+1];
c0 = fa;
c1 = da;
c2 = (3*(fb-fa)-2*da*w-db*w)/w2;
c3 = (2*(fa-fb)+da*w+db*w)/w3;
continue;
}
/*
* Calculate spline and its derivatives using power basis
*/
t = t-a;
if( needy )
{
y->ptr.p_double[pointindex] = c0+t*(c1+t*(c2+t*c3));
}
if( needd1 )
{
d1->ptr.p_double[pointindex] = c1+2*t*c2+3*t*t*c3;
}
if( needd2 )
{
d2->ptr.p_double[pointindex] = 2*c2+6*t*c3;
}
pointindex = pointindex+1;
}
}
/*************************************************************************
This function finds all roots and extrema of the spline S(x) defined at
[A,B] (interval which contains spline nodes).
It does not extrapolates function, so roots and extrema located outside
of [A,B] will not be found. It returns all isolated (including multiple)
roots and extrema.
INPUT PARAMETERS
C - spline interpolant
OUTPUT PARAMETERS
R - array[NR], contains roots of the spline.
In case there is no roots, this array has zero length.
NR - number of roots, >=0
DR - is set to True in case there is at least one interval
where spline is just a zero constant. Such degenerate
cases are not reported in the R/NR
E - array[NE], contains extrema (maximums/minimums) of
the spline. In case there is no extrema, this array
has zero length.
ET - array[NE], extrema types:
* ET[i]>0 in case I-th extrema is a minimum
* ET[i]<0 in case I-th extrema is a maximum
NE - number of extrema, >=0
DE - is set to True in case there is at least one interval
where spline is a constant. Such degenerate cases are
not reported in the E/NE.
NOTES:
1. This function does NOT report following kinds of roots:
* intervals where function is constantly zero
* roots which are outside of [A,B] (note: it CAN return A or B)
2. This function does NOT report following kinds of extrema:
* intervals where function is a constant
* extrema which are outside of (A,B) (note: it WON'T return A or B)
-- ALGLIB PROJECT --
Copyright 26.09.2011 by Bochkanov Sergey
*************************************************************************/
void spline1drootsandextrema(spline1dinterpolant* c,
/* Real */ ae_vector* r,
ae_int_t* nr,
ae_bool* dr,
/* Real */ ae_vector* e,
/* Integer */ ae_vector* et,
ae_int_t* ne,
ae_bool* de,
ae_state *_state)
{
ae_frame _frame_block;
double pl;
double ml;
double pll;
double pr;
double mr;
ae_vector tr;
ae_vector tmpr;
ae_vector tmpe;
ae_vector tmpet;
ae_vector tmpc;
double x0;
double x1;
double x2;
double ex0;
double ex1;
ae_int_t tne;
ae_int_t tnr;
ae_int_t i;
ae_int_t j;
ae_bool nstep;
ae_frame_make(_state, &_frame_block);
memset(&tr, 0, sizeof(tr));
memset(&tmpr, 0, sizeof(tmpr));
memset(&tmpe, 0, sizeof(tmpe));
memset(&tmpet, 0, sizeof(tmpet));
memset(&tmpc, 0, sizeof(tmpc));
ae_vector_clear(r);
*nr = 0;
*dr = ae_false;
ae_vector_clear(e);
ae_vector_clear(et);
*ne = 0;
*de = ae_false;
ae_vector_init(&tr, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmpr, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmpe, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmpet, 0, DT_INT, _state, ae_true);
ae_vector_init(&tmpc, 0, DT_REAL, _state, ae_true);
/*
*exception handling
*/
ae_assert(c->k==3, "Spline1DRootsAndExtrema : incorrect parameter C.K!", _state);
ae_assert(c->continuity>=0, "Spline1DRootsAndExtrema : parameter C.Continuity must not be less than 0!", _state);
/*
*initialization of variable
*/
*nr = 0;
*ne = 0;
*dr = ae_false;
*de = ae_false;
nstep = ae_true;
/*
*consider case, when C.Continuty=0
*/
if( c->continuity==0 )
{
/*
*allocation for auxiliary arrays
*'TmpR ' - it stores a time value for roots
*'TmpE ' - it stores a time value for extremums
*'TmpET '- it stores a time value for extremums type
*/
rvectorsetlengthatleast(&tmpr, 3*(c->n-1), _state);
rvectorsetlengthatleast(&tmpe, 2*(c->n-1), _state);
ivectorsetlengthatleast(&tmpet, 2*(c->n-1), _state);
/*
*start calculating
*/
for(i=0; i<=c->n-2; i++)
{
/*
*initialization pL, mL, pR, mR
*/
pl = c->c.ptr.p_double[4*i];
ml = c->c.ptr.p_double[4*i+1];
pr = c->c.ptr.p_double[4*(i+1)];
mr = c->c.ptr.p_double[4*i+1]+2*c->c.ptr.p_double[4*i+2]*(c->x.ptr.p_double[i+1]-c->x.ptr.p_double[i])+3*c->c.ptr.p_double[4*i+3]*(c->x.ptr.p_double[i+1]-c->x.ptr.p_double[i])*(c->x.ptr.p_double[i+1]-c->x.ptr.p_double[i]);
/*
*pre-searching roots and extremums
*/
solvecubicpolinom(pl, ml, pr, mr, c->x.ptr.p_double[i], c->x.ptr.p_double[i+1], &x0, &x1, &x2, &ex0, &ex1, &tnr, &tne, &tr, _state);
*dr = *dr||tnr==-1;
*de = *de||tne==-1;
/*
*searching of roots
*/
if( tnr==1&&nstep )
{
/*
*is there roots?
*/
if( *nr>0 )
{
/*
*is a next root equal a previous root?
*if is't, then write new root
*/
if( ae_fp_neq(x0,tmpr.ptr.p_double[*nr-1]) )
{
tmpr.ptr.p_double[*nr] = x0;
*nr = *nr+1;
}
}
else
{
/*
*write a first root
*/
tmpr.ptr.p_double[*nr] = x0;
*nr = *nr+1;
}
}
else
{
/*
*case when function at a segment identically to zero
*then we have to clear a root, if the one located on a
*constant segment
*/
if( tnr==-1 )
{
/*
*safe state variable as constant
*/
if( nstep )
{
nstep = ae_false;
}
/*
*clear the root, if there is
*/
if( *nr>0 )
{
if( ae_fp_eq(c->x.ptr.p_double[i],tmpr.ptr.p_double[*nr-1]) )
{
*nr = *nr-1;
}
}
/*
*change state for 'DR'
*/
if( !*dr )
{
*dr = ae_true;
}
}
else
{
nstep = ae_true;
}
}
/*
*searching of extremums
*/
if( i>0 )
{
pll = c->c.ptr.p_double[4*(i-1)];
/*
*if pL=pLL or pL=pR then
*/
if( tne==-1 )
{
if( !*de )
{
*de = ae_true;
}
}
else
{
if( ae_fp_greater(pl,pll)&&ae_fp_greater(pl,pr) )
{
/*
*maximum
*/
tmpet.ptr.p_int[*ne] = -1;
tmpe.ptr.p_double[*ne] = c->x.ptr.p_double[i];
*ne = *ne+1;
}
else
{
if( ae_fp_less(pl,pll)&&ae_fp_less(pl,pr) )
{
/*
*minimum
*/
tmpet.ptr.p_int[*ne] = 1;
tmpe.ptr.p_double[*ne] = c->x.ptr.p_double[i];
*ne = *ne+1;
}
}
}
}
}
/*
*write final result
*/
rvectorsetlengthatleast(r, *nr, _state);
rvectorsetlengthatleast(e, *ne, _state);
ivectorsetlengthatleast(et, *ne, _state);
/*
*write roots
*/
for(i=0; i<=*nr-1; i++)
{
r->ptr.p_double[i] = tmpr.ptr.p_double[i];
}
/*
*write extremums and their types
*/
for(i=0; i<=*ne-1; i++)
{
e->ptr.p_double[i] = tmpe.ptr.p_double[i];
et->ptr.p_int[i] = tmpet.ptr.p_int[i];
}
}
else
{
/*
*case, when C.Continuity>=1
*'TmpR ' - it stores a time value for roots
*'TmpC' - it stores a time value for extremums and
*their function value (TmpC={EX0,F(EX0), EX1,F(EX1), ..., EXn,F(EXn)};)
*'TmpE' - it stores a time value for extremums only
*'TmpET'- it stores a time value for extremums type
*/
rvectorsetlengthatleast(&tmpr, 2*c->n-1, _state);
rvectorsetlengthatleast(&tmpc, 4*c->n, _state);
rvectorsetlengthatleast(&tmpe, 2*c->n, _state);
ivectorsetlengthatleast(&tmpet, 2*c->n, _state);
/*
*start calculating
*/
for(i=0; i<=c->n-2; i++)
{
/*
*we calculate pL,mL, pR,mR as Fi+1(F'i+1) at left border
*/
pl = c->c.ptr.p_double[4*i];
ml = c->c.ptr.p_double[4*i+1];
pr = c->c.ptr.p_double[4*(i+1)];
mr = c->c.ptr.p_double[4*(i+1)+1];
/*
*calculating roots and extremums at [X[i],X[i+1]]
*/
solvecubicpolinom(pl, ml, pr, mr, c->x.ptr.p_double[i], c->x.ptr.p_double[i+1], &x0, &x1, &x2, &ex0, &ex1, &tnr, &tne, &tr, _state);
/*
*searching roots
*/
if( tnr>0 )
{
/*
*re-init tR
*/
if( tnr>=1 )
{
tr.ptr.p_double[0] = x0;
}
if( tnr>=2 )
{
tr.ptr.p_double[1] = x1;
}
if( tnr==3 )
{
tr.ptr.p_double[2] = x2;
}
/*
*start root selection
*/
if( *nr>0 )
{
if( ae_fp_neq(tmpr.ptr.p_double[*nr-1],x0) )
{
/*
*previous segment was't constant identical zero
*/
if( nstep )
{
for(j=0; j<=tnr-1; j++)
{
tmpr.ptr.p_double[*nr+j] = tr.ptr.p_double[j];
}
*nr = *nr+tnr;
}
else
{
/*
*previous segment was constant identical zero
*and we must ignore [NR+j-1] root
*/
for(j=1; j<=tnr-1; j++)
{
tmpr.ptr.p_double[*nr+j-1] = tr.ptr.p_double[j];
}
*nr = *nr+tnr-1;
nstep = ae_true;
}
}
else
{
for(j=1; j<=tnr-1; j++)
{
tmpr.ptr.p_double[*nr+j-1] = tr.ptr.p_double[j];
}
*nr = *nr+tnr-1;
}
}
else
{
/*
*write first root
*/
for(j=0; j<=tnr-1; j++)
{
tmpr.ptr.p_double[*nr+j] = tr.ptr.p_double[j];
}
*nr = *nr+tnr;
}
}
else
{
if( tnr==-1 )
{
/*
*decrement 'NR' if at previous step was writen a root
*(previous segment identical zero)
*/
if( *nr>0&&nstep )
{
*nr = *nr-1;
}
/*
*previous segment is't constant
*/
if( nstep )
{
nstep = ae_false;
}
/*
*rewrite 'DR'
*/
if( !*dr )
{
*dr = ae_true;
}
}
}
/*
*searching extremums
*write all term like extremums
*/
if( tne==1 )
{
if( *ne>0 )
{
/*
*just ignore identical extremums
*because he must be one
*/
if( ae_fp_neq(tmpc.ptr.p_double[*ne-2],ex0) )
{
tmpc.ptr.p_double[*ne] = ex0;
tmpc.ptr.p_double[*ne+1] = c->c.ptr.p_double[4*i]+c->c.ptr.p_double[4*i+1]*(ex0-c->x.ptr.p_double[i])+c->c.ptr.p_double[4*i+2]*(ex0-c->x.ptr.p_double[i])*(ex0-c->x.ptr.p_double[i])+c->c.ptr.p_double[4*i+3]*(ex0-c->x.ptr.p_double[i])*(ex0-c->x.ptr.p_double[i])*(ex0-c->x.ptr.p_double[i]);
*ne = *ne+2;
}
}
else
{
/*
*write first extremum and it function value
*/
tmpc.ptr.p_double[*ne] = ex0;
tmpc.ptr.p_double[*ne+1] = c->c.ptr.p_double[4*i]+c->c.ptr.p_double[4*i+1]*(ex0-c->x.ptr.p_double[i])+c->c.ptr.p_double[4*i+2]*(ex0-c->x.ptr.p_double[i])*(ex0-c->x.ptr.p_double[i])+c->c.ptr.p_double[4*i+3]*(ex0-c->x.ptr.p_double[i])*(ex0-c->x.ptr.p_double[i])*(ex0-c->x.ptr.p_double[i]);
*ne = *ne+2;
}
}
else
{
if( tne==2 )
{
if( *ne>0 )
{
/*
*ignore identical extremum
*/
if( ae_fp_neq(tmpc.ptr.p_double[*ne-2],ex0) )
{
tmpc.ptr.p_double[*ne] = ex0;
tmpc.ptr.p_double[*ne+1] = c->c.ptr.p_double[4*i]+c->c.ptr.p_double[4*i+1]*(ex0-c->x.ptr.p_double[i])+c->c.ptr.p_double[4*i+2]*(ex0-c->x.ptr.p_double[i])*(ex0-c->x.ptr.p_double[i])+c->c.ptr.p_double[4*i+3]*(ex0-c->x.ptr.p_double[i])*(ex0-c->x.ptr.p_double[i])*(ex0-c->x.ptr.p_double[i]);
*ne = *ne+2;
}
}
else
{
/*
*write first extremum
*/
tmpc.ptr.p_double[*ne] = ex0;
tmpc.ptr.p_double[*ne+1] = c->c.ptr.p_double[4*i]+c->c.ptr.p_double[4*i+1]*(ex0-c->x.ptr.p_double[i])+c->c.ptr.p_double[4*i+2]*(ex0-c->x.ptr.p_double[i])*(ex0-c->x.ptr.p_double[i])+c->c.ptr.p_double[4*i+3]*(ex0-c->x.ptr.p_double[i])*(ex0-c->x.ptr.p_double[i])*(ex0-c->x.ptr.p_double[i]);
*ne = *ne+2;
}
/*
*write second extremum
*/
tmpc.ptr.p_double[*ne] = ex1;
tmpc.ptr.p_double[*ne+1] = c->c.ptr.p_double[4*i]+c->c.ptr.p_double[4*i+1]*(ex1-c->x.ptr.p_double[i])+c->c.ptr.p_double[4*i+2]*(ex1-c->x.ptr.p_double[i])*(ex1-c->x.ptr.p_double[i])+c->c.ptr.p_double[4*i+3]*(ex1-c->x.ptr.p_double[i])*(ex1-c->x.ptr.p_double[i])*(ex1-c->x.ptr.p_double[i]);
*ne = *ne+2;
}
else
{
if( tne==-1 )
{
if( !*de )
{
*de = ae_true;
}
}
}
}
}
/*
*checking of arrays
*get number of extremums (tNe=NE/2)
*initialize pL as value F0(X[0]) and
*initialize pR as value Fn-1(X[N])
*/
tne = *ne/2;
*ne = 0;
pl = c->c.ptr.p_double[0];
pr = c->c.ptr.p_double[4*(c->n-1)];
for(i=0; i<=tne-1; i++)
{
if( i>0&&i<tne-1 )
{
if( ae_fp_greater(tmpc.ptr.p_double[2*i+1],tmpc.ptr.p_double[2*(i-1)+1])&&ae_fp_greater(tmpc.ptr.p_double[2*i+1],tmpc.ptr.p_double[2*(i+1)+1]) )
{
/*
*maximum
*/
tmpe.ptr.p_double[*ne] = tmpc.ptr.p_double[2*i];
tmpet.ptr.p_int[*ne] = -1;
*ne = *ne+1;
}
else
{
if( ae_fp_less(tmpc.ptr.p_double[2*i+1],tmpc.ptr.p_double[2*(i-1)+1])&&ae_fp_less(tmpc.ptr.p_double[2*i+1],tmpc.ptr.p_double[2*(i+1)+1]) )
{
/*
*minimum
*/
tmpe.ptr.p_double[*ne] = tmpc.ptr.p_double[2*i];
tmpet.ptr.p_int[*ne] = 1;
*ne = *ne+1;
}
}
}
else
{
if( i==0 )
{
if( ae_fp_neq(tmpc.ptr.p_double[2*i],c->x.ptr.p_double[0]) )
{
if( ae_fp_greater(tmpc.ptr.p_double[2*i+1],pl)&&ae_fp_greater(tmpc.ptr.p_double[2*i+1],tmpc.ptr.p_double[2*(i+1)+1]) )
{
/*
*maximum
*/
tmpe.ptr.p_double[*ne] = tmpc.ptr.p_double[2*i];
tmpet.ptr.p_int[*ne] = -1;
*ne = *ne+1;
}
else
{
if( ae_fp_less(tmpc.ptr.p_double[2*i+1],pl)&&ae_fp_less(tmpc.ptr.p_double[2*i+1],tmpc.ptr.p_double[2*(i+1)+1]) )
{
/*
*minimum
*/
tmpe.ptr.p_double[*ne] = tmpc.ptr.p_double[2*i];
tmpet.ptr.p_int[*ne] = 1;
*ne = *ne+1;
}
}
}
}
else
{
if( i==tne-1 )
{
if( ae_fp_neq(tmpc.ptr.p_double[2*i],c->x.ptr.p_double[c->n-1]) )
{
if( ae_fp_greater(tmpc.ptr.p_double[2*i+1],tmpc.ptr.p_double[2*(i-1)+1])&&ae_fp_greater(tmpc.ptr.p_double[2*i+1],pr) )
{
/*
*maximum
*/
tmpe.ptr.p_double[*ne] = tmpc.ptr.p_double[2*i];
tmpet.ptr.p_int[*ne] = -1;
*ne = *ne+1;
}
else
{
if( ae_fp_less(tmpc.ptr.p_double[2*i+1],tmpc.ptr.p_double[2*(i-1)+1])&&ae_fp_less(tmpc.ptr.p_double[2*i+1],pr) )
{
/*
*minimum
*/
tmpe.ptr.p_double[*ne] = tmpc.ptr.p_double[2*i];
tmpet.ptr.p_int[*ne] = 1;
*ne = *ne+1;
}
}
}
}
}
}
}
/*
*final results
*allocate R, E, ET
*/
rvectorsetlengthatleast(r, *nr, _state);
rvectorsetlengthatleast(e, *ne, _state);
ivectorsetlengthatleast(et, *ne, _state);
/*
*write result for extremus and their types
*/
for(i=0; i<=*ne-1; i++)
{
e->ptr.p_double[i] = tmpe.ptr.p_double[i];
et->ptr.p_int[i] = tmpet.ptr.p_int[i];
}
/*
*write result for roots
*/
for(i=0; i<=*nr-1; i++)
{
r->ptr.p_double[i] = tmpr.ptr.p_double[i];
}
}
ae_frame_leave(_state);
}
/*************************************************************************
Internal subroutine. Heap sort.
*************************************************************************/
void heapsortdpoints(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* d,
ae_int_t n,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector rbuf;
ae_vector ibuf;
ae_vector rbuf2;
ae_vector ibuf2;
ae_int_t i;
ae_frame_make(_state, &_frame_block);
memset(&rbuf, 0, sizeof(rbuf));
memset(&ibuf, 0, sizeof(ibuf));
memset(&rbuf2, 0, sizeof(rbuf2));
memset(&ibuf2, 0, sizeof(ibuf2));
ae_vector_init(&rbuf, 0, DT_REAL, _state, ae_true);
ae_vector_init(&ibuf, 0, DT_INT, _state, ae_true);
ae_vector_init(&rbuf2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&ibuf2, 0, DT_INT, _state, ae_true);
ae_vector_set_length(&ibuf, n, _state);
ae_vector_set_length(&rbuf, n, _state);
for(i=0; i<=n-1; i++)
{
ibuf.ptr.p_int[i] = i;
}
tagsortfasti(x, &ibuf, &rbuf2, &ibuf2, n, _state);
for(i=0; i<=n-1; i++)
{
rbuf.ptr.p_double[i] = y->ptr.p_double[ibuf.ptr.p_int[i]];
}
ae_v_move(&y->ptr.p_double[0], 1, &rbuf.ptr.p_double[0], 1, ae_v_len(0,n-1));
for(i=0; i<=n-1; i++)
{
rbuf.ptr.p_double[i] = d->ptr.p_double[ibuf.ptr.p_int[i]];
}
ae_v_move(&d->ptr.p_double[0], 1, &rbuf.ptr.p_double[0], 1, ae_v_len(0,n-1));
ae_frame_leave(_state);
}
/*************************************************************************
This procedure search roots of an quadratic equation inside [0;1] and it number of roots.
INPUT PARAMETERS:
P0 - value of a function at 0
M0 - value of a derivative at 0
P1 - value of a function at 1
M1 - value of a derivative at 1
OUTPUT PARAMETERS:
X0 - first root of an equation
X1 - second root of an equation
NR - number of roots
RESTRICTIONS OF PARAMETERS:
Parameters for this procedure has't to be zero simultaneously. Is expected,
that input polinom is't degenerate or constant identicaly ZERO.
REMARK:
The procedure always fill value for X1 and X2, even if it is't belongs to [0;1].
But first true root(even if existing one) is in X1.
Number of roots is NR.
-- ALGLIB PROJECT --
Copyright 26.09.2011 by Bochkanov Sergey
*************************************************************************/
void solvepolinom2(double p0,
double m0,
double p1,
double m1,
double* x0,
double* x1,
ae_int_t* nr,
ae_state *_state)
{
double a;
double b;
double c;
double dd;
double tmp;
double exf;
double extr;
*x0 = 0;
*x1 = 0;
*nr = 0;
/*
*calculate parameters for equation: A, B and C
*/
a = 6*p0+3*m0-6*p1+3*m1;
b = -6*p0-4*m0+6*p1-2*m1;
c = m0;
/*
*check case, when A=0
*we are considering the linear equation
*/
if( ae_fp_eq(a,(double)(0)) )
{
/*
*B<>0 and root inside [0;1]
*one root
*/
if( (ae_fp_neq(b,(double)(0))&&ae_sign(c, _state)*ae_sign(b, _state)<=0)&&ae_fp_greater_eq(ae_fabs(b, _state),ae_fabs(c, _state)) )
{
*x0 = -c/b;
*nr = 1;
return;
}
else
{
*nr = 0;
return;
}
}
/*
*consider case, when extremumu outside (0;1)
*exist one root only
*/
if( ae_fp_less_eq(ae_fabs(2*a, _state),ae_fabs(b, _state))||ae_sign(b, _state)*ae_sign(a, _state)>=0 )
{
if( ae_sign(m0, _state)*ae_sign(m1, _state)>0 )
{
*nr = 0;
return;
}
/*
*consider case, when the one exist
*same sign of derivative
*/
if( ae_sign(m0, _state)*ae_sign(m1, _state)<0 )
{
*nr = 1;
extr = -b/(2*a);
dd = b*b-4*a*c;
if( ae_fp_less(dd,(double)(0)) )
{
return;
}
*x0 = (-b-ae_sqrt(dd, _state))/(2*a);
*x1 = (-b+ae_sqrt(dd, _state))/(2*a);
if( (ae_fp_greater_eq(extr,(double)(1))&&ae_fp_less_eq(*x1,extr))||(ae_fp_less_eq(extr,(double)(0))&&ae_fp_greater_eq(*x1,extr)) )
{
*x0 = *x1;
}
return;
}
/*
*consider case, when the one is 0
*/
if( ae_fp_eq(m0,(double)(0)) )
{
*x0 = (double)(0);
*nr = 1;
return;
}
if( ae_fp_eq(m1,(double)(0)) )
{
*x0 = (double)(1);
*nr = 1;
return;
}
}
else
{
/*
*consider case, when both of derivatives is 0
*/
if( ae_fp_eq(m0,(double)(0))&&ae_fp_eq(m1,(double)(0)) )
{
*x0 = (double)(0);
*x1 = (double)(1);
*nr = 2;
return;
}
/*
*consider case, when derivative at 0 is 0, and derivative at 1 is't 0
*/
if( ae_fp_eq(m0,(double)(0))&&ae_fp_neq(m1,(double)(0)) )
{
dd = b*b-4*a*c;
if( ae_fp_less(dd,(double)(0)) )
{
*x0 = (double)(0);
*nr = 1;
return;
}
*x0 = (-b-ae_sqrt(dd, _state))/(2*a);
*x1 = (-b+ae_sqrt(dd, _state))/(2*a);
extr = -b/(2*a);
exf = a*extr*extr+b*extr+c;
if( ae_sign(exf, _state)*ae_sign(m1, _state)>0 )
{
*x0 = (double)(0);
*nr = 1;
return;
}
else
{
if( ae_fp_greater(extr,*x0) )
{
*x0 = (double)(0);
}
else
{
*x1 = (double)(0);
}
*nr = 2;
/*
*roots must placed ascending
*/
if( ae_fp_greater(*x0,*x1) )
{
tmp = *x0;
*x0 = *x1;
*x1 = tmp;
}
return;
}
}
if( ae_fp_eq(m1,(double)(0))&&ae_fp_neq(m0,(double)(0)) )
{
dd = b*b-4*a*c;
if( ae_fp_less(dd,(double)(0)) )
{
*x0 = (double)(1);
*nr = 1;
return;
}
*x0 = (-b-ae_sqrt(dd, _state))/(2*a);
*x1 = (-b+ae_sqrt(dd, _state))/(2*a);
extr = -b/(2*a);
exf = a*extr*extr+b*extr+c;
if( ae_sign(exf, _state)*ae_sign(m0, _state)>0 )
{
*x0 = (double)(1);
*nr = 1;
return;
}
else
{
if( ae_fp_less(extr,*x0) )
{
*x0 = (double)(1);
}
else
{
*x1 = (double)(1);
}
*nr = 2;
/*
*roots must placed ascending
*/
if( ae_fp_greater(*x0,*x1) )
{
tmp = *x0;
*x0 = *x1;
*x1 = tmp;
}
return;
}
}
else
{
extr = -b/(2*a);
exf = a*extr*extr+b*extr+c;
if( ae_sign(exf, _state)*ae_sign(m0, _state)>0&&ae_sign(exf, _state)*ae_sign(m1, _state)>0 )
{
*nr = 0;
return;
}
dd = b*b-4*a*c;
if( ae_fp_less(dd,(double)(0)) )
{
*nr = 0;
return;
}
*x0 = (-b-ae_sqrt(dd, _state))/(2*a);
*x1 = (-b+ae_sqrt(dd, _state))/(2*a);
/*
*if EXF and m0, EXF and m1 has different signs, then equation has two roots
*/
if( ae_sign(exf, _state)*ae_sign(m0, _state)<0&&ae_sign(exf, _state)*ae_sign(m1, _state)<0 )
{
*nr = 2;
/*
*roots must placed ascending
*/
if( ae_fp_greater(*x0,*x1) )
{
tmp = *x0;
*x0 = *x1;
*x1 = tmp;
}
return;
}
else
{
*nr = 1;
if( ae_sign(exf, _state)*ae_sign(m0, _state)<0 )
{
if( ae_fp_less(*x1,extr) )
{
*x0 = *x1;
}
return;
}
if( ae_sign(exf, _state)*ae_sign(m1, _state)<0 )
{
if( ae_fp_greater(*x1,extr) )
{
*x0 = *x1;
}
return;
}
}
}
}
}
/*************************************************************************
This procedure search roots of an cubic equation inside [A;B], it number of roots
and number of extremums.
INPUT PARAMETERS:
pA - value of a function at A
mA - value of a derivative at A
pB - value of a function at B
mB - value of a derivative at B
A0 - left border [A0;B0]
B0 - right border [A0;B0]
OUTPUT PARAMETERS:
X0 - first root of an equation
X1 - second root of an equation
X2 - third root of an equation
EX0 - first extremum of a function
EX0 - second extremum of a function
NR - number of roots
NR - number of extrmums
RESTRICTIONS OF PARAMETERS:
Length of [A;B] must be positive and is't zero, i.e. A<>B and A<B.
REMARK:
If 'NR' is -1 it's mean, than polinom has infiniti roots.
If 'NE' is -1 it's mean, than polinom has infiniti extremums.
-- ALGLIB PROJECT --
Copyright 26.09.2011 by Bochkanov Sergey
*************************************************************************/
void solvecubicpolinom(double pa,
double ma,
double pb,
double mb,
double a,
double b,
double* x0,
double* x1,
double* x2,
double* ex0,
double* ex1,
ae_int_t* nr,
ae_int_t* ne,
/* Real */ ae_vector* tempdata,
ae_state *_state)
{
ae_int_t i;
double tmpma;
double tmpmb;
double tex0;
double tex1;
*x0 = 0;
*x1 = 0;
*x2 = 0;
*ex0 = 0;
*ex1 = 0;
*nr = 0;
*ne = 0;
rvectorsetlengthatleast(tempdata, 3, _state);
/*
*case, when A>B
*/
ae_assert(ae_fp_less(a,b), "\nSolveCubicPolinom: incorrect borders for [A;B]!\n", _state);
/*
*case 1
*function can be identicaly to ZERO
*/
if( ((ae_fp_eq(ma,(double)(0))&&ae_fp_eq(mb,(double)(0)))&&ae_fp_eq(pa,pb))&&ae_fp_eq(pa,(double)(0)) )
{
*nr = -1;
*ne = -1;
return;
}
if( (ae_fp_eq(ma,(double)(0))&&ae_fp_eq(mb,(double)(0)))&&ae_fp_eq(pa,pb) )
{
*nr = 0;
*ne = -1;
return;
}
tmpma = ma*(b-a);
tmpmb = mb*(b-a);
solvepolinom2(pa, tmpma, pb, tmpmb, ex0, ex1, ne, _state);
*ex0 = spline1d_rescaleval((double)(0), (double)(1), a, b, *ex0, _state);
*ex1 = spline1d_rescaleval((double)(0), (double)(1), a, b, *ex1, _state);
/*
*case 3.1
*no extremums at [A;B]
*/
if( *ne==0 )
{
*nr = bisectmethod(pa, tmpma, pb, tmpmb, (double)(0), (double)(1), x0, _state);
if( *nr==1 )
{
*x0 = spline1d_rescaleval((double)(0), (double)(1), a, b, *x0, _state);
}
return;
}
/*
*case 3.2
*one extremum
*/
if( *ne==1 )
{
if( ae_fp_eq(*ex0,a)||ae_fp_eq(*ex0,b) )
{
*nr = bisectmethod(pa, tmpma, pb, tmpmb, (double)(0), (double)(1), x0, _state);
if( *nr==1 )
{
*x0 = spline1d_rescaleval((double)(0), (double)(1), a, b, *x0, _state);
}
return;
}
else
{
*nr = 0;
i = 0;
tex0 = spline1d_rescaleval(a, b, (double)(0), (double)(1), *ex0, _state);
*nr = bisectmethod(pa, tmpma, pb, tmpmb, (double)(0), tex0, x0, _state)+(*nr);
if( *nr>i )
{
tempdata->ptr.p_double[i] = spline1d_rescaleval((double)(0), tex0, a, *ex0, *x0, _state);
i = i+1;
}
*nr = bisectmethod(pa, tmpma, pb, tmpmb, tex0, (double)(1), x0, _state)+(*nr);
if( *nr>i )
{
*x0 = spline1d_rescaleval(tex0, (double)(1), *ex0, b, *x0, _state);
if( i>0 )
{
if( ae_fp_neq(*x0,tempdata->ptr.p_double[i-1]) )
{
tempdata->ptr.p_double[i] = *x0;
i = i+1;
}
else
{
*nr = *nr-1;
}
}
else
{
tempdata->ptr.p_double[i] = *x0;
i = i+1;
}
}
if( *nr>0 )
{
*x0 = tempdata->ptr.p_double[0];
if( *nr>1 )
{
*x1 = tempdata->ptr.p_double[1];
}
return;
}
}
return;
}
else
{
/*
*case 3.3
*two extremums(or more, but it's impossible)
*
*
*case 3.3.0
*both extremums at the border
*/
if( ae_fp_eq(*ex0,a)&&ae_fp_eq(*ex1,b) )
{
*nr = bisectmethod(pa, tmpma, pb, tmpmb, (double)(0), (double)(1), x0, _state);
if( *nr==1 )
{
*x0 = spline1d_rescaleval((double)(0), (double)(1), a, b, *x0, _state);
}
return;
}
if( ae_fp_eq(*ex0,a)&&ae_fp_neq(*ex1,b) )
{
*nr = 0;
i = 0;
tex1 = spline1d_rescaleval(a, b, (double)(0), (double)(1), *ex1, _state);
*nr = bisectmethod(pa, tmpma, pb, tmpmb, (double)(0), tex1, x0, _state)+(*nr);
if( *nr>i )
{
tempdata->ptr.p_double[i] = spline1d_rescaleval((double)(0), tex1, a, *ex1, *x0, _state);
i = i+1;
}
*nr = bisectmethod(pa, tmpma, pb, tmpmb, tex1, (double)(1), x0, _state)+(*nr);
if( *nr>i )
{
*x0 = spline1d_rescaleval(tex1, (double)(1), *ex1, b, *x0, _state);
if( ae_fp_neq(*x0,tempdata->ptr.p_double[i-1]) )
{
tempdata->ptr.p_double[i] = *x0;
i = i+1;
}
else
{
*nr = *nr-1;
}
}
if( *nr>0 )
{
*x0 = tempdata->ptr.p_double[0];
if( *nr>1 )
{
*x1 = tempdata->ptr.p_double[1];
}
return;
}
}
if( ae_fp_eq(*ex1,b)&&ae_fp_neq(*ex0,a) )
{
*nr = 0;
i = 0;
tex0 = spline1d_rescaleval(a, b, (double)(0), (double)(1), *ex0, _state);
*nr = bisectmethod(pa, tmpma, pb, tmpmb, (double)(0), tex0, x0, _state)+(*nr);
if( *nr>i )
{
tempdata->ptr.p_double[i] = spline1d_rescaleval((double)(0), tex0, a, *ex0, *x0, _state);
i = i+1;
}
*nr = bisectmethod(pa, tmpma, pb, tmpmb, tex0, (double)(1), x0, _state)+(*nr);
if( *nr>i )
{
*x0 = spline1d_rescaleval(tex0, (double)(1), *ex0, b, *x0, _state);
if( i>0 )
{
if( ae_fp_neq(*x0,tempdata->ptr.p_double[i-1]) )
{
tempdata->ptr.p_double[i] = *x0;
i = i+1;
}
else
{
*nr = *nr-1;
}
}
else
{
tempdata->ptr.p_double[i] = *x0;
i = i+1;
}
}
if( *nr>0 )
{
*x0 = tempdata->ptr.p_double[0];
if( *nr>1 )
{
*x1 = tempdata->ptr.p_double[1];
}
return;
}
}
else
{
/*
*case 3.3.2
*both extremums inside (0;1)
*/
*nr = 0;
i = 0;
tex0 = spline1d_rescaleval(a, b, (double)(0), (double)(1), *ex0, _state);
tex1 = spline1d_rescaleval(a, b, (double)(0), (double)(1), *ex1, _state);
*nr = bisectmethod(pa, tmpma, pb, tmpmb, (double)(0), tex0, x0, _state)+(*nr);
if( *nr>i )
{
tempdata->ptr.p_double[i] = spline1d_rescaleval((double)(0), tex0, a, *ex0, *x0, _state);
i = i+1;
}
*nr = bisectmethod(pa, tmpma, pb, tmpmb, tex0, tex1, x0, _state)+(*nr);
if( *nr>i )
{
*x0 = spline1d_rescaleval(tex0, tex1, *ex0, *ex1, *x0, _state);
if( i>0 )
{
if( ae_fp_neq(*x0,tempdata->ptr.p_double[i-1]) )
{
tempdata->ptr.p_double[i] = *x0;
i = i+1;
}
else
{
*nr = *nr-1;
}
}
else
{
tempdata->ptr.p_double[i] = *x0;
i = i+1;
}
}
*nr = bisectmethod(pa, tmpma, pb, tmpmb, tex1, (double)(1), x0, _state)+(*nr);
if( *nr>i )
{
*x0 = spline1d_rescaleval(tex1, (double)(1), *ex1, b, *x0, _state);
if( i>0 )
{
if( ae_fp_neq(*x0,tempdata->ptr.p_double[i-1]) )
{
tempdata->ptr.p_double[i] = *x0;
i = i+1;
}
else
{
*nr = *nr-1;
}
}
else
{
tempdata->ptr.p_double[i] = *x0;
i = i+1;
}
}
/*
*write are found roots
*/
if( *nr>0 )
{
*x0 = tempdata->ptr.p_double[0];
if( *nr>1 )
{
*x1 = tempdata->ptr.p_double[1];
}
if( *nr>2 )
{
*x2 = tempdata->ptr.p_double[2];
}
return;
}
}
}
}
/*************************************************************************
Function for searching a root at [A;B] by bisection method and return number of roots
(0 or 1)
INPUT PARAMETERS:
pA - value of a function at A
mA - value of a derivative at A
pB - value of a function at B
mB - value of a derivative at B
A0 - left border [A0;B0]
B0 - right border [A0;B0]
RESTRICTIONS OF PARAMETERS:
We assume, that B0>A0.
REMARK:
Assume, that exist one root only at [A;B], else
function may be work incorrectly.
The function dont check value A0,B0!
-- ALGLIB PROJECT --
Copyright 26.09.2011 by Bochkanov Sergey
*************************************************************************/
ae_int_t bisectmethod(double pa,
double ma,
double pb,
double mb,
double a,
double b,
double* x,
ae_state *_state)
{
double vacuum;
double eps;
double a0;
double b0;
double m;
double lf;
double rf;
double mf;
ae_int_t result;
*x = 0;
/*
*accuracy
*/
eps = 1000*(b-a)*ae_machineepsilon;
/*
*initialization left and right borders
*/
a0 = a;
b0 = b;
/*
*initialize function value at 'A' and 'B'
*/
spline1d_hermitecalc(pa, ma, pb, mb, a, &lf, &vacuum, _state);
spline1d_hermitecalc(pa, ma, pb, mb, b, &rf, &vacuum, _state);
/*
*check, that 'A' and 'B' are't roots,
*and that root exist
*/
if( ae_sign(lf, _state)*ae_sign(rf, _state)>0 )
{
result = 0;
return result;
}
else
{
if( ae_fp_eq(lf,(double)(0)) )
{
*x = a;
result = 1;
return result;
}
else
{
if( ae_fp_eq(rf,(double)(0)) )
{
*x = b;
result = 1;
return result;
}
}
}
/*
*searching a root
*/
do
{
m = (b0+a0)/2;
spline1d_hermitecalc(pa, ma, pb, mb, a0, &lf, &vacuum, _state);
spline1d_hermitecalc(pa, ma, pb, mb, b0, &rf, &vacuum, _state);
spline1d_hermitecalc(pa, ma, pb, mb, m, &mf, &vacuum, _state);
if( ae_sign(mf, _state)*ae_sign(lf, _state)<0 )
{
b0 = m;
}
else
{
if( ae_sign(mf, _state)*ae_sign(rf, _state)<0 )
{
a0 = m;
}
else
{
if( ae_fp_eq(lf,(double)(0)) )
{
*x = a0;
result = 1;
return result;
}
if( ae_fp_eq(rf,(double)(0)) )
{
*x = b0;
result = 1;
return result;
}
if( ae_fp_eq(mf,(double)(0)) )
{
*x = m;
result = 1;
return result;
}
}
}
}
while(ae_fp_greater_eq(ae_fabs(b0-a0, _state),eps));
*x = m;
result = 1;
return result;
}
/*************************************************************************
This function builds monotone cubic Hermite interpolant. This interpolant
is monotonic in [x(0),x(n-1)] and is constant outside of this interval.
In case y[] form non-monotonic sequence, interpolant is piecewise
monotonic. Say, for x=(0,1,2,3,4) and y=(0,1,2,1,0) interpolant will
monotonically grow at [0..2] and monotonically decrease at [2..4].
INPUT PARAMETERS:
X - spline nodes, array[0..N-1]. Subroutine automatically
sorts points, so caller may pass unsorted array.
Y - function values, array[0..N-1]
N - the number of points(N>=2).
OUTPUT PARAMETERS:
C - spline interpolant.
-- ALGLIB PROJECT --
Copyright 21.06.2012 by Bochkanov Sergey
*************************************************************************/
void spline1dbuildmonotone(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
spline1dinterpolant* c,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_vector d;
ae_vector ex;
ae_vector ey;
ae_vector p;
double delta;
double alpha;
double beta;
ae_int_t tmpn;
ae_int_t sn;
double ca;
double cb;
double epsilon;
ae_int_t i;
ae_int_t j;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&d, 0, sizeof(d));
memset(&ex, 0, sizeof(ex));
memset(&ey, 0, sizeof(ey));
memset(&p, 0, sizeof(p));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
_spline1dinterpolant_clear(c);
ae_vector_init(&d, 0, DT_REAL, _state, ae_true);
ae_vector_init(&ex, 0, DT_REAL, _state, ae_true);
ae_vector_init(&ey, 0, DT_REAL, _state, ae_true);
ae_vector_init(&p, 0, DT_INT, _state, ae_true);
/*
* Check lengths of arguments
*/
ae_assert(n>=2, "Spline1DBuildMonotone: N<2", _state);
ae_assert(x->cnt>=n, "Spline1DBuildMonotone: Length(X)<N", _state);
ae_assert(y->cnt>=n, "Spline1DBuildMonotone: Length(Y)<N", _state);
/*
* Check and sort points
*/
ae_assert(isfinitevector(x, n, _state), "Spline1DBuildMonotone: X contains infinite or NAN values", _state);
ae_assert(isfinitevector(y, n, _state), "Spline1DBuildMonotone: Y contains infinite or NAN values", _state);
spline1d_heapsortppoints(x, y, &p, n, _state);
ae_assert(aredistinct(x, n, _state), "Spline1DBuildMonotone: at least two consequent points are too close", _state);
epsilon = ae_machineepsilon;
n = n+2;
ae_vector_set_length(&d, n, _state);
ae_vector_set_length(&ex, n, _state);
ae_vector_set_length(&ey, n, _state);
ex.ptr.p_double[0] = x->ptr.p_double[0]-ae_fabs(x->ptr.p_double[1]-x->ptr.p_double[0], _state);
ex.ptr.p_double[n-1] = x->ptr.p_double[n-3]+ae_fabs(x->ptr.p_double[n-3]-x->ptr.p_double[n-4], _state);
ey.ptr.p_double[0] = y->ptr.p_double[0];
ey.ptr.p_double[n-1] = y->ptr.p_double[n-3];
for(i=1; i<=n-2; i++)
{
ex.ptr.p_double[i] = x->ptr.p_double[i-1];
ey.ptr.p_double[i] = y->ptr.p_double[i-1];
}
/*
* Init sign of the function for first segment
*/
i = 0;
ca = (double)(0);
do
{
ca = ey.ptr.p_double[i+1]-ey.ptr.p_double[i];
i = i+1;
}
while(!(ae_fp_neq(ca,(double)(0))||i>n-2));
if( ae_fp_neq(ca,(double)(0)) )
{
ca = ca/ae_fabs(ca, _state);
}
i = 0;
while(i<n-1)
{
/*
* Partition of the segment [X0;Xn]
*/
tmpn = 1;
for(j=i; j<=n-2; j++)
{
cb = ey.ptr.p_double[j+1]-ey.ptr.p_double[j];
if( ae_fp_greater_eq(ca*cb,(double)(0)) )
{
tmpn = tmpn+1;
}
else
{
ca = cb/ae_fabs(cb, _state);
break;
}
}
sn = i+tmpn;
ae_assert(tmpn>=2, "Spline1DBuildMonotone: internal error", _state);
/*
* Calculate derivatives for current segment
*/
d.ptr.p_double[i] = (double)(0);
d.ptr.p_double[sn-1] = (double)(0);
for(j=i+1; j<=sn-2; j++)
{
d.ptr.p_double[j] = ((ey.ptr.p_double[j]-ey.ptr.p_double[j-1])/(ex.ptr.p_double[j]-ex.ptr.p_double[j-1])+(ey.ptr.p_double[j+1]-ey.ptr.p_double[j])/(ex.ptr.p_double[j+1]-ex.ptr.p_double[j]))/2;
}
for(j=i; j<=sn-2; j++)
{
delta = (ey.ptr.p_double[j+1]-ey.ptr.p_double[j])/(ex.ptr.p_double[j+1]-ex.ptr.p_double[j]);
if( ae_fp_less_eq(ae_fabs(delta, _state),epsilon) )
{
d.ptr.p_double[j] = (double)(0);
d.ptr.p_double[j+1] = (double)(0);
}
else
{
alpha = d.ptr.p_double[j]/delta;
beta = d.ptr.p_double[j+1]/delta;
if( ae_fp_neq(alpha,(double)(0)) )
{
cb = alpha*ae_sqrt(1+ae_sqr(beta/alpha, _state), _state);
}
else
{
if( ae_fp_neq(beta,(double)(0)) )
{
cb = beta;
}
else
{
continue;
}
}
if( ae_fp_greater(cb,(double)(3)) )
{
d.ptr.p_double[j] = 3*alpha*delta/cb;
d.ptr.p_double[j+1] = 3*beta*delta/cb;
}
}
}
/*
* Transition to next segment
*/
i = sn-1;
}
spline1dbuildhermite(&ex, &ey, &d, n, c, _state);
c->continuity = 2;
ae_frame_leave(_state);
}
/*************************************************************************
Internal version of Spline1DGridDiffCubic.
Accepts pre-ordered X/Y, temporary arrays (which may be preallocated, if
you want to save time, or not) and output array (which may be preallocated
too).
Y is passed as var-parameter because we may need to force last element to
be equal to the first one (if periodic boundary conditions are specified).
-- ALGLIB PROJECT --
Copyright 03.09.2010 by Bochkanov Sergey
*************************************************************************/
static void spline1d_spline1dgriddiffcubicinternal(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t boundltype,
double boundl,
ae_int_t boundrtype,
double boundr,
/* Real */ ae_vector* d,
/* Real */ ae_vector* a1,
/* Real */ ae_vector* a2,
/* Real */ ae_vector* a3,
/* Real */ ae_vector* b,
/* Real */ ae_vector* dt,
ae_state *_state)
{
ae_int_t i;
/*
* allocate arrays
*/
if( d->cnt<n )
{
ae_vector_set_length(d, n, _state);
}
if( a1->cnt<n )
{
ae_vector_set_length(a1, n, _state);
}
if( a2->cnt<n )
{
ae_vector_set_length(a2, n, _state);
}
if( a3->cnt<n )
{
ae_vector_set_length(a3, n, _state);
}
if( b->cnt<n )
{
ae_vector_set_length(b, n, _state);
}
if( dt->cnt<n )
{
ae_vector_set_length(dt, n, _state);
}
/*
* Special cases:
* * N=2, parabolic terminated boundary condition on both ends
* * N=2, periodic boundary condition
*/
if( (n==2&&boundltype==0)&&boundrtype==0 )
{
d->ptr.p_double[0] = (y->ptr.p_double[1]-y->ptr.p_double[0])/(x->ptr.p_double[1]-x->ptr.p_double[0]);
d->ptr.p_double[1] = d->ptr.p_double[0];
return;
}
if( (n==2&&boundltype==-1)&&boundrtype==-1 )
{
d->ptr.p_double[0] = (double)(0);
d->ptr.p_double[1] = (double)(0);
return;
}
/*
* Periodic and non-periodic boundary conditions are
* two separate classes
*/
if( boundrtype==-1&&boundltype==-1 )
{
/*
* Periodic boundary conditions
*/
y->ptr.p_double[n-1] = y->ptr.p_double[0];
/*
* Boundary conditions at N-1 points
* (one point less because last point is the same as first point).
*/
a1->ptr.p_double[0] = x->ptr.p_double[1]-x->ptr.p_double[0];
a2->ptr.p_double[0] = 2*(x->ptr.p_double[1]-x->ptr.p_double[0]+x->ptr.p_double[n-1]-x->ptr.p_double[n-2]);
a3->ptr.p_double[0] = x->ptr.p_double[n-1]-x->ptr.p_double[n-2];
b->ptr.p_double[0] = 3*(y->ptr.p_double[n-1]-y->ptr.p_double[n-2])/(x->ptr.p_double[n-1]-x->ptr.p_double[n-2])*(x->ptr.p_double[1]-x->ptr.p_double[0])+3*(y->ptr.p_double[1]-y->ptr.p_double[0])/(x->ptr.p_double[1]-x->ptr.p_double[0])*(x->ptr.p_double[n-1]-x->ptr.p_double[n-2]);
for(i=1; i<=n-2; i++)
{
/*
* Altough last point is [N-2], we use X[N-1] and Y[N-1]
* (because of periodicity)
*/
a1->ptr.p_double[i] = x->ptr.p_double[i+1]-x->ptr.p_double[i];
a2->ptr.p_double[i] = 2*(x->ptr.p_double[i+1]-x->ptr.p_double[i-1]);
a3->ptr.p_double[i] = x->ptr.p_double[i]-x->ptr.p_double[i-1];
b->ptr.p_double[i] = 3*(y->ptr.p_double[i]-y->ptr.p_double[i-1])/(x->ptr.p_double[i]-x->ptr.p_double[i-1])*(x->ptr.p_double[i+1]-x->ptr.p_double[i])+3*(y->ptr.p_double[i+1]-y->ptr.p_double[i])/(x->ptr.p_double[i+1]-x->ptr.p_double[i])*(x->ptr.p_double[i]-x->ptr.p_double[i-1]);
}
/*
* Solve, add last point (with index N-1)
*/
spline1d_solvecyclictridiagonal(a1, a2, a3, b, n-1, dt, _state);
ae_v_move(&d->ptr.p_double[0], 1, &dt->ptr.p_double[0], 1, ae_v_len(0,n-2));
d->ptr.p_double[n-1] = d->ptr.p_double[0];
}
else
{
/*
* Non-periodic boundary condition.
* Left boundary conditions.
*/
if( boundltype==0 )
{
a1->ptr.p_double[0] = (double)(0);
a2->ptr.p_double[0] = (double)(1);
a3->ptr.p_double[0] = (double)(1);
b->ptr.p_double[0] = 2*(y->ptr.p_double[1]-y->ptr.p_double[0])/(x->ptr.p_double[1]-x->ptr.p_double[0]);
}
if( boundltype==1 )
{
a1->ptr.p_double[0] = (double)(0);
a2->ptr.p_double[0] = (double)(1);
a3->ptr.p_double[0] = (double)(0);
b->ptr.p_double[0] = boundl;
}
if( boundltype==2 )
{
a1->ptr.p_double[0] = (double)(0);
a2->ptr.p_double[0] = (double)(2);
a3->ptr.p_double[0] = (double)(1);
b->ptr.p_double[0] = 3*(y->ptr.p_double[1]-y->ptr.p_double[0])/(x->ptr.p_double[1]-x->ptr.p_double[0])-0.5*boundl*(x->ptr.p_double[1]-x->ptr.p_double[0]);
}
/*
* Central conditions
*/
for(i=1; i<=n-2; i++)
{
a1->ptr.p_double[i] = x->ptr.p_double[i+1]-x->ptr.p_double[i];
a2->ptr.p_double[i] = 2*(x->ptr.p_double[i+1]-x->ptr.p_double[i-1]);
a3->ptr.p_double[i] = x->ptr.p_double[i]-x->ptr.p_double[i-1];
b->ptr.p_double[i] = 3*(y->ptr.p_double[i]-y->ptr.p_double[i-1])/(x->ptr.p_double[i]-x->ptr.p_double[i-1])*(x->ptr.p_double[i+1]-x->ptr.p_double[i])+3*(y->ptr.p_double[i+1]-y->ptr.p_double[i])/(x->ptr.p_double[i+1]-x->ptr.p_double[i])*(x->ptr.p_double[i]-x->ptr.p_double[i-1]);
}
/*
* Right boundary conditions
*/
if( boundrtype==0 )
{
a1->ptr.p_double[n-1] = (double)(1);
a2->ptr.p_double[n-1] = (double)(1);
a3->ptr.p_double[n-1] = (double)(0);
b->ptr.p_double[n-1] = 2*(y->ptr.p_double[n-1]-y->ptr.p_double[n-2])/(x->ptr.p_double[n-1]-x->ptr.p_double[n-2]);
}
if( boundrtype==1 )
{
a1->ptr.p_double[n-1] = (double)(0);
a2->ptr.p_double[n-1] = (double)(1);
a3->ptr.p_double[n-1] = (double)(0);
b->ptr.p_double[n-1] = boundr;
}
if( boundrtype==2 )
{
a1->ptr.p_double[n-1] = (double)(1);
a2->ptr.p_double[n-1] = (double)(2);
a3->ptr.p_double[n-1] = (double)(0);
b->ptr.p_double[n-1] = 3*(y->ptr.p_double[n-1]-y->ptr.p_double[n-2])/(x->ptr.p_double[n-1]-x->ptr.p_double[n-2])+0.5*boundr*(x->ptr.p_double[n-1]-x->ptr.p_double[n-2]);
}
/*
* Solve
*/
spline1d_solvetridiagonal(a1, a2, a3, b, n, d, _state);
}
}
/*************************************************************************
Internal subroutine. Heap sort.
*************************************************************************/
static void spline1d_heapsortpoints(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector bufx;
ae_vector bufy;
ae_frame_make(_state, &_frame_block);
memset(&bufx, 0, sizeof(bufx));
memset(&bufy, 0, sizeof(bufy));
ae_vector_init(&bufx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bufy, 0, DT_REAL, _state, ae_true);
tagsortfastr(x, y, &bufx, &bufy, n, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Internal subroutine. Heap sort.
Accepts:
X, Y - points
P - empty or preallocated array
Returns:
X, Y - sorted by X
P - array of permutations; I-th position of output
arrays X/Y contains (X[P[I]],Y[P[I]])
*************************************************************************/
static void spline1d_heapsortppoints(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Integer */ ae_vector* p,
ae_int_t n,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector rbuf;
ae_vector ibuf;
ae_int_t i;
ae_frame_make(_state, &_frame_block);
memset(&rbuf, 0, sizeof(rbuf));
memset(&ibuf, 0, sizeof(ibuf));
ae_vector_init(&rbuf, 0, DT_REAL, _state, ae_true);
ae_vector_init(&ibuf, 0, DT_INT, _state, ae_true);
if( p->cnt<n )
{
ae_vector_set_length(p, n, _state);
}
ae_vector_set_length(&rbuf, n, _state);
for(i=0; i<=n-1; i++)
{
p->ptr.p_int[i] = i;
}
tagsortfasti(x, p, &rbuf, &ibuf, n, _state);
for(i=0; i<=n-1; i++)
{
rbuf.ptr.p_double[i] = y->ptr.p_double[p->ptr.p_int[i]];
}
ae_v_move(&y->ptr.p_double[0], 1, &rbuf.ptr.p_double[0], 1, ae_v_len(0,n-1));
ae_frame_leave(_state);
}
/*************************************************************************
Internal subroutine. Tridiagonal solver. Solves
( B[0] C[0]
( A[1] B[1] C[1] )
( A[2] B[2] C[2] )
( .......... ) * X = D
( .......... )
( A[N-2] B[N-2] C[N-2] )
( A[N-1] B[N-1] )
*************************************************************************/
static void spline1d_solvetridiagonal(/* Real */ ae_vector* a,
/* Real */ ae_vector* b,
/* Real */ ae_vector* c,
/* Real */ ae_vector* d,
ae_int_t n,
/* Real */ ae_vector* x,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _b;
ae_vector _d;
ae_int_t k;
double t;
ae_frame_make(_state, &_frame_block);
memset(&_b, 0, sizeof(_b));
memset(&_d, 0, sizeof(_d));
ae_vector_init_copy(&_b, b, _state, ae_true);
b = &_b;
ae_vector_init_copy(&_d, d, _state, ae_true);
d = &_d;
if( x->cnt<n )
{
ae_vector_set_length(x, n, _state);
}
for(k=1; k<=n-1; k++)
{
t = a->ptr.p_double[k]/b->ptr.p_double[k-1];
b->ptr.p_double[k] = b->ptr.p_double[k]-t*c->ptr.p_double[k-1];
d->ptr.p_double[k] = d->ptr.p_double[k]-t*d->ptr.p_double[k-1];
}
x->ptr.p_double[n-1] = d->ptr.p_double[n-1]/b->ptr.p_double[n-1];
for(k=n-2; k>=0; k--)
{
x->ptr.p_double[k] = (d->ptr.p_double[k]-c->ptr.p_double[k]*x->ptr.p_double[k+1])/b->ptr.p_double[k];
}
ae_frame_leave(_state);
}
/*************************************************************************
Internal subroutine. Cyclic tridiagonal solver. Solves
( B[0] C[0] A[0] )
( A[1] B[1] C[1] )
( A[2] B[2] C[2] )
( .......... ) * X = D
( .......... )
( A[N-2] B[N-2] C[N-2] )
( C[N-1] A[N-1] B[N-1] )
*************************************************************************/
static void spline1d_solvecyclictridiagonal(/* Real */ ae_vector* a,
/* Real */ ae_vector* b,
/* Real */ ae_vector* c,
/* Real */ ae_vector* d,
ae_int_t n,
/* Real */ ae_vector* x,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _b;
ae_int_t k;
double alpha;
double beta;
double gamma;
ae_vector y;
ae_vector z;
ae_vector u;
ae_frame_make(_state, &_frame_block);
memset(&_b, 0, sizeof(_b));
memset(&y, 0, sizeof(y));
memset(&z, 0, sizeof(z));
memset(&u, 0, sizeof(u));
ae_vector_init_copy(&_b, b, _state, ae_true);
b = &_b;
ae_vector_init(&y, 0, DT_REAL, _state, ae_true);
ae_vector_init(&z, 0, DT_REAL, _state, ae_true);
ae_vector_init(&u, 0, DT_REAL, _state, ae_true);
if( x->cnt<n )
{
ae_vector_set_length(x, n, _state);
}
beta = a->ptr.p_double[0];
alpha = c->ptr.p_double[n-1];
gamma = -b->ptr.p_double[0];
b->ptr.p_double[0] = 2*b->ptr.p_double[0];
b->ptr.p_double[n-1] = b->ptr.p_double[n-1]-alpha*beta/gamma;
ae_vector_set_length(&u, n, _state);
for(k=0; k<=n-1; k++)
{
u.ptr.p_double[k] = (double)(0);
}
u.ptr.p_double[0] = gamma;
u.ptr.p_double[n-1] = alpha;
spline1d_solvetridiagonal(a, b, c, d, n, &y, _state);
spline1d_solvetridiagonal(a, b, c, &u, n, &z, _state);
for(k=0; k<=n-1; k++)
{
x->ptr.p_double[k] = y.ptr.p_double[k]-(y.ptr.p_double[0]+beta/gamma*y.ptr.p_double[n-1])/(1+z.ptr.p_double[0]+beta/gamma*z.ptr.p_double[n-1])*z.ptr.p_double[k];
}
ae_frame_leave(_state);
}
/*************************************************************************
Internal subroutine. Three-point differentiation
*************************************************************************/
static double spline1d_diffthreepoint(double t,
double x0,
double f0,
double x1,
double f1,
double x2,
double f2,
ae_state *_state)
{
double a;
double b;
double result;
t = t-x0;
x1 = x1-x0;
x2 = x2-x0;
a = (f2-f0-x2/x1*(f1-f0))/(ae_sqr(x2, _state)-x1*x2);
b = (f1-f0-a*ae_sqr(x1, _state))/x1;
result = 2*a*t+b;
return result;
}
/*************************************************************************
Procedure for calculating value of a function is providet in the form of
Hermite polinom
INPUT PARAMETERS:
P0 - value of a function at 0
M0 - value of a derivative at 0
P1 - value of a function at 1
M1 - value of a derivative at 1
T - point inside [0;1]
OUTPUT PARAMETERS:
S - value of a function at T
B0 - value of a derivative function at T
-- ALGLIB PROJECT --
Copyright 26.09.2011 by Bochkanov Sergey
*************************************************************************/
static void spline1d_hermitecalc(double p0,
double m0,
double p1,
double m1,
double t,
double* s,
double* ds,
ae_state *_state)
{
*s = 0;
*ds = 0;
*s = p0*(1+2*t)*(1-t)*(1-t)+m0*t*(1-t)*(1-t)+p1*(3-2*t)*t*t+m1*t*t*(t-1);
*ds = -p0*6*t*(1-t)+m0*(1-t)*(1-3*t)+p1*6*t*(1-t)+m1*t*(3*t-2);
}
/*************************************************************************
Function for mapping from [A0;B0] to [A1;B1]
INPUT PARAMETERS:
A0 - left border [A0;B0]
B0 - right border [A0;B0]
A1 - left border [A1;B1]
B1 - right border [A1;B1]
T - value inside [A0;B0]
RESTRICTIONS OF PARAMETERS:
We assume, that B0>A0 and B1>A1. But we chech, that T is inside [A0;B0],
and if T<A0 then T become A1, if T>B0 then T - B1.
INPUT PARAMETERS:
A0 - left border for segment [A0;B0] from 'T' is converted to [A1;B1]
B0 - right border for segment [A0;B0] from 'T' is converted to [A1;B1]
A1 - left border for segment [A1;B1] to 'T' is converted from [A0;B0]
B1 - right border for segment [A1;B1] to 'T' is converted from [A0;B0]
T - the parameter is mapped from [A0;B0] to [A1;B1]
Result:
is converted value for 'T' from [A0;B0] to [A1;B1]
REMARK:
The function dont check value A0,B0 and A1,B1!
-- ALGLIB PROJECT --
Copyright 26.09.2011 by Bochkanov Sergey
*************************************************************************/
static double spline1d_rescaleval(double a0,
double b0,
double a1,
double b1,
double t,
ae_state *_state)
{
double result;
/*
*return left border
*/
if( ae_fp_less_eq(t,a0) )
{
result = a1;
return result;
}
/*
*return right border
*/
if( ae_fp_greater_eq(t,b0) )
{
result = b1;
return result;
}
/*
*return value between left and right borders
*/
result = (b1-a1)*(t-a0)/(b0-a0)+a1;
return result;
}
void _spline1dinterpolant_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
spline1dinterpolant *p = (spline1dinterpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->x, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->c, 0, DT_REAL, _state, make_automatic);
}
void _spline1dinterpolant_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
spline1dinterpolant *dst = (spline1dinterpolant*)_dst;
spline1dinterpolant *src = (spline1dinterpolant*)_src;
dst->periodic = src->periodic;
dst->n = src->n;
dst->k = src->k;
dst->continuity = src->continuity;
ae_vector_init_copy(&dst->x, &src->x, _state, make_automatic);
ae_vector_init_copy(&dst->c, &src->c, _state, make_automatic);
}
void _spline1dinterpolant_clear(void* _p)
{
spline1dinterpolant *p = (spline1dinterpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->x);
ae_vector_clear(&p->c);
}
void _spline1dinterpolant_destroy(void* _p)
{
spline1dinterpolant *p = (spline1dinterpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->x);
ae_vector_destroy(&p->c);
}
void _spline1dfitreport_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
spline1dfitreport *p = (spline1dfitreport*)_p;
ae_touch_ptr((void*)p);
}
void _spline1dfitreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
spline1dfitreport *dst = (spline1dfitreport*)_dst;
spline1dfitreport *src = (spline1dfitreport*)_src;
dst->taskrcond = src->taskrcond;
dst->rmserror = src->rmserror;
dst->avgerror = src->avgerror;
dst->avgrelerror = src->avgrelerror;
dst->maxerror = src->maxerror;
}
void _spline1dfitreport_clear(void* _p)
{
spline1dfitreport *p = (spline1dfitreport*)_p;
ae_touch_ptr((void*)p);
}
void _spline1dfitreport_destroy(void* _p)
{
spline1dfitreport *p = (spline1dfitreport*)_p;
ae_touch_ptr((void*)p);
}
#endif
#if defined(AE_COMPILE_PARAMETRIC) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This function builds non-periodic 2-dimensional parametric spline which
starts at (X[0],Y[0]) and ends at (X[N-1],Y[N-1]).
INPUT PARAMETERS:
XY - points, array[0..N-1,0..1].
XY[I,0:1] corresponds to the Ith point.
Order of points is important!
N - points count, N>=5 for Akima splines, N>=2 for other types of
splines.
ST - spline type:
* 0 Akima spline
* 1 parabolically terminated Catmull-Rom spline (Tension=0)
* 2 parabolically terminated cubic spline
PT - parameterization type:
* 0 uniform
* 1 chord length
* 2 centripetal
OUTPUT PARAMETERS:
P - parametric spline interpolant
NOTES:
* this function assumes that there all consequent points are distinct.
I.e. (x0,y0)<>(x1,y1), (x1,y1)<>(x2,y2), (x2,y2)<>(x3,y3) and so on.
However, non-consequent points may coincide, i.e. we can have (x0,y0)=
=(x2,y2).
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline2build(/* Real */ ae_matrix* xy,
ae_int_t n,
ae_int_t st,
ae_int_t pt,
pspline2interpolant* p,
ae_state *_state)
{
ae_frame _frame_block;
ae_matrix _xy;
ae_vector tmp;
ae_frame_make(_state, &_frame_block);
memset(&_xy, 0, sizeof(_xy));
memset(&tmp, 0, sizeof(tmp));
ae_matrix_init_copy(&_xy, xy, _state, ae_true);
xy = &_xy;
_pspline2interpolant_clear(p);
ae_vector_init(&tmp, 0, DT_REAL, _state, ae_true);
ae_assert(st>=0&&st<=2, "PSpline2Build: incorrect spline type!", _state);
ae_assert(pt>=0&&pt<=2, "PSpline2Build: incorrect parameterization type!", _state);
if( st==0 )
{
ae_assert(n>=5, "PSpline2Build: N<5 (minimum value for Akima splines)!", _state);
}
else
{
ae_assert(n>=2, "PSpline2Build: N<2!", _state);
}
/*
* Prepare
*/
p->n = n;
p->periodic = ae_false;
ae_vector_set_length(&tmp, n, _state);
/*
* Build parameterization, check that all parameters are distinct
*/
parametric_pspline2par(xy, n, pt, &p->p, _state);
ae_assert(aredistinct(&p->p, n, _state), "PSpline2Build: consequent points are too close!", _state);
/*
* Build splines
*/
if( st==0 )
{
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][0], xy->stride, ae_v_len(0,n-1));
spline1dbuildakima(&p->p, &tmp, n, &p->x, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][1], xy->stride, ae_v_len(0,n-1));
spline1dbuildakima(&p->p, &tmp, n, &p->y, _state);
}
if( st==1 )
{
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][0], xy->stride, ae_v_len(0,n-1));
spline1dbuildcatmullrom(&p->p, &tmp, n, 0, 0.0, &p->x, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][1], xy->stride, ae_v_len(0,n-1));
spline1dbuildcatmullrom(&p->p, &tmp, n, 0, 0.0, &p->y, _state);
}
if( st==2 )
{
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][0], xy->stride, ae_v_len(0,n-1));
spline1dbuildcubic(&p->p, &tmp, n, 0, 0.0, 0, 0.0, &p->x, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][1], xy->stride, ae_v_len(0,n-1));
spline1dbuildcubic(&p->p, &tmp, n, 0, 0.0, 0, 0.0, &p->y, _state);
}
ae_frame_leave(_state);
}
/*************************************************************************
This function builds non-periodic 3-dimensional parametric spline which
starts at (X[0],Y[0],Z[0]) and ends at (X[N-1],Y[N-1],Z[N-1]).
Same as PSpline2Build() function, but for 3D, so we won't duplicate its
description here.
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline3build(/* Real */ ae_matrix* xy,
ae_int_t n,
ae_int_t st,
ae_int_t pt,
pspline3interpolant* p,
ae_state *_state)
{
ae_frame _frame_block;
ae_matrix _xy;
ae_vector tmp;
ae_frame_make(_state, &_frame_block);
memset(&_xy, 0, sizeof(_xy));
memset(&tmp, 0, sizeof(tmp));
ae_matrix_init_copy(&_xy, xy, _state, ae_true);
xy = &_xy;
_pspline3interpolant_clear(p);
ae_vector_init(&tmp, 0, DT_REAL, _state, ae_true);
ae_assert(st>=0&&st<=2, "PSpline3Build: incorrect spline type!", _state);
ae_assert(pt>=0&&pt<=2, "PSpline3Build: incorrect parameterization type!", _state);
if( st==0 )
{
ae_assert(n>=5, "PSpline3Build: N<5 (minimum value for Akima splines)!", _state);
}
else
{
ae_assert(n>=2, "PSpline3Build: N<2!", _state);
}
/*
* Prepare
*/
p->n = n;
p->periodic = ae_false;
ae_vector_set_length(&tmp, n, _state);
/*
* Build parameterization, check that all parameters are distinct
*/
parametric_pspline3par(xy, n, pt, &p->p, _state);
ae_assert(aredistinct(&p->p, n, _state), "PSpline3Build: consequent points are too close!", _state);
/*
* Build splines
*/
if( st==0 )
{
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][0], xy->stride, ae_v_len(0,n-1));
spline1dbuildakima(&p->p, &tmp, n, &p->x, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][1], xy->stride, ae_v_len(0,n-1));
spline1dbuildakima(&p->p, &tmp, n, &p->y, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][2], xy->stride, ae_v_len(0,n-1));
spline1dbuildakima(&p->p, &tmp, n, &p->z, _state);
}
if( st==1 )
{
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][0], xy->stride, ae_v_len(0,n-1));
spline1dbuildcatmullrom(&p->p, &tmp, n, 0, 0.0, &p->x, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][1], xy->stride, ae_v_len(0,n-1));
spline1dbuildcatmullrom(&p->p, &tmp, n, 0, 0.0, &p->y, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][2], xy->stride, ae_v_len(0,n-1));
spline1dbuildcatmullrom(&p->p, &tmp, n, 0, 0.0, &p->z, _state);
}
if( st==2 )
{
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][0], xy->stride, ae_v_len(0,n-1));
spline1dbuildcubic(&p->p, &tmp, n, 0, 0.0, 0, 0.0, &p->x, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][1], xy->stride, ae_v_len(0,n-1));
spline1dbuildcubic(&p->p, &tmp, n, 0, 0.0, 0, 0.0, &p->y, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xy->ptr.pp_double[0][2], xy->stride, ae_v_len(0,n-1));
spline1dbuildcubic(&p->p, &tmp, n, 0, 0.0, 0, 0.0, &p->z, _state);
}
ae_frame_leave(_state);
}
/*************************************************************************
This function builds periodic 2-dimensional parametric spline which
starts at (X[0],Y[0]), goes through all points to (X[N-1],Y[N-1]) and then
back to (X[0],Y[0]).
INPUT PARAMETERS:
XY - points, array[0..N-1,0..1].
XY[I,0:1] corresponds to the Ith point.
XY[N-1,0:1] must be different from XY[0,0:1].
Order of points is important!
N - points count, N>=3 for other types of splines.
ST - spline type:
* 1 Catmull-Rom spline (Tension=0) with cyclic boundary conditions
* 2 cubic spline with cyclic boundary conditions
PT - parameterization type:
* 0 uniform
* 1 chord length
* 2 centripetal
OUTPUT PARAMETERS:
P - parametric spline interpolant
NOTES:
* this function assumes that there all consequent points are distinct.
I.e. (x0,y0)<>(x1,y1), (x1,y1)<>(x2,y2), (x2,y2)<>(x3,y3) and so on.
However, non-consequent points may coincide, i.e. we can have (x0,y0)=
=(x2,y2).
* last point of sequence is NOT equal to the first point. You shouldn't
make curve "explicitly periodic" by making them equal.
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline2buildperiodic(/* Real */ ae_matrix* xy,
ae_int_t n,
ae_int_t st,
ae_int_t pt,
pspline2interpolant* p,
ae_state *_state)
{
ae_frame _frame_block;
ae_matrix _xy;
ae_matrix xyp;
ae_vector tmp;
ae_frame_make(_state, &_frame_block);
memset(&_xy, 0, sizeof(_xy));
memset(&xyp, 0, sizeof(xyp));
memset(&tmp, 0, sizeof(tmp));
ae_matrix_init_copy(&_xy, xy, _state, ae_true);
xy = &_xy;
_pspline2interpolant_clear(p);
ae_matrix_init(&xyp, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp, 0, DT_REAL, _state, ae_true);
ae_assert(st>=1&&st<=2, "PSpline2BuildPeriodic: incorrect spline type!", _state);
ae_assert(pt>=0&&pt<=2, "PSpline2BuildPeriodic: incorrect parameterization type!", _state);
ae_assert(n>=3, "PSpline2BuildPeriodic: N<3!", _state);
/*
* Prepare
*/
p->n = n;
p->periodic = ae_true;
ae_vector_set_length(&tmp, n+1, _state);
ae_matrix_set_length(&xyp, n+1, 2, _state);
ae_v_move(&xyp.ptr.pp_double[0][0], xyp.stride, &xy->ptr.pp_double[0][0], xy->stride, ae_v_len(0,n-1));
ae_v_move(&xyp.ptr.pp_double[0][1], xyp.stride, &xy->ptr.pp_double[0][1], xy->stride, ae_v_len(0,n-1));
ae_v_move(&xyp.ptr.pp_double[n][0], 1, &xy->ptr.pp_double[0][0], 1, ae_v_len(0,1));
/*
* Build parameterization, check that all parameters are distinct
*/
parametric_pspline2par(&xyp, n+1, pt, &p->p, _state);
ae_assert(aredistinct(&p->p, n+1, _state), "PSpline2BuildPeriodic: consequent (or first and last) points are too close!", _state);
/*
* Build splines
*/
if( st==1 )
{
ae_v_move(&tmp.ptr.p_double[0], 1, &xyp.ptr.pp_double[0][0], xyp.stride, ae_v_len(0,n));
spline1dbuildcatmullrom(&p->p, &tmp, n+1, -1, 0.0, &p->x, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xyp.ptr.pp_double[0][1], xyp.stride, ae_v_len(0,n));
spline1dbuildcatmullrom(&p->p, &tmp, n+1, -1, 0.0, &p->y, _state);
}
if( st==2 )
{
ae_v_move(&tmp.ptr.p_double[0], 1, &xyp.ptr.pp_double[0][0], xyp.stride, ae_v_len(0,n));
spline1dbuildcubic(&p->p, &tmp, n+1, -1, 0.0, -1, 0.0, &p->x, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xyp.ptr.pp_double[0][1], xyp.stride, ae_v_len(0,n));
spline1dbuildcubic(&p->p, &tmp, n+1, -1, 0.0, -1, 0.0, &p->y, _state);
}
ae_frame_leave(_state);
}
/*************************************************************************
This function builds periodic 3-dimensional parametric spline which
starts at (X[0],Y[0],Z[0]), goes through all points to (X[N-1],Y[N-1],Z[N-1])
and then back to (X[0],Y[0],Z[0]).
Same as PSpline2Build() function, but for 3D, so we won't duplicate its
description here.
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline3buildperiodic(/* Real */ ae_matrix* xy,
ae_int_t n,
ae_int_t st,
ae_int_t pt,
pspline3interpolant* p,
ae_state *_state)
{
ae_frame _frame_block;
ae_matrix _xy;
ae_matrix xyp;
ae_vector tmp;
ae_frame_make(_state, &_frame_block);
memset(&_xy, 0, sizeof(_xy));
memset(&xyp, 0, sizeof(xyp));
memset(&tmp, 0, sizeof(tmp));
ae_matrix_init_copy(&_xy, xy, _state, ae_true);
xy = &_xy;
_pspline3interpolant_clear(p);
ae_matrix_init(&xyp, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp, 0, DT_REAL, _state, ae_true);
ae_assert(st>=1&&st<=2, "PSpline3BuildPeriodic: incorrect spline type!", _state);
ae_assert(pt>=0&&pt<=2, "PSpline3BuildPeriodic: incorrect parameterization type!", _state);
ae_assert(n>=3, "PSpline3BuildPeriodic: N<3!", _state);
/*
* Prepare
*/
p->n = n;
p->periodic = ae_true;
ae_vector_set_length(&tmp, n+1, _state);
ae_matrix_set_length(&xyp, n+1, 3, _state);
ae_v_move(&xyp.ptr.pp_double[0][0], xyp.stride, &xy->ptr.pp_double[0][0], xy->stride, ae_v_len(0,n-1));
ae_v_move(&xyp.ptr.pp_double[0][1], xyp.stride, &xy->ptr.pp_double[0][1], xy->stride, ae_v_len(0,n-1));
ae_v_move(&xyp.ptr.pp_double[0][2], xyp.stride, &xy->ptr.pp_double[0][2], xy->stride, ae_v_len(0,n-1));
ae_v_move(&xyp.ptr.pp_double[n][0], 1, &xy->ptr.pp_double[0][0], 1, ae_v_len(0,2));
/*
* Build parameterization, check that all parameters are distinct
*/
parametric_pspline3par(&xyp, n+1, pt, &p->p, _state);
ae_assert(aredistinct(&p->p, n+1, _state), "PSplineBuild2Periodic: consequent (or first and last) points are too close!", _state);
/*
* Build splines
*/
if( st==1 )
{
ae_v_move(&tmp.ptr.p_double[0], 1, &xyp.ptr.pp_double[0][0], xyp.stride, ae_v_len(0,n));
spline1dbuildcatmullrom(&p->p, &tmp, n+1, -1, 0.0, &p->x, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xyp.ptr.pp_double[0][1], xyp.stride, ae_v_len(0,n));
spline1dbuildcatmullrom(&p->p, &tmp, n+1, -1, 0.0, &p->y, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xyp.ptr.pp_double[0][2], xyp.stride, ae_v_len(0,n));
spline1dbuildcatmullrom(&p->p, &tmp, n+1, -1, 0.0, &p->z, _state);
}
if( st==2 )
{
ae_v_move(&tmp.ptr.p_double[0], 1, &xyp.ptr.pp_double[0][0], xyp.stride, ae_v_len(0,n));
spline1dbuildcubic(&p->p, &tmp, n+1, -1, 0.0, -1, 0.0, &p->x, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xyp.ptr.pp_double[0][1], xyp.stride, ae_v_len(0,n));
spline1dbuildcubic(&p->p, &tmp, n+1, -1, 0.0, -1, 0.0, &p->y, _state);
ae_v_move(&tmp.ptr.p_double[0], 1, &xyp.ptr.pp_double[0][2], xyp.stride, ae_v_len(0,n));
spline1dbuildcubic(&p->p, &tmp, n+1, -1, 0.0, -1, 0.0, &p->z, _state);
}
ae_frame_leave(_state);
}
/*************************************************************************
This function returns vector of parameter values correspoding to points.
I.e. for P created from (X[0],Y[0])...(X[N-1],Y[N-1]) and U=TValues(P) we
have
(X[0],Y[0]) = PSpline2Calc(P,U[0]),
(X[1],Y[1]) = PSpline2Calc(P,U[1]),
(X[2],Y[2]) = PSpline2Calc(P,U[2]),
...
INPUT PARAMETERS:
P - parametric spline interpolant
OUTPUT PARAMETERS:
N - array size
T - array[0..N-1]
NOTES:
* for non-periodic splines U[0]=0, U[0]<U[1]<...<U[N-1], U[N-1]=1
* for periodic splines U[0]=0, U[0]<U[1]<...<U[N-1], U[N-1]<1
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline2parametervalues(pspline2interpolant* p,
ae_int_t* n,
/* Real */ ae_vector* t,
ae_state *_state)
{
*n = 0;
ae_vector_clear(t);
ae_assert(p->n>=2, "PSpline2ParameterValues: internal error!", _state);
*n = p->n;
ae_vector_set_length(t, *n, _state);
ae_v_move(&t->ptr.p_double[0], 1, &p->p.ptr.p_double[0], 1, ae_v_len(0,*n-1));
t->ptr.p_double[0] = (double)(0);
if( !p->periodic )
{
t->ptr.p_double[*n-1] = (double)(1);
}
}
/*************************************************************************
This function returns vector of parameter values correspoding to points.
Same as PSpline2ParameterValues(), but for 3D.
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline3parametervalues(pspline3interpolant* p,
ae_int_t* n,
/* Real */ ae_vector* t,
ae_state *_state)
{
*n = 0;
ae_vector_clear(t);
ae_assert(p->n>=2, "PSpline3ParameterValues: internal error!", _state);
*n = p->n;
ae_vector_set_length(t, *n, _state);
ae_v_move(&t->ptr.p_double[0], 1, &p->p.ptr.p_double[0], 1, ae_v_len(0,*n-1));
t->ptr.p_double[0] = (double)(0);
if( !p->periodic )
{
t->ptr.p_double[*n-1] = (double)(1);
}
}
/*************************************************************************
This function calculates the value of the parametric spline for a given
value of parameter T
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-position
Y - Y-position
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline2calc(pspline2interpolant* p,
double t,
double* x,
double* y,
ae_state *_state)
{
*x = 0;
*y = 0;
if( p->periodic )
{
t = t-ae_ifloor(t, _state);
}
*x = spline1dcalc(&p->x, t, _state);
*y = spline1dcalc(&p->y, t, _state);
}
/*************************************************************************
This function calculates the value of the parametric spline for a given
value of parameter T.
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-position
Y - Y-position
Z - Z-position
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline3calc(pspline3interpolant* p,
double t,
double* x,
double* y,
double* z,
ae_state *_state)
{
*x = 0;
*y = 0;
*z = 0;
if( p->periodic )
{
t = t-ae_ifloor(t, _state);
}
*x = spline1dcalc(&p->x, t, _state);
*y = spline1dcalc(&p->y, t, _state);
*z = spline1dcalc(&p->z, t, _state);
}
/*************************************************************************
This function calculates tangent vector for a given value of parameter T
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-component of tangent vector (normalized)
Y - Y-component of tangent vector (normalized)
NOTE:
X^2+Y^2 is either 1 (for non-zero tangent vector) or 0.
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline2tangent(pspline2interpolant* p,
double t,
double* x,
double* y,
ae_state *_state)
{
double v;
double v0;
double v1;
*x = 0;
*y = 0;
if( p->periodic )
{
t = t-ae_ifloor(t, _state);
}
pspline2diff(p, t, &v0, x, &v1, y, _state);
if( ae_fp_neq(*x,(double)(0))||ae_fp_neq(*y,(double)(0)) )
{
/*
* this code is a bit more complex than X^2+Y^2 to avoid
* overflow for large values of X and Y.
*/
v = safepythag2(*x, *y, _state);
*x = *x/v;
*y = *y/v;
}
}
/*************************************************************************
This function calculates tangent vector for a given value of parameter T
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-component of tangent vector (normalized)
Y - Y-component of tangent vector (normalized)
Z - Z-component of tangent vector (normalized)
NOTE:
X^2+Y^2+Z^2 is either 1 (for non-zero tangent vector) or 0.
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline3tangent(pspline3interpolant* p,
double t,
double* x,
double* y,
double* z,
ae_state *_state)
{
double v;
double v0;
double v1;
double v2;
*x = 0;
*y = 0;
*z = 0;
if( p->periodic )
{
t = t-ae_ifloor(t, _state);
}
pspline3diff(p, t, &v0, x, &v1, y, &v2, z, _state);
if( (ae_fp_neq(*x,(double)(0))||ae_fp_neq(*y,(double)(0)))||ae_fp_neq(*z,(double)(0)) )
{
v = safepythag3(*x, *y, *z, _state);
*x = *x/v;
*y = *y/v;
*z = *z/v;
}
}
/*************************************************************************
This function calculates derivative, i.e. it returns (dX/dT,dY/dT).
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-value
DX - X-derivative
Y - Y-value
DY - Y-derivative
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline2diff(pspline2interpolant* p,
double t,
double* x,
double* dx,
double* y,
double* dy,
ae_state *_state)
{
double d2s;
*x = 0;
*dx = 0;
*y = 0;
*dy = 0;
if( p->periodic )
{
t = t-ae_ifloor(t, _state);
}
spline1ddiff(&p->x, t, x, dx, &d2s, _state);
spline1ddiff(&p->y, t, y, dy, &d2s, _state);
}
/*************************************************************************
This function calculates derivative, i.e. it returns (dX/dT,dY/dT,dZ/dT).
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-value
DX - X-derivative
Y - Y-value
DY - Y-derivative
Z - Z-value
DZ - Z-derivative
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline3diff(pspline3interpolant* p,
double t,
double* x,
double* dx,
double* y,
double* dy,
double* z,
double* dz,
ae_state *_state)
{
double d2s;
*x = 0;
*dx = 0;
*y = 0;
*dy = 0;
*z = 0;
*dz = 0;
if( p->periodic )
{
t = t-ae_ifloor(t, _state);
}
spline1ddiff(&p->x, t, x, dx, &d2s, _state);
spline1ddiff(&p->y, t, y, dy, &d2s, _state);
spline1ddiff(&p->z, t, z, dz, &d2s, _state);
}
/*************************************************************************
This function calculates first and second derivative with respect to T.
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-value
DX - derivative
D2X - second derivative
Y - Y-value
DY - derivative
D2Y - second derivative
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline2diff2(pspline2interpolant* p,
double t,
double* x,
double* dx,
double* d2x,
double* y,
double* dy,
double* d2y,
ae_state *_state)
{
*x = 0;
*dx = 0;
*d2x = 0;
*y = 0;
*dy = 0;
*d2y = 0;
if( p->periodic )
{
t = t-ae_ifloor(t, _state);
}
spline1ddiff(&p->x, t, x, dx, d2x, _state);
spline1ddiff(&p->y, t, y, dy, d2y, _state);
}
/*************************************************************************
This function calculates first and second derivative with respect to T.
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-value
DX - derivative
D2X - second derivative
Y - Y-value
DY - derivative
D2Y - second derivative
Z - Z-value
DZ - derivative
D2Z - second derivative
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
void pspline3diff2(pspline3interpolant* p,
double t,
double* x,
double* dx,
double* d2x,
double* y,
double* dy,
double* d2y,
double* z,
double* dz,
double* d2z,
ae_state *_state)
{
*x = 0;
*dx = 0;
*d2x = 0;
*y = 0;
*dy = 0;
*d2y = 0;
*z = 0;
*dz = 0;
*d2z = 0;
if( p->periodic )
{
t = t-ae_ifloor(t, _state);
}
spline1ddiff(&p->x, t, x, dx, d2x, _state);
spline1ddiff(&p->y, t, y, dy, d2y, _state);
spline1ddiff(&p->z, t, z, dz, d2z, _state);
}
/*************************************************************************
This function calculates arc length, i.e. length of curve between t=a
and t=b.
INPUT PARAMETERS:
P - parametric spline interpolant
A,B - parameter values corresponding to arc ends:
* B>A will result in positive length returned
* B<A will result in negative length returned
RESULT:
length of arc starting at T=A and ending at T=B.
-- ALGLIB PROJECT --
Copyright 30.05.2010 by Bochkanov Sergey
*************************************************************************/
double pspline2arclength(pspline2interpolant* p,
double a,
double b,
ae_state *_state)
{
ae_frame _frame_block;
autogkstate state;
autogkreport rep;
double sx;
double dsx;
double d2sx;
double sy;
double dsy;
double d2sy;
double result;
ae_frame_make(_state, &_frame_block);
memset(&state, 0, sizeof(state));
memset(&rep, 0, sizeof(rep));
_autogkstate_init(&state, _state, ae_true);
_autogkreport_init(&rep, _state, ae_true);
autogksmooth(a, b, &state, _state);
while(autogkiteration(&state, _state))
{
spline1ddiff(&p->x, state.x, &sx, &dsx, &d2sx, _state);
spline1ddiff(&p->y, state.x, &sy, &dsy, &d2sy, _state);
state.f = safepythag2(dsx, dsy, _state);
}
autogkresults(&state, &result, &rep, _state);
ae_assert(rep.terminationtype>0, "PSpline2ArcLength: internal error!", _state);
ae_frame_leave(_state);
return result;
}
/*************************************************************************
This function calculates arc length, i.e. length of curve between t=a
and t=b.
INPUT PARAMETERS:
P - parametric spline interpolant
A,B - parameter values corresponding to arc ends:
* B>A will result in positive length returned
* B<A will result in negative length returned
RESULT:
length of arc starting at T=A and ending at T=B.
-- ALGLIB PROJECT --
Copyright 30.05.2010 by Bochkanov Sergey
*************************************************************************/
double pspline3arclength(pspline3interpolant* p,
double a,
double b,
ae_state *_state)
{
ae_frame _frame_block;
autogkstate state;
autogkreport rep;
double sx;
double dsx;
double d2sx;
double sy;
double dsy;
double d2sy;
double sz;
double dsz;
double d2sz;
double result;
ae_frame_make(_state, &_frame_block);
memset(&state, 0, sizeof(state));
memset(&rep, 0, sizeof(rep));
_autogkstate_init(&state, _state, ae_true);
_autogkreport_init(&rep, _state, ae_true);
autogksmooth(a, b, &state, _state);
while(autogkiteration(&state, _state))
{
spline1ddiff(&p->x, state.x, &sx, &dsx, &d2sx, _state);
spline1ddiff(&p->y, state.x, &sy, &dsy, &d2sy, _state);
spline1ddiff(&p->z, state.x, &sz, &dsz, &d2sz, _state);
state.f = safepythag3(dsx, dsy, dsz, _state);
}
autogkresults(&state, &result, &rep, _state);
ae_assert(rep.terminationtype>0, "PSpline3ArcLength: internal error!", _state);
ae_frame_leave(_state);
return result;
}
/*************************************************************************
This subroutine fits piecewise linear curve to points with Ramer-Douglas-
Peucker algorithm. This function performs PARAMETRIC fit, i.e. it can be
used to fit curves like circles.
On input it accepts dataset which describes parametric multidimensional
curve X(t), with X being vector, and t taking values in [0,N), where N is
a number of points in dataset. As result, it returns reduced dataset X2,
which can be used to build parametric curve X2(t), which approximates
X(t) with desired precision (or has specified number of sections).
INPUT PARAMETERS:
X - array of multidimensional points:
* at least N elements, leading N elements are used if more
than N elements were specified
* order of points is IMPORTANT because it is parametric
fit
* each row of array is one point which has D coordinates
N - number of elements in X
D - number of dimensions (elements per row of X)
StopM - stopping condition - desired number of sections:
* at most M sections are generated by this function
* less than M sections can be generated if we have N<M
(or some X are non-distinct).
* zero StopM means that algorithm does not stop after
achieving some pre-specified section count
StopEps - stopping condition - desired precision:
* algorithm stops after error in each section is at most Eps
* zero Eps means that algorithm does not stop after
achieving some pre-specified precision
OUTPUT PARAMETERS:
X2 - array of corner points for piecewise approximation,
has length NSections+1 or zero (for NSections=0).
Idx2 - array of indexes (parameter values):
* has length NSections+1 or zero (for NSections=0).
* each element of Idx2 corresponds to same-numbered
element of X2
* each element of Idx2 is index of corresponding element
of X2 at original array X, i.e. I-th row of X2 is
Idx2[I]-th row of X.
* elements of Idx2 can be treated as parameter values
which should be used when building new parametric curve
* Idx2[0]=0, Idx2[NSections]=N-1
NSections- number of sections found by algorithm, NSections<=M,
NSections can be zero for degenerate datasets
(N<=1 or all X[] are non-distinct).
NOTE: algorithm stops after:
a) dividing curve into StopM sections
b) achieving required precision StopEps
c) dividing curve into N-1 sections
If both StopM and StopEps are non-zero, algorithm is stopped by the
FIRST criterion which is satisfied. In case both StopM and StopEps
are zero, algorithm stops because of (c).
-- ALGLIB --
Copyright 02.10.2014 by Bochkanov Sergey
*************************************************************************/
void parametricrdpfixed(/* Real */ ae_matrix* x,
ae_int_t n,
ae_int_t d,
ae_int_t stopm,
double stopeps,
/* Real */ ae_matrix* x2,
/* Integer */ ae_vector* idx2,
ae_int_t* nsections,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_bool allsame;
ae_int_t k0;
ae_int_t k1;
ae_int_t k2;
double e0;
double e1;
ae_int_t idx0;
ae_int_t idx1;
ae_int_t worstidx;
double worsterror;
ae_matrix sections;
ae_vector heaperrors;
ae_vector heaptags;
ae_vector buf0;
ae_vector buf1;
ae_frame_make(_state, &_frame_block);
memset(&sections, 0, sizeof(sections));
memset(&heaperrors, 0, sizeof(heaperrors));
memset(&heaptags, 0, sizeof(heaptags));
memset(&buf0, 0, sizeof(buf0));
memset(&buf1, 0, sizeof(buf1));
ae_matrix_clear(x2);
ae_vector_clear(idx2);
*nsections = 0;
ae_matrix_init(&sections, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&heaperrors, 0, DT_REAL, _state, ae_true);
ae_vector_init(&heaptags, 0, DT_INT, _state, ae_true);
ae_vector_init(&buf0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&buf1, 0, DT_REAL, _state, ae_true);
ae_assert(n>=0, "LSTFitPiecewiseLinearParametricRDP: N<0", _state);
ae_assert(d>=1, "LSTFitPiecewiseLinearParametricRDP: D<=0", _state);
ae_assert(stopm>=0, "LSTFitPiecewiseLinearParametricRDP: StopM<1", _state);
ae_assert(ae_isfinite(stopeps, _state)&&ae_fp_greater_eq(stopeps,(double)(0)), "LSTFitPiecewiseLinearParametricRDP: StopEps<0 or is infinite", _state);
ae_assert(x->rows>=n, "LSTFitPiecewiseLinearParametricRDP: Rows(X)<N", _state);
ae_assert(x->cols>=d, "LSTFitPiecewiseLinearParametricRDP: Cols(X)<D", _state);
ae_assert(apservisfinitematrix(x, n, d, _state), "LSTFitPiecewiseLinearParametricRDP: X contains infinite/NAN values", _state);
/*
* Handle degenerate cases
*/
if( n<=1 )
{
*nsections = 0;
ae_frame_leave(_state);
return;
}
allsame = ae_true;
for(i=1; i<=n-1; i++)
{
for(j=0; j<=d-1; j++)
{
allsame = allsame&&ae_fp_eq(x->ptr.pp_double[i][j],x->ptr.pp_double[0][j]);
}
}
if( allsame )
{
*nsections = 0;
ae_frame_leave(_state);
return;
}
/*
* Prepare first section
*/
parametric_rdpanalyzesectionpar(x, 0, n-1, d, &worstidx, &worsterror, _state);
ae_matrix_set_length(&sections, n, 4, _state);
ae_vector_set_length(&heaperrors, n, _state);
ae_vector_set_length(&heaptags, n, _state);
*nsections = 1;
sections.ptr.pp_double[0][0] = (double)(0);
sections.ptr.pp_double[0][1] = (double)(n-1);
sections.ptr.pp_double[0][2] = (double)(worstidx);
sections.ptr.pp_double[0][3] = worsterror;
heaperrors.ptr.p_double[0] = worsterror;
heaptags.ptr.p_int[0] = 0;
ae_assert(ae_fp_eq(sections.ptr.pp_double[0][1],(double)(n-1)), "RDP algorithm: integrity check failed", _state);
/*
* Main loop.
* Repeatedly find section with worst error and divide it.
* Terminate after M-th section, or because of other reasons (see loop internals).
*/
for(;;)
{
/*
* Break loop if one of the stopping conditions was met.
* Store index of worst section to K.
*/
if( ae_fp_eq(heaperrors.ptr.p_double[0],(double)(0)) )
{
break;
}
if( ae_fp_greater(stopeps,(double)(0))&&ae_fp_less_eq(heaperrors.ptr.p_double[0],stopeps) )
{
break;
}
if( stopm>0&&*nsections>=stopm )
{
break;
}
k = heaptags.ptr.p_int[0];
/*
* K-th section is divided in two:
* * first one spans interval from X[Sections[K,0]] to X[Sections[K,2]]
* * second one spans interval from X[Sections[K,2]] to X[Sections[K,1]]
*
* First section is stored at K-th position, second one is appended to the table.
* Then we update heap which stores pairs of (error,section_index)
*/
k0 = ae_round(sections.ptr.pp_double[k][0], _state);
k1 = ae_round(sections.ptr.pp_double[k][1], _state);
k2 = ae_round(sections.ptr.pp_double[k][2], _state);
parametric_rdpanalyzesectionpar(x, k0, k2, d, &idx0, &e0, _state);
parametric_rdpanalyzesectionpar(x, k2, k1, d, &idx1, &e1, _state);
sections.ptr.pp_double[k][0] = (double)(k0);
sections.ptr.pp_double[k][1] = (double)(k2);
sections.ptr.pp_double[k][2] = (double)(idx0);
sections.ptr.pp_double[k][3] = e0;
tagheapreplacetopi(&heaperrors, &heaptags, *nsections, e0, k, _state);
sections.ptr.pp_double[*nsections][0] = (double)(k2);
sections.ptr.pp_double[*nsections][1] = (double)(k1);
sections.ptr.pp_double[*nsections][2] = (double)(idx1);
sections.ptr.pp_double[*nsections][3] = e1;
tagheappushi(&heaperrors, &heaptags, nsections, e1, *nsections, _state);
}
/*
* Convert from sections to indexes
*/
ae_vector_set_length(&buf0, *nsections+1, _state);
for(i=0; i<=*nsections-1; i++)
{
buf0.ptr.p_double[i] = (double)(ae_round(sections.ptr.pp_double[i][0], _state));
}
buf0.ptr.p_double[*nsections] = (double)(n-1);
tagsortfast(&buf0, &buf1, *nsections+1, _state);
ae_vector_set_length(idx2, *nsections+1, _state);
for(i=0; i<=*nsections; i++)
{
idx2->ptr.p_int[i] = ae_round(buf0.ptr.p_double[i], _state);
}
ae_assert(idx2->ptr.p_int[0]==0, "RDP algorithm: integrity check failed", _state);
ae_assert(idx2->ptr.p_int[*nsections]==n-1, "RDP algorithm: integrity check failed", _state);
/*
* Output sections:
* * first NSection elements of X2/Y2 are filled by x/y at left boundaries of sections
* * last element of X2/Y2 is filled by right boundary of rightmost section
* * X2/Y2 is sorted by ascending of X2
*/
ae_matrix_set_length(x2, *nsections+1, d, _state);
for(i=0; i<=*nsections; i++)
{
for(j=0; j<=d-1; j++)
{
x2->ptr.pp_double[i][j] = x->ptr.pp_double[idx2->ptr.p_int[i]][j];
}
}
ae_frame_leave(_state);
}
/*************************************************************************
Builds non-periodic parameterization for 2-dimensional spline
*************************************************************************/
static void parametric_pspline2par(/* Real */ ae_matrix* xy,
ae_int_t n,
ae_int_t pt,
/* Real */ ae_vector* p,
ae_state *_state)
{
double v;
ae_int_t i;
ae_vector_clear(p);
ae_assert(pt>=0&&pt<=2, "PSpline2Par: internal error!", _state);
/*
* Build parameterization:
* * fill by non-normalized values
* * normalize them so we have P[0]=0, P[N-1]=1.
*/
ae_vector_set_length(p, n, _state);
if( pt==0 )
{
for(i=0; i<=n-1; i++)
{
p->ptr.p_double[i] = (double)(i);
}
}
if( pt==1 )
{
p->ptr.p_double[0] = (double)(0);
for(i=1; i<=n-1; i++)
{
p->ptr.p_double[i] = p->ptr.p_double[i-1]+safepythag2(xy->ptr.pp_double[i][0]-xy->ptr.pp_double[i-1][0], xy->ptr.pp_double[i][1]-xy->ptr.pp_double[i-1][1], _state);
}
}
if( pt==2 )
{
p->ptr.p_double[0] = (double)(0);
for(i=1; i<=n-1; i++)
{
p->ptr.p_double[i] = p->ptr.p_double[i-1]+ae_sqrt(safepythag2(xy->ptr.pp_double[i][0]-xy->ptr.pp_double[i-1][0], xy->ptr.pp_double[i][1]-xy->ptr.pp_double[i-1][1], _state), _state);
}
}
v = 1/p->ptr.p_double[n-1];
ae_v_muld(&p->ptr.p_double[0], 1, ae_v_len(0,n-1), v);
}
/*************************************************************************
Builds non-periodic parameterization for 3-dimensional spline
*************************************************************************/
static void parametric_pspline3par(/* Real */ ae_matrix* xy,
ae_int_t n,
ae_int_t pt,
/* Real */ ae_vector* p,
ae_state *_state)
{
double v;
ae_int_t i;
ae_vector_clear(p);
ae_assert(pt>=0&&pt<=2, "PSpline3Par: internal error!", _state);
/*
* Build parameterization:
* * fill by non-normalized values
* * normalize them so we have P[0]=0, P[N-1]=1.
*/
ae_vector_set_length(p, n, _state);
if( pt==0 )
{
for(i=0; i<=n-1; i++)
{
p->ptr.p_double[i] = (double)(i);
}
}
if( pt==1 )
{
p->ptr.p_double[0] = (double)(0);
for(i=1; i<=n-1; i++)
{
p->ptr.p_double[i] = p->ptr.p_double[i-1]+safepythag3(xy->ptr.pp_double[i][0]-xy->ptr.pp_double[i-1][0], xy->ptr.pp_double[i][1]-xy->ptr.pp_double[i-1][1], xy->ptr.pp_double[i][2]-xy->ptr.pp_double[i-1][2], _state);
}
}
if( pt==2 )
{
p->ptr.p_double[0] = (double)(0);
for(i=1; i<=n-1; i++)
{
p->ptr.p_double[i] = p->ptr.p_double[i-1]+ae_sqrt(safepythag3(xy->ptr.pp_double[i][0]-xy->ptr.pp_double[i-1][0], xy->ptr.pp_double[i][1]-xy->ptr.pp_double[i-1][1], xy->ptr.pp_double[i][2]-xy->ptr.pp_double[i-1][2], _state), _state);
}
}
v = 1/p->ptr.p_double[n-1];
ae_v_muld(&p->ptr.p_double[0], 1, ae_v_len(0,n-1), v);
}
/*************************************************************************
This function analyzes section of curve for processing by RDP algorithm:
given set of points X,Y with indexes [I0,I1] it returns point with
worst deviation from linear model (PARAMETRIC version which sees curve
as X(t) with vector X).
Input parameters:
XY - array
I0,I1 - interval (boundaries included) to process
D - number of dimensions
OUTPUT PARAMETERS:
WorstIdx - index of worst point
WorstError - error at worst point
NOTE: this function guarantees that it returns exactly zero for a section
with less than 3 points.
-- ALGLIB PROJECT --
Copyright 02.10.2014 by Bochkanov Sergey
*************************************************************************/
static void parametric_rdpanalyzesectionpar(/* Real */ ae_matrix* xy,
ae_int_t i0,
ae_int_t i1,
ae_int_t d,
ae_int_t* worstidx,
double* worsterror,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
double v;
double d2;
double ts;
double vv;
*worstidx = 0;
*worsterror = 0;
/*
* Quick exit for 0, 1, 2 points
*/
if( i1-i0+1<3 )
{
*worstidx = i0;
*worsterror = 0.0;
return;
}
/*
* Estimate D2 - squared distance between XY[I1] and XY[I0].
* In case D2=0 handle it as special case.
*/
d2 = 0.0;
for(j=0; j<=d-1; j++)
{
d2 = d2+ae_sqr(xy->ptr.pp_double[i1][j]-xy->ptr.pp_double[i0][j], _state);
}
if( ae_fp_eq(d2,(double)(0)) )
{
/*
* First and last points are equal, interval evaluation is
* trivial - we just calculate distance from all points to
* the first/last one.
*/
*worstidx = i0;
*worsterror = 0.0;
for(i=i0+1; i<=i1-1; i++)
{
vv = 0.0;
for(j=0; j<=d-1; j++)
{
v = xy->ptr.pp_double[i][j]-xy->ptr.pp_double[i0][j];
vv = vv+v*v;
}
vv = ae_sqrt(vv, _state);
if( ae_fp_greater(vv,*worsterror) )
{
*worsterror = vv;
*worstidx = i;
}
}
return;
}
/*
* General case
*
* Current section of curve is modeled as x(t) = d*t+c, where
* d = XY[I1]-XY[I0]
* c = XY[I0]
* t is in [0,1]
*/
*worstidx = i0;
*worsterror = 0.0;
for(i=i0+1; i<=i1-1; i++)
{
/*
* Determine t_s - parameter value for projected point.
*/
ts = (double)(i-i0)/(double)(i1-i0);
/*
* Estimate error norm
*/
vv = 0.0;
for(j=0; j<=d-1; j++)
{
v = (xy->ptr.pp_double[i1][j]-xy->ptr.pp_double[i0][j])*ts-(xy->ptr.pp_double[i][j]-xy->ptr.pp_double[i0][j]);
vv = vv+ae_sqr(v, _state);
}
vv = ae_sqrt(vv, _state);
if( ae_fp_greater(vv,*worsterror) )
{
*worsterror = vv;
*worstidx = i;
}
}
}
void _pspline2interpolant_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
pspline2interpolant *p = (pspline2interpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->p, 0, DT_REAL, _state, make_automatic);
_spline1dinterpolant_init(&p->x, _state, make_automatic);
_spline1dinterpolant_init(&p->y, _state, make_automatic);
}
void _pspline2interpolant_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
pspline2interpolant *dst = (pspline2interpolant*)_dst;
pspline2interpolant *src = (pspline2interpolant*)_src;
dst->n = src->n;
dst->periodic = src->periodic;
ae_vector_init_copy(&dst->p, &src->p, _state, make_automatic);
_spline1dinterpolant_init_copy(&dst->x, &src->x, _state, make_automatic);
_spline1dinterpolant_init_copy(&dst->y, &src->y, _state, make_automatic);
}
void _pspline2interpolant_clear(void* _p)
{
pspline2interpolant *p = (pspline2interpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->p);
_spline1dinterpolant_clear(&p->x);
_spline1dinterpolant_clear(&p->y);
}
void _pspline2interpolant_destroy(void* _p)
{
pspline2interpolant *p = (pspline2interpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->p);
_spline1dinterpolant_destroy(&p->x);
_spline1dinterpolant_destroy(&p->y);
}
void _pspline3interpolant_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
pspline3interpolant *p = (pspline3interpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->p, 0, DT_REAL, _state, make_automatic);
_spline1dinterpolant_init(&p->x, _state, make_automatic);
_spline1dinterpolant_init(&p->y, _state, make_automatic);
_spline1dinterpolant_init(&p->z, _state, make_automatic);
}
void _pspline3interpolant_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
pspline3interpolant *dst = (pspline3interpolant*)_dst;
pspline3interpolant *src = (pspline3interpolant*)_src;
dst->n = src->n;
dst->periodic = src->periodic;
ae_vector_init_copy(&dst->p, &src->p, _state, make_automatic);
_spline1dinterpolant_init_copy(&dst->x, &src->x, _state, make_automatic);
_spline1dinterpolant_init_copy(&dst->y, &src->y, _state, make_automatic);
_spline1dinterpolant_init_copy(&dst->z, &src->z, _state, make_automatic);
}
void _pspline3interpolant_clear(void* _p)
{
pspline3interpolant *p = (pspline3interpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->p);
_spline1dinterpolant_clear(&p->x);
_spline1dinterpolant_clear(&p->y);
_spline1dinterpolant_clear(&p->z);
}
void _pspline3interpolant_destroy(void* _p)
{
pspline3interpolant *p = (pspline3interpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->p);
_spline1dinterpolant_destroy(&p->x);
_spline1dinterpolant_destroy(&p->y);
_spline1dinterpolant_destroy(&p->z);
}
#endif
#if defined(AE_COMPILE_SPLINE3D) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This subroutine calculates the value of the trilinear or tricubic spline at
the given point (X,Y,Z).
INPUT PARAMETERS:
C - coefficients table.
Built by BuildBilinearSpline or BuildBicubicSpline.
X, Y,
Z - point
Result:
S(x,y,z)
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
double spline3dcalc(spline3dinterpolant* c,
double x,
double y,
double z,
ae_state *_state)
{
double v;
double vx;
double vy;
double vxy;
double result;
ae_assert(c->stype==-1||c->stype==-3, "Spline3DCalc: incorrect C (incorrect parameter C.SType)", _state);
ae_assert((ae_isfinite(x, _state)&&ae_isfinite(y, _state))&&ae_isfinite(z, _state), "Spline3DCalc: X=NaN/Infinite, Y=NaN/Infinite or Z=NaN/Infinite", _state);
if( c->d!=1 )
{
result = (double)(0);
return result;
}
spline3d_spline3ddiff(c, x, y, z, &v, &vx, &vy, &vxy, _state);
result = v;
return result;
}
/*************************************************************************
This subroutine performs linear transformation of the spline argument.
INPUT PARAMETERS:
C - spline interpolant
AX, BX - transformation coefficients: x = A*u + B
AY, BY - transformation coefficients: y = A*v + B
AZ, BZ - transformation coefficients: z = A*w + B
OUTPUT PARAMETERS:
C - transformed spline
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline3dlintransxyz(spline3dinterpolant* c,
double ax,
double bx,
double ay,
double by,
double az,
double bz,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector x;
ae_vector y;
ae_vector z;
ae_vector f;
ae_vector v;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t di;
ae_frame_make(_state, &_frame_block);
memset(&x, 0, sizeof(x));
memset(&y, 0, sizeof(y));
memset(&z, 0, sizeof(z));
memset(&f, 0, sizeof(f));
memset(&v, 0, sizeof(v));
ae_vector_init(&x, 0, DT_REAL, _state, ae_true);
ae_vector_init(&y, 0, DT_REAL, _state, ae_true);
ae_vector_init(&z, 0, DT_REAL, _state, ae_true);
ae_vector_init(&f, 0, DT_REAL, _state, ae_true);
ae_vector_init(&v, 0, DT_REAL, _state, ae_true);
ae_assert(c->stype==-3||c->stype==-1, "Spline3DLinTransXYZ: incorrect C (incorrect parameter C.SType)", _state);
ae_vector_set_length(&x, c->n, _state);
ae_vector_set_length(&y, c->m, _state);
ae_vector_set_length(&z, c->l, _state);
ae_vector_set_length(&f, c->m*c->n*c->l*c->d, _state);
for(j=0; j<=c->n-1; j++)
{
x.ptr.p_double[j] = c->x.ptr.p_double[j];
}
for(i=0; i<=c->m-1; i++)
{
y.ptr.p_double[i] = c->y.ptr.p_double[i];
}
for(i=0; i<=c->l-1; i++)
{
z.ptr.p_double[i] = c->z.ptr.p_double[i];
}
/*
* Handle different combinations of zero/nonzero AX/AY/AZ
*/
if( (ae_fp_neq(ax,(double)(0))&&ae_fp_neq(ay,(double)(0)))&&ae_fp_neq(az,(double)(0)) )
{
ae_v_move(&f.ptr.p_double[0], 1, &c->f.ptr.p_double[0], 1, ae_v_len(0,c->m*c->n*c->l*c->d-1));
}
if( (ae_fp_eq(ax,(double)(0))&&ae_fp_neq(ay,(double)(0)))&&ae_fp_neq(az,(double)(0)) )
{
for(i=0; i<=c->m-1; i++)
{
for(j=0; j<=c->l-1; j++)
{
spline3dcalcv(c, bx, y.ptr.p_double[i], z.ptr.p_double[j], &v, _state);
for(k=0; k<=c->n-1; k++)
{
for(di=0; di<=c->d-1; di++)
{
f.ptr.p_double[c->d*(c->n*(c->m*j+i)+k)+di] = v.ptr.p_double[di];
}
}
}
}
ax = (double)(1);
bx = (double)(0);
}
if( (ae_fp_neq(ax,(double)(0))&&ae_fp_eq(ay,(double)(0)))&&ae_fp_neq(az,(double)(0)) )
{
for(i=0; i<=c->n-1; i++)
{
for(j=0; j<=c->l-1; j++)
{
spline3dcalcv(c, x.ptr.p_double[i], by, z.ptr.p_double[j], &v, _state);
for(k=0; k<=c->m-1; k++)
{
for(di=0; di<=c->d-1; di++)
{
f.ptr.p_double[c->d*(c->n*(c->m*j+k)+i)+di] = v.ptr.p_double[di];
}
}
}
}
ay = (double)(1);
by = (double)(0);
}
if( (ae_fp_neq(ax,(double)(0))&&ae_fp_neq(ay,(double)(0)))&&ae_fp_eq(az,(double)(0)) )
{
for(i=0; i<=c->n-1; i++)
{
for(j=0; j<=c->m-1; j++)
{
spline3dcalcv(c, x.ptr.p_double[i], y.ptr.p_double[j], bz, &v, _state);
for(k=0; k<=c->l-1; k++)
{
for(di=0; di<=c->d-1; di++)
{
f.ptr.p_double[c->d*(c->n*(c->m*k+j)+i)+di] = v.ptr.p_double[di];
}
}
}
}
az = (double)(1);
bz = (double)(0);
}
if( (ae_fp_eq(ax,(double)(0))&&ae_fp_eq(ay,(double)(0)))&&ae_fp_neq(az,(double)(0)) )
{
for(i=0; i<=c->l-1; i++)
{
spline3dcalcv(c, bx, by, z.ptr.p_double[i], &v, _state);
for(k=0; k<=c->m-1; k++)
{
for(j=0; j<=c->n-1; j++)
{
for(di=0; di<=c->d-1; di++)
{
f.ptr.p_double[c->d*(c->n*(c->m*i+k)+j)+di] = v.ptr.p_double[di];
}
}
}
}
ax = (double)(1);
bx = (double)(0);
ay = (double)(1);
by = (double)(0);
}
if( (ae_fp_eq(ax,(double)(0))&&ae_fp_neq(ay,(double)(0)))&&ae_fp_eq(az,(double)(0)) )
{
for(i=0; i<=c->m-1; i++)
{
spline3dcalcv(c, bx, y.ptr.p_double[i], bz, &v, _state);
for(k=0; k<=c->l-1; k++)
{
for(j=0; j<=c->n-1; j++)
{
for(di=0; di<=c->d-1; di++)
{
f.ptr.p_double[c->d*(c->n*(c->m*k+i)+j)+di] = v.ptr.p_double[di];
}
}
}
}
ax = (double)(1);
bx = (double)(0);
az = (double)(1);
bz = (double)(0);
}
if( (ae_fp_neq(ax,(double)(0))&&ae_fp_eq(ay,(double)(0)))&&ae_fp_eq(az,(double)(0)) )
{
for(i=0; i<=c->n-1; i++)
{
spline3dcalcv(c, x.ptr.p_double[i], by, bz, &v, _state);
for(k=0; k<=c->l-1; k++)
{
for(j=0; j<=c->m-1; j++)
{
for(di=0; di<=c->d-1; di++)
{
f.ptr.p_double[c->d*(c->n*(c->m*k+j)+i)+di] = v.ptr.p_double[di];
}
}
}
}
ay = (double)(1);
by = (double)(0);
az = (double)(1);
bz = (double)(0);
}
if( (ae_fp_eq(ax,(double)(0))&&ae_fp_eq(ay,(double)(0)))&&ae_fp_eq(az,(double)(0)) )
{
spline3dcalcv(c, bx, by, bz, &v, _state);
for(k=0; k<=c->l-1; k++)
{
for(j=0; j<=c->m-1; j++)
{
for(i=0; i<=c->n-1; i++)
{
for(di=0; di<=c->d-1; di++)
{
f.ptr.p_double[c->d*(c->n*(c->m*k+j)+i)+di] = v.ptr.p_double[di];
}
}
}
}
ax = (double)(1);
bx = (double)(0);
ay = (double)(1);
by = (double)(0);
az = (double)(1);
bz = (double)(0);
}
/*
* General case: AX<>0, AY<>0, AZ<>0
* Unpack, scale and pack again.
*/
for(i=0; i<=c->n-1; i++)
{
x.ptr.p_double[i] = (x.ptr.p_double[i]-bx)/ax;
}
for(i=0; i<=c->m-1; i++)
{
y.ptr.p_double[i] = (y.ptr.p_double[i]-by)/ay;
}
for(i=0; i<=c->l-1; i++)
{
z.ptr.p_double[i] = (z.ptr.p_double[i]-bz)/az;
}
if( c->stype==-1 )
{
spline3dbuildtrilinearv(&x, c->n, &y, c->m, &z, c->l, &f, c->d, c, _state);
}
ae_frame_leave(_state);
}
/*************************************************************************
This subroutine performs linear transformation of the spline.
INPUT PARAMETERS:
C - spline interpolant.
A, B- transformation coefficients: S2(x,y) = A*S(x,y,z) + B
OUTPUT PARAMETERS:
C - transformed spline
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline3dlintransf(spline3dinterpolant* c,
double a,
double b,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector x;
ae_vector y;
ae_vector z;
ae_vector f;
ae_int_t i;
ae_int_t j;
ae_frame_make(_state, &_frame_block);
memset(&x, 0, sizeof(x));
memset(&y, 0, sizeof(y));
memset(&z, 0, sizeof(z));
memset(&f, 0, sizeof(f));
ae_vector_init(&x, 0, DT_REAL, _state, ae_true);
ae_vector_init(&y, 0, DT_REAL, _state, ae_true);
ae_vector_init(&z, 0, DT_REAL, _state, ae_true);
ae_vector_init(&f, 0, DT_REAL, _state, ae_true);
ae_assert(c->stype==-3||c->stype==-1, "Spline3DLinTransF: incorrect C (incorrect parameter C.SType)", _state);
ae_vector_set_length(&x, c->n, _state);
ae_vector_set_length(&y, c->m, _state);
ae_vector_set_length(&z, c->l, _state);
ae_vector_set_length(&f, c->m*c->n*c->l*c->d, _state);
for(j=0; j<=c->n-1; j++)
{
x.ptr.p_double[j] = c->x.ptr.p_double[j];
}
for(i=0; i<=c->m-1; i++)
{
y.ptr.p_double[i] = c->y.ptr.p_double[i];
}
for(i=0; i<=c->l-1; i++)
{
z.ptr.p_double[i] = c->z.ptr.p_double[i];
}
for(i=0; i<=c->m*c->n*c->l*c->d-1; i++)
{
f.ptr.p_double[i] = a*c->f.ptr.p_double[i]+b;
}
if( c->stype==-1 )
{
spline3dbuildtrilinearv(&x, c->n, &y, c->m, &z, c->l, &f, c->d, c, _state);
}
ae_frame_leave(_state);
}
/*************************************************************************
This subroutine makes the copy of the spline model.
INPUT PARAMETERS:
C - spline interpolant
OUTPUT PARAMETERS:
CC - spline copy
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline3dcopy(spline3dinterpolant* c,
spline3dinterpolant* cc,
ae_state *_state)
{
ae_int_t tblsize;
_spline3dinterpolant_clear(cc);
ae_assert(c->k==1||c->k==3, "Spline3DCopy: incorrect C (incorrect parameter C.K)", _state);
cc->k = c->k;
cc->n = c->n;
cc->m = c->m;
cc->l = c->l;
cc->d = c->d;
tblsize = c->n*c->m*c->l*c->d;
cc->stype = c->stype;
ae_vector_set_length(&cc->x, cc->n, _state);
ae_vector_set_length(&cc->y, cc->m, _state);
ae_vector_set_length(&cc->z, cc->l, _state);
ae_vector_set_length(&cc->f, tblsize, _state);
ae_v_move(&cc->x.ptr.p_double[0], 1, &c->x.ptr.p_double[0], 1, ae_v_len(0,cc->n-1));
ae_v_move(&cc->y.ptr.p_double[0], 1, &c->y.ptr.p_double[0], 1, ae_v_len(0,cc->m-1));
ae_v_move(&cc->z.ptr.p_double[0], 1, &c->z.ptr.p_double[0], 1, ae_v_len(0,cc->l-1));
ae_v_move(&cc->f.ptr.p_double[0], 1, &c->f.ptr.p_double[0], 1, ae_v_len(0,tblsize-1));
}
/*************************************************************************
Trilinear spline resampling
INPUT PARAMETERS:
A - array[0..OldXCount*OldYCount*OldZCount-1], function
values at the old grid, :
A[0] x=0,y=0,z=0
A[1] x=1,y=0,z=0
A[..] ...
A[..] x=oldxcount-1,y=0,z=0
A[..] x=0,y=1,z=0
A[..] ...
...
OldZCount - old Z-count, OldZCount>1
OldYCount - old Y-count, OldYCount>1
OldXCount - old X-count, OldXCount>1
NewZCount - new Z-count, NewZCount>1
NewYCount - new Y-count, NewYCount>1
NewXCount - new X-count, NewXCount>1
OUTPUT PARAMETERS:
B - array[0..NewXCount*NewYCount*NewZCount-1], function
values at the new grid:
B[0] x=0,y=0,z=0
B[1] x=1,y=0,z=0
B[..] ...
B[..] x=newxcount-1,y=0,z=0
B[..] x=0,y=1,z=0
B[..] ...
...
-- ALGLIB routine --
26.04.2012
Copyright by Bochkanov Sergey
*************************************************************************/
void spline3dresampletrilinear(/* Real */ ae_vector* a,
ae_int_t oldzcount,
ae_int_t oldycount,
ae_int_t oldxcount,
ae_int_t newzcount,
ae_int_t newycount,
ae_int_t newxcount,
/* Real */ ae_vector* b,
ae_state *_state)
{
double xd;
double yd;
double zd;
double c0;
double c1;
double c2;
double c3;
ae_int_t ix;
ae_int_t iy;
ae_int_t iz;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_vector_clear(b);
ae_assert((oldycount>1&&oldzcount>1)&&oldxcount>1, "Spline3DResampleTrilinear: length/width/height less than 1", _state);
ae_assert((newycount>1&&newzcount>1)&&newxcount>1, "Spline3DResampleTrilinear: length/width/height less than 1", _state);
ae_assert(a->cnt>=oldycount*oldzcount*oldxcount, "Spline3DResampleTrilinear: length/width/height less than 1", _state);
ae_vector_set_length(b, newxcount*newycount*newzcount, _state);
for(i=0; i<=newxcount-1; i++)
{
for(j=0; j<=newycount-1; j++)
{
for(k=0; k<=newzcount-1; k++)
{
ix = i*(oldxcount-1)/(newxcount-1);
if( ix==oldxcount-1 )
{
ix = oldxcount-2;
}
xd = (double)(i*(oldxcount-1))/(double)(newxcount-1)-ix;
iy = j*(oldycount-1)/(newycount-1);
if( iy==oldycount-1 )
{
iy = oldycount-2;
}
yd = (double)(j*(oldycount-1))/(double)(newycount-1)-iy;
iz = k*(oldzcount-1)/(newzcount-1);
if( iz==oldzcount-1 )
{
iz = oldzcount-2;
}
zd = (double)(k*(oldzcount-1))/(double)(newzcount-1)-iz;
c0 = a->ptr.p_double[oldxcount*(oldycount*iz+iy)+ix]*(1-xd)+a->ptr.p_double[oldxcount*(oldycount*iz+iy)+(ix+1)]*xd;
c1 = a->ptr.p_double[oldxcount*(oldycount*iz+(iy+1))+ix]*(1-xd)+a->ptr.p_double[oldxcount*(oldycount*iz+(iy+1))+(ix+1)]*xd;
c2 = a->ptr.p_double[oldxcount*(oldycount*(iz+1)+iy)+ix]*(1-xd)+a->ptr.p_double[oldxcount*(oldycount*(iz+1)+iy)+(ix+1)]*xd;
c3 = a->ptr.p_double[oldxcount*(oldycount*(iz+1)+(iy+1))+ix]*(1-xd)+a->ptr.p_double[oldxcount*(oldycount*(iz+1)+(iy+1))+(ix+1)]*xd;
c0 = c0*(1-yd)+c1*yd;
c1 = c2*(1-yd)+c3*yd;
b->ptr.p_double[newxcount*(newycount*k+j)+i] = c0*(1-zd)+c1*zd;
}
}
}
}
/*************************************************************************
This subroutine builds trilinear vector-valued spline.
INPUT PARAMETERS:
X - spline abscissas, array[0..N-1]
Y - spline ordinates, array[0..M-1]
Z - spline applicates, array[0..L-1]
F - function values, array[0..M*N*L*D-1]:
* first D elements store D values at (X[0],Y[0],Z[0])
* next D elements store D values at (X[1],Y[0],Z[0])
* next D elements store D values at (X[2],Y[0],Z[0])
* ...
* next D elements store D values at (X[0],Y[1],Z[0])
* next D elements store D values at (X[1],Y[1],Z[0])
* next D elements store D values at (X[2],Y[1],Z[0])
* ...
* next D elements store D values at (X[0],Y[0],Z[1])
* next D elements store D values at (X[1],Y[0],Z[1])
* next D elements store D values at (X[2],Y[0],Z[1])
* ...
* general form - D function values at (X[i],Y[j]) are stored
at F[D*(N*(M*K+J)+I)...D*(N*(M*K+J)+I)+D-1].
M,N,
L - grid size, M>=2, N>=2, L>=2
D - vector dimension, D>=1
OUTPUT PARAMETERS:
C - spline interpolant
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline3dbuildtrilinearv(/* Real */ ae_vector* x,
ae_int_t n,
/* Real */ ae_vector* y,
ae_int_t m,
/* Real */ ae_vector* z,
ae_int_t l,
/* Real */ ae_vector* f,
ae_int_t d,
spline3dinterpolant* c,
ae_state *_state)
{
double t;
ae_int_t tblsize;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t i0;
ae_int_t j0;
_spline3dinterpolant_clear(c);
ae_assert(m>=2, "Spline3DBuildTrilinearV: M<2", _state);
ae_assert(n>=2, "Spline3DBuildTrilinearV: N<2", _state);
ae_assert(l>=2, "Spline3DBuildTrilinearV: L<2", _state);
ae_assert(d>=1, "Spline3DBuildTrilinearV: D<1", _state);
ae_assert((x->cnt>=n&&y->cnt>=m)&&z->cnt>=l, "Spline3DBuildTrilinearV: length of X, Y or Z is too short (Length(X/Y/Z)<N/M/L)", _state);
ae_assert((isfinitevector(x, n, _state)&&isfinitevector(y, m, _state))&&isfinitevector(z, l, _state), "Spline3DBuildTrilinearV: X, Y or Z contains NaN or Infinite value", _state);
tblsize = n*m*l*d;
ae_assert(f->cnt>=tblsize, "Spline3DBuildTrilinearV: length of F is too short (Length(F)<N*M*L*D)", _state);
ae_assert(isfinitevector(f, tblsize, _state), "Spline3DBuildTrilinearV: F contains NaN or Infinite value", _state);
/*
* Fill interpolant
*/
c->k = 1;
c->n = n;
c->m = m;
c->l = l;
c->d = d;
c->stype = -1;
ae_vector_set_length(&c->x, c->n, _state);
ae_vector_set_length(&c->y, c->m, _state);
ae_vector_set_length(&c->z, c->l, _state);
ae_vector_set_length(&c->f, tblsize, _state);
for(i=0; i<=c->n-1; i++)
{
c->x.ptr.p_double[i] = x->ptr.p_double[i];
}
for(i=0; i<=c->m-1; i++)
{
c->y.ptr.p_double[i] = y->ptr.p_double[i];
}
for(i=0; i<=c->l-1; i++)
{
c->z.ptr.p_double[i] = z->ptr.p_double[i];
}
for(i=0; i<=tblsize-1; i++)
{
c->f.ptr.p_double[i] = f->ptr.p_double[i];
}
/*
* Sort points:
* * sort x;
* * sort y;
* * sort z.
*/
for(j=0; j<=c->n-1; j++)
{
k = j;
for(i=j+1; i<=c->n-1; i++)
{
if( ae_fp_less(c->x.ptr.p_double[i],c->x.ptr.p_double[k]) )
{
k = i;
}
}
if( k!=j )
{
for(i=0; i<=c->m-1; i++)
{
for(j0=0; j0<=c->l-1; j0++)
{
for(i0=0; i0<=c->d-1; i0++)
{
t = c->f.ptr.p_double[c->d*(c->n*(c->m*j0+i)+j)+i0];
c->f.ptr.p_double[c->d*(c->n*(c->m*j0+i)+j)+i0] = c->f.ptr.p_double[c->d*(c->n*(c->m*j0+i)+k)+i0];
c->f.ptr.p_double[c->d*(c->n*(c->m*j0+i)+k)+i0] = t;
}
}
}
t = c->x.ptr.p_double[j];
c->x.ptr.p_double[j] = c->x.ptr.p_double[k];
c->x.ptr.p_double[k] = t;
}
}
for(i=0; i<=c->m-1; i++)
{
k = i;
for(j=i+1; j<=c->m-1; j++)
{
if( ae_fp_less(c->y.ptr.p_double[j],c->y.ptr.p_double[k]) )
{
k = j;
}
}
if( k!=i )
{
for(j=0; j<=c->n-1; j++)
{
for(j0=0; j0<=c->l-1; j0++)
{
for(i0=0; i0<=c->d-1; i0++)
{
t = c->f.ptr.p_double[c->d*(c->n*(c->m*j0+i)+j)+i0];
c->f.ptr.p_double[c->d*(c->n*(c->m*j0+i)+j)+i0] = c->f.ptr.p_double[c->d*(c->n*(c->m*j0+k)+j)+i0];
c->f.ptr.p_double[c->d*(c->n*(c->m*j0+k)+j)+i0] = t;
}
}
}
t = c->y.ptr.p_double[i];
c->y.ptr.p_double[i] = c->y.ptr.p_double[k];
c->y.ptr.p_double[k] = t;
}
}
for(k=0; k<=c->l-1; k++)
{
i = k;
for(j=i+1; j<=c->l-1; j++)
{
if( ae_fp_less(c->z.ptr.p_double[j],c->z.ptr.p_double[i]) )
{
i = j;
}
}
if( i!=k )
{
for(j=0; j<=c->m-1; j++)
{
for(j0=0; j0<=c->n-1; j0++)
{
for(i0=0; i0<=c->d-1; i0++)
{
t = c->f.ptr.p_double[c->d*(c->n*(c->m*k+j)+j0)+i0];
c->f.ptr.p_double[c->d*(c->n*(c->m*k+j)+j0)+i0] = c->f.ptr.p_double[c->d*(c->n*(c->m*i+j)+j0)+i0];
c->f.ptr.p_double[c->d*(c->n*(c->m*i+j)+j0)+i0] = t;
}
}
}
t = c->z.ptr.p_double[k];
c->z.ptr.p_double[k] = c->z.ptr.p_double[i];
c->z.ptr.p_double[i] = t;
}
}
}
/*************************************************************************
This subroutine calculates bilinear or bicubic vector-valued spline at the
given point (X,Y,Z).
INPUT PARAMETERS:
C - spline interpolant.
X, Y,
Z - point
F - output buffer, possibly preallocated array. In case array size
is large enough to store result, it is not reallocated. Array
which is too short will be reallocated
OUTPUT PARAMETERS:
F - array[D] (or larger) which stores function values
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline3dcalcvbuf(spline3dinterpolant* c,
double x,
double y,
double z,
/* Real */ ae_vector* f,
ae_state *_state)
{
double xd;
double yd;
double zd;
double c0;
double c1;
double c2;
double c3;
ae_int_t ix;
ae_int_t iy;
ae_int_t iz;
ae_int_t l;
ae_int_t r;
ae_int_t h;
ae_int_t i;
ae_assert(c->stype==-1||c->stype==-3, "Spline3DCalcVBuf: incorrect C (incorrect parameter C.SType)", _state);
ae_assert((ae_isfinite(x, _state)&&ae_isfinite(y, _state))&&ae_isfinite(z, _state), "Spline3DCalcVBuf: X, Y or Z contains NaN/Infinite", _state);
rvectorsetlengthatleast(f, c->d, _state);
/*
* Binary search in the [ x[0], ..., x[n-2] ] (x[n-1] is not included)
*/
l = 0;
r = c->n-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->x.ptr.p_double[h],x) )
{
r = h;
}
else
{
l = h;
}
}
ix = l;
/*
* Binary search in the [ y[0], ..., y[n-2] ] (y[n-1] is not included)
*/
l = 0;
r = c->m-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->y.ptr.p_double[h],y) )
{
r = h;
}
else
{
l = h;
}
}
iy = l;
/*
* Binary search in the [ z[0], ..., z[n-2] ] (z[n-1] is not included)
*/
l = 0;
r = c->l-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->z.ptr.p_double[h],z) )
{
r = h;
}
else
{
l = h;
}
}
iz = l;
xd = (x-c->x.ptr.p_double[ix])/(c->x.ptr.p_double[ix+1]-c->x.ptr.p_double[ix]);
yd = (y-c->y.ptr.p_double[iy])/(c->y.ptr.p_double[iy+1]-c->y.ptr.p_double[iy]);
zd = (z-c->z.ptr.p_double[iz])/(c->z.ptr.p_double[iz+1]-c->z.ptr.p_double[iz]);
for(i=0; i<=c->d-1; i++)
{
/*
* Trilinear interpolation
*/
if( c->stype==-1 )
{
c0 = c->f.ptr.p_double[c->d*(c->n*(c->m*iz+iy)+ix)+i]*(1-xd)+c->f.ptr.p_double[c->d*(c->n*(c->m*iz+iy)+(ix+1))+i]*xd;
c1 = c->f.ptr.p_double[c->d*(c->n*(c->m*iz+(iy+1))+ix)+i]*(1-xd)+c->f.ptr.p_double[c->d*(c->n*(c->m*iz+(iy+1))+(ix+1))+i]*xd;
c2 = c->f.ptr.p_double[c->d*(c->n*(c->m*(iz+1)+iy)+ix)+i]*(1-xd)+c->f.ptr.p_double[c->d*(c->n*(c->m*(iz+1)+iy)+(ix+1))+i]*xd;
c3 = c->f.ptr.p_double[c->d*(c->n*(c->m*(iz+1)+(iy+1))+ix)+i]*(1-xd)+c->f.ptr.p_double[c->d*(c->n*(c->m*(iz+1)+(iy+1))+(ix+1))+i]*xd;
c0 = c0*(1-yd)+c1*yd;
c1 = c2*(1-yd)+c3*yd;
f->ptr.p_double[i] = c0*(1-zd)+c1*zd;
}
}
}
/*************************************************************************
This subroutine calculates trilinear or tricubic vector-valued spline at the
given point (X,Y,Z).
INPUT PARAMETERS:
C - spline interpolant.
X, Y,
Z - point
OUTPUT PARAMETERS:
F - array[D] which stores function values. F is out-parameter and
it is reallocated after call to this function. In case you
want to reuse previously allocated F, you may use
Spline2DCalcVBuf(), which reallocates F only when it is too
small.
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline3dcalcv(spline3dinterpolant* c,
double x,
double y,
double z,
/* Real */ ae_vector* f,
ae_state *_state)
{
ae_vector_clear(f);
ae_assert(c->stype==-1||c->stype==-3, "Spline3DCalcV: incorrect C (incorrect parameter C.SType)", _state);
ae_assert((ae_isfinite(x, _state)&&ae_isfinite(y, _state))&&ae_isfinite(z, _state), "Spline3DCalcV: X=NaN/Infinite, Y=NaN/Infinite or Z=NaN/Infinite", _state);
ae_vector_set_length(f, c->d, _state);
spline3dcalcvbuf(c, x, y, z, f, _state);
}
/*************************************************************************
This subroutine unpacks tri-dimensional spline into the coefficients table
INPUT PARAMETERS:
C - spline interpolant.
Result:
N - grid size (X)
M - grid size (Y)
L - grid size (Z)
D - number of components
SType- spline type. Currently, only one spline type is supported:
trilinear spline, as indicated by SType=1.
Tbl - spline coefficients: [0..(N-1)*(M-1)*(L-1)*D-1, 0..13].
For T=0..D-1 (component index), I = 0...N-2 (x index),
J=0..M-2 (y index), K=0..L-2 (z index):
Q := T + I*D + J*D*(N-1) + K*D*(N-1)*(M-1),
Q-th row stores decomposition for T-th component of the
vector-valued function
Tbl[Q,0] = X[i]
Tbl[Q,1] = X[i+1]
Tbl[Q,2] = Y[j]
Tbl[Q,3] = Y[j+1]
Tbl[Q,4] = Z[k]
Tbl[Q,5] = Z[k+1]
Tbl[Q,6] = C000
Tbl[Q,7] = C100
Tbl[Q,8] = C010
Tbl[Q,9] = C110
Tbl[Q,10]= C001
Tbl[Q,11]= C101
Tbl[Q,12]= C011
Tbl[Q,13]= C111
On each grid square spline is equals to:
S(x) = SUM(c[i,j,k]*(x^i)*(y^j)*(z^k), i=0..1, j=0..1, k=0..1)
t = x-x[j]
u = y-y[i]
v = z-z[k]
NOTE: format of Tbl is given for SType=1. Future versions of
ALGLIB can use different formats for different values of
SType.
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline3dunpackv(spline3dinterpolant* c,
ae_int_t* n,
ae_int_t* m,
ae_int_t* l,
ae_int_t* d,
ae_int_t* stype,
/* Real */ ae_matrix* tbl,
ae_state *_state)
{
ae_int_t p;
ae_int_t ci;
ae_int_t cj;
ae_int_t ck;
double du;
double dv;
double dw;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t di;
ae_int_t i0;
*n = 0;
*m = 0;
*l = 0;
*d = 0;
*stype = 0;
ae_matrix_clear(tbl);
ae_assert(c->stype==-1, "Spline3DUnpackV: incorrect C (incorrect parameter C.SType)", _state);
*n = c->n;
*m = c->m;
*l = c->l;
*d = c->d;
*stype = ae_iabs(c->stype, _state);
ae_matrix_set_length(tbl, (*n-1)*(*m-1)*(*l-1)*(*d), 14, _state);
/*
* Fill
*/
for(i=0; i<=*n-2; i++)
{
for(j=0; j<=*m-2; j++)
{
for(k=0; k<=*l-2; k++)
{
for(di=0; di<=*d-1; di++)
{
p = *d*((*n-1)*((*m-1)*k+j)+i)+di;
tbl->ptr.pp_double[p][0] = c->x.ptr.p_double[i];
tbl->ptr.pp_double[p][1] = c->x.ptr.p_double[i+1];
tbl->ptr.pp_double[p][2] = c->y.ptr.p_double[j];
tbl->ptr.pp_double[p][3] = c->y.ptr.p_double[j+1];
tbl->ptr.pp_double[p][4] = c->z.ptr.p_double[k];
tbl->ptr.pp_double[p][5] = c->z.ptr.p_double[k+1];
du = 1/(tbl->ptr.pp_double[p][1]-tbl->ptr.pp_double[p][0]);
dv = 1/(tbl->ptr.pp_double[p][3]-tbl->ptr.pp_double[p][2]);
dw = 1/(tbl->ptr.pp_double[p][5]-tbl->ptr.pp_double[p][4]);
/*
* Trilinear interpolation
*/
if( c->stype==-1 )
{
for(i0=6; i0<=13; i0++)
{
tbl->ptr.pp_double[p][i0] = (double)(0);
}
tbl->ptr.pp_double[p][6+2*(2*0+0)+0] = c->f.ptr.p_double[*d*(*n*(*m*k+j)+i)+di];
tbl->ptr.pp_double[p][6+2*(2*0+0)+1] = c->f.ptr.p_double[*d*(*n*(*m*k+j)+(i+1))+di]-c->f.ptr.p_double[*d*(*n*(*m*k+j)+i)+di];
tbl->ptr.pp_double[p][6+2*(2*0+1)+0] = c->f.ptr.p_double[*d*(*n*(*m*k+(j+1))+i)+di]-c->f.ptr.p_double[*d*(*n*(*m*k+j)+i)+di];
tbl->ptr.pp_double[p][6+2*(2*0+1)+1] = c->f.ptr.p_double[*d*(*n*(*m*k+(j+1))+(i+1))+di]-c->f.ptr.p_double[*d*(*n*(*m*k+(j+1))+i)+di]-c->f.ptr.p_double[*d*(*n*(*m*k+j)+(i+1))+di]+c->f.ptr.p_double[*d*(*n*(*m*k+j)+i)+di];
tbl->ptr.pp_double[p][6+2*(2*1+0)+0] = c->f.ptr.p_double[*d*(*n*(*m*(k+1)+j)+i)+di]-c->f.ptr.p_double[*d*(*n*(*m*k+j)+i)+di];
tbl->ptr.pp_double[p][6+2*(2*1+0)+1] = c->f.ptr.p_double[*d*(*n*(*m*(k+1)+j)+(i+1))+di]-c->f.ptr.p_double[*d*(*n*(*m*(k+1)+j)+i)+di]-c->f.ptr.p_double[*d*(*n*(*m*k+j)+(i+1))+di]+c->f.ptr.p_double[*d*(*n*(*m*k+j)+i)+di];
tbl->ptr.pp_double[p][6+2*(2*1+1)+0] = c->f.ptr.p_double[*d*(*n*(*m*(k+1)+(j+1))+i)+di]-c->f.ptr.p_double[*d*(*n*(*m*(k+1)+j)+i)+di]-c->f.ptr.p_double[*d*(*n*(*m*k+(j+1))+i)+di]+c->f.ptr.p_double[*d*(*n*(*m*k+j)+i)+di];
tbl->ptr.pp_double[p][6+2*(2*1+1)+1] = c->f.ptr.p_double[*d*(*n*(*m*(k+1)+(j+1))+(i+1))+di]-c->f.ptr.p_double[*d*(*n*(*m*(k+1)+(j+1))+i)+di]-c->f.ptr.p_double[*d*(*n*(*m*(k+1)+j)+(i+1))+di]+c->f.ptr.p_double[*d*(*n*(*m*(k+1)+j)+i)+di]-c->f.ptr.p_double[*d*(*n*(*m*k+(j+1))+(i+1))+di]+c->f.ptr.p_double[*d*(*n*(*m*k+(j+1))+i)+di]+c->f.ptr.p_double[*d*(*n*(*m*k+j)+(i+1))+di]-c->f.ptr.p_double[*d*(*n*(*m*k+j)+i)+di];
}
/*
* Rescale Cij
*/
for(ci=0; ci<=1; ci++)
{
for(cj=0; cj<=1; cj++)
{
for(ck=0; ck<=1; ck++)
{
tbl->ptr.pp_double[p][6+2*(2*ck+cj)+ci] = tbl->ptr.pp_double[p][6+2*(2*ck+cj)+ci]*ae_pow(du, (double)(ci), _state)*ae_pow(dv, (double)(cj), _state)*ae_pow(dw, (double)(ck), _state);
}
}
}
}
}
}
}
}
/*************************************************************************
This subroutine calculates the value of the trilinear(or tricubic;possible
will be later) spline at the given point X(and its derivatives; possible
will be later).
INPUT PARAMETERS:
C - spline interpolant.
X, Y, Z - point
OUTPUT PARAMETERS:
F - S(x,y,z)
FX - dS(x,y,z)/dX
FY - dS(x,y,z)/dY
FXY - d2S(x,y,z)/dXdY
-- ALGLIB PROJECT --
Copyright 26.04.2012 by Bochkanov Sergey
*************************************************************************/
static void spline3d_spline3ddiff(spline3dinterpolant* c,
double x,
double y,
double z,
double* f,
double* fx,
double* fy,
double* fxy,
ae_state *_state)
{
double xd;
double yd;
double zd;
double c0;
double c1;
double c2;
double c3;
ae_int_t ix;
ae_int_t iy;
ae_int_t iz;
ae_int_t l;
ae_int_t r;
ae_int_t h;
*f = 0;
*fx = 0;
*fy = 0;
*fxy = 0;
ae_assert(c->stype==-1||c->stype==-3, "Spline3DDiff: incorrect C (incorrect parameter C.SType)", _state);
ae_assert(ae_isfinite(x, _state)&&ae_isfinite(y, _state), "Spline3DDiff: X or Y contains NaN or Infinite value", _state);
/*
* Prepare F, dF/dX, dF/dY, d2F/dXdY
*/
*f = (double)(0);
*fx = (double)(0);
*fy = (double)(0);
*fxy = (double)(0);
if( c->d!=1 )
{
return;
}
/*
* Binary search in the [ x[0], ..., x[n-2] ] (x[n-1] is not included)
*/
l = 0;
r = c->n-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->x.ptr.p_double[h],x) )
{
r = h;
}
else
{
l = h;
}
}
ix = l;
/*
* Binary search in the [ y[0], ..., y[n-2] ] (y[n-1] is not included)
*/
l = 0;
r = c->m-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->y.ptr.p_double[h],y) )
{
r = h;
}
else
{
l = h;
}
}
iy = l;
/*
* Binary search in the [ z[0], ..., z[n-2] ] (z[n-1] is not included)
*/
l = 0;
r = c->l-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->z.ptr.p_double[h],z) )
{
r = h;
}
else
{
l = h;
}
}
iz = l;
xd = (x-c->x.ptr.p_double[ix])/(c->x.ptr.p_double[ix+1]-c->x.ptr.p_double[ix]);
yd = (y-c->y.ptr.p_double[iy])/(c->y.ptr.p_double[iy+1]-c->y.ptr.p_double[iy]);
zd = (z-c->z.ptr.p_double[iz])/(c->z.ptr.p_double[iz+1]-c->z.ptr.p_double[iz]);
/*
* Trilinear interpolation
*/
if( c->stype==-1 )
{
c0 = c->f.ptr.p_double[c->n*(c->m*iz+iy)+ix]*(1-xd)+c->f.ptr.p_double[c->n*(c->m*iz+iy)+(ix+1)]*xd;
c1 = c->f.ptr.p_double[c->n*(c->m*iz+(iy+1))+ix]*(1-xd)+c->f.ptr.p_double[c->n*(c->m*iz+(iy+1))+(ix+1)]*xd;
c2 = c->f.ptr.p_double[c->n*(c->m*(iz+1)+iy)+ix]*(1-xd)+c->f.ptr.p_double[c->n*(c->m*(iz+1)+iy)+(ix+1)]*xd;
c3 = c->f.ptr.p_double[c->n*(c->m*(iz+1)+(iy+1))+ix]*(1-xd)+c->f.ptr.p_double[c->n*(c->m*(iz+1)+(iy+1))+(ix+1)]*xd;
c0 = c0*(1-yd)+c1*yd;
c1 = c2*(1-yd)+c3*yd;
*f = c0*(1-zd)+c1*zd;
}
}
void _spline3dinterpolant_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
spline3dinterpolant *p = (spline3dinterpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->x, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->y, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->z, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->f, 0, DT_REAL, _state, make_automatic);
}
void _spline3dinterpolant_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
spline3dinterpolant *dst = (spline3dinterpolant*)_dst;
spline3dinterpolant *src = (spline3dinterpolant*)_src;
dst->k = src->k;
dst->stype = src->stype;
dst->n = src->n;
dst->m = src->m;
dst->l = src->l;
dst->d = src->d;
ae_vector_init_copy(&dst->x, &src->x, _state, make_automatic);
ae_vector_init_copy(&dst->y, &src->y, _state, make_automatic);
ae_vector_init_copy(&dst->z, &src->z, _state, make_automatic);
ae_vector_init_copy(&dst->f, &src->f, _state, make_automatic);
}
void _spline3dinterpolant_clear(void* _p)
{
spline3dinterpolant *p = (spline3dinterpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->x);
ae_vector_clear(&p->y);
ae_vector_clear(&p->z);
ae_vector_clear(&p->f);
}
void _spline3dinterpolant_destroy(void* _p)
{
spline3dinterpolant *p = (spline3dinterpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->x);
ae_vector_destroy(&p->y);
ae_vector_destroy(&p->z);
ae_vector_destroy(&p->f);
}
#endif
#if defined(AE_COMPILE_POLINT) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
Conversion from barycentric representation to Chebyshev basis.
This function has O(N^2) complexity.
INPUT PARAMETERS:
P - polynomial in barycentric form
A,B - base interval for Chebyshev polynomials (see below)
A<>B
OUTPUT PARAMETERS
T - coefficients of Chebyshev representation;
P(x) = sum { T[i]*Ti(2*(x-A)/(B-A)-1), i=0..N-1 },
where Ti - I-th Chebyshev polynomial.
NOTES:
barycentric interpolant passed as P may be either polynomial obtained
from polynomial interpolation/ fitting or rational function which is
NOT polynomial. We can't distinguish between these two cases, and this
algorithm just tries to work assuming that P IS a polynomial. If not,
algorithm will return results, but they won't have any meaning.
-- ALGLIB --
Copyright 30.09.2010 by Bochkanov Sergey
*************************************************************************/
void polynomialbar2cheb(barycentricinterpolant* p,
double a,
double b,
/* Real */ ae_vector* t,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_int_t k;
ae_vector vp;
ae_vector vx;
ae_vector tk;
ae_vector tk1;
double v;
ae_frame_make(_state, &_frame_block);
memset(&vp, 0, sizeof(vp));
memset(&vx, 0, sizeof(vx));
memset(&tk, 0, sizeof(tk));
memset(&tk1, 0, sizeof(tk1));
ae_vector_clear(t);
ae_vector_init(&vp, 0, DT_REAL, _state, ae_true);
ae_vector_init(&vx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tk, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tk1, 0, DT_REAL, _state, ae_true);
ae_assert(ae_isfinite(a, _state), "PolynomialBar2Cheb: A is not finite!", _state);
ae_assert(ae_isfinite(b, _state), "PolynomialBar2Cheb: B is not finite!", _state);
ae_assert(ae_fp_neq(a,b), "PolynomialBar2Cheb: A=B!", _state);
ae_assert(p->n>0, "PolynomialBar2Cheb: P is not correctly initialized barycentric interpolant!", _state);
/*
* Calculate function values on a Chebyshev grid
*/
ae_vector_set_length(&vp, p->n, _state);
ae_vector_set_length(&vx, p->n, _state);
for(i=0; i<=p->n-1; i++)
{
vx.ptr.p_double[i] = ae_cos(ae_pi*(i+0.5)/p->n, _state);
vp.ptr.p_double[i] = barycentriccalc(p, 0.5*(vx.ptr.p_double[i]+1)*(b-a)+a, _state);
}
/*
* T[0]
*/
ae_vector_set_length(t, p->n, _state);
v = (double)(0);
for(i=0; i<=p->n-1; i++)
{
v = v+vp.ptr.p_double[i];
}
t->ptr.p_double[0] = v/p->n;
/*
* other T's.
*
* NOTES:
* 1. TK stores T{k} on VX, TK1 stores T{k-1} on VX
* 2. we can do same calculations with fast DCT, but it
* * adds dependencies
* * still leaves us with O(N^2) algorithm because
* preparation of function values is O(N^2) process
*/
if( p->n>1 )
{
ae_vector_set_length(&tk, p->n, _state);
ae_vector_set_length(&tk1, p->n, _state);
for(i=0; i<=p->n-1; i++)
{
tk.ptr.p_double[i] = vx.ptr.p_double[i];
tk1.ptr.p_double[i] = (double)(1);
}
for(k=1; k<=p->n-1; k++)
{
/*
* calculate discrete product of function vector and TK
*/
v = ae_v_dotproduct(&tk.ptr.p_double[0], 1, &vp.ptr.p_double[0], 1, ae_v_len(0,p->n-1));
t->ptr.p_double[k] = v/(0.5*p->n);
/*
* Update TK and TK1
*/
for(i=0; i<=p->n-1; i++)
{
v = 2*vx.ptr.p_double[i]*tk.ptr.p_double[i]-tk1.ptr.p_double[i];
tk1.ptr.p_double[i] = tk.ptr.p_double[i];
tk.ptr.p_double[i] = v;
}
}
}
ae_frame_leave(_state);
}
/*************************************************************************
Conversion from Chebyshev basis to barycentric representation.
This function has O(N^2) complexity.
INPUT PARAMETERS:
T - coefficients of Chebyshev representation;
P(x) = sum { T[i]*Ti(2*(x-A)/(B-A)-1), i=0..N },
where Ti - I-th Chebyshev polynomial.
N - number of coefficients:
* if given, only leading N elements of T are used
* if not given, automatically determined from size of T
A,B - base interval for Chebyshev polynomials (see above)
A<B
OUTPUT PARAMETERS
P - polynomial in barycentric form
-- ALGLIB --
Copyright 30.09.2010 by Bochkanov Sergey
*************************************************************************/
void polynomialcheb2bar(/* Real */ ae_vector* t,
ae_int_t n,
double a,
double b,
barycentricinterpolant* p,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_int_t k;
ae_vector y;
double tk;
double tk1;
double vx;
double vy;
double v;
ae_frame_make(_state, &_frame_block);
memset(&y, 0, sizeof(y));
_barycentricinterpolant_clear(p);
ae_vector_init(&y, 0, DT_REAL, _state, ae_true);
ae_assert(ae_isfinite(a, _state), "PolynomialBar2Cheb: A is not finite!", _state);
ae_assert(ae_isfinite(b, _state), "PolynomialBar2Cheb: B is not finite!", _state);
ae_assert(ae_fp_neq(a,b), "PolynomialBar2Cheb: A=B!", _state);
ae_assert(n>=1, "PolynomialBar2Cheb: N<1", _state);
ae_assert(t->cnt>=n, "PolynomialBar2Cheb: Length(T)<N", _state);
ae_assert(isfinitevector(t, n, _state), "PolynomialBar2Cheb: T[] contains INF or NAN", _state);
/*
* Calculate function values on a Chebyshev grid spanning [-1,+1]
*/
ae_vector_set_length(&y, n, _state);
for(i=0; i<=n-1; i++)
{
/*
* Calculate value on a grid spanning [-1,+1]
*/
vx = ae_cos(ae_pi*(i+0.5)/n, _state);
vy = t->ptr.p_double[0];
tk1 = (double)(1);
tk = vx;
for(k=1; k<=n-1; k++)
{
vy = vy+t->ptr.p_double[k]*tk;
v = 2*vx*tk-tk1;
tk1 = tk;
tk = v;
}
y.ptr.p_double[i] = vy;
}
/*
* Build barycentric interpolant, map grid from [-1,+1] to [A,B]
*/
polynomialbuildcheb1(a, b, &y, n, p, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Conversion from barycentric representation to power basis.
This function has O(N^2) complexity.
INPUT PARAMETERS:
P - polynomial in barycentric form
C - offset (see below); 0.0 is used as default value.
S - scale (see below); 1.0 is used as default value. S<>0.
OUTPUT PARAMETERS
A - coefficients, P(x) = sum { A[i]*((X-C)/S)^i, i=0..N-1 }
N - number of coefficients (polynomial degree plus 1)
NOTES:
1. this function accepts offset and scale, which can be set to improve
numerical properties of polynomial. For example, if P was obtained as
result of interpolation on [-1,+1], you can set C=0 and S=1 and
represent P as sum of 1, x, x^2, x^3 and so on. In most cases you it
is exactly what you need.
However, if your interpolation model was built on [999,1001], you will
see significant growth of numerical errors when using {1, x, x^2, x^3}
as basis. Representing P as sum of 1, (x-1000), (x-1000)^2, (x-1000)^3
will be better option. Such representation can be obtained by using
1000.0 as offset C and 1.0 as scale S.
2. power basis is ill-conditioned and tricks described above can't solve
this problem completely. This function will return coefficients in
any case, but for N>8 they will become unreliable. However, N's
less than 5 are pretty safe.
3. barycentric interpolant passed as P may be either polynomial obtained
from polynomial interpolation/ fitting or rational function which is
NOT polynomial. We can't distinguish between these two cases, and this
algorithm just tries to work assuming that P IS a polynomial. If not,
algorithm will return results, but they won't have any meaning.
-- ALGLIB --
Copyright 30.09.2010 by Bochkanov Sergey
*************************************************************************/
void polynomialbar2pow(barycentricinterpolant* p,
double c,
double s,
/* Real */ ae_vector* a,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_int_t k;
double e;
double d;
ae_vector vp;
ae_vector vx;
ae_vector tk;
ae_vector tk1;
ae_vector t;
double v;
double c0;
double s0;
double va;
double vb;
ae_vector vai;
ae_vector vbi;
double minx;
double maxx;
ae_frame_make(_state, &_frame_block);
memset(&vp, 0, sizeof(vp));
memset(&vx, 0, sizeof(vx));
memset(&tk, 0, sizeof(tk));
memset(&tk1, 0, sizeof(tk1));
memset(&t, 0, sizeof(t));
memset(&vai, 0, sizeof(vai));
memset(&vbi, 0, sizeof(vbi));
ae_vector_clear(a);
ae_vector_init(&vp, 0, DT_REAL, _state, ae_true);
ae_vector_init(&vx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tk, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tk1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&t, 0, DT_REAL, _state, ae_true);
ae_vector_init(&vai, 0, DT_REAL, _state, ae_true);
ae_vector_init(&vbi, 0, DT_REAL, _state, ae_true);
/*
* We have barycentric model built using set of points X[], and we
* want to convert it to power basis centered about point C with
* scale S: I-th basis function is ((X-C)/S)^i.
*
* We use following three-stage algorithm:
*
* 1. we build Chebyshev representation of polynomial using
* intermediate center C0 and scale S0, which are derived from X[]:
* C0 = 0.5*(min(X)+max(X)), S0 = 0.5*(max(X)-min(X)). Chebyshev
* representation is built by sampling points around center C0,
* with typical distance between them proportional to S0.
* 2. then we transform form Chebyshev basis to intermediate power
* basis, using same center/scale C0/S0.
* 3. after that, we apply linear transformation to intermediate
* power basis which moves it to final center/scale C/S.
*
* The idea of such multi-stage algorithm is that it is much easier to
* transform barycentric model to Chebyshev basis, and only later to
* power basis, than transforming it directly to power basis. It is
* also more numerically stable to sample points using intermediate C0/S0,
* which are derived from user-supplied model, than using "final" C/S,
* which may be unsuitable for sampling (say, if S=1, we may have stability
* problems when working with models built from dataset with non-unit
* scale of abscissas).
*/
ae_assert(ae_isfinite(c, _state), "PolynomialBar2Pow: C is not finite!", _state);
ae_assert(ae_isfinite(s, _state), "PolynomialBar2Pow: S is not finite!", _state);
ae_assert(ae_fp_neq(s,(double)(0)), "PolynomialBar2Pow: S=0!", _state);
ae_assert(p->n>0, "PolynomialBar2Pow: P is not correctly initialized barycentric interpolant!", _state);
/*
* Select intermediate center/scale
*/
minx = p->x.ptr.p_double[0];
maxx = p->x.ptr.p_double[0];
for(i=1; i<=p->n-1; i++)
{
minx = ae_minreal(minx, p->x.ptr.p_double[i], _state);
maxx = ae_maxreal(maxx, p->x.ptr.p_double[i], _state);
}
if( ae_fp_eq(minx,maxx) )
{
c0 = minx;
s0 = 1.0;
}
else
{
c0 = 0.5*(maxx+minx);
s0 = 0.5*(maxx-minx);
}
/*
* Calculate function values on a Chebyshev grid using intermediate C0/S0
*/
ae_vector_set_length(&vp, p->n+1, _state);
ae_vector_set_length(&vx, p->n, _state);
for(i=0; i<=p->n-1; i++)
{
vx.ptr.p_double[i] = ae_cos(ae_pi*(i+0.5)/p->n, _state);
vp.ptr.p_double[i] = barycentriccalc(p, s0*vx.ptr.p_double[i]+c0, _state);
}
/*
* T[0]
*/
ae_vector_set_length(&t, p->n, _state);
v = (double)(0);
for(i=0; i<=p->n-1; i++)
{
v = v+vp.ptr.p_double[i];
}
t.ptr.p_double[0] = v/p->n;
/*
* other T's.
*
* NOTES:
* 1. TK stores T{k} on VX, TK1 stores T{k-1} on VX
* 2. we can do same calculations with fast DCT, but it
* * adds dependencies
* * still leaves us with O(N^2) algorithm because
* preparation of function values is O(N^2) process
*/
if( p->n>1 )
{
ae_vector_set_length(&tk, p->n, _state);
ae_vector_set_length(&tk1, p->n, _state);
for(i=0; i<=p->n-1; i++)
{
tk.ptr.p_double[i] = vx.ptr.p_double[i];
tk1.ptr.p_double[i] = (double)(1);
}
for(k=1; k<=p->n-1; k++)
{
/*
* calculate discrete product of function vector and TK
*/
v = ae_v_dotproduct(&tk.ptr.p_double[0], 1, &vp.ptr.p_double[0], 1, ae_v_len(0,p->n-1));
t.ptr.p_double[k] = v/(0.5*p->n);
/*
* Update TK and TK1
*/
for(i=0; i<=p->n-1; i++)
{
v = 2*vx.ptr.p_double[i]*tk.ptr.p_double[i]-tk1.ptr.p_double[i];
tk1.ptr.p_double[i] = tk.ptr.p_double[i];
tk.ptr.p_double[i] = v;
}
}
}
/*
* Convert from Chebyshev basis to power basis
*/
ae_vector_set_length(a, p->n, _state);
for(i=0; i<=p->n-1; i++)
{
a->ptr.p_double[i] = (double)(0);
}
d = (double)(0);
for(i=0; i<=p->n-1; i++)
{
for(k=i; k<=p->n-1; k++)
{
e = a->ptr.p_double[k];
a->ptr.p_double[k] = (double)(0);
if( i<=1&&k==i )
{
a->ptr.p_double[k] = (double)(1);
}
else
{
if( i!=0 )
{
a->ptr.p_double[k] = 2*d;
}
if( k>i+1 )
{
a->ptr.p_double[k] = a->ptr.p_double[k]-a->ptr.p_double[k-2];
}
}
d = e;
}
d = a->ptr.p_double[i];
e = (double)(0);
k = i;
while(k<=p->n-1)
{
e = e+a->ptr.p_double[k]*t.ptr.p_double[k];
k = k+2;
}
a->ptr.p_double[i] = e;
}
/*
* Apply linear transformation which converts basis from intermediate
* one Fi=((x-C0)/S0)^i to final one Fi=((x-C)/S)^i.
*
* We have y=(x-C0)/S0, z=(x-C)/S, and coefficients A[] for basis Fi(y).
* Because we have y=A*z+B, for A=s/s0 and B=c/s0-c0/s0, we can perform
* substitution and get coefficients A_new[] in basis Fi(z).
*/
ae_assert(vp.cnt>=p->n+1, "PolynomialBar2Pow: internal error", _state);
ae_assert(t.cnt>=p->n, "PolynomialBar2Pow: internal error", _state);
for(i=0; i<=p->n-1; i++)
{
t.ptr.p_double[i] = 0.0;
}
va = s/s0;
vb = c/s0-c0/s0;
ae_vector_set_length(&vai, p->n, _state);
ae_vector_set_length(&vbi, p->n, _state);
vai.ptr.p_double[0] = (double)(1);
vbi.ptr.p_double[0] = (double)(1);
for(k=1; k<=p->n-1; k++)
{
vai.ptr.p_double[k] = vai.ptr.p_double[k-1]*va;
vbi.ptr.p_double[k] = vbi.ptr.p_double[k-1]*vb;
}
for(k=0; k<=p->n-1; k++)
{
/*
* Generate set of binomial coefficients in VP[]
*/
if( k>0 )
{
vp.ptr.p_double[k] = (double)(1);
for(i=k-1; i>=1; i--)
{
vp.ptr.p_double[i] = vp.ptr.p_double[i]+vp.ptr.p_double[i-1];
}
vp.ptr.p_double[0] = (double)(1);
}
else
{
vp.ptr.p_double[0] = (double)(1);
}
/*
* Update T[] with expansion of K-th basis function
*/
for(i=0; i<=k; i++)
{
t.ptr.p_double[i] = t.ptr.p_double[i]+a->ptr.p_double[k]*vai.ptr.p_double[i]*vbi.ptr.p_double[k-i]*vp.ptr.p_double[i];
}
}
for(k=0; k<=p->n-1; k++)
{
a->ptr.p_double[k] = t.ptr.p_double[k];
}
ae_frame_leave(_state);
}
/*************************************************************************
Conversion from power basis to barycentric representation.
This function has O(N^2) complexity.
INPUT PARAMETERS:
A - coefficients, P(x) = sum { A[i]*((X-C)/S)^i, i=0..N-1 }
N - number of coefficients (polynomial degree plus 1)
* if given, only leading N elements of A are used
* if not given, automatically determined from size of A
C - offset (see below); 0.0 is used as default value.
S - scale (see below); 1.0 is used as default value. S<>0.
OUTPUT PARAMETERS
P - polynomial in barycentric form
NOTES:
1. this function accepts offset and scale, which can be set to improve
numerical properties of polynomial. For example, if you interpolate on
[-1,+1], you can set C=0 and S=1 and convert from sum of 1, x, x^2,
x^3 and so on. In most cases you it is exactly what you need.
However, if your interpolation model was built on [999,1001], you will
see significant growth of numerical errors when using {1, x, x^2, x^3}
as input basis. Converting from sum of 1, (x-1000), (x-1000)^2,
(x-1000)^3 will be better option (you have to specify 1000.0 as offset
C and 1.0 as scale S).
2. power basis is ill-conditioned and tricks described above can't solve
this problem completely. This function will return barycentric model
in any case, but for N>8 accuracy well degrade. However, N's less than
5 are pretty safe.
-- ALGLIB --
Copyright 30.09.2010 by Bochkanov Sergey
*************************************************************************/
void polynomialpow2bar(/* Real */ ae_vector* a,
ae_int_t n,
double c,
double s,
barycentricinterpolant* p,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_int_t k;
ae_vector y;
double vx;
double vy;
double px;
ae_frame_make(_state, &_frame_block);
memset(&y, 0, sizeof(y));
_barycentricinterpolant_clear(p);
ae_vector_init(&y, 0, DT_REAL, _state, ae_true);
ae_assert(ae_isfinite(c, _state), "PolynomialPow2Bar: C is not finite!", _state);
ae_assert(ae_isfinite(s, _state), "PolynomialPow2Bar: S is not finite!", _state);
ae_assert(ae_fp_neq(s,(double)(0)), "PolynomialPow2Bar: S is zero!", _state);
ae_assert(n>=1, "PolynomialPow2Bar: N<1", _state);
ae_assert(a->cnt>=n, "PolynomialPow2Bar: Length(A)<N", _state);
ae_assert(isfinitevector(a, n, _state), "PolynomialPow2Bar: A[] contains INF or NAN", _state);
/*
* Calculate function values on a Chebyshev grid spanning [-1,+1]
*/
ae_vector_set_length(&y, n, _state);
for(i=0; i<=n-1; i++)
{
/*
* Calculate value on a grid spanning [-1,+1]
*/
vx = ae_cos(ae_pi*(i+0.5)/n, _state);
vy = a->ptr.p_double[0];
px = vx;
for(k=1; k<=n-1; k++)
{
vy = vy+px*a->ptr.p_double[k];
px = px*vx;
}
y.ptr.p_double[i] = vy;
}
/*
* Build barycentric interpolant, map grid from [-1,+1] to [A,B]
*/
polynomialbuildcheb1(c-s, c+s, &y, n, p, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Lagrange intepolant: generation of the model on the general grid.
This function has O(N^2) complexity.
INPUT PARAMETERS:
X - abscissas, array[0..N-1]
Y - function values, array[0..N-1]
N - number of points, N>=1
OUTPUT PARAMETERS
P - barycentric model which represents Lagrange interpolant
(see ratint unit info and BarycentricCalc() description for
more information).
-- ALGLIB --
Copyright 02.12.2009 by Bochkanov Sergey
*************************************************************************/
void polynomialbuild(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
barycentricinterpolant* p,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_int_t j;
ae_int_t k;
ae_vector w;
double b;
double a;
double v;
double mx;
ae_vector sortrbuf;
ae_vector sortrbuf2;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&w, 0, sizeof(w));
memset(&sortrbuf, 0, sizeof(sortrbuf));
memset(&sortrbuf2, 0, sizeof(sortrbuf2));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
_barycentricinterpolant_clear(p);
ae_vector_init(&w, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sortrbuf, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sortrbuf2, 0, DT_REAL, _state, ae_true);
ae_assert(n>0, "PolynomialBuild: N<=0!", _state);
ae_assert(x->cnt>=n, "PolynomialBuild: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "PolynomialBuild: Length(Y)<N!", _state);
ae_assert(isfinitevector(x, n, _state), "PolynomialBuild: X contains infinite or NaN values!", _state);
ae_assert(isfinitevector(y, n, _state), "PolynomialBuild: Y contains infinite or NaN values!", _state);
tagsortfastr(x, y, &sortrbuf, &sortrbuf2, n, _state);
ae_assert(aredistinct(x, n, _state), "PolynomialBuild: at least two consequent points are too close!", _state);
/*
* calculate W[j]
* multi-pass algorithm is used to avoid overflow
*/
ae_vector_set_length(&w, n, _state);
a = x->ptr.p_double[0];
b = x->ptr.p_double[0];
for(j=0; j<=n-1; j++)
{
w.ptr.p_double[j] = (double)(1);
a = ae_minreal(a, x->ptr.p_double[j], _state);
b = ae_maxreal(b, x->ptr.p_double[j], _state);
}
for(k=0; k<=n-1; k++)
{
/*
* W[K] is used instead of 0.0 because
* cycle on J does not touch K-th element
* and we MUST get maximum from ALL elements
*/
mx = ae_fabs(w.ptr.p_double[k], _state);
for(j=0; j<=n-1; j++)
{
if( j!=k )
{
v = (b-a)/(x->ptr.p_double[j]-x->ptr.p_double[k]);
w.ptr.p_double[j] = w.ptr.p_double[j]*v;
mx = ae_maxreal(mx, ae_fabs(w.ptr.p_double[j], _state), _state);
}
}
if( k%5==0 )
{
/*
* every 5-th run we renormalize W[]
*/
v = 1/mx;
ae_v_muld(&w.ptr.p_double[0], 1, ae_v_len(0,n-1), v);
}
}
barycentricbuildxyw(x, y, &w, n, p, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Lagrange intepolant: generation of the model on equidistant grid.
This function has O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
Y - function values at the nodes, array[0..N-1]
N - number of points, N>=1
for N=1 a constant model is constructed.
OUTPUT PARAMETERS
P - barycentric model which represents Lagrange interpolant
(see ratint unit info and BarycentricCalc() description for
more information).
-- ALGLIB --
Copyright 03.12.2009 by Bochkanov Sergey
*************************************************************************/
void polynomialbuildeqdist(double a,
double b,
/* Real */ ae_vector* y,
ae_int_t n,
barycentricinterpolant* p,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_vector w;
ae_vector x;
double v;
ae_frame_make(_state, &_frame_block);
memset(&w, 0, sizeof(w));
memset(&x, 0, sizeof(x));
_barycentricinterpolant_clear(p);
ae_vector_init(&w, 0, DT_REAL, _state, ae_true);
ae_vector_init(&x, 0, DT_REAL, _state, ae_true);
ae_assert(n>0, "PolynomialBuildEqDist: N<=0!", _state);
ae_assert(y->cnt>=n, "PolynomialBuildEqDist: Length(Y)<N!", _state);
ae_assert(ae_isfinite(a, _state), "PolynomialBuildEqDist: A is infinite or NaN!", _state);
ae_assert(ae_isfinite(b, _state), "PolynomialBuildEqDist: B is infinite or NaN!", _state);
ae_assert(isfinitevector(y, n, _state), "PolynomialBuildEqDist: Y contains infinite or NaN values!", _state);
ae_assert(ae_fp_neq(b,a), "PolynomialBuildEqDist: B=A!", _state);
ae_assert(ae_fp_neq(a+(b-a)/n,a), "PolynomialBuildEqDist: B is too close to A!", _state);
/*
* Special case: N=1
*/
if( n==1 )
{
ae_vector_set_length(&x, 1, _state);
ae_vector_set_length(&w, 1, _state);
x.ptr.p_double[0] = 0.5*(b+a);
w.ptr.p_double[0] = (double)(1);
barycentricbuildxyw(&x, y, &w, 1, p, _state);
ae_frame_leave(_state);
return;
}
/*
* general case
*/
ae_vector_set_length(&x, n, _state);
ae_vector_set_length(&w, n, _state);
v = (double)(1);
for(i=0; i<=n-1; i++)
{
w.ptr.p_double[i] = v;
x.ptr.p_double[i] = a+(b-a)*i/(n-1);
v = -v*(n-1-i);
v = v/(i+1);
}
barycentricbuildxyw(&x, y, &w, n, p, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Lagrange intepolant on Chebyshev grid (first kind).
This function has O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
Y - function values at the nodes, array[0..N-1],
Y[I] = Y(0.5*(B+A) + 0.5*(B-A)*Cos(PI*(2*i+1)/(2*n)))
N - number of points, N>=1
for N=1 a constant model is constructed.
OUTPUT PARAMETERS
P - barycentric model which represents Lagrange interpolant
(see ratint unit info and BarycentricCalc() description for
more information).
-- ALGLIB --
Copyright 03.12.2009 by Bochkanov Sergey
*************************************************************************/
void polynomialbuildcheb1(double a,
double b,
/* Real */ ae_vector* y,
ae_int_t n,
barycentricinterpolant* p,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_vector w;
ae_vector x;
double v;
double t;
ae_frame_make(_state, &_frame_block);
memset(&w, 0, sizeof(w));
memset(&x, 0, sizeof(x));
_barycentricinterpolant_clear(p);
ae_vector_init(&w, 0, DT_REAL, _state, ae_true);
ae_vector_init(&x, 0, DT_REAL, _state, ae_true);
ae_assert(n>0, "PolynomialBuildCheb1: N<=0!", _state);
ae_assert(y->cnt>=n, "PolynomialBuildCheb1: Length(Y)<N!", _state);
ae_assert(ae_isfinite(a, _state), "PolynomialBuildCheb1: A is infinite or NaN!", _state);
ae_assert(ae_isfinite(b, _state), "PolynomialBuildCheb1: B is infinite or NaN!", _state);
ae_assert(isfinitevector(y, n, _state), "PolynomialBuildCheb1: Y contains infinite or NaN values!", _state);
ae_assert(ae_fp_neq(b,a), "PolynomialBuildCheb1: B=A!", _state);
/*
* Special case: N=1
*/
if( n==1 )
{
ae_vector_set_length(&x, 1, _state);
ae_vector_set_length(&w, 1, _state);
x.ptr.p_double[0] = 0.5*(b+a);
w.ptr.p_double[0] = (double)(1);
barycentricbuildxyw(&x, y, &w, 1, p, _state);
ae_frame_leave(_state);
return;
}
/*
* general case
*/
ae_vector_set_length(&x, n, _state);
ae_vector_set_length(&w, n, _state);
v = (double)(1);
for(i=0; i<=n-1; i++)
{
t = ae_tan(0.5*ae_pi*(2*i+1)/(2*n), _state);
w.ptr.p_double[i] = 2*v*t/(1+ae_sqr(t, _state));
x.ptr.p_double[i] = 0.5*(b+a)+0.5*(b-a)*(1-ae_sqr(t, _state))/(1+ae_sqr(t, _state));
v = -v;
}
barycentricbuildxyw(&x, y, &w, n, p, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Lagrange intepolant on Chebyshev grid (second kind).
This function has O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
Y - function values at the nodes, array[0..N-1],
Y[I] = Y(0.5*(B+A) + 0.5*(B-A)*Cos(PI*i/(n-1)))
N - number of points, N>=1
for N=1 a constant model is constructed.
OUTPUT PARAMETERS
P - barycentric model which represents Lagrange interpolant
(see ratint unit info and BarycentricCalc() description for
more information).
-- ALGLIB --
Copyright 03.12.2009 by Bochkanov Sergey
*************************************************************************/
void polynomialbuildcheb2(double a,
double b,
/* Real */ ae_vector* y,
ae_int_t n,
barycentricinterpolant* p,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_vector w;
ae_vector x;
double v;
ae_frame_make(_state, &_frame_block);
memset(&w, 0, sizeof(w));
memset(&x, 0, sizeof(x));
_barycentricinterpolant_clear(p);
ae_vector_init(&w, 0, DT_REAL, _state, ae_true);
ae_vector_init(&x, 0, DT_REAL, _state, ae_true);
ae_assert(n>0, "PolynomialBuildCheb2: N<=0!", _state);
ae_assert(y->cnt>=n, "PolynomialBuildCheb2: Length(Y)<N!", _state);
ae_assert(ae_isfinite(a, _state), "PolynomialBuildCheb2: A is infinite or NaN!", _state);
ae_assert(ae_isfinite(b, _state), "PolynomialBuildCheb2: B is infinite or NaN!", _state);
ae_assert(ae_fp_neq(b,a), "PolynomialBuildCheb2: B=A!", _state);
ae_assert(isfinitevector(y, n, _state), "PolynomialBuildCheb2: Y contains infinite or NaN values!", _state);
/*
* Special case: N=1
*/
if( n==1 )
{
ae_vector_set_length(&x, 1, _state);
ae_vector_set_length(&w, 1, _state);
x.ptr.p_double[0] = 0.5*(b+a);
w.ptr.p_double[0] = (double)(1);
barycentricbuildxyw(&x, y, &w, 1, p, _state);
ae_frame_leave(_state);
return;
}
/*
* general case
*/
ae_vector_set_length(&x, n, _state);
ae_vector_set_length(&w, n, _state);
v = (double)(1);
for(i=0; i<=n-1; i++)
{
if( i==0||i==n-1 )
{
w.ptr.p_double[i] = v*0.5;
}
else
{
w.ptr.p_double[i] = v;
}
x.ptr.p_double[i] = 0.5*(b+a)+0.5*(b-a)*ae_cos(ae_pi*i/(n-1), _state);
v = -v;
}
barycentricbuildxyw(&x, y, &w, n, p, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Fast equidistant polynomial interpolation function with O(N) complexity
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
F - function values, array[0..N-1]
N - number of points on equidistant grid, N>=1
for N=1 a constant model is constructed.
T - position where P(x) is calculated
RESULT
value of the Lagrange interpolant at T
IMPORTANT
this function provides fast interface which is not overflow-safe
nor it is very precise.
the best option is to use PolynomialBuildEqDist()/BarycentricCalc()
subroutines unless you are pretty sure that your data will not result
in overflow.
-- ALGLIB --
Copyright 02.12.2009 by Bochkanov Sergey
*************************************************************************/
double polynomialcalceqdist(double a,
double b,
/* Real */ ae_vector* f,
ae_int_t n,
double t,
ae_state *_state)
{
double s1;
double s2;
double v;
double threshold;
double s;
double h;
ae_int_t i;
ae_int_t j;
double w;
double x;
double result;
ae_assert(n>0, "PolynomialCalcEqDist: N<=0!", _state);
ae_assert(f->cnt>=n, "PolynomialCalcEqDist: Length(F)<N!", _state);
ae_assert(ae_isfinite(a, _state), "PolynomialCalcEqDist: A is infinite or NaN!", _state);
ae_assert(ae_isfinite(b, _state), "PolynomialCalcEqDist: B is infinite or NaN!", _state);
ae_assert(isfinitevector(f, n, _state), "PolynomialCalcEqDist: F contains infinite or NaN values!", _state);
ae_assert(ae_fp_neq(b,a), "PolynomialCalcEqDist: B=A!", _state);
ae_assert(!ae_isinf(t, _state), "PolynomialCalcEqDist: T is infinite!", _state);
/*
* Special case: T is NAN
*/
if( ae_isnan(t, _state) )
{
result = _state->v_nan;
return result;
}
/*
* Special case: N=1
*/
if( n==1 )
{
result = f->ptr.p_double[0];
return result;
}
/*
* First, decide: should we use "safe" formula (guarded
* against overflow) or fast one?
*/
threshold = ae_sqrt(ae_minrealnumber, _state);
j = 0;
s = t-a;
for(i=1; i<=n-1; i++)
{
x = a+(double)i/(double)(n-1)*(b-a);
if( ae_fp_less(ae_fabs(t-x, _state),ae_fabs(s, _state)) )
{
s = t-x;
j = i;
}
}
if( ae_fp_eq(s,(double)(0)) )
{
result = f->ptr.p_double[j];
return result;
}
if( ae_fp_greater(ae_fabs(s, _state),threshold) )
{
/*
* use fast formula
*/
j = -1;
s = 1.0;
}
/*
* Calculate using safe or fast barycentric formula
*/
s1 = (double)(0);
s2 = (double)(0);
w = 1.0;
h = (b-a)/(n-1);
for(i=0; i<=n-1; i++)
{
if( i!=j )
{
v = s*w/(t-(a+i*h));
s1 = s1+v*f->ptr.p_double[i];
s2 = s2+v;
}
else
{
v = w;
s1 = s1+v*f->ptr.p_double[i];
s2 = s2+v;
}
w = -w*(n-1-i);
w = w/(i+1);
}
result = s1/s2;
return result;
}
/*************************************************************************
Fast polynomial interpolation function on Chebyshev points (first kind)
with O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
F - function values, array[0..N-1]
N - number of points on Chebyshev grid (first kind),
X[i] = 0.5*(B+A) + 0.5*(B-A)*Cos(PI*(2*i+1)/(2*n))
for N=1 a constant model is constructed.
T - position where P(x) is calculated
RESULT
value of the Lagrange interpolant at T
IMPORTANT
this function provides fast interface which is not overflow-safe
nor it is very precise.
the best option is to use PolIntBuildCheb1()/BarycentricCalc()
subroutines unless you are pretty sure that your data will not result
in overflow.
-- ALGLIB --
Copyright 02.12.2009 by Bochkanov Sergey
*************************************************************************/
double polynomialcalccheb1(double a,
double b,
/* Real */ ae_vector* f,
ae_int_t n,
double t,
ae_state *_state)
{
double s1;
double s2;
double v;
double threshold;
double s;
ae_int_t i;
ae_int_t j;
double a0;
double delta;
double alpha;
double beta;
double ca;
double sa;
double tempc;
double temps;
double x;
double w;
double p1;
double result;
ae_assert(n>0, "PolynomialCalcCheb1: N<=0!", _state);
ae_assert(f->cnt>=n, "PolynomialCalcCheb1: Length(F)<N!", _state);
ae_assert(ae_isfinite(a, _state), "PolynomialCalcCheb1: A is infinite or NaN!", _state);
ae_assert(ae_isfinite(b, _state), "PolynomialCalcCheb1: B is infinite or NaN!", _state);
ae_assert(isfinitevector(f, n, _state), "PolynomialCalcCheb1: F contains infinite or NaN values!", _state);
ae_assert(ae_fp_neq(b,a), "PolynomialCalcCheb1: B=A!", _state);
ae_assert(!ae_isinf(t, _state), "PolynomialCalcCheb1: T is infinite!", _state);
/*
* Special case: T is NAN
*/
if( ae_isnan(t, _state) )
{
result = _state->v_nan;
return result;
}
/*
* Special case: N=1
*/
if( n==1 )
{
result = f->ptr.p_double[0];
return result;
}
/*
* Prepare information for the recurrence formula
* used to calculate sin(pi*(2j+1)/(2n+2)) and
* cos(pi*(2j+1)/(2n+2)):
*
* A0 = pi/(2n+2)
* Delta = pi/(n+1)
* Alpha = 2 sin^2 (Delta/2)
* Beta = sin(Delta)
*
* so that sin(..) = sin(A0+j*delta) and cos(..) = cos(A0+j*delta).
* Then we use
*
* sin(x+delta) = sin(x) - (alpha*sin(x) - beta*cos(x))
* cos(x+delta) = cos(x) - (alpha*cos(x) - beta*sin(x))
*
* to repeatedly calculate sin(..) and cos(..).
*/
threshold = ae_sqrt(ae_minrealnumber, _state);
t = (t-0.5*(a+b))/(0.5*(b-a));
a0 = ae_pi/(2*(n-1)+2);
delta = 2*ae_pi/(2*(n-1)+2);
alpha = 2*ae_sqr(ae_sin(delta/2, _state), _state);
beta = ae_sin(delta, _state);
/*
* First, decide: should we use "safe" formula (guarded
* against overflow) or fast one?
*/
ca = ae_cos(a0, _state);
sa = ae_sin(a0, _state);
j = 0;
x = ca;
s = t-x;
for(i=1; i<=n-1; i++)
{
/*
* Next X[i]
*/
temps = sa-(alpha*sa-beta*ca);
tempc = ca-(alpha*ca+beta*sa);
sa = temps;
ca = tempc;
x = ca;
/*
* Use X[i]
*/
if( ae_fp_less(ae_fabs(t-x, _state),ae_fabs(s, _state)) )
{
s = t-x;
j = i;
}
}
if( ae_fp_eq(s,(double)(0)) )
{
result = f->ptr.p_double[j];
return result;
}
if( ae_fp_greater(ae_fabs(s, _state),threshold) )
{
/*
* use fast formula
*/
j = -1;
s = 1.0;
}
/*
* Calculate using safe or fast barycentric formula
*/
s1 = (double)(0);
s2 = (double)(0);
ca = ae_cos(a0, _state);
sa = ae_sin(a0, _state);
p1 = 1.0;
for(i=0; i<=n-1; i++)
{
/*
* Calculate X[i], W[i]
*/
x = ca;
w = p1*sa;
/*
* Proceed
*/
if( i!=j )
{
v = s*w/(t-x);
s1 = s1+v*f->ptr.p_double[i];
s2 = s2+v;
}
else
{
v = w;
s1 = s1+v*f->ptr.p_double[i];
s2 = s2+v;
}
/*
* Next CA, SA, P1
*/
temps = sa-(alpha*sa-beta*ca);
tempc = ca-(alpha*ca+beta*sa);
sa = temps;
ca = tempc;
p1 = -p1;
}
result = s1/s2;
return result;
}
/*************************************************************************
Fast polynomial interpolation function on Chebyshev points (second kind)
with O(N) complexity.
INPUT PARAMETERS:
A - left boundary of [A,B]
B - right boundary of [A,B]
F - function values, array[0..N-1]
N - number of points on Chebyshev grid (second kind),
X[i] = 0.5*(B+A) + 0.5*(B-A)*Cos(PI*i/(n-1))
for N=1 a constant model is constructed.
T - position where P(x) is calculated
RESULT
value of the Lagrange interpolant at T
IMPORTANT
this function provides fast interface which is not overflow-safe
nor it is very precise.
the best option is to use PolIntBuildCheb2()/BarycentricCalc()
subroutines unless you are pretty sure that your data will not result
in overflow.
-- ALGLIB --
Copyright 02.12.2009 by Bochkanov Sergey
*************************************************************************/
double polynomialcalccheb2(double a,
double b,
/* Real */ ae_vector* f,
ae_int_t n,
double t,
ae_state *_state)
{
double s1;
double s2;
double v;
double threshold;
double s;
ae_int_t i;
ae_int_t j;
double a0;
double delta;
double alpha;
double beta;
double ca;
double sa;
double tempc;
double temps;
double x;
double w;
double p1;
double result;
ae_assert(n>0, "PolynomialCalcCheb2: N<=0!", _state);
ae_assert(f->cnt>=n, "PolynomialCalcCheb2: Length(F)<N!", _state);
ae_assert(ae_isfinite(a, _state), "PolynomialCalcCheb2: A is infinite or NaN!", _state);
ae_assert(ae_isfinite(b, _state), "PolynomialCalcCheb2: B is infinite or NaN!", _state);
ae_assert(ae_fp_neq(b,a), "PolynomialCalcCheb2: B=A!", _state);
ae_assert(isfinitevector(f, n, _state), "PolynomialCalcCheb2: F contains infinite or NaN values!", _state);
ae_assert(!ae_isinf(t, _state), "PolynomialCalcEqDist: T is infinite!", _state);
/*
* Special case: T is NAN
*/
if( ae_isnan(t, _state) )
{
result = _state->v_nan;
return result;
}
/*
* Special case: N=1
*/
if( n==1 )
{
result = f->ptr.p_double[0];
return result;
}
/*
* Prepare information for the recurrence formula
* used to calculate sin(pi*i/n) and
* cos(pi*i/n):
*
* A0 = 0
* Delta = pi/n
* Alpha = 2 sin^2 (Delta/2)
* Beta = sin(Delta)
*
* so that sin(..) = sin(A0+j*delta) and cos(..) = cos(A0+j*delta).
* Then we use
*
* sin(x+delta) = sin(x) - (alpha*sin(x) - beta*cos(x))
* cos(x+delta) = cos(x) - (alpha*cos(x) - beta*sin(x))
*
* to repeatedly calculate sin(..) and cos(..).
*/
threshold = ae_sqrt(ae_minrealnumber, _state);
t = (t-0.5*(a+b))/(0.5*(b-a));
a0 = 0.0;
delta = ae_pi/(n-1);
alpha = 2*ae_sqr(ae_sin(delta/2, _state), _state);
beta = ae_sin(delta, _state);
/*
* First, decide: should we use "safe" formula (guarded
* against overflow) or fast one?
*/
ca = ae_cos(a0, _state);
sa = ae_sin(a0, _state);
j = 0;
x = ca;
s = t-x;
for(i=1; i<=n-1; i++)
{
/*
* Next X[i]
*/
temps = sa-(alpha*sa-beta*ca);
tempc = ca-(alpha*ca+beta*sa);
sa = temps;
ca = tempc;
x = ca;
/*
* Use X[i]
*/
if( ae_fp_less(ae_fabs(t-x, _state),ae_fabs(s, _state)) )
{
s = t-x;
j = i;
}
}
if( ae_fp_eq(s,(double)(0)) )
{
result = f->ptr.p_double[j];
return result;
}
if( ae_fp_greater(ae_fabs(s, _state),threshold) )
{
/*
* use fast formula
*/
j = -1;
s = 1.0;
}
/*
* Calculate using safe or fast barycentric formula
*/
s1 = (double)(0);
s2 = (double)(0);
ca = ae_cos(a0, _state);
sa = ae_sin(a0, _state);
p1 = 1.0;
for(i=0; i<=n-1; i++)
{
/*
* Calculate X[i], W[i]
*/
x = ca;
if( i==0||i==n-1 )
{
w = 0.5*p1;
}
else
{
w = 1.0*p1;
}
/*
* Proceed
*/
if( i!=j )
{
v = s*w/(t-x);
s1 = s1+v*f->ptr.p_double[i];
s2 = s2+v;
}
else
{
v = w;
s1 = s1+v*f->ptr.p_double[i];
s2 = s2+v;
}
/*
* Next CA, SA, P1
*/
temps = sa-(alpha*sa-beta*ca);
tempc = ca-(alpha*ca+beta*sa);
sa = temps;
ca = tempc;
p1 = -p1;
}
result = s1/s2;
return result;
}
#endif
#if defined(AE_COMPILE_LSFIT) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This subroutine fits piecewise linear curve to points with Ramer-Douglas-
Peucker algorithm, which stops after generating specified number of linear
sections.
IMPORTANT:
* it does NOT perform least-squares fitting; it builds curve, but this
curve does not minimize some least squares metric. See description of
RDP algorithm (say, in Wikipedia) for more details on WHAT is performed.
* this function does NOT work with parametric curves (i.e. curves which
can be represented as {X(t),Y(t)}. It works with curves which can be
represented as Y(X). Thus, it is impossible to model figures like
circles with this functions.
If you want to work with parametric curves, you should use
ParametricRDPFixed() function provided by "Parametric" subpackage of
"Interpolation" package.
INPUT PARAMETERS:
X - array of X-coordinates:
* at least N elements
* can be unordered (points are automatically sorted)
* this function may accept non-distinct X (see below for
more information on handling of such inputs)
Y - array of Y-coordinates:
* at least N elements
N - number of elements in X/Y
M - desired number of sections:
* at most M sections are generated by this function
* less than M sections can be generated if we have N<M
(or some X are non-distinct).
OUTPUT PARAMETERS:
X2 - X-values of corner points for piecewise approximation,
has length NSections+1 or zero (for NSections=0).
Y2 - Y-values of corner points,
has length NSections+1 or zero (for NSections=0).
NSections- number of sections found by algorithm, NSections<=M,
NSections can be zero for degenerate datasets
(N<=1 or all X[] are non-distinct).
NOTE: X2/Y2 are ordered arrays, i.e. (X2[0],Y2[0]) is a first point of
curve, (X2[NSection-1],Y2[NSection-1]) is the last point.
-- ALGLIB --
Copyright 02.10.2014 by Bochkanov Sergey
*************************************************************************/
void lstfitpiecewiselinearrdpfixed(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t m,
/* Real */ ae_vector* x2,
/* Real */ ae_vector* y2,
ae_int_t* nsections,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t k0;
ae_int_t k1;
ae_int_t k2;
ae_vector buf0;
ae_vector buf1;
ae_matrix sections;
ae_vector points;
double v;
ae_int_t worstidx;
double worsterror;
ae_int_t idx0;
ae_int_t idx1;
double e0;
double e1;
ae_vector heaperrors;
ae_vector heaptags;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&buf0, 0, sizeof(buf0));
memset(&buf1, 0, sizeof(buf1));
memset(&sections, 0, sizeof(sections));
memset(&points, 0, sizeof(points));
memset(&heaperrors, 0, sizeof(heaperrors));
memset(&heaptags, 0, sizeof(heaptags));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
ae_vector_clear(x2);
ae_vector_clear(y2);
*nsections = 0;
ae_vector_init(&buf0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&buf1, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&sections, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&points, 0, DT_REAL, _state, ae_true);
ae_vector_init(&heaperrors, 0, DT_REAL, _state, ae_true);
ae_vector_init(&heaptags, 0, DT_INT, _state, ae_true);
ae_assert(n>=0, "LSTFitPiecewiseLinearRDPFixed: N<0", _state);
ae_assert(m>=1, "LSTFitPiecewiseLinearRDPFixed: M<1", _state);
ae_assert(x->cnt>=n, "LSTFitPiecewiseLinearRDPFixed: Length(X)<N", _state);
ae_assert(y->cnt>=n, "LSTFitPiecewiseLinearRDPFixed: Length(Y)<N", _state);
if( n<=1 )
{
*nsections = 0;
ae_frame_leave(_state);
return;
}
/*
* Sort points.
* Handle possible ties (tied values are replaced by their mean)
*/
tagsortfastr(x, y, &buf0, &buf1, n, _state);
i = 0;
while(i<=n-1)
{
j = i+1;
v = y->ptr.p_double[i];
while(j<=n-1&&ae_fp_eq(x->ptr.p_double[j],x->ptr.p_double[i]))
{
v = v+y->ptr.p_double[j];
j = j+1;
}
v = v/(j-i);
for(k=i; k<=j-1; k++)
{
y->ptr.p_double[k] = v;
}
i = j;
}
/*
* Handle degenerate case x[0]=x[N-1]
*/
if( ae_fp_eq(x->ptr.p_double[n-1],x->ptr.p_double[0]) )
{
*nsections = 0;
ae_frame_leave(_state);
return;
}
/*
* Prepare first section
*/
lsfit_rdpanalyzesection(x, y, 0, n-1, &worstidx, &worsterror, _state);
ae_matrix_set_length(&sections, m, 4, _state);
ae_vector_set_length(&heaperrors, m, _state);
ae_vector_set_length(&heaptags, m, _state);
*nsections = 1;
sections.ptr.pp_double[0][0] = (double)(0);
sections.ptr.pp_double[0][1] = (double)(n-1);
sections.ptr.pp_double[0][2] = (double)(worstidx);
sections.ptr.pp_double[0][3] = worsterror;
heaperrors.ptr.p_double[0] = worsterror;
heaptags.ptr.p_int[0] = 0;
ae_assert(ae_fp_eq(sections.ptr.pp_double[0][1],(double)(n-1)), "RDP algorithm: integrity check failed", _state);
/*
* Main loop.
* Repeatedly find section with worst error and divide it.
* Terminate after M-th section, or because of other reasons (see loop internals).
*/
while(*nsections<m)
{
/*
* Break if worst section has zero error.
* Store index of worst section to K.
*/
if( ae_fp_eq(heaperrors.ptr.p_double[0],(double)(0)) )
{
break;
}
k = heaptags.ptr.p_int[0];
/*
* K-th section is divided in two:
* * first one spans interval from X[Sections[K,0]] to X[Sections[K,2]]
* * second one spans interval from X[Sections[K,2]] to X[Sections[K,1]]
*
* First section is stored at K-th position, second one is appended to the table.
* Then we update heap which stores pairs of (error,section_index)
*/
k0 = ae_round(sections.ptr.pp_double[k][0], _state);
k1 = ae_round(sections.ptr.pp_double[k][1], _state);
k2 = ae_round(sections.ptr.pp_double[k][2], _state);
lsfit_rdpanalyzesection(x, y, k0, k2, &idx0, &e0, _state);
lsfit_rdpanalyzesection(x, y, k2, k1, &idx1, &e1, _state);
sections.ptr.pp_double[k][0] = (double)(k0);
sections.ptr.pp_double[k][1] = (double)(k2);
sections.ptr.pp_double[k][2] = (double)(idx0);
sections.ptr.pp_double[k][3] = e0;
tagheapreplacetopi(&heaperrors, &heaptags, *nsections, e0, k, _state);
sections.ptr.pp_double[*nsections][0] = (double)(k2);
sections.ptr.pp_double[*nsections][1] = (double)(k1);
sections.ptr.pp_double[*nsections][2] = (double)(idx1);
sections.ptr.pp_double[*nsections][3] = e1;
tagheappushi(&heaperrors, &heaptags, nsections, e1, *nsections, _state);
}
/*
* Convert from sections to points
*/
ae_vector_set_length(&points, *nsections+1, _state);
k = ae_round(sections.ptr.pp_double[0][1], _state);
for(i=0; i<=*nsections-1; i++)
{
points.ptr.p_double[i] = (double)(ae_round(sections.ptr.pp_double[i][0], _state));
if( ae_fp_greater(x->ptr.p_double[ae_round(sections.ptr.pp_double[i][1], _state)],x->ptr.p_double[k]) )
{
k = ae_round(sections.ptr.pp_double[i][1], _state);
}
}
points.ptr.p_double[*nsections] = (double)(k);
tagsortfast(&points, &buf0, *nsections+1, _state);
/*
* Output sections:
* * first NSection elements of X2/Y2 are filled by x/y at left boundaries of sections
* * last element of X2/Y2 is filled by right boundary of rightmost section
* * X2/Y2 is sorted by ascending of X2
*/
ae_vector_set_length(x2, *nsections+1, _state);
ae_vector_set_length(y2, *nsections+1, _state);
for(i=0; i<=*nsections; i++)
{
x2->ptr.p_double[i] = x->ptr.p_double[ae_round(points.ptr.p_double[i], _state)];
y2->ptr.p_double[i] = y->ptr.p_double[ae_round(points.ptr.p_double[i], _state)];
}
ae_frame_leave(_state);
}
/*************************************************************************
This subroutine fits piecewise linear curve to points with Ramer-Douglas-
Peucker algorithm, which stops after achieving desired precision.
IMPORTANT:
* it performs non-least-squares fitting; it builds curve, but this curve
does not minimize some least squares metric. See description of RDP
algorithm (say, in Wikipedia) for more details on WHAT is performed.
* this function does NOT work with parametric curves (i.e. curves which
can be represented as {X(t),Y(t)}. It works with curves which can be
represented as Y(X). Thus, it is impossible to model figures like circles
with this functions.
If you want to work with parametric curves, you should use
ParametricRDPFixed() function provided by "Parametric" subpackage of
"Interpolation" package.
INPUT PARAMETERS:
X - array of X-coordinates:
* at least N elements
* can be unordered (points are automatically sorted)
* this function may accept non-distinct X (see below for
more information on handling of such inputs)
Y - array of Y-coordinates:
* at least N elements
N - number of elements in X/Y
Eps - positive number, desired precision.
OUTPUT PARAMETERS:
X2 - X-values of corner points for piecewise approximation,
has length NSections+1 or zero (for NSections=0).
Y2 - Y-values of corner points,
has length NSections+1 or zero (for NSections=0).
NSections- number of sections found by algorithm,
NSections can be zero for degenerate datasets
(N<=1 or all X[] are non-distinct).
NOTE: X2/Y2 are ordered arrays, i.e. (X2[0],Y2[0]) is a first point of
curve, (X2[NSection-1],Y2[NSection-1]) is the last point.
-- ALGLIB --
Copyright 02.10.2014 by Bochkanov Sergey
*************************************************************************/
void lstfitpiecewiselinearrdp(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
double eps,
/* Real */ ae_vector* x2,
/* Real */ ae_vector* y2,
ae_int_t* nsections,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_vector buf0;
ae_vector buf1;
ae_vector xtmp;
ae_vector ytmp;
double v;
ae_int_t npts;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&buf0, 0, sizeof(buf0));
memset(&buf1, 0, sizeof(buf1));
memset(&xtmp, 0, sizeof(xtmp));
memset(&ytmp, 0, sizeof(ytmp));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
ae_vector_clear(x2);
ae_vector_clear(y2);
*nsections = 0;
ae_vector_init(&buf0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&buf1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&xtmp, 0, DT_REAL, _state, ae_true);
ae_vector_init(&ytmp, 0, DT_REAL, _state, ae_true);
ae_assert(n>=0, "LSTFitPiecewiseLinearRDP: N<0", _state);
ae_assert(ae_fp_greater(eps,(double)(0)), "LSTFitPiecewiseLinearRDP: Eps<=0", _state);
ae_assert(x->cnt>=n, "LSTFitPiecewiseLinearRDP: Length(X)<N", _state);
ae_assert(y->cnt>=n, "LSTFitPiecewiseLinearRDP: Length(Y)<N", _state);
if( n<=1 )
{
*nsections = 0;
ae_frame_leave(_state);
return;
}
/*
* Sort points.
* Handle possible ties (tied values are replaced by their mean)
*/
tagsortfastr(x, y, &buf0, &buf1, n, _state);
i = 0;
while(i<=n-1)
{
j = i+1;
v = y->ptr.p_double[i];
while(j<=n-1&&ae_fp_eq(x->ptr.p_double[j],x->ptr.p_double[i]))
{
v = v+y->ptr.p_double[j];
j = j+1;
}
v = v/(j-i);
for(k=i; k<=j-1; k++)
{
y->ptr.p_double[k] = v;
}
i = j;
}
/*
* Handle degenerate case x[0]=x[N-1]
*/
if( ae_fp_eq(x->ptr.p_double[n-1],x->ptr.p_double[0]) )
{
*nsections = 0;
ae_frame_leave(_state);
return;
}
/*
* Prepare data for recursive algorithm
*/
ae_vector_set_length(&xtmp, n, _state);
ae_vector_set_length(&ytmp, n, _state);
npts = 2;
xtmp.ptr.p_double[0] = x->ptr.p_double[0];
ytmp.ptr.p_double[0] = y->ptr.p_double[0];
xtmp.ptr.p_double[1] = x->ptr.p_double[n-1];
ytmp.ptr.p_double[1] = y->ptr.p_double[n-1];
lsfit_rdprecursive(x, y, 0, n-1, eps, &xtmp, &ytmp, &npts, _state);
/*
* Output sections:
* * first NSection elements of X2/Y2 are filled by x/y at left boundaries of sections
* * last element of X2/Y2 is filled by right boundary of rightmost section
* * X2/Y2 is sorted by ascending of X2
*/
*nsections = npts-1;
ae_vector_set_length(x2, npts, _state);
ae_vector_set_length(y2, npts, _state);
for(i=0; i<=*nsections; i++)
{
x2->ptr.p_double[i] = xtmp.ptr.p_double[i];
y2->ptr.p_double[i] = ytmp.ptr.p_double[i];
}
tagsortfastr(x2, y2, &buf0, &buf1, npts, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Fitting by polynomials in barycentric form. This function provides simple
unterface for unconstrained unweighted fitting. See PolynomialFitWC() if
you need constrained fitting.
Task is linear, so linear least squares solver is used. Complexity of this
computational scheme is O(N*M^2), mostly dominated by least squares solver
SEE ALSO:
PolynomialFitWC()
NOTES:
you can convert P from barycentric form to the power or Chebyshev
basis with PolynomialBar2Pow() or PolynomialBar2Cheb() functions from
POLINT subpackage.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
N - number of points, N>0
* if given, only leading N elements of X/Y are used
* if not given, automatically determined from sizes of X/Y
M - number of basis functions (= polynomial_degree + 1), M>=1
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearW() subroutine:
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
P - interpolant in barycentric form.
Rep - report, same format as in LSFitLinearW() subroutine.
Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
-- ALGLIB PROJECT --
Copyright 10.12.2009 by Bochkanov Sergey
*************************************************************************/
void polynomialfit(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t m,
ae_int_t* info,
barycentricinterpolant* p,
polynomialfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_vector w;
ae_vector xc;
ae_vector yc;
ae_vector dc;
ae_frame_make(_state, &_frame_block);
memset(&w, 0, sizeof(w));
memset(&xc, 0, sizeof(xc));
memset(&yc, 0, sizeof(yc));
memset(&dc, 0, sizeof(dc));
*info = 0;
_barycentricinterpolant_clear(p);
_polynomialfitreport_clear(rep);
ae_vector_init(&w, 0, DT_REAL, _state, ae_true);
ae_vector_init(&xc, 0, DT_REAL, _state, ae_true);
ae_vector_init(&yc, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dc, 0, DT_INT, _state, ae_true);
ae_assert(n>0, "PolynomialFit: N<=0!", _state);
ae_assert(m>0, "PolynomialFit: M<=0!", _state);
ae_assert(x->cnt>=n, "PolynomialFit: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "PolynomialFit: Length(Y)<N!", _state);
ae_assert(isfinitevector(x, n, _state), "PolynomialFit: X contains infinite or NaN values!", _state);
ae_assert(isfinitevector(y, n, _state), "PolynomialFit: Y contains infinite or NaN values!", _state);
ae_vector_set_length(&w, n, _state);
for(i=0; i<=n-1; i++)
{
w.ptr.p_double[i] = (double)(1);
}
polynomialfitwc(x, y, &w, n, &xc, &yc, &dc, 0, m, info, p, rep, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Weighted fitting by polynomials in barycentric form, with constraints on
function values or first derivatives.
Small regularizing term is used when solving constrained tasks (to improve
stability).
Task is linear, so linear least squares solver is used. Complexity of this
computational scheme is O(N*M^2), mostly dominated by least squares solver
SEE ALSO:
PolynomialFit()
NOTES:
you can convert P from barycentric form to the power or Chebyshev
basis with PolynomialBar2Pow() or PolynomialBar2Cheb() functions from
POLINT subpackage.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
W - weights, array[0..N-1]
Each summand in square sum of approximation deviations from
given values is multiplied by the square of corresponding
weight. Fill it by 1's if you don't want to solve weighted
task.
N - number of points, N>0.
* if given, only leading N elements of X/Y/W are used
* if not given, automatically determined from sizes of X/Y/W
XC - points where polynomial values/derivatives are constrained,
array[0..K-1].
YC - values of constraints, array[0..K-1]
DC - array[0..K-1], types of constraints:
* DC[i]=0 means that P(XC[i])=YC[i]
* DC[i]=1 means that P'(XC[i])=YC[i]
SEE BELOW FOR IMPORTANT INFORMATION ON CONSTRAINTS
K - number of constraints, 0<=K<M.
K=0 means no constraints (XC/YC/DC are not used in such cases)
M - number of basis functions (= polynomial_degree + 1), M>=1
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearW() subroutine:
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
-3 means inconsistent constraints
P - interpolant in barycentric form.
Rep - report, same format as in LSFitLinearW() subroutine.
Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
SETTING CONSTRAINTS - DANGERS AND OPPORTUNITIES:
Setting constraints can lead to undesired results, like ill-conditioned
behavior, or inconsistency being detected. From the other side, it allows
us to improve quality of the fit. Here we summarize our experience with
constrained regression splines:
* even simple constraints can be inconsistent, see Wikipedia article on
this subject: http://en.wikipedia.org/wiki/Birkhoff_interpolation
* the greater is M (given fixed constraints), the more chances that
constraints will be consistent
* in the general case, consistency of constraints is NOT GUARANTEED.
* in the one special cases, however, we can guarantee consistency. This
case is: M>1 and constraints on the function values (NOT DERIVATIVES)
Our final recommendation is to use constraints WHEN AND ONLY when you
can't solve your task without them. Anything beyond special cases given
above is not guaranteed and may result in inconsistency.
-- ALGLIB PROJECT --
Copyright 10.12.2009 by Bochkanov Sergey
*************************************************************************/
void polynomialfitwc(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
ae_int_t n,
/* Real */ ae_vector* xc,
/* Real */ ae_vector* yc,
/* Integer */ ae_vector* dc,
ae_int_t k,
ae_int_t m,
ae_int_t* info,
barycentricinterpolant* p,
polynomialfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_vector _w;
ae_vector _xc;
ae_vector _yc;
double xa;
double xb;
double sa;
double sb;
ae_vector xoriginal;
ae_vector yoriginal;
ae_vector y2;
ae_vector w2;
ae_vector tmp;
ae_vector tmp2;
ae_vector bx;
ae_vector by;
ae_vector bw;
ae_int_t i;
ae_int_t j;
double u;
double v;
double s;
ae_int_t relcnt;
lsfitreport lrep;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&_w, 0, sizeof(_w));
memset(&_xc, 0, sizeof(_xc));
memset(&_yc, 0, sizeof(_yc));
memset(&xoriginal, 0, sizeof(xoriginal));
memset(&yoriginal, 0, sizeof(yoriginal));
memset(&y2, 0, sizeof(y2));
memset(&w2, 0, sizeof(w2));
memset(&tmp, 0, sizeof(tmp));
memset(&tmp2, 0, sizeof(tmp2));
memset(&bx, 0, sizeof(bx));
memset(&by, 0, sizeof(by));
memset(&bw, 0, sizeof(bw));
memset(&lrep, 0, sizeof(lrep));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
ae_vector_init_copy(&_w, w, _state, ae_true);
w = &_w;
ae_vector_init_copy(&_xc, xc, _state, ae_true);
xc = &_xc;
ae_vector_init_copy(&_yc, yc, _state, ae_true);
yc = &_yc;
*info = 0;
_barycentricinterpolant_clear(p);
_polynomialfitreport_clear(rep);
ae_vector_init(&xoriginal, 0, DT_REAL, _state, ae_true);
ae_vector_init(&yoriginal, 0, DT_REAL, _state, ae_true);
ae_vector_init(&y2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&w2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&by, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bw, 0, DT_REAL, _state, ae_true);
_lsfitreport_init(&lrep, _state, ae_true);
ae_assert(n>0, "PolynomialFitWC: N<=0!", _state);
ae_assert(m>0, "PolynomialFitWC: M<=0!", _state);
ae_assert(k>=0, "PolynomialFitWC: K<0!", _state);
ae_assert(k<m, "PolynomialFitWC: K>=M!", _state);
ae_assert(x->cnt>=n, "PolynomialFitWC: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "PolynomialFitWC: Length(Y)<N!", _state);
ae_assert(w->cnt>=n, "PolynomialFitWC: Length(W)<N!", _state);
ae_assert(xc->cnt>=k, "PolynomialFitWC: Length(XC)<K!", _state);
ae_assert(yc->cnt>=k, "PolynomialFitWC: Length(YC)<K!", _state);
ae_assert(dc->cnt>=k, "PolynomialFitWC: Length(DC)<K!", _state);
ae_assert(isfinitevector(x, n, _state), "PolynomialFitWC: X contains infinite or NaN values!", _state);
ae_assert(isfinitevector(y, n, _state), "PolynomialFitWC: Y contains infinite or NaN values!", _state);
ae_assert(isfinitevector(w, n, _state), "PolynomialFitWC: X contains infinite or NaN values!", _state);
ae_assert(isfinitevector(xc, k, _state), "PolynomialFitWC: XC contains infinite or NaN values!", _state);
ae_assert(isfinitevector(yc, k, _state), "PolynomialFitWC: YC contains infinite or NaN values!", _state);
for(i=0; i<=k-1; i++)
{
ae_assert(dc->ptr.p_int[i]==0||dc->ptr.p_int[i]==1, "PolynomialFitWC: one of DC[] is not 0 or 1!", _state);
}
/*
* Scale X, Y, XC, YC.
* Solve scaled problem using internal Chebyshev fitting function.
*/
lsfitscalexy(x, y, w, n, xc, yc, dc, k, &xa, &xb, &sa, &sb, &xoriginal, &yoriginal, _state);
lsfit_internalchebyshevfit(x, y, w, n, xc, yc, dc, k, m, info, &tmp, &lrep, _state);
if( *info<0 )
{
ae_frame_leave(_state);
return;
}
/*
* Generate barycentric model and scale it
* * BX, BY store barycentric model nodes
* * FMatrix is reused (remember - it is at least MxM, what we need)
*
* Model intialization is done in O(M^2). In principle, it can be
* done in O(M*log(M)), but before it we solved task with O(N*M^2)
* complexity, so it is only a small amount of total time spent.
*/
ae_vector_set_length(&bx, m, _state);
ae_vector_set_length(&by, m, _state);
ae_vector_set_length(&bw, m, _state);
ae_vector_set_length(&tmp2, m, _state);
s = (double)(1);
for(i=0; i<=m-1; i++)
{
if( m!=1 )
{
u = ae_cos(ae_pi*i/(m-1), _state);
}
else
{
u = (double)(0);
}
v = (double)(0);
for(j=0; j<=m-1; j++)
{
if( j==0 )
{
tmp2.ptr.p_double[j] = (double)(1);
}
else
{
if( j==1 )
{
tmp2.ptr.p_double[j] = u;
}
else
{
tmp2.ptr.p_double[j] = 2*u*tmp2.ptr.p_double[j-1]-tmp2.ptr.p_double[j-2];
}
}
v = v+tmp.ptr.p_double[j]*tmp2.ptr.p_double[j];
}
bx.ptr.p_double[i] = u;
by.ptr.p_double[i] = v;
bw.ptr.p_double[i] = s;
if( i==0||i==m-1 )
{
bw.ptr.p_double[i] = 0.5*bw.ptr.p_double[i];
}
s = -s;
}
barycentricbuildxyw(&bx, &by, &bw, m, p, _state);
barycentriclintransx(p, 2/(xb-xa), -(xa+xb)/(xb-xa), _state);
barycentriclintransy(p, sb-sa, sa, _state);
/*
* Scale absolute errors obtained from LSFitLinearW.
* Relative error should be calculated separately
* (because of shifting/scaling of the task)
*/
rep->taskrcond = lrep.taskrcond;
rep->rmserror = lrep.rmserror*(sb-sa);
rep->avgerror = lrep.avgerror*(sb-sa);
rep->maxerror = lrep.maxerror*(sb-sa);
rep->avgrelerror = (double)(0);
relcnt = 0;
for(i=0; i<=n-1; i++)
{
if( ae_fp_neq(yoriginal.ptr.p_double[i],(double)(0)) )
{
rep->avgrelerror = rep->avgrelerror+ae_fabs(barycentriccalc(p, xoriginal.ptr.p_double[i], _state)-yoriginal.ptr.p_double[i], _state)/ae_fabs(yoriginal.ptr.p_double[i], _state);
relcnt = relcnt+1;
}
}
if( relcnt!=0 )
{
rep->avgrelerror = rep->avgrelerror/relcnt;
}
ae_frame_leave(_state);
}
/*************************************************************************
This function calculates value of four-parameter logistic (4PL) model at
specified point X. 4PL model has following form:
F(x|A,B,C,D) = D+(A-D)/(1+Power(x/C,B))
INPUT PARAMETERS:
X - current point, X>=0:
* zero X is correctly handled even for B<=0
* negative X results in exception.
A, B, C, D- parameters of 4PL model:
* A is unconstrained
* B is unconstrained; zero or negative values are handled
correctly.
* C>0, non-positive value results in exception
* D is unconstrained
RESULT:
model value at X
NOTE: if B=0, denominator is assumed to be equal to 2.0 even for zero X
(strictly speaking, 0^0 is undefined).
NOTE: this function also throws exception if all input parameters are
correct, but overflow was detected during calculations.
NOTE: this function performs a lot of checks; if you need really high
performance, consider evaluating model yourself, without checking
for degenerate cases.
-- ALGLIB PROJECT --
Copyright 14.05.2014 by Bochkanov Sergey
*************************************************************************/
double logisticcalc4(double x,
double a,
double b,
double c,
double d,
ae_state *_state)
{
double result;
ae_assert(ae_isfinite(x, _state), "LogisticCalc4: X is not finite", _state);
ae_assert(ae_isfinite(a, _state), "LogisticCalc4: A is not finite", _state);
ae_assert(ae_isfinite(b, _state), "LogisticCalc4: B is not finite", _state);
ae_assert(ae_isfinite(c, _state), "LogisticCalc4: C is not finite", _state);
ae_assert(ae_isfinite(d, _state), "LogisticCalc4: D is not finite", _state);
ae_assert(ae_fp_greater_eq(x,(double)(0)), "LogisticCalc4: X is negative", _state);
ae_assert(ae_fp_greater(c,(double)(0)), "LogisticCalc4: C is non-positive", _state);
/*
* Check for degenerate cases
*/
if( ae_fp_eq(b,(double)(0)) )
{
result = 0.5*(a+d);
return result;
}
if( ae_fp_eq(x,(double)(0)) )
{
if( ae_fp_greater(b,(double)(0)) )
{
result = a;
}
else
{
result = d;
}
return result;
}
/*
* General case
*/
result = d+(a-d)/(1.0+ae_pow(x/c, b, _state));
ae_assert(ae_isfinite(result, _state), "LogisticCalc4: overflow during calculations", _state);
return result;
}
/*************************************************************************
This function calculates value of five-parameter logistic (5PL) model at
specified point X. 5PL model has following form:
F(x|A,B,C,D,G) = D+(A-D)/Power(1+Power(x/C,B),G)
INPUT PARAMETERS:
X - current point, X>=0:
* zero X is correctly handled even for B<=0
* negative X results in exception.
A, B, C, D, G- parameters of 5PL model:
* A is unconstrained
* B is unconstrained; zero or negative values are handled
correctly.
* C>0, non-positive value results in exception
* D is unconstrained
* G>0, non-positive value results in exception
RESULT:
model value at X
NOTE: if B=0, denominator is assumed to be equal to Power(2.0,G) even for
zero X (strictly speaking, 0^0 is undefined).
NOTE: this function also throws exception if all input parameters are
correct, but overflow was detected during calculations.
NOTE: this function performs a lot of checks; if you need really high
performance, consider evaluating model yourself, without checking
for degenerate cases.
-- ALGLIB PROJECT --
Copyright 14.05.2014 by Bochkanov Sergey
*************************************************************************/
double logisticcalc5(double x,
double a,
double b,
double c,
double d,
double g,
ae_state *_state)
{
double result;
ae_assert(ae_isfinite(x, _state), "LogisticCalc5: X is not finite", _state);
ae_assert(ae_isfinite(a, _state), "LogisticCalc5: A is not finite", _state);
ae_assert(ae_isfinite(b, _state), "LogisticCalc5: B is not finite", _state);
ae_assert(ae_isfinite(c, _state), "LogisticCalc5: C is not finite", _state);
ae_assert(ae_isfinite(d, _state), "LogisticCalc5: D is not finite", _state);
ae_assert(ae_isfinite(g, _state), "LogisticCalc5: G is not finite", _state);
ae_assert(ae_fp_greater_eq(x,(double)(0)), "LogisticCalc5: X is negative", _state);
ae_assert(ae_fp_greater(c,(double)(0)), "LogisticCalc5: C is non-positive", _state);
ae_assert(ae_fp_greater(g,(double)(0)), "LogisticCalc5: G is non-positive", _state);
/*
* Check for degenerate cases
*/
if( ae_fp_eq(b,(double)(0)) )
{
result = d+(a-d)/ae_pow(2.0, g, _state);
return result;
}
if( ae_fp_eq(x,(double)(0)) )
{
if( ae_fp_greater(b,(double)(0)) )
{
result = a;
}
else
{
result = d;
}
return result;
}
/*
* General case
*/
result = d+(a-d)/ae_pow(1.0+ae_pow(x/c, b, _state), g, _state);
ae_assert(ae_isfinite(result, _state), "LogisticCalc5: overflow during calculations", _state);
return result;
}
/*************************************************************************
This function fits four-parameter logistic (4PL) model to data provided
by user. 4PL model has following form:
F(x|A,B,C,D) = D+(A-D)/(1+Power(x/C,B))
Here:
* A, D - unconstrained (see LogisticFit4EC() for constrained 4PL)
* B>=0
* C>0
IMPORTANT: output of this function is constrained in such way that B>0.
Because 4PL model is symmetric with respect to B, there is no
need to explore B<0. Constraining B makes algorithm easier
to stabilize and debug.
Users who for some reason prefer to work with negative B's
should transform output themselves (swap A and D, replace B by
-B).
4PL fitting is implemented as follows:
* we perform small number of restarts from random locations which helps to
solve problem of bad local extrema. Locations are only partially random
- we use input data to determine good initial guess, but we include
controlled amount of randomness.
* we perform Levenberg-Marquardt fitting with very tight constraints on
parameters B and C - it allows us to find good initial guess for the
second stage without risk of running into "flat spot".
* second Levenberg-Marquardt round is performed without excessive
constraints. Results from the previous round are used as initial guess.
* after fitting is done, we compare results with best values found so far,
rewrite "best solution" if needed, and move to next random location.
Overall algorithm is very stable and is not prone to bad local extrema.
Furthermore, it automatically scales when input data have very large or
very small range.
INPUT PARAMETERS:
X - array[N], stores X-values.
MUST include only non-negative numbers (but may include
zero values). Can be unsorted.
Y - array[N], values to fit.
N - number of points. If N is less than length of X/Y, only
leading N elements are used.
OUTPUT PARAMETERS:
A, B, C, D- parameters of 4PL model
Rep - fitting report. This structure has many fields, but ONLY
ONES LISTED BELOW ARE SET:
* Rep.IterationsCount - number of iterations performed
* Rep.RMSError - root-mean-square error
* Rep.AvgError - average absolute error
* Rep.AvgRelError - average relative error (calculated for
non-zero Y-values)
* Rep.MaxError - maximum absolute error
* Rep.R2 - coefficient of determination, R-squared. This
coefficient is calculated as R2=1-RSS/TSS (in case
of nonlinear regression there are multiple ways to
define R2, each of them giving different results).
NOTE: for stability reasons the B parameter is restricted by [1/1000,1000]
range. It prevents algorithm from making trial steps deep into the
area of bad parameters.
NOTE: after you obtained coefficients, you can evaluate model with
LogisticCalc4() function.
NOTE: if you need better control over fitting process than provided by this
function, you may use LogisticFit45X().
NOTE: step is automatically scaled according to scale of parameters being
fitted before we compare its length with EpsX. Thus, this function
can be used to fit data with very small or very large values without
changing EpsX.
-- ALGLIB PROJECT --
Copyright 14.02.2014 by Bochkanov Sergey
*************************************************************************/
void logisticfit4(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
double* a,
double* b,
double* c,
double* d,
lsfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
double g;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
*a = 0;
*b = 0;
*c = 0;
*d = 0;
_lsfitreport_clear(rep);
logisticfit45x(x, y, n, _state->v_nan, _state->v_nan, ae_true, 0.0, 0.0, 0, a, b, c, d, &g, rep, _state);
ae_frame_leave(_state);
}
/*************************************************************************
This function fits four-parameter logistic (4PL) model to data provided
by user, with optional constraints on parameters A and D. 4PL model has
following form:
F(x|A,B,C,D) = D+(A-D)/(1+Power(x/C,B))
Here:
* A, D - with optional equality constraints
* B>=0
* C>0
IMPORTANT: output of this function is constrained in such way that B>0.
Because 4PL model is symmetric with respect to B, there is no
need to explore B<0. Constraining B makes algorithm easier
to stabilize and debug.
Users who for some reason prefer to work with negative B's
should transform output themselves (swap A and D, replace B by
-B).
4PL fitting is implemented as follows:
* we perform small number of restarts from random locations which helps to
solve problem of bad local extrema. Locations are only partially random
- we use input data to determine good initial guess, but we include
controlled amount of randomness.
* we perform Levenberg-Marquardt fitting with very tight constraints on
parameters B and C - it allows us to find good initial guess for the
second stage without risk of running into "flat spot".
* second Levenberg-Marquardt round is performed without excessive
constraints. Results from the previous round are used as initial guess.
* after fitting is done, we compare results with best values found so far,
rewrite "best solution" if needed, and move to next random location.
Overall algorithm is very stable and is not prone to bad local extrema.
Furthermore, it automatically scales when input data have very large or
very small range.
INPUT PARAMETERS:
X - array[N], stores X-values.
MUST include only non-negative numbers (but may include
zero values). Can be unsorted.
Y - array[N], values to fit.
N - number of points. If N is less than length of X/Y, only
leading N elements are used.
CnstrLeft- optional equality constraint for model value at the left
boundary (at X=0). Specify NAN (Not-a-Number) if you do
not need constraint on the model value at X=0 (in C++ you
can pass alglib::fp_nan as parameter, in C# it will be
Double.NaN).
See below, section "EQUALITY CONSTRAINTS" for more
information about constraints.
CnstrRight- optional equality constraint for model value at X=infinity.
Specify NAN (Not-a-Number) if you do not need constraint
on the model value (in C++ you can pass alglib::fp_nan as
parameter, in C# it will be Double.NaN).
See below, section "EQUALITY CONSTRAINTS" for more
information about constraints.
OUTPUT PARAMETERS:
A, B, C, D- parameters of 4PL model
Rep - fitting report. This structure has many fields, but ONLY
ONES LISTED BELOW ARE SET:
* Rep.IterationsCount - number of iterations performed
* Rep.RMSError - root-mean-square error
* Rep.AvgError - average absolute error
* Rep.AvgRelError - average relative error (calculated for
non-zero Y-values)
* Rep.MaxError - maximum absolute error
* Rep.R2 - coefficient of determination, R-squared. This
coefficient is calculated as R2=1-RSS/TSS (in case
of nonlinear regression there are multiple ways to
define R2, each of them giving different results).
NOTE: for stability reasons the B parameter is restricted by [1/1000,1000]
range. It prevents algorithm from making trial steps deep into the
area of bad parameters.
NOTE: after you obtained coefficients, you can evaluate model with
LogisticCalc4() function.
NOTE: if you need better control over fitting process than provided by this
function, you may use LogisticFit45X().
NOTE: step is automatically scaled according to scale of parameters being
fitted before we compare its length with EpsX. Thus, this function
can be used to fit data with very small or very large values without
changing EpsX.
EQUALITY CONSTRAINTS ON PARAMETERS
4PL/5PL solver supports equality constraints on model values at the left
boundary (X=0) and right boundary (X=infinity). These constraints are
completely optional and you can specify both of them, only one - or no
constraints at all.
Parameter CnstrLeft contains left constraint (or NAN for unconstrained
fitting), and CnstrRight contains right one. For 4PL, left constraint
ALWAYS corresponds to parameter A, and right one is ALWAYS constraint on
D. That's because 4PL model is normalized in such way that B>=0.
-- ALGLIB PROJECT --
Copyright 14.02.2014 by Bochkanov Sergey
*************************************************************************/
void logisticfit4ec(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
double cnstrleft,
double cnstrright,
double* a,
double* b,
double* c,
double* d,
lsfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
double g;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
*a = 0;
*b = 0;
*c = 0;
*d = 0;
_lsfitreport_clear(rep);
logisticfit45x(x, y, n, cnstrleft, cnstrright, ae_true, 0.0, 0.0, 0, a, b, c, d, &g, rep, _state);
ae_frame_leave(_state);
}
/*************************************************************************
This function fits five-parameter logistic (5PL) model to data provided
by user. 5PL model has following form:
F(x|A,B,C,D,G) = D+(A-D)/Power(1+Power(x/C,B),G)
Here:
* A, D - unconstrained
* B - unconstrained
* C>0
* G>0
IMPORTANT: unlike in 4PL fitting, output of this function is NOT
constrained in such way that B is guaranteed to be positive.
Furthermore, unlike 4PL, 5PL model is NOT symmetric with
respect to B, so you can NOT transform model to equivalent one,
with B having desired sign (>0 or <0).
5PL fitting is implemented as follows:
* we perform small number of restarts from random locations which helps to
solve problem of bad local extrema. Locations are only partially random
- we use input data to determine good initial guess, but we include
controlled amount of randomness.
* we perform Levenberg-Marquardt fitting with very tight constraints on
parameters B and C - it allows us to find good initial guess for the
second stage without risk of running into "flat spot". Parameter G is
fixed at G=1.
* second Levenberg-Marquardt round is performed without excessive
constraints on B and C, but with G still equal to 1. Results from the
previous round are used as initial guess.
* third Levenberg-Marquardt round relaxes constraints on G and tries two
different models - one with B>0 and one with B<0.
* after fitting is done, we compare results with best values found so far,
rewrite "best solution" if needed, and move to next random location.
Overall algorithm is very stable and is not prone to bad local extrema.
Furthermore, it automatically scales when input data have very large or
very small range.
INPUT PARAMETERS:
X - array[N], stores X-values.
MUST include only non-negative numbers (but may include
zero values). Can be unsorted.
Y - array[N], values to fit.
N - number of points. If N is less than length of X/Y, only
leading N elements are used.
OUTPUT PARAMETERS:
A,B,C,D,G- parameters of 5PL model
Rep - fitting report. This structure has many fields, but ONLY
ONES LISTED BELOW ARE SET:
* Rep.IterationsCount - number of iterations performed
* Rep.RMSError - root-mean-square error
* Rep.AvgError - average absolute error
* Rep.AvgRelError - average relative error (calculated for
non-zero Y-values)
* Rep.MaxError - maximum absolute error
* Rep.R2 - coefficient of determination, R-squared. This
coefficient is calculated as R2=1-RSS/TSS (in case
of nonlinear regression there are multiple ways to
define R2, each of them giving different results).
NOTE: for better stability B parameter is restricted by [+-1/1000,+-1000]
range, and G is restricted by [1/10,10] range. It prevents algorithm
from making trial steps deep into the area of bad parameters.
NOTE: after you obtained coefficients, you can evaluate model with
LogisticCalc5() function.
NOTE: if you need better control over fitting process than provided by this
function, you may use LogisticFit45X().
NOTE: step is automatically scaled according to scale of parameters being
fitted before we compare its length with EpsX. Thus, this function
can be used to fit data with very small or very large values without
changing EpsX.
-- ALGLIB PROJECT --
Copyright 14.02.2014 by Bochkanov Sergey
*************************************************************************/
void logisticfit5(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
double* a,
double* b,
double* c,
double* d,
double* g,
lsfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
*a = 0;
*b = 0;
*c = 0;
*d = 0;
*g = 0;
_lsfitreport_clear(rep);
logisticfit45x(x, y, n, _state->v_nan, _state->v_nan, ae_false, 0.0, 0.0, 0, a, b, c, d, g, rep, _state);
ae_frame_leave(_state);
}
/*************************************************************************
This function fits five-parameter logistic (5PL) model to data provided
by user, subject to optional equality constraints on parameters A and D.
5PL model has following form:
F(x|A,B,C,D,G) = D+(A-D)/Power(1+Power(x/C,B),G)
Here:
* A, D - with optional equality constraints
* B - unconstrained
* C>0
* G>0
IMPORTANT: unlike in 4PL fitting, output of this function is NOT
constrained in such way that B is guaranteed to be positive.
Furthermore, unlike 4PL, 5PL model is NOT symmetric with
respect to B, so you can NOT transform model to equivalent one,
with B having desired sign (>0 or <0).
5PL fitting is implemented as follows:
* we perform small number of restarts from random locations which helps to
solve problem of bad local extrema. Locations are only partially random
- we use input data to determine good initial guess, but we include
controlled amount of randomness.
* we perform Levenberg-Marquardt fitting with very tight constraints on
parameters B and C - it allows us to find good initial guess for the
second stage without risk of running into "flat spot". Parameter G is
fixed at G=1.
* second Levenberg-Marquardt round is performed without excessive
constraints on B and C, but with G still equal to 1. Results from the
previous round are used as initial guess.
* third Levenberg-Marquardt round relaxes constraints on G and tries two
different models - one with B>0 and one with B<0.
* after fitting is done, we compare results with best values found so far,
rewrite "best solution" if needed, and move to next random location.
Overall algorithm is very stable and is not prone to bad local extrema.
Furthermore, it automatically scales when input data have very large or
very small range.
INPUT PARAMETERS:
X - array[N], stores X-values.
MUST include only non-negative numbers (but may include
zero values). Can be unsorted.
Y - array[N], values to fit.
N - number of points. If N is less than length of X/Y, only
leading N elements are used.
CnstrLeft- optional equality constraint for model value at the left
boundary (at X=0). Specify NAN (Not-a-Number) if you do
not need constraint on the model value at X=0 (in C++ you
can pass alglib::fp_nan as parameter, in C# it will be
Double.NaN).
See below, section "EQUALITY CONSTRAINTS" for more
information about constraints.
CnstrRight- optional equality constraint for model value at X=infinity.
Specify NAN (Not-a-Number) if you do not need constraint
on the model value (in C++ you can pass alglib::fp_nan as
parameter, in C# it will be Double.NaN).
See below, section "EQUALITY CONSTRAINTS" for more
information about constraints.
OUTPUT PARAMETERS:
A,B,C,D,G- parameters of 5PL model
Rep - fitting report. This structure has many fields, but ONLY
ONES LISTED BELOW ARE SET:
* Rep.IterationsCount - number of iterations performed
* Rep.RMSError - root-mean-square error
* Rep.AvgError - average absolute error
* Rep.AvgRelError - average relative error (calculated for
non-zero Y-values)
* Rep.MaxError - maximum absolute error
* Rep.R2 - coefficient of determination, R-squared. This
coefficient is calculated as R2=1-RSS/TSS (in case
of nonlinear regression there are multiple ways to
define R2, each of them giving different results).
NOTE: for better stability B parameter is restricted by [+-1/1000,+-1000]
range, and G is restricted by [1/10,10] range. It prevents algorithm
from making trial steps deep into the area of bad parameters.
NOTE: after you obtained coefficients, you can evaluate model with
LogisticCalc5() function.
NOTE: if you need better control over fitting process than provided by this
function, you may use LogisticFit45X().
NOTE: step is automatically scaled according to scale of parameters being
fitted before we compare its length with EpsX. Thus, this function
can be used to fit data with very small or very large values without
changing EpsX.
EQUALITY CONSTRAINTS ON PARAMETERS
5PL solver supports equality constraints on model values at the left
boundary (X=0) and right boundary (X=infinity). These constraints are
completely optional and you can specify both of them, only one - or no
constraints at all.
Parameter CnstrLeft contains left constraint (or NAN for unconstrained
fitting), and CnstrRight contains right one.
Unlike 4PL one, 5PL model is NOT symmetric with respect to change in sign
of B. Thus, negative B's are possible, and left constraint may constrain
parameter A (for positive B's) - or parameter D (for negative B's).
Similarly changes meaning of right constraint.
You do not have to decide what parameter to constrain - algorithm will
automatically determine correct parameters as fitting progresses. However,
question highlighted above is important when you interpret fitting results.
-- ALGLIB PROJECT --
Copyright 14.02.2014 by Bochkanov Sergey
*************************************************************************/
void logisticfit5ec(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
double cnstrleft,
double cnstrright,
double* a,
double* b,
double* c,
double* d,
double* g,
lsfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
*a = 0;
*b = 0;
*c = 0;
*d = 0;
*g = 0;
_lsfitreport_clear(rep);
logisticfit45x(x, y, n, cnstrleft, cnstrright, ae_false, 0.0, 0.0, 0, a, b, c, d, g, rep, _state);
ae_frame_leave(_state);
}
/*************************************************************************
This is "expert" 4PL/5PL fitting function, which can be used if you need
better control over fitting process than provided by LogisticFit4() or
LogisticFit5().
This function fits model of the form
F(x|A,B,C,D) = D+(A-D)/(1+Power(x/C,B)) (4PL model)
or
F(x|A,B,C,D,G) = D+(A-D)/Power(1+Power(x/C,B),G) (5PL model)
Here:
* A, D - unconstrained
* B>=0 for 4PL, unconstrained for 5PL
* C>0
* G>0 (if present)
INPUT PARAMETERS:
X - array[N], stores X-values.
MUST include only non-negative numbers (but may include
zero values). Can be unsorted.
Y - array[N], values to fit.
N - number of points. If N is less than length of X/Y, only
leading N elements are used.
CnstrLeft- optional equality constraint for model value at the left
boundary (at X=0). Specify NAN (Not-a-Number) if you do
not need constraint on the model value at X=0 (in C++ you
can pass alglib::fp_nan as parameter, in C# it will be
Double.NaN).
See below, section "EQUALITY CONSTRAINTS" for more
information about constraints.
CnstrRight- optional equality constraint for model value at X=infinity.
Specify NAN (Not-a-Number) if you do not need constraint
on the model value (in C++ you can pass alglib::fp_nan as
parameter, in C# it will be Double.NaN).
See below, section "EQUALITY CONSTRAINTS" for more
information about constraints.
Is4PL - whether 4PL or 5PL models are fitted
LambdaV - regularization coefficient, LambdaV>=0.
Set it to zero unless you know what you are doing.
EpsX - stopping condition (step size), EpsX>=0.
Zero value means that small step is automatically chosen.
See notes below for more information.
RsCnt - number of repeated restarts from random points. 4PL/5PL
models are prone to problem of bad local extrema. Utilizing
multiple random restarts allows us to improve algorithm
convergence.
RsCnt>=0.
Zero value means that function automatically choose small
amount of restarts (recommended).
OUTPUT PARAMETERS:
A, B, C, D- parameters of 4PL model
G - parameter of 5PL model; for Is4PL=True, G=1 is returned.
Rep - fitting report. This structure has many fields, but ONLY
ONES LISTED BELOW ARE SET:
* Rep.IterationsCount - number of iterations performed
* Rep.RMSError - root-mean-square error
* Rep.AvgError - average absolute error
* Rep.AvgRelError - average relative error (calculated for
non-zero Y-values)
* Rep.MaxError - maximum absolute error
* Rep.R2 - coefficient of determination, R-squared. This
coefficient is calculated as R2=1-RSS/TSS (in case
of nonlinear regression there are multiple ways to
define R2, each of them giving different results).
NOTE: for better stability B parameter is restricted by [+-1/1000,+-1000]
range, and G is restricted by [1/10,10] range. It prevents algorithm
from making trial steps deep into the area of bad parameters.
NOTE: after you obtained coefficients, you can evaluate model with
LogisticCalc5() function.
NOTE: step is automatically scaled according to scale of parameters being
fitted before we compare its length with EpsX. Thus, this function
can be used to fit data with very small or very large values without
changing EpsX.
EQUALITY CONSTRAINTS ON PARAMETERS
4PL/5PL solver supports equality constraints on model values at the left
boundary (X=0) and right boundary (X=infinity). These constraints are
completely optional and you can specify both of them, only one - or no
constraints at all.
Parameter CnstrLeft contains left constraint (or NAN for unconstrained
fitting), and CnstrRight contains right one. For 4PL, left constraint
ALWAYS corresponds to parameter A, and right one is ALWAYS constraint on
D. That's because 4PL model is normalized in such way that B>=0.
For 5PL model things are different. Unlike 4PL one, 5PL model is NOT
symmetric with respect to change in sign of B. Thus, negative B's are
possible, and left constraint may constrain parameter A (for positive B's)
- or parameter D (for negative B's). Similarly changes meaning of right
constraint.
You do not have to decide what parameter to constrain - algorithm will
automatically determine correct parameters as fitting progresses. However,
question highlighted above is important when you interpret fitting results.
-- ALGLIB PROJECT --
Copyright 14.02.2014 by Bochkanov Sergey
*************************************************************************/
void logisticfit45x(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
double cnstrleft,
double cnstrright,
ae_bool is4pl,
double lambdav,
double epsx,
ae_int_t rscnt,
double* a,
double* b,
double* c,
double* d,
double* g,
lsfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_int_t i;
ae_int_t outerit;
ae_int_t nz;
double v;
ae_vector p0;
ae_vector p1;
ae_vector p2;
ae_vector bndl;
ae_vector bndu;
ae_vector s;
ae_vector bndl1;
ae_vector bndu1;
ae_vector bndl2;
ae_vector bndu2;
ae_matrix z;
hqrndstate rs;
minlmstate state;
minlmreport replm;
ae_int_t maxits;
double fbest;
double flast;
double scalex;
double scaley;
ae_vector bufx;
ae_vector bufy;
double fposb;
double fnegb;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&p0, 0, sizeof(p0));
memset(&p1, 0, sizeof(p1));
memset(&p2, 0, sizeof(p2));
memset(&bndl, 0, sizeof(bndl));
memset(&bndu, 0, sizeof(bndu));
memset(&s, 0, sizeof(s));
memset(&bndl1, 0, sizeof(bndl1));
memset(&bndu1, 0, sizeof(bndu1));
memset(&bndl2, 0, sizeof(bndl2));
memset(&bndu2, 0, sizeof(bndu2));
memset(&z, 0, sizeof(z));
memset(&rs, 0, sizeof(rs));
memset(&state, 0, sizeof(state));
memset(&replm, 0, sizeof(replm));
memset(&bufx, 0, sizeof(bufx));
memset(&bufy, 0, sizeof(bufy));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
*a = 0;
*b = 0;
*c = 0;
*d = 0;
*g = 0;
_lsfitreport_clear(rep);
ae_vector_init(&p0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&p1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&p2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bndl, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bndu, 0, DT_REAL, _state, ae_true);
ae_vector_init(&s, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bndl1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bndu1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bndl2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bndu2, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&z, 0, 0, DT_REAL, _state, ae_true);
_hqrndstate_init(&rs, _state, ae_true);
_minlmstate_init(&state, _state, ae_true);
_minlmreport_init(&replm, _state, ae_true);
ae_vector_init(&bufx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bufy, 0, DT_REAL, _state, ae_true);
ae_assert(ae_isfinite(epsx, _state), "LogisticFitX: EpsX is infinite/NAN", _state);
ae_assert(ae_isfinite(lambdav, _state), "LogisticFitX: LambdaV is infinite/NAN", _state);
ae_assert(ae_isfinite(cnstrleft, _state)||ae_isnan(cnstrleft, _state), "LogisticFitX: CnstrLeft is NOT finite or NAN", _state);
ae_assert(ae_isfinite(cnstrright, _state)||ae_isnan(cnstrright, _state), "LogisticFitX: CnstrRight is NOT finite or NAN", _state);
ae_assert(ae_fp_greater_eq(lambdav,(double)(0)), "LogisticFitX: negative LambdaV", _state);
ae_assert(n>0, "LogisticFitX: N<=0", _state);
ae_assert(rscnt>=0, "LogisticFitX: RsCnt<0", _state);
ae_assert(ae_fp_greater_eq(epsx,(double)(0)), "LogisticFitX: EpsX<0", _state);
ae_assert(x->cnt>=n, "LogisticFitX: Length(X)<N", _state);
ae_assert(y->cnt>=n, "LogisticFitX: Length(Y)<N", _state);
ae_assert(isfinitevector(x, n, _state), "LogisticFitX: X contains infinite/NAN values", _state);
ae_assert(isfinitevector(y, n, _state), "LogisticFitX: X contains infinite/NAN values", _state);
hqrndseed(2211, 1033044, &rs, _state);
lsfit_clearreport(rep, _state);
if( ae_fp_eq(epsx,(double)(0)) )
{
epsx = 1.0E-10;
}
if( rscnt==0 )
{
rscnt = 4;
}
maxits = 1000;
/*
* Sort points by X.
* Determine number of zero and non-zero values.
*/
tagsortfastr(x, y, &bufx, &bufy, n, _state);
ae_assert(ae_fp_greater_eq(x->ptr.p_double[0],(double)(0)), "LogisticFitX: some X[] are negative", _state);
nz = n;
for(i=0; i<=n-1; i++)
{
if( ae_fp_greater(x->ptr.p_double[i],(double)(0)) )
{
nz = i;
break;
}
}
/*
* For NZ=N (all X[] are zero) special code is used.
* For NZ<N we use general-purpose code.
*/
rep->iterationscount = 0;
if( nz==n )
{
/*
* NZ=N, degenerate problem.
* No need to run optimizer.
*/
v = 0.0;
for(i=0; i<=n-1; i++)
{
v = v+y->ptr.p_double[i];
}
v = v/n;
if( ae_isfinite(cnstrleft, _state) )
{
*a = cnstrleft;
}
else
{
*a = v;
}
*b = (double)(1);
*c = (double)(1);
if( ae_isfinite(cnstrright, _state) )
{
*d = cnstrright;
}
else
{
*d = *a;
}
*g = (double)(1);
lsfit_logisticfit45errors(x, y, n, *a, *b, *c, *d, *g, rep, _state);
ae_frame_leave(_state);
return;
}
/*
* Non-degenerate problem.
* Determine scale of data.
*/
scalex = x->ptr.p_double[nz+(n-nz)/2];
ae_assert(ae_fp_greater(scalex,(double)(0)), "LogisticFitX: internal error", _state);
v = 0.0;
for(i=0; i<=n-1; i++)
{
v = v+y->ptr.p_double[i];
}
v = v/n;
scaley = 0.0;
for(i=0; i<=n-1; i++)
{
scaley = scaley+ae_sqr(y->ptr.p_double[i]-v, _state);
}
scaley = ae_sqrt(scaley/n, _state);
if( ae_fp_eq(scaley,(double)(0)) )
{
scaley = 1.0;
}
ae_vector_set_length(&s, 5, _state);
s.ptr.p_double[0] = scaley;
s.ptr.p_double[1] = 0.1;
s.ptr.p_double[2] = scalex;
s.ptr.p_double[3] = scaley;
s.ptr.p_double[4] = 0.1;
ae_vector_set_length(&p0, 5, _state);
p0.ptr.p_double[0] = (double)(0);
p0.ptr.p_double[1] = (double)(0);
p0.ptr.p_double[2] = (double)(0);
p0.ptr.p_double[3] = (double)(0);
p0.ptr.p_double[4] = (double)(0);
ae_vector_set_length(&bndl, 5, _state);
ae_vector_set_length(&bndu, 5, _state);
ae_vector_set_length(&bndl1, 5, _state);
ae_vector_set_length(&bndu1, 5, _state);
ae_vector_set_length(&bndl2, 5, _state);
ae_vector_set_length(&bndu2, 5, _state);
minlmcreatevj(5, n+5, &p0, &state, _state);
minlmsetscale(&state, &s, _state);
minlmsetcond(&state, epsx, maxits, _state);
minlmsetxrep(&state, ae_true, _state);
ae_vector_set_length(&p1, 5, _state);
ae_vector_set_length(&p2, 5, _state);
/*
* Is it 4PL problem?
*/
if( is4pl )
{
/*
* Run outer iterations
*/
*a = (double)(0);
*b = (double)(1);
*c = (double)(1);
*d = (double)(1);
*g = (double)(1);
fbest = ae_maxrealnumber;
for(outerit=0; outerit<=rscnt-1; outerit++)
{
/*
* Prepare initial point; use B>0
*/
if( ae_isfinite(cnstrleft, _state) )
{
p1.ptr.p_double[0] = cnstrleft;
}
else
{
p1.ptr.p_double[0] = y->ptr.p_double[0]+0.15*scaley*(hqrnduniformr(&rs, _state)-0.5);
}
p1.ptr.p_double[1] = 0.5+hqrnduniformr(&rs, _state);
p1.ptr.p_double[2] = x->ptr.p_double[nz+hqrnduniformi(&rs, n-nz, _state)];
if( ae_isfinite(cnstrright, _state) )
{
p1.ptr.p_double[3] = cnstrright;
}
else
{
p1.ptr.p_double[3] = y->ptr.p_double[n-1]+0.25*scaley*(hqrnduniformr(&rs, _state)-0.5);
}
p1.ptr.p_double[4] = 1.0;
/*
* Run optimization with tight constraints and increased regularization
*/
if( ae_isfinite(cnstrleft, _state) )
{
bndl.ptr.p_double[0] = cnstrleft;
bndu.ptr.p_double[0] = cnstrleft;
}
else
{
bndl.ptr.p_double[0] = _state->v_neginf;
bndu.ptr.p_double[0] = _state->v_posinf;
}
bndl.ptr.p_double[1] = 0.5;
bndu.ptr.p_double[1] = 2.0;
bndl.ptr.p_double[2] = 0.5*scalex;
bndu.ptr.p_double[2] = 2.0*scalex;
if( ae_isfinite(cnstrright, _state) )
{
bndl.ptr.p_double[3] = cnstrright;
bndu.ptr.p_double[3] = cnstrright;
}
else
{
bndl.ptr.p_double[3] = _state->v_neginf;
bndu.ptr.p_double[3] = _state->v_posinf;
}
bndl.ptr.p_double[4] = 1.0;
bndu.ptr.p_double[4] = 1.0;
minlmsetbc(&state, &bndl, &bndu, _state);
lsfit_logisticfitinternal(x, y, n, is4pl, 100*lambdav, &state, &replm, &p1, &flast, _state);
rep->iterationscount = rep->iterationscount+replm.iterationscount;
/*
* Relax constraints, run optimization one more time
*/
bndl.ptr.p_double[1] = 0.1;
bndu.ptr.p_double[1] = 10.0;
bndl.ptr.p_double[2] = ae_machineepsilon*scalex;
bndu.ptr.p_double[2] = scalex/ae_machineepsilon;
minlmsetbc(&state, &bndl, &bndu, _state);
lsfit_logisticfitinternal(x, y, n, is4pl, lambdav, &state, &replm, &p1, &flast, _state);
rep->iterationscount = rep->iterationscount+replm.iterationscount;
/*
* Relax constraints more, run optimization one more time
*/
bndl.ptr.p_double[1] = 0.01;
bndu.ptr.p_double[1] = 100.0;
minlmsetbc(&state, &bndl, &bndu, _state);
lsfit_logisticfitinternal(x, y, n, is4pl, lambdav, &state, &replm, &p1, &flast, _state);
rep->iterationscount = rep->iterationscount+replm.iterationscount;
/*
* Relax constraints ever more, run optimization one more time
*/
bndl.ptr.p_double[1] = 0.001;
bndu.ptr.p_double[1] = 1000.0;
minlmsetbc(&state, &bndl, &bndu, _state);
lsfit_logisticfitinternal(x, y, n, is4pl, lambdav, &state, &replm, &p1, &flast, _state);
rep->iterationscount = rep->iterationscount+replm.iterationscount;
/*
* Compare results with best value found so far.
*/
if( ae_fp_less(flast,fbest) )
{
*a = p1.ptr.p_double[0];
*b = p1.ptr.p_double[1];
*c = p1.ptr.p_double[2];
*d = p1.ptr.p_double[3];
*g = p1.ptr.p_double[4];
fbest = flast;
}
}
lsfit_logisticfit45errors(x, y, n, *a, *b, *c, *d, *g, rep, _state);
ae_frame_leave(_state);
return;
}
/*
* Well.... we have 5PL fit, and we have to test two separate branches:
* B>0 and B<0, because of asymmetry in the curve. First, we run optimization
* with tight constraints two times, in order to determine better sign for B.
*
* Run outer iterations
*/
*a = (double)(0);
*b = (double)(1);
*c = (double)(1);
*d = (double)(1);
*g = (double)(1);
fbest = ae_maxrealnumber;
for(outerit=0; outerit<=rscnt-1; outerit++)
{
/*
* First, we try positive B.
*/
p1.ptr.p_double[0] = y->ptr.p_double[0]+0.15*scaley*(hqrnduniformr(&rs, _state)-0.5);
p1.ptr.p_double[1] = 0.5+hqrnduniformr(&rs, _state);
p1.ptr.p_double[2] = x->ptr.p_double[nz+hqrnduniformi(&rs, n-nz, _state)];
p1.ptr.p_double[3] = y->ptr.p_double[n-1]+0.25*scaley*(hqrnduniformr(&rs, _state)-0.5);
p1.ptr.p_double[4] = 1.0;
bndl1.ptr.p_double[0] = _state->v_neginf;
bndu1.ptr.p_double[0] = _state->v_posinf;
bndl1.ptr.p_double[1] = 0.5;
bndu1.ptr.p_double[1] = 2.0;
bndl1.ptr.p_double[2] = 0.5*scalex;
bndu1.ptr.p_double[2] = 2.0*scalex;
bndl1.ptr.p_double[3] = _state->v_neginf;
bndu1.ptr.p_double[3] = _state->v_posinf;
bndl1.ptr.p_double[4] = 0.5;
bndu1.ptr.p_double[4] = 2.0;
if( ae_isfinite(cnstrleft, _state) )
{
p1.ptr.p_double[0] = cnstrleft;
bndl1.ptr.p_double[0] = cnstrleft;
bndu1.ptr.p_double[0] = cnstrleft;
}
if( ae_isfinite(cnstrright, _state) )
{
p1.ptr.p_double[3] = cnstrright;
bndl1.ptr.p_double[3] = cnstrright;
bndu1.ptr.p_double[3] = cnstrright;
}
minlmsetbc(&state, &bndl1, &bndu1, _state);
lsfit_logisticfitinternal(x, y, n, is4pl, 100*lambdav, &state, &replm, &p1, &fposb, _state);
rep->iterationscount = rep->iterationscount+replm.iterationscount;
/*
* Second attempt - with negative B (constraints are still tight).
*/
p2.ptr.p_double[0] = y->ptr.p_double[n-1]+0.15*scaley*(hqrnduniformr(&rs, _state)-0.5);
p2.ptr.p_double[1] = -(0.5+hqrnduniformr(&rs, _state));
p2.ptr.p_double[2] = x->ptr.p_double[nz+hqrnduniformi(&rs, n-nz, _state)];
p2.ptr.p_double[3] = y->ptr.p_double[0]+0.25*scaley*(hqrnduniformr(&rs, _state)-0.5);
p2.ptr.p_double[4] = 1.0;
bndl2.ptr.p_double[0] = _state->v_neginf;
bndu2.ptr.p_double[0] = _state->v_posinf;
bndl2.ptr.p_double[1] = -2.0;
bndu2.ptr.p_double[1] = -0.5;
bndl2.ptr.p_double[2] = 0.5*scalex;
bndu2.ptr.p_double[2] = 2.0*scalex;
bndl2.ptr.p_double[3] = _state->v_neginf;
bndu2.ptr.p_double[3] = _state->v_posinf;
bndl2.ptr.p_double[4] = 0.5;
bndu2.ptr.p_double[4] = 2.0;
if( ae_isfinite(cnstrleft, _state) )
{
p2.ptr.p_double[3] = cnstrleft;
bndl2.ptr.p_double[3] = cnstrleft;
bndu2.ptr.p_double[3] = cnstrleft;
}
if( ae_isfinite(cnstrright, _state) )
{
p2.ptr.p_double[0] = cnstrright;
bndl2.ptr.p_double[0] = cnstrright;
bndu2.ptr.p_double[0] = cnstrright;
}
minlmsetbc(&state, &bndl2, &bndu2, _state);
lsfit_logisticfitinternal(x, y, n, is4pl, 100*lambdav, &state, &replm, &p2, &fnegb, _state);
rep->iterationscount = rep->iterationscount+replm.iterationscount;
/*
* Select best version of B sign
*/
if( ae_fp_less(fposb,fnegb) )
{
/*
* Prepare relaxed constraints assuming that B is positive
*/
bndl1.ptr.p_double[1] = 0.1;
bndu1.ptr.p_double[1] = 10.0;
bndl1.ptr.p_double[2] = ae_machineepsilon*scalex;
bndu1.ptr.p_double[2] = scalex/ae_machineepsilon;
bndl1.ptr.p_double[4] = 0.1;
bndu1.ptr.p_double[4] = 10.0;
minlmsetbc(&state, &bndl1, &bndu1, _state);
lsfit_logisticfitinternal(x, y, n, is4pl, lambdav, &state, &replm, &p1, &flast, _state);
rep->iterationscount = rep->iterationscount+replm.iterationscount;
/*
* Prepare stronger relaxation of constraints
*/
bndl1.ptr.p_double[1] = 0.01;
bndu1.ptr.p_double[1] = 100.0;
minlmsetbc(&state, &bndl1, &bndu1, _state);
lsfit_logisticfitinternal(x, y, n, is4pl, lambdav, &state, &replm, &p1, &flast, _state);
rep->iterationscount = rep->iterationscount+replm.iterationscount;
/*
* Prepare stronger relaxation of constraints
*/
bndl1.ptr.p_double[1] = 0.001;
bndu1.ptr.p_double[1] = 1000.0;
minlmsetbc(&state, &bndl1, &bndu1, _state);
lsfit_logisticfitinternal(x, y, n, is4pl, lambdav, &state, &replm, &p1, &flast, _state);
rep->iterationscount = rep->iterationscount+replm.iterationscount;
/*
* Compare results with best value found so far.
*/
if( ae_fp_less(flast,fbest) )
{
*a = p1.ptr.p_double[0];
*b = p1.ptr.p_double[1];
*c = p1.ptr.p_double[2];
*d = p1.ptr.p_double[3];
*g = p1.ptr.p_double[4];
fbest = flast;
}
}
else
{
/*
* Prepare relaxed constraints assuming that B is negative
*/
bndl2.ptr.p_double[1] = -10.0;
bndu2.ptr.p_double[1] = -0.1;
bndl2.ptr.p_double[2] = ae_machineepsilon*scalex;
bndu2.ptr.p_double[2] = scalex/ae_machineepsilon;
bndl2.ptr.p_double[4] = 0.1;
bndu2.ptr.p_double[4] = 10.0;
minlmsetbc(&state, &bndl2, &bndu2, _state);
lsfit_logisticfitinternal(x, y, n, is4pl, lambdav, &state, &replm, &p2, &flast, _state);
rep->iterationscount = rep->iterationscount+replm.iterationscount;
/*
* Prepare stronger relaxation
*/
bndl2.ptr.p_double[1] = -100.0;
bndu2.ptr.p_double[1] = -0.01;
minlmsetbc(&state, &bndl2, &bndu2, _state);
lsfit_logisticfitinternal(x, y, n, is4pl, lambdav, &state, &replm, &p2, &flast, _state);
rep->iterationscount = rep->iterationscount+replm.iterationscount;
/*
* Prepare stronger relaxation
*/
bndl2.ptr.p_double[1] = -1000.0;
bndu2.ptr.p_double[1] = -0.001;
minlmsetbc(&state, &bndl2, &bndu2, _state);
lsfit_logisticfitinternal(x, y, n, is4pl, lambdav, &state, &replm, &p2, &flast, _state);
rep->iterationscount = rep->iterationscount+replm.iterationscount;
/*
* Compare results with best value found so far.
*/
if( ae_fp_less(flast,fbest) )
{
*a = p2.ptr.p_double[0];
*b = p2.ptr.p_double[1];
*c = p2.ptr.p_double[2];
*d = p2.ptr.p_double[3];
*g = p2.ptr.p_double[4];
fbest = flast;
}
}
}
lsfit_logisticfit45errors(x, y, n, *a, *b, *c, *d, *g, rep, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Weghted rational least squares fitting using Floater-Hormann rational
functions with optimal D chosen from [0,9], with constraints and
individual weights.
Equidistant grid with M node on [min(x),max(x)] is used to build basis
functions. Different values of D are tried, optimal D (least WEIGHTED root
mean square error) is chosen. Task is linear, so linear least squares
solver is used. Complexity of this computational scheme is O(N*M^2)
(mostly dominated by the least squares solver).
SEE ALSO
* BarycentricFitFloaterHormann(), "lightweight" fitting without invididual
weights and constraints.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
W - weights, array[0..N-1]
Each summand in square sum of approximation deviations from
given values is multiplied by the square of corresponding
weight. Fill it by 1's if you don't want to solve weighted
task.
N - number of points, N>0.
XC - points where function values/derivatives are constrained,
array[0..K-1].
YC - values of constraints, array[0..K-1]
DC - array[0..K-1], types of constraints:
* DC[i]=0 means that S(XC[i])=YC[i]
* DC[i]=1 means that S'(XC[i])=YC[i]
SEE BELOW FOR IMPORTANT INFORMATION ON CONSTRAINTS
K - number of constraints, 0<=K<M.
K=0 means no constraints (XC/YC/DC are not used in such cases)
M - number of basis functions ( = number_of_nodes), M>=2.
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearWC() subroutine.
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
-3 means inconsistent constraints
-1 means another errors in parameters passed
(N<=0, for example)
B - barycentric interpolant.
Rep - report, same format as in LSFitLinearWC() subroutine.
Following fields are set:
* DBest best value of the D parameter
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroutine doesn't calculate task's condition number for K<>0.
SETTING CONSTRAINTS - DANGERS AND OPPORTUNITIES:
Setting constraints can lead to undesired results, like ill-conditioned
behavior, or inconsistency being detected. From the other side, it allows
us to improve quality of the fit. Here we summarize our experience with
constrained barycentric interpolants:
* excessive constraints can be inconsistent. Floater-Hormann basis
functions aren't as flexible as splines (although they are very smooth).
* the more evenly constraints are spread across [min(x),max(x)], the more
chances that they will be consistent
* the greater is M (given fixed constraints), the more chances that
constraints will be consistent
* in the general case, consistency of constraints IS NOT GUARANTEED.
* in the several special cases, however, we CAN guarantee consistency.
* one of this cases is constraints on the function VALUES at the interval
boundaries. Note that consustency of the constraints on the function
DERIVATIVES is NOT guaranteed (you can use in such cases cubic splines
which are more flexible).
* another special case is ONE constraint on the function value (OR, but
not AND, derivative) anywhere in the interval
Our final recommendation is to use constraints WHEN AND ONLY WHEN you
can't solve your task without them. Anything beyond special cases given
above is not guaranteed and may result in inconsistency.
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentricfitfloaterhormannwc(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
ae_int_t n,
/* Real */ ae_vector* xc,
/* Real */ ae_vector* yc,
/* Integer */ ae_vector* dc,
ae_int_t k,
ae_int_t m,
ae_int_t* info,
barycentricinterpolant* b,
barycentricfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t d;
ae_int_t i;
double wrmscur;
double wrmsbest;
barycentricinterpolant locb;
barycentricfitreport locrep;
ae_int_t locinfo;
ae_frame_make(_state, &_frame_block);
memset(&locb, 0, sizeof(locb));
memset(&locrep, 0, sizeof(locrep));
*info = 0;
_barycentricinterpolant_clear(b);
_barycentricfitreport_clear(rep);
_barycentricinterpolant_init(&locb, _state, ae_true);
_barycentricfitreport_init(&locrep, _state, ae_true);
ae_assert(n>0, "BarycentricFitFloaterHormannWC: N<=0!", _state);
ae_assert(m>0, "BarycentricFitFloaterHormannWC: M<=0!", _state);
ae_assert(k>=0, "BarycentricFitFloaterHormannWC: K<0!", _state);
ae_assert(k<m, "BarycentricFitFloaterHormannWC: K>=M!", _state);
ae_assert(x->cnt>=n, "BarycentricFitFloaterHormannWC: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "BarycentricFitFloaterHormannWC: Length(Y)<N!", _state);
ae_assert(w->cnt>=n, "BarycentricFitFloaterHormannWC: Length(W)<N!", _state);
ae_assert(xc->cnt>=k, "BarycentricFitFloaterHormannWC: Length(XC)<K!", _state);
ae_assert(yc->cnt>=k, "BarycentricFitFloaterHormannWC: Length(YC)<K!", _state);
ae_assert(dc->cnt>=k, "BarycentricFitFloaterHormannWC: Length(DC)<K!", _state);
ae_assert(isfinitevector(x, n, _state), "BarycentricFitFloaterHormannWC: X contains infinite or NaN values!", _state);
ae_assert(isfinitevector(y, n, _state), "BarycentricFitFloaterHormannWC: Y contains infinite or NaN values!", _state);
ae_assert(isfinitevector(w, n, _state), "BarycentricFitFloaterHormannWC: X contains infinite or NaN values!", _state);
ae_assert(isfinitevector(xc, k, _state), "BarycentricFitFloaterHormannWC: XC contains infinite or NaN values!", _state);
ae_assert(isfinitevector(yc, k, _state), "BarycentricFitFloaterHormannWC: YC contains infinite or NaN values!", _state);
for(i=0; i<=k-1; i++)
{
ae_assert(dc->ptr.p_int[i]==0||dc->ptr.p_int[i]==1, "BarycentricFitFloaterHormannWC: one of DC[] is not 0 or 1!", _state);
}
/*
* Find optimal D
*
* Info is -3 by default (degenerate constraints).
* If LocInfo will always be equal to -3, Info will remain equal to -3.
* If at least once LocInfo will be -4, Info will be -4.
*/
wrmsbest = ae_maxrealnumber;
rep->dbest = -1;
*info = -3;
for(d=0; d<=ae_minint(9, n-1, _state); d++)
{
lsfit_barycentricfitwcfixedd(x, y, w, n, xc, yc, dc, k, m, d, &locinfo, &locb, &locrep, _state);
ae_assert((locinfo==-4||locinfo==-3)||locinfo>0, "BarycentricFitFloaterHormannWC: unexpected result from BarycentricFitWCFixedD!", _state);
if( locinfo>0 )
{
/*
* Calculate weghted RMS
*/
wrmscur = (double)(0);
for(i=0; i<=n-1; i++)
{
wrmscur = wrmscur+ae_sqr(w->ptr.p_double[i]*(y->ptr.p_double[i]-barycentriccalc(&locb, x->ptr.p_double[i], _state)), _state);
}
wrmscur = ae_sqrt(wrmscur/n, _state);
if( ae_fp_less(wrmscur,wrmsbest)||rep->dbest<0 )
{
barycentriccopy(&locb, b, _state);
rep->dbest = d;
*info = 1;
rep->rmserror = locrep.rmserror;
rep->avgerror = locrep.avgerror;
rep->avgrelerror = locrep.avgrelerror;
rep->maxerror = locrep.maxerror;
rep->taskrcond = locrep.taskrcond;
wrmsbest = wrmscur;
}
}
else
{
if( locinfo!=-3&&*info<0 )
{
*info = locinfo;
}
}
}
ae_frame_leave(_state);
}
/*************************************************************************
Rational least squares fitting using Floater-Hormann rational functions
with optimal D chosen from [0,9].
Equidistant grid with M node on [min(x),max(x)] is used to build basis
functions. Different values of D are tried, optimal D (least root mean
square error) is chosen. Task is linear, so linear least squares solver
is used. Complexity of this computational scheme is O(N*M^2) (mostly
dominated by the least squares solver).
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
N - number of points, N>0.
M - number of basis functions ( = number_of_nodes), M>=2.
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearWC() subroutine.
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
-3 means inconsistent constraints
B - barycentric interpolant.
Rep - report, same format as in LSFitLinearWC() subroutine.
Following fields are set:
* DBest best value of the D parameter
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
void barycentricfitfloaterhormann(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t m,
ae_int_t* info,
barycentricinterpolant* b,
barycentricfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector w;
ae_vector xc;
ae_vector yc;
ae_vector dc;
ae_int_t i;
ae_frame_make(_state, &_frame_block);
memset(&w, 0, sizeof(w));
memset(&xc, 0, sizeof(xc));
memset(&yc, 0, sizeof(yc));
memset(&dc, 0, sizeof(dc));
*info = 0;
_barycentricinterpolant_clear(b);
_barycentricfitreport_clear(rep);
ae_vector_init(&w, 0, DT_REAL, _state, ae_true);
ae_vector_init(&xc, 0, DT_REAL, _state, ae_true);
ae_vector_init(&yc, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dc, 0, DT_INT, _state, ae_true);
ae_assert(n>0, "BarycentricFitFloaterHormann: N<=0!", _state);
ae_assert(m>0, "BarycentricFitFloaterHormann: M<=0!", _state);
ae_assert(x->cnt>=n, "BarycentricFitFloaterHormann: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "BarycentricFitFloaterHormann: Length(Y)<N!", _state);
ae_assert(isfinitevector(x, n, _state), "BarycentricFitFloaterHormann: X contains infinite or NaN values!", _state);
ae_assert(isfinitevector(y, n, _state), "BarycentricFitFloaterHormann: Y contains infinite or NaN values!", _state);
ae_vector_set_length(&w, n, _state);
for(i=0; i<=n-1; i++)
{
w.ptr.p_double[i] = (double)(1);
}
barycentricfitfloaterhormannwc(x, y, &w, n, &xc, &yc, &dc, 0, m, info, b, rep, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Weighted fitting by cubic spline, with constraints on function values or
derivatives.
Equidistant grid with M-2 nodes on [min(x,xc),max(x,xc)] is used to build
basis functions. Basis functions are cubic splines with continuous second
derivatives and non-fixed first derivatives at interval ends. Small
regularizing term is used when solving constrained tasks (to improve
stability).
Task is linear, so linear least squares solver is used. Complexity of this
computational scheme is O(N*M^2), mostly dominated by least squares solver
SEE ALSO
Spline1DFitHermiteWC() - fitting by Hermite splines (more flexible,
less smooth)
Spline1DFitCubic() - "lightweight" fitting by cubic splines,
without invididual weights and constraints
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
W - weights, array[0..N-1]
Each summand in square sum of approximation deviations from
given values is multiplied by the square of corresponding
weight. Fill it by 1's if you don't want to solve weighted
task.
N - number of points (optional):
* N>0
* if given, only first N elements of X/Y/W are processed
* if not given, automatically determined from X/Y/W sizes
XC - points where spline values/derivatives are constrained,
array[0..K-1].
YC - values of constraints, array[0..K-1]
DC - array[0..K-1], types of constraints:
* DC[i]=0 means that S(XC[i])=YC[i]
* DC[i]=1 means that S'(XC[i])=YC[i]
SEE BELOW FOR IMPORTANT INFORMATION ON CONSTRAINTS
K - number of constraints (optional):
* 0<=K<M.
* K=0 means no constraints (XC/YC/DC are not used)
* if given, only first K elements of XC/YC/DC are used
* if not given, automatically determined from XC/YC/DC
M - number of basis functions ( = number_of_nodes+2), M>=4.
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearWC() subroutine.
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
-3 means inconsistent constraints
S - spline interpolant.
Rep - report, same format as in LSFitLinearWC() subroutine.
Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
SETTING CONSTRAINTS - DANGERS AND OPPORTUNITIES:
Setting constraints can lead to undesired results, like ill-conditioned
behavior, or inconsistency being detected. From the other side, it allows
us to improve quality of the fit. Here we summarize our experience with
constrained regression splines:
* excessive constraints can be inconsistent. Splines are piecewise cubic
functions, and it is easy to create an example, where large number of
constraints concentrated in small area will result in inconsistency.
Just because spline is not flexible enough to satisfy all of them. And
same constraints spread across the [min(x),max(x)] will be perfectly
consistent.
* the more evenly constraints are spread across [min(x),max(x)], the more
chances that they will be consistent
* the greater is M (given fixed constraints), the more chances that
constraints will be consistent
* in the general case, consistency of constraints IS NOT GUARANTEED.
* in the several special cases, however, we CAN guarantee consistency.
* one of this cases is constraints on the function values AND/OR its
derivatives at the interval boundaries.
* another special case is ONE constraint on the function value (OR, but
not AND, derivative) anywhere in the interval
Our final recommendation is to use constraints WHEN AND ONLY WHEN you
can't solve your task without them. Anything beyond special cases given
above is not guaranteed and may result in inconsistency.
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
void spline1dfitcubicwc(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
ae_int_t n,
/* Real */ ae_vector* xc,
/* Real */ ae_vector* yc,
/* Integer */ ae_vector* dc,
ae_int_t k,
ae_int_t m,
ae_int_t* info,
spline1dinterpolant* s,
spline1dfitreport* rep,
ae_state *_state)
{
ae_int_t i;
*info = 0;
_spline1dinterpolant_clear(s);
_spline1dfitreport_clear(rep);
ae_assert(n>=1, "Spline1DFitCubicWC: N<1!", _state);
ae_assert(m>=4, "Spline1DFitCubicWC: M<4!", _state);
ae_assert(k>=0, "Spline1DFitCubicWC: K<0!", _state);
ae_assert(k<m, "Spline1DFitCubicWC: K>=M!", _state);
ae_assert(x->cnt>=n, "Spline1DFitCubicWC: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DFitCubicWC: Length(Y)<N!", _state);
ae_assert(w->cnt>=n, "Spline1DFitCubicWC: Length(W)<N!", _state);
ae_assert(xc->cnt>=k, "Spline1DFitCubicWC: Length(XC)<K!", _state);
ae_assert(yc->cnt>=k, "Spline1DFitCubicWC: Length(YC)<K!", _state);
ae_assert(dc->cnt>=k, "Spline1DFitCubicWC: Length(DC)<K!", _state);
ae_assert(isfinitevector(x, n, _state), "Spline1DFitCubicWC: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, n, _state), "Spline1DFitCubicWC: Y contains infinite or NAN values!", _state);
ae_assert(isfinitevector(w, n, _state), "Spline1DFitCubicWC: Y contains infinite or NAN values!", _state);
ae_assert(isfinitevector(xc, k, _state), "Spline1DFitCubicWC: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(yc, k, _state), "Spline1DFitCubicWC: Y contains infinite or NAN values!", _state);
for(i=0; i<=k-1; i++)
{
ae_assert(dc->ptr.p_int[i]==0||dc->ptr.p_int[i]==1, "Spline1DFitCubicWC: DC[i] is neither 0 or 1!", _state);
}
lsfit_spline1dfitinternal(0, x, y, w, n, xc, yc, dc, k, m, info, s, rep, _state);
}
/*************************************************************************
Weighted fitting by Hermite spline, with constraints on function values
or first derivatives.
Equidistant grid with M nodes on [min(x,xc),max(x,xc)] is used to build
basis functions. Basis functions are Hermite splines. Small regularizing
term is used when solving constrained tasks (to improve stability).
Task is linear, so linear least squares solver is used. Complexity of this
computational scheme is O(N*M^2), mostly dominated by least squares solver
SEE ALSO
Spline1DFitCubicWC() - fitting by Cubic splines (less flexible,
more smooth)
Spline1DFitHermite() - "lightweight" Hermite fitting, without
invididual weights and constraints
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
W - weights, array[0..N-1]
Each summand in square sum of approximation deviations from
given values is multiplied by the square of corresponding
weight. Fill it by 1's if you don't want to solve weighted
task.
N - number of points (optional):
* N>0
* if given, only first N elements of X/Y/W are processed
* if not given, automatically determined from X/Y/W sizes
XC - points where spline values/derivatives are constrained,
array[0..K-1].
YC - values of constraints, array[0..K-1]
DC - array[0..K-1], types of constraints:
* DC[i]=0 means that S(XC[i])=YC[i]
* DC[i]=1 means that S'(XC[i])=YC[i]
SEE BELOW FOR IMPORTANT INFORMATION ON CONSTRAINTS
K - number of constraints (optional):
* 0<=K<M.
* K=0 means no constraints (XC/YC/DC are not used)
* if given, only first K elements of XC/YC/DC are used
* if not given, automatically determined from XC/YC/DC
M - number of basis functions (= 2 * number of nodes),
M>=4,
M IS EVEN!
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearW() subroutine:
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
-3 means inconsistent constraints
-2 means odd M was passed (which is not supported)
-1 means another errors in parameters passed
(N<=0, for example)
S - spline interpolant.
Rep - report, same format as in LSFitLinearW() subroutine.
Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
IMPORTANT:
this subroitine supports only even M's
ORDER OF POINTS
Subroutine automatically sorts points, so caller may pass unsorted array.
SETTING CONSTRAINTS - DANGERS AND OPPORTUNITIES:
Setting constraints can lead to undesired results, like ill-conditioned
behavior, or inconsistency being detected. From the other side, it allows
us to improve quality of the fit. Here we summarize our experience with
constrained regression splines:
* excessive constraints can be inconsistent. Splines are piecewise cubic
functions, and it is easy to create an example, where large number of
constraints concentrated in small area will result in inconsistency.
Just because spline is not flexible enough to satisfy all of them. And
same constraints spread across the [min(x),max(x)] will be perfectly
consistent.
* the more evenly constraints are spread across [min(x),max(x)], the more
chances that they will be consistent
* the greater is M (given fixed constraints), the more chances that
constraints will be consistent
* in the general case, consistency of constraints is NOT GUARANTEED.
* in the several special cases, however, we can guarantee consistency.
* one of this cases is M>=4 and constraints on the function value
(AND/OR its derivative) at the interval boundaries.
* another special case is M>=4 and ONE constraint on the function value
(OR, BUT NOT AND, derivative) anywhere in [min(x),max(x)]
Our final recommendation is to use constraints WHEN AND ONLY when you
can't solve your task without them. Anything beyond special cases given
above is not guaranteed and may result in inconsistency.
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
void spline1dfithermitewc(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
ae_int_t n,
/* Real */ ae_vector* xc,
/* Real */ ae_vector* yc,
/* Integer */ ae_vector* dc,
ae_int_t k,
ae_int_t m,
ae_int_t* info,
spline1dinterpolant* s,
spline1dfitreport* rep,
ae_state *_state)
{
ae_int_t i;
*info = 0;
_spline1dinterpolant_clear(s);
_spline1dfitreport_clear(rep);
ae_assert(n>=1, "Spline1DFitHermiteWC: N<1!", _state);
ae_assert(m>=4, "Spline1DFitHermiteWC: M<4!", _state);
ae_assert(m%2==0, "Spline1DFitHermiteWC: M is odd!", _state);
ae_assert(k>=0, "Spline1DFitHermiteWC: K<0!", _state);
ae_assert(k<m, "Spline1DFitHermiteWC: K>=M!", _state);
ae_assert(x->cnt>=n, "Spline1DFitHermiteWC: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DFitHermiteWC: Length(Y)<N!", _state);
ae_assert(w->cnt>=n, "Spline1DFitHermiteWC: Length(W)<N!", _state);
ae_assert(xc->cnt>=k, "Spline1DFitHermiteWC: Length(XC)<K!", _state);
ae_assert(yc->cnt>=k, "Spline1DFitHermiteWC: Length(YC)<K!", _state);
ae_assert(dc->cnt>=k, "Spline1DFitHermiteWC: Length(DC)<K!", _state);
ae_assert(isfinitevector(x, n, _state), "Spline1DFitHermiteWC: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, n, _state), "Spline1DFitHermiteWC: Y contains infinite or NAN values!", _state);
ae_assert(isfinitevector(w, n, _state), "Spline1DFitHermiteWC: Y contains infinite or NAN values!", _state);
ae_assert(isfinitevector(xc, k, _state), "Spline1DFitHermiteWC: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(yc, k, _state), "Spline1DFitHermiteWC: Y contains infinite or NAN values!", _state);
for(i=0; i<=k-1; i++)
{
ae_assert(dc->ptr.p_int[i]==0||dc->ptr.p_int[i]==1, "Spline1DFitHermiteWC: DC[i] is neither 0 or 1!", _state);
}
lsfit_spline1dfitinternal(1, x, y, w, n, xc, yc, dc, k, m, info, s, rep, _state);
}
/*************************************************************************
Least squares fitting by cubic spline.
This subroutine is "lightweight" alternative for more complex and feature-
rich Spline1DFitCubicWC(). See Spline1DFitCubicWC() for more information
about subroutine parameters (we don't duplicate it here because of length)
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
void spline1dfitcubic(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t m,
ae_int_t* info,
spline1dinterpolant* s,
spline1dfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_vector w;
ae_vector xc;
ae_vector yc;
ae_vector dc;
ae_frame_make(_state, &_frame_block);
memset(&w, 0, sizeof(w));
memset(&xc, 0, sizeof(xc));
memset(&yc, 0, sizeof(yc));
memset(&dc, 0, sizeof(dc));
*info = 0;
_spline1dinterpolant_clear(s);
_spline1dfitreport_clear(rep);
ae_vector_init(&w, 0, DT_REAL, _state, ae_true);
ae_vector_init(&xc, 0, DT_REAL, _state, ae_true);
ae_vector_init(&yc, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dc, 0, DT_INT, _state, ae_true);
ae_assert(n>=1, "Spline1DFitCubic: N<1!", _state);
ae_assert(m>=4, "Spline1DFitCubic: M<4!", _state);
ae_assert(x->cnt>=n, "Spline1DFitCubic: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DFitCubic: Length(Y)<N!", _state);
ae_assert(isfinitevector(x, n, _state), "Spline1DFitCubic: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, n, _state), "Spline1DFitCubic: Y contains infinite or NAN values!", _state);
ae_vector_set_length(&w, n, _state);
for(i=0; i<=n-1; i++)
{
w.ptr.p_double[i] = (double)(1);
}
spline1dfitcubicwc(x, y, &w, n, &xc, &yc, &dc, 0, m, info, s, rep, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Least squares fitting by Hermite spline.
This subroutine is "lightweight" alternative for more complex and feature-
rich Spline1DFitHermiteWC(). See Spline1DFitHermiteWC() description for
more information about subroutine parameters (we don't duplicate it here
because of length).
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
void spline1dfithermite(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t m,
ae_int_t* info,
spline1dinterpolant* s,
spline1dfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_vector w;
ae_vector xc;
ae_vector yc;
ae_vector dc;
ae_frame_make(_state, &_frame_block);
memset(&w, 0, sizeof(w));
memset(&xc, 0, sizeof(xc));
memset(&yc, 0, sizeof(yc));
memset(&dc, 0, sizeof(dc));
*info = 0;
_spline1dinterpolant_clear(s);
_spline1dfitreport_clear(rep);
ae_vector_init(&w, 0, DT_REAL, _state, ae_true);
ae_vector_init(&xc, 0, DT_REAL, _state, ae_true);
ae_vector_init(&yc, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dc, 0, DT_INT, _state, ae_true);
ae_assert(n>=1, "Spline1DFitHermite: N<1!", _state);
ae_assert(m>=4, "Spline1DFitHermite: M<4!", _state);
ae_assert(m%2==0, "Spline1DFitHermite: M is odd!", _state);
ae_assert(x->cnt>=n, "Spline1DFitHermite: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DFitHermite: Length(Y)<N!", _state);
ae_assert(isfinitevector(x, n, _state), "Spline1DFitHermite: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, n, _state), "Spline1DFitHermite: Y contains infinite or NAN values!", _state);
ae_vector_set_length(&w, n, _state);
for(i=0; i<=n-1; i++)
{
w.ptr.p_double[i] = (double)(1);
}
spline1dfithermitewc(x, y, &w, n, &xc, &yc, &dc, 0, m, info, s, rep, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Weighted linear least squares fitting.
QR decomposition is used to reduce task to MxM, then triangular solver or
SVD-based solver is used depending on condition number of the system. It
allows to maximize speed and retain decent accuracy.
IMPORTANT: if you want to perform polynomial fitting, it may be more
convenient to use PolynomialFit() function. This function gives
best results on polynomial problems and solves numerical
stability issues which arise when you fit high-degree
polynomials to your data.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
Y - array[0..N-1] Function values in N points.
W - array[0..N-1] Weights corresponding to function values.
Each summand in square sum of approximation deviations
from given values is multiplied by the square of
corresponding weight.
FMatrix - a table of basis functions values, array[0..N-1, 0..M-1].
FMatrix[I, J] - value of J-th basis function in I-th point.
N - number of points used. N>=1.
M - number of basis functions, M>=1.
OUTPUT PARAMETERS:
Info - error code:
* -4 internal SVD decomposition subroutine failed (very
rare and for degenerate systems only)
* -1 incorrect N/M were specified
* 1 task is solved
C - decomposition coefficients, array[0..M-1]
Rep - fitting report. Following fields are set:
* Rep.TaskRCond reciprocal of condition number
* R2 non-adjusted coefficient of determination
(non-weighted)
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
ERRORS IN PARAMETERS
This solver also calculates different kinds of errors in parameters and
fills corresponding fields of report:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(F*CovPar*F')),
where F is functions matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
NOTE: covariance matrix is estimated using correction for degrees
of freedom (covariances are divided by N-M instead of dividing
by N).
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitlinearw(/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
/* Real */ ae_matrix* fmatrix,
ae_int_t n,
ae_int_t m,
ae_int_t* info,
/* Real */ ae_vector* c,
lsfitreport* rep,
ae_state *_state)
{
*info = 0;
ae_vector_clear(c);
_lsfitreport_clear(rep);
ae_assert(n>=1, "LSFitLinearW: N<1!", _state);
ae_assert(m>=1, "LSFitLinearW: M<1!", _state);
ae_assert(y->cnt>=n, "LSFitLinearW: length(Y)<N!", _state);
ae_assert(isfinitevector(y, n, _state), "LSFitLinearW: Y contains infinite or NaN values!", _state);
ae_assert(w->cnt>=n, "LSFitLinearW: length(W)<N!", _state);
ae_assert(isfinitevector(w, n, _state), "LSFitLinearW: W contains infinite or NaN values!", _state);
ae_assert(fmatrix->rows>=n, "LSFitLinearW: rows(FMatrix)<N!", _state);
ae_assert(fmatrix->cols>=m, "LSFitLinearW: cols(FMatrix)<M!", _state);
ae_assert(apservisfinitematrix(fmatrix, n, m, _state), "LSFitLinearW: FMatrix contains infinite or NaN values!", _state);
lsfit_lsfitlinearinternal(y, w, fmatrix, n, m, info, c, rep, _state);
}
/*************************************************************************
Weighted constained linear least squares fitting.
This is variation of LSFitLinearW(), which searchs for min|A*x=b| given
that K additional constaints C*x=bc are satisfied. It reduces original
task to modified one: min|B*y-d| WITHOUT constraints, then LSFitLinearW()
is called.
IMPORTANT: if you want to perform polynomial fitting, it may be more
convenient to use PolynomialFit() function. This function gives
best results on polynomial problems and solves numerical
stability issues which arise when you fit high-degree
polynomials to your data.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
Y - array[0..N-1] Function values in N points.
W - array[0..N-1] Weights corresponding to function values.
Each summand in square sum of approximation deviations
from given values is multiplied by the square of
corresponding weight.
FMatrix - a table of basis functions values, array[0..N-1, 0..M-1].
FMatrix[I,J] - value of J-th basis function in I-th point.
CMatrix - a table of constaints, array[0..K-1,0..M].
I-th row of CMatrix corresponds to I-th linear constraint:
CMatrix[I,0]*C[0] + ... + CMatrix[I,M-1]*C[M-1] = CMatrix[I,M]
N - number of points used. N>=1.
M - number of basis functions, M>=1.
K - number of constraints, 0 <= K < M
K=0 corresponds to absence of constraints.
OUTPUT PARAMETERS:
Info - error code:
* -4 internal SVD decomposition subroutine failed (very
rare and for degenerate systems only)
* -3 either too many constraints (M or more),
degenerate constraints (some constraints are
repetead twice) or inconsistent constraints were
specified.
* 1 task is solved
C - decomposition coefficients, array[0..M-1]
Rep - fitting report. Following fields are set:
* R2 non-adjusted coefficient of determination
(non-weighted)
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
ERRORS IN PARAMETERS
This solver also calculates different kinds of errors in parameters and
fills corresponding fields of report:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(F*CovPar*F')),
where F is functions matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
IMPORTANT: errors in parameters are calculated without taking into
account boundary/linear constraints! Presence of constraints
changes distribution of errors, but there is no easy way to
account for constraints when you calculate covariance matrix.
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
NOTE: covariance matrix is estimated using correction for degrees
of freedom (covariances are divided by N-M instead of dividing
by N).
-- ALGLIB --
Copyright 07.09.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitlinearwc(/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
/* Real */ ae_matrix* fmatrix,
/* Real */ ae_matrix* cmatrix,
ae_int_t n,
ae_int_t m,
ae_int_t k,
ae_int_t* info,
/* Real */ ae_vector* c,
lsfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _y;
ae_matrix _cmatrix;
ae_int_t i;
ae_int_t j;
ae_vector tau;
ae_matrix q;
ae_matrix f2;
ae_vector tmp;
ae_vector c0;
double v;
ae_frame_make(_state, &_frame_block);
memset(&_y, 0, sizeof(_y));
memset(&_cmatrix, 0, sizeof(_cmatrix));
memset(&tau, 0, sizeof(tau));
memset(&q, 0, sizeof(q));
memset(&f2, 0, sizeof(f2));
memset(&tmp, 0, sizeof(tmp));
memset(&c0, 0, sizeof(c0));
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
ae_matrix_init_copy(&_cmatrix, cmatrix, _state, ae_true);
cmatrix = &_cmatrix;
*info = 0;
ae_vector_clear(c);
_lsfitreport_clear(rep);
ae_vector_init(&tau, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&q, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&f2, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp, 0, DT_REAL, _state, ae_true);
ae_vector_init(&c0, 0, DT_REAL, _state, ae_true);
ae_assert(n>=1, "LSFitLinearWC: N<1!", _state);
ae_assert(m>=1, "LSFitLinearWC: M<1!", _state);
ae_assert(k>=0, "LSFitLinearWC: K<0!", _state);
ae_assert(y->cnt>=n, "LSFitLinearWC: length(Y)<N!", _state);
ae_assert(isfinitevector(y, n, _state), "LSFitLinearWC: Y contains infinite or NaN values!", _state);
ae_assert(w->cnt>=n, "LSFitLinearWC: length(W)<N!", _state);
ae_assert(isfinitevector(w, n, _state), "LSFitLinearWC: W contains infinite or NaN values!", _state);
ae_assert(fmatrix->rows>=n, "LSFitLinearWC: rows(FMatrix)<N!", _state);
ae_assert(fmatrix->cols>=m, "LSFitLinearWC: cols(FMatrix)<M!", _state);
ae_assert(apservisfinitematrix(fmatrix, n, m, _state), "LSFitLinearWC: FMatrix contains infinite or NaN values!", _state);
ae_assert(cmatrix->rows>=k, "LSFitLinearWC: rows(CMatrix)<K!", _state);
ae_assert(cmatrix->cols>=m+1||k==0, "LSFitLinearWC: cols(CMatrix)<M+1!", _state);
ae_assert(apservisfinitematrix(cmatrix, k, m+1, _state), "LSFitLinearWC: CMatrix contains infinite or NaN values!", _state);
if( k>=m )
{
*info = -3;
ae_frame_leave(_state);
return;
}
/*
* Solve
*/
if( k==0 )
{
/*
* no constraints
*/
lsfit_lsfitlinearinternal(y, w, fmatrix, n, m, info, c, rep, _state);
}
else
{
/*
* First, find general form solution of constraints system:
* * factorize C = L*Q
* * unpack Q
* * fill upper part of C with zeros (for RCond)
*
* We got C=C0+Q2'*y where Q2 is lower M-K rows of Q.
*/
rmatrixlq(cmatrix, k, m, &tau, _state);
rmatrixlqunpackq(cmatrix, k, m, &tau, m, &q, _state);
for(i=0; i<=k-1; i++)
{
for(j=i+1; j<=m-1; j++)
{
cmatrix->ptr.pp_double[i][j] = 0.0;
}
}
if( ae_fp_less(rmatrixlurcondinf(cmatrix, k, _state),1000*ae_machineepsilon) )
{
*info = -3;
ae_frame_leave(_state);
return;
}
ae_vector_set_length(&tmp, k, _state);
for(i=0; i<=k-1; i++)
{
if( i>0 )
{
v = ae_v_dotproduct(&cmatrix->ptr.pp_double[i][0], 1, &tmp.ptr.p_double[0], 1, ae_v_len(0,i-1));
}
else
{
v = (double)(0);
}
tmp.ptr.p_double[i] = (cmatrix->ptr.pp_double[i][m]-v)/cmatrix->ptr.pp_double[i][i];
}
ae_vector_set_length(&c0, m, _state);
for(i=0; i<=m-1; i++)
{
c0.ptr.p_double[i] = (double)(0);
}
for(i=0; i<=k-1; i++)
{
v = tmp.ptr.p_double[i];
ae_v_addd(&c0.ptr.p_double[0], 1, &q.ptr.pp_double[i][0], 1, ae_v_len(0,m-1), v);
}
/*
* Second, prepare modified matrix F2 = F*Q2' and solve modified task
*/
ae_vector_set_length(&tmp, ae_maxint(n, m, _state)+1, _state);
ae_matrix_set_length(&f2, n, m-k, _state);
matrixvectormultiply(fmatrix, 0, n-1, 0, m-1, ae_false, &c0, 0, m-1, -1.0, y, 0, n-1, 1.0, _state);
rmatrixgemm(n, m-k, m, 1.0, fmatrix, 0, 0, 0, &q, k, 0, 1, 0.0, &f2, 0, 0, _state);
lsfit_lsfitlinearinternal(y, w, &f2, n, m-k, info, &tmp, rep, _state);
rep->taskrcond = (double)(-1);
if( *info<=0 )
{
ae_frame_leave(_state);
return;
}
/*
* then, convert back to original answer: C = C0 + Q2'*Y0
*/
ae_vector_set_length(c, m, _state);
ae_v_move(&c->ptr.p_double[0], 1, &c0.ptr.p_double[0], 1, ae_v_len(0,m-1));
matrixvectormultiply(&q, k, m-1, 0, m-1, ae_true, &tmp, 0, m-k-1, 1.0, c, 0, m-1, 1.0, _state);
}
ae_frame_leave(_state);
}
/*************************************************************************
Linear least squares fitting.
QR decomposition is used to reduce task to MxM, then triangular solver or
SVD-based solver is used depending on condition number of the system. It
allows to maximize speed and retain decent accuracy.
IMPORTANT: if you want to perform polynomial fitting, it may be more
convenient to use PolynomialFit() function. This function gives
best results on polynomial problems and solves numerical
stability issues which arise when you fit high-degree
polynomials to your data.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
Y - array[0..N-1] Function values in N points.
FMatrix - a table of basis functions values, array[0..N-1, 0..M-1].
FMatrix[I, J] - value of J-th basis function in I-th point.
N - number of points used. N>=1.
M - number of basis functions, M>=1.
OUTPUT PARAMETERS:
Info - error code:
* -4 internal SVD decomposition subroutine failed (very
rare and for degenerate systems only)
* 1 task is solved
C - decomposition coefficients, array[0..M-1]
Rep - fitting report. Following fields are set:
* Rep.TaskRCond reciprocal of condition number
* R2 non-adjusted coefficient of determination
(non-weighted)
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
ERRORS IN PARAMETERS
This solver also calculates different kinds of errors in parameters and
fills corresponding fields of report:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(F*CovPar*F')),
where F is functions matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
NOTE: covariance matrix is estimated using correction for degrees
of freedom (covariances are divided by N-M instead of dividing
by N).
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitlinear(/* Real */ ae_vector* y,
/* Real */ ae_matrix* fmatrix,
ae_int_t n,
ae_int_t m,
ae_int_t* info,
/* Real */ ae_vector* c,
lsfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector w;
ae_int_t i;
ae_frame_make(_state, &_frame_block);
memset(&w, 0, sizeof(w));
*info = 0;
ae_vector_clear(c);
_lsfitreport_clear(rep);
ae_vector_init(&w, 0, DT_REAL, _state, ae_true);
ae_assert(n>=1, "LSFitLinear: N<1!", _state);
ae_assert(m>=1, "LSFitLinear: M<1!", _state);
ae_assert(y->cnt>=n, "LSFitLinear: length(Y)<N!", _state);
ae_assert(isfinitevector(y, n, _state), "LSFitLinear: Y contains infinite or NaN values!", _state);
ae_assert(fmatrix->rows>=n, "LSFitLinear: rows(FMatrix)<N!", _state);
ae_assert(fmatrix->cols>=m, "LSFitLinear: cols(FMatrix)<M!", _state);
ae_assert(apservisfinitematrix(fmatrix, n, m, _state), "LSFitLinear: FMatrix contains infinite or NaN values!", _state);
ae_vector_set_length(&w, n, _state);
for(i=0; i<=n-1; i++)
{
w.ptr.p_double[i] = (double)(1);
}
lsfit_lsfitlinearinternal(y, &w, fmatrix, n, m, info, c, rep, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Constained linear least squares fitting.
This is variation of LSFitLinear(), which searchs for min|A*x=b| given
that K additional constaints C*x=bc are satisfied. It reduces original
task to modified one: min|B*y-d| WITHOUT constraints, then LSFitLinear()
is called.
IMPORTANT: if you want to perform polynomial fitting, it may be more
convenient to use PolynomialFit() function. This function gives
best results on polynomial problems and solves numerical
stability issues which arise when you fit high-degree
polynomials to your data.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
Y - array[0..N-1] Function values in N points.
FMatrix - a table of basis functions values, array[0..N-1, 0..M-1].
FMatrix[I,J] - value of J-th basis function in I-th point.
CMatrix - a table of constaints, array[0..K-1,0..M].
I-th row of CMatrix corresponds to I-th linear constraint:
CMatrix[I,0]*C[0] + ... + CMatrix[I,M-1]*C[M-1] = CMatrix[I,M]
N - number of points used. N>=1.
M - number of basis functions, M>=1.
K - number of constraints, 0 <= K < M
K=0 corresponds to absence of constraints.
OUTPUT PARAMETERS:
Info - error code:
* -4 internal SVD decomposition subroutine failed (very
rare and for degenerate systems only)
* -3 either too many constraints (M or more),
degenerate constraints (some constraints are
repetead twice) or inconsistent constraints were
specified.
* 1 task is solved
C - decomposition coefficients, array[0..M-1]
Rep - fitting report. Following fields are set:
* R2 non-adjusted coefficient of determination
(non-weighted)
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
ERRORS IN PARAMETERS
This solver also calculates different kinds of errors in parameters and
fills corresponding fields of report:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(F*CovPar*F')),
where F is functions matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
IMPORTANT: errors in parameters are calculated without taking into
account boundary/linear constraints! Presence of constraints
changes distribution of errors, but there is no easy way to
account for constraints when you calculate covariance matrix.
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
NOTE: covariance matrix is estimated using correction for degrees
of freedom (covariances are divided by N-M instead of dividing
by N).
-- ALGLIB --
Copyright 07.09.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitlinearc(/* Real */ ae_vector* y,
/* Real */ ae_matrix* fmatrix,
/* Real */ ae_matrix* cmatrix,
ae_int_t n,
ae_int_t m,
ae_int_t k,
ae_int_t* info,
/* Real */ ae_vector* c,
lsfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _y;
ae_vector w;
ae_int_t i;
ae_frame_make(_state, &_frame_block);
memset(&_y, 0, sizeof(_y));
memset(&w, 0, sizeof(w));
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
*info = 0;
ae_vector_clear(c);
_lsfitreport_clear(rep);
ae_vector_init(&w, 0, DT_REAL, _state, ae_true);
ae_assert(n>=1, "LSFitLinearC: N<1!", _state);
ae_assert(m>=1, "LSFitLinearC: M<1!", _state);
ae_assert(k>=0, "LSFitLinearC: K<0!", _state);
ae_assert(y->cnt>=n, "LSFitLinearC: length(Y)<N!", _state);
ae_assert(isfinitevector(y, n, _state), "LSFitLinearC: Y contains infinite or NaN values!", _state);
ae_assert(fmatrix->rows>=n, "LSFitLinearC: rows(FMatrix)<N!", _state);
ae_assert(fmatrix->cols>=m, "LSFitLinearC: cols(FMatrix)<M!", _state);
ae_assert(apservisfinitematrix(fmatrix, n, m, _state), "LSFitLinearC: FMatrix contains infinite or NaN values!", _state);
ae_assert(cmatrix->rows>=k, "LSFitLinearC: rows(CMatrix)<K!", _state);
ae_assert(cmatrix->cols>=m+1||k==0, "LSFitLinearC: cols(CMatrix)<M+1!", _state);
ae_assert(apservisfinitematrix(cmatrix, k, m+1, _state), "LSFitLinearC: CMatrix contains infinite or NaN values!", _state);
ae_vector_set_length(&w, n, _state);
for(i=0; i<=n-1; i++)
{
w.ptr.p_double[i] = (double)(1);
}
lsfitlinearwc(y, &w, fmatrix, cmatrix, n, m, k, info, c, rep, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Weighted nonlinear least squares fitting using function values only.
Combination of numerical differentiation and secant updates is used to
obtain function Jacobian.
Nonlinear task min(F(c)) is solved, where
F(c) = (w[0]*(f(c,x[0])-y[0]))^2 + ... + (w[n-1]*(f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* w is an N-dimensional vector of weight coefficients,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses only f(c,x[i]).
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
W - weights, array[0..N-1]
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
DiffStep- numerical differentiation step;
should not be very small or large;
large = loss of accuracy
small = growth of round-off errors
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 18.10.2008 by Bochkanov Sergey
*************************************************************************/
void lsfitcreatewf(/* Real */ ae_matrix* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
/* Real */ ae_vector* c,
ae_int_t n,
ae_int_t m,
ae_int_t k,
double diffstep,
lsfitstate* state,
ae_state *_state)
{
ae_int_t i;
_lsfitstate_clear(state);
ae_assert(n>=1, "LSFitCreateWF: N<1!", _state);
ae_assert(m>=1, "LSFitCreateWF: M<1!", _state);
ae_assert(k>=1, "LSFitCreateWF: K<1!", _state);
ae_assert(c->cnt>=k, "LSFitCreateWF: length(C)<K!", _state);
ae_assert(isfinitevector(c, k, _state), "LSFitCreateWF: C contains infinite or NaN values!", _state);
ae_assert(y->cnt>=n, "LSFitCreateWF: length(Y)<N!", _state);
ae_assert(isfinitevector(y, n, _state), "LSFitCreateWF: Y contains infinite or NaN values!", _state);
ae_assert(w->cnt>=n, "LSFitCreateWF: length(W)<N!", _state);
ae_assert(isfinitevector(w, n, _state), "LSFitCreateWF: W contains infinite or NaN values!", _state);
ae_assert(x->rows>=n, "LSFitCreateWF: rows(X)<N!", _state);
ae_assert(x->cols>=m, "LSFitCreateWF: cols(X)<M!", _state);
ae_assert(apservisfinitematrix(x, n, m, _state), "LSFitCreateWF: X contains infinite or NaN values!", _state);
ae_assert(ae_isfinite(diffstep, _state), "LSFitCreateWF: DiffStep is not finite!", _state);
ae_assert(ae_fp_greater(diffstep,(double)(0)), "LSFitCreateWF: DiffStep<=0!", _state);
state->teststep = (double)(0);
state->diffstep = diffstep;
state->npoints = n;
state->nweights = n;
state->wkind = 1;
state->m = m;
state->k = k;
lsfitsetcond(state, 0.0, 0, _state);
lsfitsetstpmax(state, 0.0, _state);
lsfitsetxrep(state, ae_false, _state);
ae_matrix_set_length(&state->taskx, n, m, _state);
ae_vector_set_length(&state->tasky, n, _state);
ae_vector_set_length(&state->taskw, n, _state);
ae_vector_set_length(&state->c, k, _state);
ae_vector_set_length(&state->c0, k, _state);
ae_vector_set_length(&state->c1, k, _state);
ae_v_move(&state->c0.ptr.p_double[0], 1, &c->ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_v_move(&state->c1.ptr.p_double[0], 1, &c->ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_vector_set_length(&state->x, m, _state);
ae_v_move(&state->taskw.ptr.p_double[0], 1, &w->ptr.p_double[0], 1, ae_v_len(0,n-1));
for(i=0; i<=n-1; i++)
{
ae_v_move(&state->taskx.ptr.pp_double[i][0], 1, &x->ptr.pp_double[i][0], 1, ae_v_len(0,m-1));
state->tasky.ptr.p_double[i] = y->ptr.p_double[i];
}
ae_vector_set_length(&state->s, k, _state);
ae_vector_set_length(&state->bndl, k, _state);
ae_vector_set_length(&state->bndu, k, _state);
for(i=0; i<=k-1; i++)
{
state->s.ptr.p_double[i] = 1.0;
state->bndl.ptr.p_double[i] = _state->v_neginf;
state->bndu.ptr.p_double[i] = _state->v_posinf;
}
state->optalgo = 0;
state->prevnpt = -1;
state->prevalgo = -1;
state->nec = 0;
state->nic = 0;
minlmcreatev(k, n, &state->c0, diffstep, &state->optstate, _state);
lsfit_lsfitclearrequestfields(state, _state);
ae_vector_set_length(&state->rstate.ia, 6+1, _state);
ae_vector_set_length(&state->rstate.ra, 8+1, _state);
state->rstate.stage = -1;
}
/*************************************************************************
Nonlinear least squares fitting using function values only.
Combination of numerical differentiation and secant updates is used to
obtain function Jacobian.
Nonlinear task min(F(c)) is solved, where
F(c) = (f(c,x[0])-y[0])^2 + ... + (f(c,x[n-1])-y[n-1])^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* w is an N-dimensional vector of weight coefficients,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses only f(c,x[i]).
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
DiffStep- numerical differentiation step;
should not be very small or large;
large = loss of accuracy
small = growth of round-off errors
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 18.10.2008 by Bochkanov Sergey
*************************************************************************/
void lsfitcreatef(/* Real */ ae_matrix* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* c,
ae_int_t n,
ae_int_t m,
ae_int_t k,
double diffstep,
lsfitstate* state,
ae_state *_state)
{
ae_int_t i;
_lsfitstate_clear(state);
ae_assert(n>=1, "LSFitCreateF: N<1!", _state);
ae_assert(m>=1, "LSFitCreateF: M<1!", _state);
ae_assert(k>=1, "LSFitCreateF: K<1!", _state);
ae_assert(c->cnt>=k, "LSFitCreateF: length(C)<K!", _state);
ae_assert(isfinitevector(c, k, _state), "LSFitCreateF: C contains infinite or NaN values!", _state);
ae_assert(y->cnt>=n, "LSFitCreateF: length(Y)<N!", _state);
ae_assert(isfinitevector(y, n, _state), "LSFitCreateF: Y contains infinite or NaN values!", _state);
ae_assert(x->rows>=n, "LSFitCreateF: rows(X)<N!", _state);
ae_assert(x->cols>=m, "LSFitCreateF: cols(X)<M!", _state);
ae_assert(apservisfinitematrix(x, n, m, _state), "LSFitCreateF: X contains infinite or NaN values!", _state);
ae_assert(x->rows>=n, "LSFitCreateF: rows(X)<N!", _state);
ae_assert(x->cols>=m, "LSFitCreateF: cols(X)<M!", _state);
ae_assert(apservisfinitematrix(x, n, m, _state), "LSFitCreateF: X contains infinite or NaN values!", _state);
ae_assert(ae_isfinite(diffstep, _state), "LSFitCreateF: DiffStep is not finite!", _state);
ae_assert(ae_fp_greater(diffstep,(double)(0)), "LSFitCreateF: DiffStep<=0!", _state);
state->teststep = (double)(0);
state->diffstep = diffstep;
state->npoints = n;
state->wkind = 0;
state->m = m;
state->k = k;
lsfitsetcond(state, 0.0, 0, _state);
lsfitsetstpmax(state, 0.0, _state);
lsfitsetxrep(state, ae_false, _state);
ae_matrix_set_length(&state->taskx, n, m, _state);
ae_vector_set_length(&state->tasky, n, _state);
ae_vector_set_length(&state->c, k, _state);
ae_vector_set_length(&state->c0, k, _state);
ae_vector_set_length(&state->c1, k, _state);
ae_v_move(&state->c0.ptr.p_double[0], 1, &c->ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_v_move(&state->c1.ptr.p_double[0], 1, &c->ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_vector_set_length(&state->x, m, _state);
for(i=0; i<=n-1; i++)
{
ae_v_move(&state->taskx.ptr.pp_double[i][0], 1, &x->ptr.pp_double[i][0], 1, ae_v_len(0,m-1));
state->tasky.ptr.p_double[i] = y->ptr.p_double[i];
}
ae_vector_set_length(&state->s, k, _state);
ae_vector_set_length(&state->bndl, k, _state);
ae_vector_set_length(&state->bndu, k, _state);
for(i=0; i<=k-1; i++)
{
state->s.ptr.p_double[i] = 1.0;
state->bndl.ptr.p_double[i] = _state->v_neginf;
state->bndu.ptr.p_double[i] = _state->v_posinf;
}
state->optalgo = 0;
state->prevnpt = -1;
state->prevalgo = -1;
state->nec = 0;
state->nic = 0;
minlmcreatev(k, n, &state->c0, diffstep, &state->optstate, _state);
lsfit_lsfitclearrequestfields(state, _state);
ae_vector_set_length(&state->rstate.ia, 6+1, _state);
ae_vector_set_length(&state->rstate.ra, 8+1, _state);
state->rstate.stage = -1;
}
/*************************************************************************
Weighted nonlinear least squares fitting using gradient only.
Nonlinear task min(F(c)) is solved, where
F(c) = (w[0]*(f(c,x[0])-y[0]))^2 + ... + (w[n-1]*(f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* w is an N-dimensional vector of weight coefficients,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses only f(c,x[i]) and its gradient.
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
W - weights, array[0..N-1]
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
CheapFG - boolean flag, which is:
* True if both function and gradient calculation complexity
are less than O(M^2). An improved algorithm can
be used which corresponds to FGJ scheme from
MINLM unit.
* False otherwise.
Standard Jacibian-bases Levenberg-Marquardt algo
will be used (FJ scheme).
OUTPUT PARAMETERS:
State - structure which stores algorithm state
See also:
LSFitResults
LSFitCreateFG (fitting without weights)
LSFitCreateWFGH (fitting using Hessian)
LSFitCreateFGH (fitting using Hessian, without weights)
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitcreatewfg(/* Real */ ae_matrix* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
/* Real */ ae_vector* c,
ae_int_t n,
ae_int_t m,
ae_int_t k,
ae_bool cheapfg,
lsfitstate* state,
ae_state *_state)
{
ae_int_t i;
_lsfitstate_clear(state);
ae_assert(n>=1, "LSFitCreateWFG: N<1!", _state);
ae_assert(m>=1, "LSFitCreateWFG: M<1!", _state);
ae_assert(k>=1, "LSFitCreateWFG: K<1!", _state);
ae_assert(c->cnt>=k, "LSFitCreateWFG: length(C)<K!", _state);
ae_assert(isfinitevector(c, k, _state), "LSFitCreateWFG: C contains infinite or NaN values!", _state);
ae_assert(y->cnt>=n, "LSFitCreateWFG: length(Y)<N!", _state);
ae_assert(isfinitevector(y, n, _state), "LSFitCreateWFG: Y contains infinite or NaN values!", _state);
ae_assert(w->cnt>=n, "LSFitCreateWFG: length(W)<N!", _state);
ae_assert(isfinitevector(w, n, _state), "LSFitCreateWFG: W contains infinite or NaN values!", _state);
ae_assert(x->rows>=n, "LSFitCreateWFG: rows(X)<N!", _state);
ae_assert(x->cols>=m, "LSFitCreateWFG: cols(X)<M!", _state);
ae_assert(apservisfinitematrix(x, n, m, _state), "LSFitCreateWFG: X contains infinite or NaN values!", _state);
state->teststep = (double)(0);
state->diffstep = (double)(0);
state->npoints = n;
state->nweights = n;
state->wkind = 1;
state->m = m;
state->k = k;
lsfitsetcond(state, 0.0, 0, _state);
lsfitsetstpmax(state, 0.0, _state);
lsfitsetxrep(state, ae_false, _state);
ae_matrix_set_length(&state->taskx, n, m, _state);
ae_vector_set_length(&state->tasky, n, _state);
ae_vector_set_length(&state->taskw, n, _state);
ae_vector_set_length(&state->c, k, _state);
ae_vector_set_length(&state->c0, k, _state);
ae_vector_set_length(&state->c1, k, _state);
ae_v_move(&state->c0.ptr.p_double[0], 1, &c->ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_v_move(&state->c1.ptr.p_double[0], 1, &c->ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_vector_set_length(&state->x, m, _state);
ae_vector_set_length(&state->g, k, _state);
ae_v_move(&state->taskw.ptr.p_double[0], 1, &w->ptr.p_double[0], 1, ae_v_len(0,n-1));
for(i=0; i<=n-1; i++)
{
ae_v_move(&state->taskx.ptr.pp_double[i][0], 1, &x->ptr.pp_double[i][0], 1, ae_v_len(0,m-1));
state->tasky.ptr.p_double[i] = y->ptr.p_double[i];
}
ae_vector_set_length(&state->s, k, _state);
ae_vector_set_length(&state->bndl, k, _state);
ae_vector_set_length(&state->bndu, k, _state);
for(i=0; i<=k-1; i++)
{
state->s.ptr.p_double[i] = 1.0;
state->bndl.ptr.p_double[i] = _state->v_neginf;
state->bndu.ptr.p_double[i] = _state->v_posinf;
}
state->optalgo = 1;
state->prevnpt = -1;
state->prevalgo = -1;
state->nec = 0;
state->nic = 0;
if( cheapfg )
{
minlmcreatevgj(k, n, &state->c0, &state->optstate, _state);
}
else
{
minlmcreatevj(k, n, &state->c0, &state->optstate, _state);
}
lsfit_lsfitclearrequestfields(state, _state);
ae_vector_set_length(&state->rstate.ia, 6+1, _state);
ae_vector_set_length(&state->rstate.ra, 8+1, _state);
state->rstate.stage = -1;
}
/*************************************************************************
Nonlinear least squares fitting using gradient only, without individual
weights.
Nonlinear task min(F(c)) is solved, where
F(c) = ((f(c,x[0])-y[0]))^2 + ... + ((f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses only f(c,x[i]) and its gradient.
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
CheapFG - boolean flag, which is:
* True if both function and gradient calculation complexity
are less than O(M^2). An improved algorithm can
be used which corresponds to FGJ scheme from
MINLM unit.
* False otherwise.
Standard Jacibian-bases Levenberg-Marquardt algo
will be used (FJ scheme).
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitcreatefg(/* Real */ ae_matrix* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* c,
ae_int_t n,
ae_int_t m,
ae_int_t k,
ae_bool cheapfg,
lsfitstate* state,
ae_state *_state)
{
ae_int_t i;
_lsfitstate_clear(state);
ae_assert(n>=1, "LSFitCreateFG: N<1!", _state);
ae_assert(m>=1, "LSFitCreateFG: M<1!", _state);
ae_assert(k>=1, "LSFitCreateFG: K<1!", _state);
ae_assert(c->cnt>=k, "LSFitCreateFG: length(C)<K!", _state);
ae_assert(isfinitevector(c, k, _state), "LSFitCreateFG: C contains infinite or NaN values!", _state);
ae_assert(y->cnt>=n, "LSFitCreateFG: length(Y)<N!", _state);
ae_assert(isfinitevector(y, n, _state), "LSFitCreateFG: Y contains infinite or NaN values!", _state);
ae_assert(x->rows>=n, "LSFitCreateFG: rows(X)<N!", _state);
ae_assert(x->cols>=m, "LSFitCreateFG: cols(X)<M!", _state);
ae_assert(apservisfinitematrix(x, n, m, _state), "LSFitCreateFG: X contains infinite or NaN values!", _state);
ae_assert(x->rows>=n, "LSFitCreateFG: rows(X)<N!", _state);
ae_assert(x->cols>=m, "LSFitCreateFG: cols(X)<M!", _state);
ae_assert(apservisfinitematrix(x, n, m, _state), "LSFitCreateFG: X contains infinite or NaN values!", _state);
state->teststep = (double)(0);
state->diffstep = (double)(0);
state->npoints = n;
state->wkind = 0;
state->m = m;
state->k = k;
lsfitsetcond(state, 0.0, 0, _state);
lsfitsetstpmax(state, 0.0, _state);
lsfitsetxrep(state, ae_false, _state);
ae_matrix_set_length(&state->taskx, n, m, _state);
ae_vector_set_length(&state->tasky, n, _state);
ae_vector_set_length(&state->c, k, _state);
ae_vector_set_length(&state->c0, k, _state);
ae_vector_set_length(&state->c1, k, _state);
ae_v_move(&state->c0.ptr.p_double[0], 1, &c->ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_v_move(&state->c1.ptr.p_double[0], 1, &c->ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_vector_set_length(&state->x, m, _state);
ae_vector_set_length(&state->g, k, _state);
for(i=0; i<=n-1; i++)
{
ae_v_move(&state->taskx.ptr.pp_double[i][0], 1, &x->ptr.pp_double[i][0], 1, ae_v_len(0,m-1));
state->tasky.ptr.p_double[i] = y->ptr.p_double[i];
}
ae_vector_set_length(&state->s, k, _state);
ae_vector_set_length(&state->bndl, k, _state);
ae_vector_set_length(&state->bndu, k, _state);
for(i=0; i<=k-1; i++)
{
state->s.ptr.p_double[i] = 1.0;
state->bndl.ptr.p_double[i] = _state->v_neginf;
state->bndu.ptr.p_double[i] = _state->v_posinf;
}
state->optalgo = 1;
state->prevnpt = -1;
state->prevalgo = -1;
state->nec = 0;
state->nic = 0;
if( cheapfg )
{
minlmcreatevgj(k, n, &state->c0, &state->optstate, _state);
}
else
{
minlmcreatevj(k, n, &state->c0, &state->optstate, _state);
}
lsfit_lsfitclearrequestfields(state, _state);
ae_vector_set_length(&state->rstate.ia, 6+1, _state);
ae_vector_set_length(&state->rstate.ra, 8+1, _state);
state->rstate.stage = -1;
}
/*************************************************************************
Weighted nonlinear least squares fitting using gradient/Hessian.
Nonlinear task min(F(c)) is solved, where
F(c) = (w[0]*(f(c,x[0])-y[0]))^2 + ... + (w[n-1]*(f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* w is an N-dimensional vector of weight coefficients,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses f(c,x[i]), its gradient and its Hessian.
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
W - weights, array[0..N-1]
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitcreatewfgh(/* Real */ ae_matrix* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
/* Real */ ae_vector* c,
ae_int_t n,
ae_int_t m,
ae_int_t k,
lsfitstate* state,
ae_state *_state)
{
ae_int_t i;
_lsfitstate_clear(state);
ae_assert(n>=1, "LSFitCreateWFGH: N<1!", _state);
ae_assert(m>=1, "LSFitCreateWFGH: M<1!", _state);
ae_assert(k>=1, "LSFitCreateWFGH: K<1!", _state);
ae_assert(c->cnt>=k, "LSFitCreateWFGH: length(C)<K!", _state);
ae_assert(isfinitevector(c, k, _state), "LSFitCreateWFGH: C contains infinite or NaN values!", _state);
ae_assert(y->cnt>=n, "LSFitCreateWFGH: length(Y)<N!", _state);
ae_assert(isfinitevector(y, n, _state), "LSFitCreateWFGH: Y contains infinite or NaN values!", _state);
ae_assert(w->cnt>=n, "LSFitCreateWFGH: length(W)<N!", _state);
ae_assert(isfinitevector(w, n, _state), "LSFitCreateWFGH: W contains infinite or NaN values!", _state);
ae_assert(x->rows>=n, "LSFitCreateWFGH: rows(X)<N!", _state);
ae_assert(x->cols>=m, "LSFitCreateWFGH: cols(X)<M!", _state);
ae_assert(apservisfinitematrix(x, n, m, _state), "LSFitCreateWFGH: X contains infinite or NaN values!", _state);
state->teststep = (double)(0);
state->diffstep = (double)(0);
state->npoints = n;
state->nweights = n;
state->wkind = 1;
state->m = m;
state->k = k;
lsfitsetcond(state, 0.0, 0, _state);
lsfitsetstpmax(state, 0.0, _state);
lsfitsetxrep(state, ae_false, _state);
ae_matrix_set_length(&state->taskx, n, m, _state);
ae_vector_set_length(&state->tasky, n, _state);
ae_vector_set_length(&state->taskw, n, _state);
ae_vector_set_length(&state->c, k, _state);
ae_vector_set_length(&state->c0, k, _state);
ae_vector_set_length(&state->c1, k, _state);
ae_v_move(&state->c0.ptr.p_double[0], 1, &c->ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_v_move(&state->c1.ptr.p_double[0], 1, &c->ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_matrix_set_length(&state->h, k, k, _state);
ae_vector_set_length(&state->x, m, _state);
ae_vector_set_length(&state->g, k, _state);
ae_v_move(&state->taskw.ptr.p_double[0], 1, &w->ptr.p_double[0], 1, ae_v_len(0,n-1));
for(i=0; i<=n-1; i++)
{
ae_v_move(&state->taskx.ptr.pp_double[i][0], 1, &x->ptr.pp_double[i][0], 1, ae_v_len(0,m-1));
state->tasky.ptr.p_double[i] = y->ptr.p_double[i];
}
ae_vector_set_length(&state->s, k, _state);
ae_vector_set_length(&state->bndl, k, _state);
ae_vector_set_length(&state->bndu, k, _state);
for(i=0; i<=k-1; i++)
{
state->s.ptr.p_double[i] = 1.0;
state->bndl.ptr.p_double[i] = _state->v_neginf;
state->bndu.ptr.p_double[i] = _state->v_posinf;
}
state->optalgo = 2;
state->prevnpt = -1;
state->prevalgo = -1;
state->nec = 0;
state->nic = 0;
minlmcreatefgh(k, &state->c0, &state->optstate, _state);
lsfit_lsfitclearrequestfields(state, _state);
ae_vector_set_length(&state->rstate.ia, 6+1, _state);
ae_vector_set_length(&state->rstate.ra, 8+1, _state);
state->rstate.stage = -1;
}
/*************************************************************************
Nonlinear least squares fitting using gradient/Hessian, without individial
weights.
Nonlinear task min(F(c)) is solved, where
F(c) = ((f(c,x[0])-y[0]))^2 + ... + ((f(c,x[n-1])-y[n-1]))^2,
* N is a number of points,
* M is a dimension of a space points belong to,
* K is a dimension of a space of parameters being fitted,
* x is a set of N points, each of them is an M-dimensional vector,
* c is a K-dimensional vector of parameters being fitted
This subroutine uses f(c,x[i]), its gradient and its Hessian.
INPUT PARAMETERS:
X - array[0..N-1,0..M-1], points (one row = one point)
Y - array[0..N-1], function values.
C - array[0..K-1], initial approximation to the solution,
N - number of points, N>1
M - dimension of space
K - number of parameters being fitted
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitcreatefgh(/* Real */ ae_matrix* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* c,
ae_int_t n,
ae_int_t m,
ae_int_t k,
lsfitstate* state,
ae_state *_state)
{
ae_int_t i;
_lsfitstate_clear(state);
ae_assert(n>=1, "LSFitCreateFGH: N<1!", _state);
ae_assert(m>=1, "LSFitCreateFGH: M<1!", _state);
ae_assert(k>=1, "LSFitCreateFGH: K<1!", _state);
ae_assert(c->cnt>=k, "LSFitCreateFGH: length(C)<K!", _state);
ae_assert(isfinitevector(c, k, _state), "LSFitCreateFGH: C contains infinite or NaN values!", _state);
ae_assert(y->cnt>=n, "LSFitCreateFGH: length(Y)<N!", _state);
ae_assert(isfinitevector(y, n, _state), "LSFitCreateFGH: Y contains infinite or NaN values!", _state);
ae_assert(x->rows>=n, "LSFitCreateFGH: rows(X)<N!", _state);
ae_assert(x->cols>=m, "LSFitCreateFGH: cols(X)<M!", _state);
ae_assert(apservisfinitematrix(x, n, m, _state), "LSFitCreateFGH: X contains infinite or NaN values!", _state);
state->teststep = (double)(0);
state->diffstep = (double)(0);
state->npoints = n;
state->wkind = 0;
state->m = m;
state->k = k;
lsfitsetcond(state, 0.0, 0, _state);
lsfitsetstpmax(state, 0.0, _state);
lsfitsetxrep(state, ae_false, _state);
ae_matrix_set_length(&state->taskx, n, m, _state);
ae_vector_set_length(&state->tasky, n, _state);
ae_vector_set_length(&state->c, k, _state);
ae_vector_set_length(&state->c0, k, _state);
ae_vector_set_length(&state->c1, k, _state);
ae_v_move(&state->c0.ptr.p_double[0], 1, &c->ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_v_move(&state->c1.ptr.p_double[0], 1, &c->ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_matrix_set_length(&state->h, k, k, _state);
ae_vector_set_length(&state->x, m, _state);
ae_vector_set_length(&state->g, k, _state);
for(i=0; i<=n-1; i++)
{
ae_v_move(&state->taskx.ptr.pp_double[i][0], 1, &x->ptr.pp_double[i][0], 1, ae_v_len(0,m-1));
state->tasky.ptr.p_double[i] = y->ptr.p_double[i];
}
ae_vector_set_length(&state->s, k, _state);
ae_vector_set_length(&state->bndl, k, _state);
ae_vector_set_length(&state->bndu, k, _state);
for(i=0; i<=k-1; i++)
{
state->s.ptr.p_double[i] = 1.0;
state->bndl.ptr.p_double[i] = _state->v_neginf;
state->bndu.ptr.p_double[i] = _state->v_posinf;
}
state->optalgo = 2;
state->prevnpt = -1;
state->prevalgo = -1;
state->nec = 0;
state->nic = 0;
minlmcreatefgh(k, &state->c0, &state->optstate, _state);
lsfit_lsfitclearrequestfields(state, _state);
ae_vector_set_length(&state->rstate.ia, 6+1, _state);
ae_vector_set_length(&state->rstate.ra, 8+1, _state);
state->rstate.stage = -1;
}
/*************************************************************************
Stopping conditions for nonlinear least squares fitting.
INPUT PARAMETERS:
State - structure which stores algorithm state
EpsX - >=0
The subroutine finishes its work if on k+1-th iteration
the condition |v|<=EpsX is fulfilled, where:
* |.| means Euclidian norm
* v - scaled step vector, v[i]=dx[i]/s[i]
* dx - ste pvector, dx=X(k+1)-X(k)
* s - scaling coefficients set by LSFitSetScale()
MaxIts - maximum number of iterations. If MaxIts=0, the number of
iterations is unlimited. Only Levenberg-Marquardt
iterations are counted (L-BFGS/CG iterations are NOT
counted because their cost is very low compared to that of
LM).
NOTE
Passing EpsX=0 and MaxIts=0 (simultaneously) will lead to automatic
stopping criterion selection (according to the scheme used by MINLM unit).
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitsetcond(lsfitstate* state,
double epsx,
ae_int_t maxits,
ae_state *_state)
{
ae_assert(ae_isfinite(epsx, _state), "LSFitSetCond: EpsX is not finite!", _state);
ae_assert(ae_fp_greater_eq(epsx,(double)(0)), "LSFitSetCond: negative EpsX!", _state);
ae_assert(maxits>=0, "LSFitSetCond: negative MaxIts!", _state);
state->epsx = epsx;
state->maxits = maxits;
}
/*************************************************************************
This function sets maximum step length
INPUT PARAMETERS:
State - structure which stores algorithm state
StpMax - maximum step length, >=0. Set StpMax to 0.0, if you don't
want to limit step length.
Use this subroutine when you optimize target function which contains exp()
or other fast growing functions, and optimization algorithm makes too
large steps which leads to overflow. This function allows us to reject
steps that are too large (and therefore expose us to the possible
overflow) without actually calculating function value at the x+stp*d.
NOTE: non-zero StpMax leads to moderate performance degradation because
intermediate step of preconditioned L-BFGS optimization is incompatible
with limits on step size.
-- ALGLIB --
Copyright 02.04.2010 by Bochkanov Sergey
*************************************************************************/
void lsfitsetstpmax(lsfitstate* state, double stpmax, ae_state *_state)
{
ae_assert(ae_fp_greater_eq(stpmax,(double)(0)), "LSFitSetStpMax: StpMax<0!", _state);
state->stpmax = stpmax;
}
/*************************************************************************
This function turns on/off reporting.
INPUT PARAMETERS:
State - structure which stores algorithm state
NeedXRep- whether iteration reports are needed or not
When reports are needed, State.C (current parameters) and State.F (current
value of fitting function) are reported.
-- ALGLIB --
Copyright 15.08.2010 by Bochkanov Sergey
*************************************************************************/
void lsfitsetxrep(lsfitstate* state, ae_bool needxrep, ae_state *_state)
{
state->xrep = needxrep;
}
/*************************************************************************
This function sets scaling coefficients for underlying optimizer.
ALGLIB optimizers use scaling matrices to test stopping conditions (step
size and gradient are scaled before comparison with tolerances). Scale of
the I-th variable is a translation invariant measure of:
a) "how large" the variable is
b) how large the step should be to make significant changes in the function
Generally, scale is NOT considered to be a form of preconditioner. But LM
optimizer is unique in that it uses scaling matrix both in the stopping
condition tests and as Marquardt damping factor.
Proper scaling is very important for the algorithm performance. It is less
important for the quality of results, but still has some influence (it is
easier to converge when variables are properly scaled, so premature
stopping is possible when very badly scalled variables are combined with
relaxed stopping conditions).
INPUT PARAMETERS:
State - structure stores algorithm state
S - array[N], non-zero scaling coefficients
S[i] may be negative, sign doesn't matter.
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void lsfitsetscale(lsfitstate* state,
/* Real */ ae_vector* s,
ae_state *_state)
{
ae_int_t i;
ae_assert(s->cnt>=state->k, "LSFitSetScale: Length(S)<K", _state);
for(i=0; i<=state->k-1; i++)
{
ae_assert(ae_isfinite(s->ptr.p_double[i], _state), "LSFitSetScale: S contains infinite or NAN elements", _state);
ae_assert(ae_fp_neq(s->ptr.p_double[i],(double)(0)), "LSFitSetScale: S contains infinite or NAN elements", _state);
state->s.ptr.p_double[i] = ae_fabs(s->ptr.p_double[i], _state);
}
}
/*************************************************************************
This function sets boundary constraints for underlying optimizer
Boundary constraints are inactive by default (after initial creation).
They are preserved until explicitly turned off with another SetBC() call.
INPUT PARAMETERS:
State - structure stores algorithm state
BndL - lower bounds, array[K].
If some (all) variables are unbounded, you may specify
very small number or -INF (latter is recommended because
it will allow solver to use better algorithm).
BndU - upper bounds, array[K].
If some (all) variables are unbounded, you may specify
very large number or +INF (latter is recommended because
it will allow solver to use better algorithm).
NOTE 1: it is possible to specify BndL[i]=BndU[i]. In this case I-th
variable will be "frozen" at X[i]=BndL[i]=BndU[i].
NOTE 2: unlike other constrained optimization algorithms, this solver has
following useful properties:
* bound constraints are always satisfied exactly
* function is evaluated only INSIDE area specified by bound constraints
-- ALGLIB --
Copyright 14.01.2011 by Bochkanov Sergey
*************************************************************************/
void lsfitsetbc(lsfitstate* state,
/* Real */ ae_vector* bndl,
/* Real */ ae_vector* bndu,
ae_state *_state)
{
ae_int_t i;
ae_int_t k;
k = state->k;
ae_assert(bndl->cnt>=k, "LSFitSetBC: Length(BndL)<K", _state);
ae_assert(bndu->cnt>=k, "LSFitSetBC: Length(BndU)<K", _state);
for(i=0; i<=k-1; i++)
{
ae_assert(ae_isfinite(bndl->ptr.p_double[i], _state)||ae_isneginf(bndl->ptr.p_double[i], _state), "LSFitSetBC: BndL contains NAN or +INF", _state);
ae_assert(ae_isfinite(bndu->ptr.p_double[i], _state)||ae_isposinf(bndu->ptr.p_double[i], _state), "LSFitSetBC: BndU contains NAN or -INF", _state);
if( ae_isfinite(bndl->ptr.p_double[i], _state)&&ae_isfinite(bndu->ptr.p_double[i], _state) )
{
ae_assert(ae_fp_less_eq(bndl->ptr.p_double[i],bndu->ptr.p_double[i]), "LSFitSetBC: BndL[i]>BndU[i]", _state);
}
state->bndl.ptr.p_double[i] = bndl->ptr.p_double[i];
state->bndu.ptr.p_double[i] = bndu->ptr.p_double[i];
}
}
/*************************************************************************
This function sets linear constraints for underlying optimizer
Linear constraints are inactive by default (after initial creation).
They are preserved until explicitly turned off with another SetLC() call.
INPUT PARAMETERS:
State - structure stores algorithm state
C - linear constraints, array[K,N+1].
Each row of C represents one constraint, either equality
or inequality (see below):
* first N elements correspond to coefficients,
* last element corresponds to the right part.
All elements of C (including right part) must be finite.
CT - type of constraints, array[K]:
* if CT[i]>0, then I-th constraint is C[i,*]*x >= C[i,n+1]
* if CT[i]=0, then I-th constraint is C[i,*]*x = C[i,n+1]
* if CT[i]<0, then I-th constraint is C[i,*]*x <= C[i,n+1]
K - number of equality/inequality constraints, K>=0:
* if given, only leading K elements of C/CT are used
* if not given, automatically determined from sizes of C/CT
IMPORTANT: if you have linear constraints, it is strongly recommended to
set scale of variables with lsfitsetscale(). QP solver which is
used to calculate linearly constrained steps heavily relies on
good scaling of input problems.
NOTE: linear (non-box) constraints are satisfied only approximately -
there always exists some violation due to numerical errors and
algorithmic limitations.
NOTE: general linear constraints add significant overhead to solution
process. Although solver performs roughly same amount of iterations
(when compared with similar box-only constrained problem), each
iteration now involves solution of linearly constrained QP
subproblem, which requires ~3-5 times more Cholesky decompositions.
Thus, if you can reformulate your problem in such way this it has
only box constraints, it may be beneficial to do so.
-- ALGLIB --
Copyright 29.04.2017 by Bochkanov Sergey
*************************************************************************/
void lsfitsetlc(lsfitstate* state,
/* Real */ ae_matrix* c,
/* Integer */ ae_vector* ct,
ae_int_t k,
ae_state *_state)
{
ae_int_t i;
ae_int_t n;
n = state->k;
/*
* First, check for errors in the inputs
*/
ae_assert(k>=0, "LSFitSetLC: K<0", _state);
ae_assert(c->cols>=n+1||k==0, "LSFitSetLC: Cols(C)<N+1", _state);
ae_assert(c->rows>=k, "LSFitSetLC: Rows(C)<K", _state);
ae_assert(ct->cnt>=k, "LSFitSetLC: Length(CT)<K", _state);
ae_assert(apservisfinitematrix(c, k, n+1, _state), "LSFitSetLC: C contains infinite or NaN values!", _state);
/*
* Handle zero K
*/
if( k==0 )
{
state->nec = 0;
state->nic = 0;
return;
}
/*
* Equality constraints are stored first, in the upper
* NEC rows of State.CLEIC matrix. Inequality constraints
* are stored in the next NIC rows.
*
* NOTE: we convert inequality constraints to the form
* A*x<=b before copying them.
*/
rmatrixsetlengthatleast(&state->cleic, k, n+1, _state);
state->nec = 0;
state->nic = 0;
for(i=0; i<=k-1; i++)
{
if( ct->ptr.p_int[i]==0 )
{
ae_v_move(&state->cleic.ptr.pp_double[state->nec][0], 1, &c->ptr.pp_double[i][0], 1, ae_v_len(0,n));
state->nec = state->nec+1;
}
}
for(i=0; i<=k-1; i++)
{
if( ct->ptr.p_int[i]!=0 )
{
if( ct->ptr.p_int[i]>0 )
{
ae_v_moveneg(&state->cleic.ptr.pp_double[state->nec+state->nic][0], 1, &c->ptr.pp_double[i][0], 1, ae_v_len(0,n));
}
else
{
ae_v_move(&state->cleic.ptr.pp_double[state->nec+state->nic][0], 1, &c->ptr.pp_double[i][0], 1, ae_v_len(0,n));
}
state->nic = state->nic+1;
}
}
}
/*************************************************************************
NOTES:
1. this algorithm is somewhat unusual because it works with parameterized
function f(C,X), where X is a function argument (we have many points
which are characterized by different argument values), and C is a
parameter to fit.
For example, if we want to do linear fit by f(c0,c1,x) = c0*x+c1, then
x will be argument, and {c0,c1} will be parameters.
It is important to understand that this algorithm finds minimum in the
space of function PARAMETERS (not arguments), so it needs derivatives
of f() with respect to C, not X.
In the example above it will need f=c0*x+c1 and {df/dc0,df/dc1} = {x,1}
instead of {df/dx} = {c0}.
2. Callback functions accept C as the first parameter, and X as the second
3. If state was created with LSFitCreateFG(), algorithm needs just
function and its gradient, but if state was created with
LSFitCreateFGH(), algorithm will need function, gradient and Hessian.
According to the said above, there ase several versions of this
function, which accept different sets of callbacks.
This flexibility opens way to subtle errors - you may create state with
LSFitCreateFGH() (optimization using Hessian), but call function which
does not accept Hessian. So when algorithm will request Hessian, there
will be no callback to call. In this case exception will be thrown.
Be careful to avoid such errors because there is no way to find them at
compile time - you can see them at runtime only.
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
ae_bool lsfititeration(lsfitstate* state, ae_state *_state)
{
double lx;
double lf;
double ld;
double rx;
double rf;
double rd;
ae_int_t n;
ae_int_t m;
ae_int_t k;
double v;
double vv;
double relcnt;
ae_int_t i;
ae_int_t j;
ae_int_t j1;
ae_int_t info;
ae_bool result;
/*
* Reverse communication preparations
* I know it looks ugly, but it works the same way
* anywhere from C++ to Python.
*
* This code initializes locals by:
* * random values determined during code
* generation - on first subroutine call
* * values from previous call - on subsequent calls
*/
if( state->rstate.stage>=0 )
{
n = state->rstate.ia.ptr.p_int[0];
m = state->rstate.ia.ptr.p_int[1];
k = state->rstate.ia.ptr.p_int[2];
i = state->rstate.ia.ptr.p_int[3];
j = state->rstate.ia.ptr.p_int[4];
j1 = state->rstate.ia.ptr.p_int[5];
info = state->rstate.ia.ptr.p_int[6];
lx = state->rstate.ra.ptr.p_double[0];
lf = state->rstate.ra.ptr.p_double[1];
ld = state->rstate.ra.ptr.p_double[2];
rx = state->rstate.ra.ptr.p_double[3];
rf = state->rstate.ra.ptr.p_double[4];
rd = state->rstate.ra.ptr.p_double[5];
v = state->rstate.ra.ptr.p_double[6];
vv = state->rstate.ra.ptr.p_double[7];
relcnt = state->rstate.ra.ptr.p_double[8];
}
else
{
n = 359;
m = -58;
k = -919;
i = -909;
j = 81;
j1 = 255;
info = 74;
lx = -788;
lf = 809;
ld = 205;
rx = -838;
rf = 939;
rd = -526;
v = 763;
vv = -541;
relcnt = -698;
}
if( state->rstate.stage==0 )
{
goto lbl_0;
}
if( state->rstate.stage==1 )
{
goto lbl_1;
}
if( state->rstate.stage==2 )
{
goto lbl_2;
}
if( state->rstate.stage==3 )
{
goto lbl_3;
}
if( state->rstate.stage==4 )
{
goto lbl_4;
}
if( state->rstate.stage==5 )
{
goto lbl_5;
}
if( state->rstate.stage==6 )
{
goto lbl_6;
}
if( state->rstate.stage==7 )
{
goto lbl_7;
}
if( state->rstate.stage==8 )
{
goto lbl_8;
}
if( state->rstate.stage==9 )
{
goto lbl_9;
}
if( state->rstate.stage==10 )
{
goto lbl_10;
}
if( state->rstate.stage==11 )
{
goto lbl_11;
}
if( state->rstate.stage==12 )
{
goto lbl_12;
}
if( state->rstate.stage==13 )
{
goto lbl_13;
}
/*
* Routine body
*/
/*
* Init
*/
if( state->wkind==1 )
{
ae_assert(state->npoints==state->nweights, "LSFitFit: number of points is not equal to the number of weights", _state);
}
state->repvaridx = -1;
n = state->npoints;
m = state->m;
k = state->k;
ivectorsetlengthatleast(&state->tmpct, state->nec+state->nic, _state);
for(i=0; i<=state->nec-1; i++)
{
state->tmpct.ptr.p_int[i] = 0;
}
for(i=0; i<=state->nic-1; i++)
{
state->tmpct.ptr.p_int[state->nec+i] = -1;
}
minlmsetcond(&state->optstate, state->epsx, state->maxits, _state);
minlmsetstpmax(&state->optstate, state->stpmax, _state);
minlmsetxrep(&state->optstate, state->xrep, _state);
minlmsetscale(&state->optstate, &state->s, _state);
minlmsetbc(&state->optstate, &state->bndl, &state->bndu, _state);
minlmsetlc(&state->optstate, &state->cleic, &state->tmpct, state->nec+state->nic, _state);
/*
* Check that user-supplied gradient is correct
*/
lsfit_lsfitclearrequestfields(state, _state);
if( !(ae_fp_greater(state->teststep,(double)(0))&&state->optalgo==1) )
{
goto lbl_14;
}
for(i=0; i<=k-1; i++)
{
state->c.ptr.p_double[i] = state->c0.ptr.p_double[i];
if( ae_isfinite(state->bndl.ptr.p_double[i], _state) )
{
state->c.ptr.p_double[i] = ae_maxreal(state->c.ptr.p_double[i], state->bndl.ptr.p_double[i], _state);
}
if( ae_isfinite(state->bndu.ptr.p_double[i], _state) )
{
state->c.ptr.p_double[i] = ae_minreal(state->c.ptr.p_double[i], state->bndu.ptr.p_double[i], _state);
}
}
state->needfg = ae_true;
i = 0;
lbl_16:
if( i>k-1 )
{
goto lbl_18;
}
ae_assert(ae_fp_less_eq(state->bndl.ptr.p_double[i],state->c.ptr.p_double[i])&&ae_fp_less_eq(state->c.ptr.p_double[i],state->bndu.ptr.p_double[i]), "LSFitIteration: internal error(State.C is out of bounds)", _state);
v = state->c.ptr.p_double[i];
j = 0;
lbl_19:
if( j>n-1 )
{
goto lbl_21;
}
ae_v_move(&state->x.ptr.p_double[0], 1, &state->taskx.ptr.pp_double[j][0], 1, ae_v_len(0,m-1));
state->c.ptr.p_double[i] = v-state->teststep*state->s.ptr.p_double[i];
if( ae_isfinite(state->bndl.ptr.p_double[i], _state) )
{
state->c.ptr.p_double[i] = ae_maxreal(state->c.ptr.p_double[i], state->bndl.ptr.p_double[i], _state);
}
lx = state->c.ptr.p_double[i];
state->rstate.stage = 0;
goto lbl_rcomm;
lbl_0:
lf = state->f;
ld = state->g.ptr.p_double[i];
state->c.ptr.p_double[i] = v+state->teststep*state->s.ptr.p_double[i];
if( ae_isfinite(state->bndu.ptr.p_double[i], _state) )
{
state->c.ptr.p_double[i] = ae_minreal(state->c.ptr.p_double[i], state->bndu.ptr.p_double[i], _state);
}
rx = state->c.ptr.p_double[i];
state->rstate.stage = 1;
goto lbl_rcomm;
lbl_1:
rf = state->f;
rd = state->g.ptr.p_double[i];
state->c.ptr.p_double[i] = (lx+rx)/2;
if( ae_isfinite(state->bndl.ptr.p_double[i], _state) )
{
state->c.ptr.p_double[i] = ae_maxreal(state->c.ptr.p_double[i], state->bndl.ptr.p_double[i], _state);
}
if( ae_isfinite(state->bndu.ptr.p_double[i], _state) )
{
state->c.ptr.p_double[i] = ae_minreal(state->c.ptr.p_double[i], state->bndu.ptr.p_double[i], _state);
}
state->rstate.stage = 2;
goto lbl_rcomm;
lbl_2:
state->c.ptr.p_double[i] = v;
if( !derivativecheck(lf, ld, rf, rd, state->f, state->g.ptr.p_double[i], rx-lx, _state) )
{
state->repvaridx = i;
state->repterminationtype = -7;
result = ae_false;
return result;
}
j = j+1;
goto lbl_19;
lbl_21:
i = i+1;
goto lbl_16;
lbl_18:
state->needfg = ae_false;
lbl_14:
/*
* Fill WCur by weights:
* * for WKind=0 unit weights are chosen
* * for WKind=1 we use user-supplied weights stored in State.TaskW
*/
rvectorsetlengthatleast(&state->wcur, n, _state);
for(i=0; i<=n-1; i++)
{
state->wcur.ptr.p_double[i] = 1.0;
if( state->wkind==1 )
{
state->wcur.ptr.p_double[i] = state->taskw.ptr.p_double[i];
}
}
/*
* Optimize
*/
lbl_22:
if( !minlmiteration(&state->optstate, _state) )
{
goto lbl_23;
}
if( !state->optstate.needfi )
{
goto lbl_24;
}
/*
* calculate f[] = wi*(f(xi,c)-yi)
*/
i = 0;
lbl_26:
if( i>n-1 )
{
goto lbl_28;
}
ae_v_move(&state->c.ptr.p_double[0], 1, &state->optstate.x.ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_v_move(&state->x.ptr.p_double[0], 1, &state->taskx.ptr.pp_double[i][0], 1, ae_v_len(0,m-1));
state->pointindex = i;
lsfit_lsfitclearrequestfields(state, _state);
state->needf = ae_true;
state->rstate.stage = 3;
goto lbl_rcomm;
lbl_3:
state->needf = ae_false;
vv = state->wcur.ptr.p_double[i];
state->optstate.fi.ptr.p_double[i] = vv*(state->f-state->tasky.ptr.p_double[i]);
i = i+1;
goto lbl_26;
lbl_28:
goto lbl_22;
lbl_24:
if( !state->optstate.needf )
{
goto lbl_29;
}
/*
* calculate F = sum (wi*(f(xi,c)-yi))^2
*/
state->optstate.f = (double)(0);
i = 0;
lbl_31:
if( i>n-1 )
{
goto lbl_33;
}
ae_v_move(&state->c.ptr.p_double[0], 1, &state->optstate.x.ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_v_move(&state->x.ptr.p_double[0], 1, &state->taskx.ptr.pp_double[i][0], 1, ae_v_len(0,m-1));
state->pointindex = i;
lsfit_lsfitclearrequestfields(state, _state);
state->needf = ae_true;
state->rstate.stage = 4;
goto lbl_rcomm;
lbl_4:
state->needf = ae_false;
vv = state->wcur.ptr.p_double[i];
state->optstate.f = state->optstate.f+ae_sqr(vv*(state->f-state->tasky.ptr.p_double[i]), _state);
i = i+1;
goto lbl_31;
lbl_33:
goto lbl_22;
lbl_29:
if( !state->optstate.needfg )
{
goto lbl_34;
}
/*
* calculate F/gradF
*/
state->optstate.f = (double)(0);
for(i=0; i<=k-1; i++)
{
state->optstate.g.ptr.p_double[i] = (double)(0);
}
i = 0;
lbl_36:
if( i>n-1 )
{
goto lbl_38;
}
ae_v_move(&state->c.ptr.p_double[0], 1, &state->optstate.x.ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_v_move(&state->x.ptr.p_double[0], 1, &state->taskx.ptr.pp_double[i][0], 1, ae_v_len(0,m-1));
state->pointindex = i;
lsfit_lsfitclearrequestfields(state, _state);
state->needfg = ae_true;
state->rstate.stage = 5;
goto lbl_rcomm;
lbl_5:
state->needfg = ae_false;
vv = state->wcur.ptr.p_double[i];
state->optstate.f = state->optstate.f+ae_sqr(vv*(state->f-state->tasky.ptr.p_double[i]), _state);
v = ae_sqr(vv, _state)*2*(state->f-state->tasky.ptr.p_double[i]);
ae_v_addd(&state->optstate.g.ptr.p_double[0], 1, &state->g.ptr.p_double[0], 1, ae_v_len(0,k-1), v);
i = i+1;
goto lbl_36;
lbl_38:
goto lbl_22;
lbl_34:
if( !state->optstate.needfij )
{
goto lbl_39;
}
/*
* calculate Fi/jac(Fi)
*/
i = 0;
lbl_41:
if( i>n-1 )
{
goto lbl_43;
}
ae_v_move(&state->c.ptr.p_double[0], 1, &state->optstate.x.ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_v_move(&state->x.ptr.p_double[0], 1, &state->taskx.ptr.pp_double[i][0], 1, ae_v_len(0,m-1));
state->pointindex = i;
lsfit_lsfitclearrequestfields(state, _state);
state->needfg = ae_true;
state->rstate.stage = 6;
goto lbl_rcomm;
lbl_6:
state->needfg = ae_false;
vv = state->wcur.ptr.p_double[i];
state->optstate.fi.ptr.p_double[i] = vv*(state->f-state->tasky.ptr.p_double[i]);
ae_v_moved(&state->optstate.j.ptr.pp_double[i][0], 1, &state->g.ptr.p_double[0], 1, ae_v_len(0,k-1), vv);
i = i+1;
goto lbl_41;
lbl_43:
goto lbl_22;
lbl_39:
if( !state->optstate.needfgh )
{
goto lbl_44;
}
/*
* calculate F/grad(F)/hess(F)
*/
state->optstate.f = (double)(0);
for(i=0; i<=k-1; i++)
{
state->optstate.g.ptr.p_double[i] = (double)(0);
}
for(i=0; i<=k-1; i++)
{
for(j=0; j<=k-1; j++)
{
state->optstate.h.ptr.pp_double[i][j] = (double)(0);
}
}
i = 0;
lbl_46:
if( i>n-1 )
{
goto lbl_48;
}
ae_v_move(&state->c.ptr.p_double[0], 1, &state->optstate.x.ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_v_move(&state->x.ptr.p_double[0], 1, &state->taskx.ptr.pp_double[i][0], 1, ae_v_len(0,m-1));
state->pointindex = i;
lsfit_lsfitclearrequestfields(state, _state);
state->needfgh = ae_true;
state->rstate.stage = 7;
goto lbl_rcomm;
lbl_7:
state->needfgh = ae_false;
vv = state->wcur.ptr.p_double[i];
state->optstate.f = state->optstate.f+ae_sqr(vv*(state->f-state->tasky.ptr.p_double[i]), _state);
v = ae_sqr(vv, _state)*2*(state->f-state->tasky.ptr.p_double[i]);
ae_v_addd(&state->optstate.g.ptr.p_double[0], 1, &state->g.ptr.p_double[0], 1, ae_v_len(0,k-1), v);
for(j=0; j<=k-1; j++)
{
v = 2*ae_sqr(vv, _state)*state->g.ptr.p_double[j];
ae_v_addd(&state->optstate.h.ptr.pp_double[j][0], 1, &state->g.ptr.p_double[0], 1, ae_v_len(0,k-1), v);
v = 2*ae_sqr(vv, _state)*(state->f-state->tasky.ptr.p_double[i]);
ae_v_addd(&state->optstate.h.ptr.pp_double[j][0], 1, &state->h.ptr.pp_double[j][0], 1, ae_v_len(0,k-1), v);
}
i = i+1;
goto lbl_46;
lbl_48:
goto lbl_22;
lbl_44:
if( !state->optstate.xupdated )
{
goto lbl_49;
}
/*
* Report new iteration
*/
ae_v_move(&state->c.ptr.p_double[0], 1, &state->optstate.x.ptr.p_double[0], 1, ae_v_len(0,k-1));
state->f = state->optstate.f;
lsfit_lsfitclearrequestfields(state, _state);
state->xupdated = ae_true;
state->rstate.stage = 8;
goto lbl_rcomm;
lbl_8:
state->xupdated = ae_false;
goto lbl_22;
lbl_49:
goto lbl_22;
lbl_23:
/*
* Extract results
*
* NOTE: reverse communication protocol used by this unit does NOT
* allow us to reallocate State.C[] array. Thus, we extract
* results to the temporary variable in order to avoid possible
* reallocation.
*/
minlmresults(&state->optstate, &state->c1, &state->optrep, _state);
state->repterminationtype = state->optrep.terminationtype;
state->repiterationscount = state->optrep.iterationscount;
/*
* calculate errors
*/
if( state->repterminationtype<=0 )
{
goto lbl_51;
}
/*
* Calculate RMS/Avg/Max/... errors
*/
state->reprmserror = (double)(0);
state->repwrmserror = (double)(0);
state->repavgerror = (double)(0);
state->repavgrelerror = (double)(0);
state->repmaxerror = (double)(0);
relcnt = (double)(0);
i = 0;
lbl_53:
if( i>n-1 )
{
goto lbl_55;
}
ae_v_move(&state->c.ptr.p_double[0], 1, &state->c1.ptr.p_double[0], 1, ae_v_len(0,k-1));
ae_v_move(&state->x.ptr.p_double[0], 1, &state->taskx.ptr.pp_double[i][0], 1, ae_v_len(0,m-1));
state->pointindex = i;
lsfit_lsfitclearrequestfields(state, _state);
state->needf = ae_true;
state->rstate.stage = 9;
goto lbl_rcomm;
lbl_9:
state->needf = ae_false;
v = state->f;
vv = state->wcur.ptr.p_double[i];
state->reprmserror = state->reprmserror+ae_sqr(v-state->tasky.ptr.p_double[i], _state);
state->repwrmserror = state->repwrmserror+ae_sqr(vv*(v-state->tasky.ptr.p_double[i]), _state);
state->repavgerror = state->repavgerror+ae_fabs(v-state->tasky.ptr.p_double[i], _state);
if( ae_fp_neq(state->tasky.ptr.p_double[i],(double)(0)) )
{
state->repavgrelerror = state->repavgrelerror+ae_fabs(v-state->tasky.ptr.p_double[i], _state)/ae_fabs(state->tasky.ptr.p_double[i], _state);
relcnt = relcnt+1;
}
state->repmaxerror = ae_maxreal(state->repmaxerror, ae_fabs(v-state->tasky.ptr.p_double[i], _state), _state);
i = i+1;
goto lbl_53;
lbl_55:
state->reprmserror = ae_sqrt(state->reprmserror/n, _state);
state->repwrmserror = ae_sqrt(state->repwrmserror/n, _state);
state->repavgerror = state->repavgerror/n;
if( ae_fp_neq(relcnt,(double)(0)) )
{
state->repavgrelerror = state->repavgrelerror/relcnt;
}
/*
* Calculate covariance matrix
*/
rmatrixsetlengthatleast(&state->tmpjac, n, k, _state);
rvectorsetlengthatleast(&state->tmpf, n, _state);
rvectorsetlengthatleast(&state->tmp, k, _state);
if( ae_fp_less_eq(state->diffstep,(double)(0)) )
{
goto lbl_56;
}
/*
* Compute Jacobian by means of numerical differentiation
*/
lsfit_lsfitclearrequestfields(state, _state);
state->needf = ae_true;
i = 0;
lbl_58:
if( i>n-1 )
{
goto lbl_60;
}
ae_v_move(&state->x.ptr.p_double[0], 1, &state->taskx.ptr.pp_double[i][0], 1, ae_v_len(0,m-1));
state->pointindex = i;
state->rstate.stage = 10;
goto lbl_rcomm;
lbl_10:
state->tmpf.ptr.p_double[i] = state->f;
j = 0;
lbl_61:
if( j>k-1 )
{
goto lbl_63;
}
v = state->c.ptr.p_double[j];
lx = v-state->diffstep*state->s.ptr.p_double[j];
state->c.ptr.p_double[j] = lx;
if( ae_isfinite(state->bndl.ptr.p_double[j], _state) )
{
state->c.ptr.p_double[j] = ae_maxreal(state->c.ptr.p_double[j], state->bndl.ptr.p_double[j], _state);
}
state->rstate.stage = 11;
goto lbl_rcomm;
lbl_11:
lf = state->f;
rx = v+state->diffstep*state->s.ptr.p_double[j];
state->c.ptr.p_double[j] = rx;
if( ae_isfinite(state->bndu.ptr.p_double[j], _state) )
{
state->c.ptr.p_double[j] = ae_minreal(state->c.ptr.p_double[j], state->bndu.ptr.p_double[j], _state);
}
state->rstate.stage = 12;
goto lbl_rcomm;
lbl_12:
rf = state->f;
state->c.ptr.p_double[j] = v;
if( ae_fp_neq(rx,lx) )
{
state->tmpjac.ptr.pp_double[i][j] = (rf-lf)/(rx-lx);
}
else
{
state->tmpjac.ptr.pp_double[i][j] = (double)(0);
}
j = j+1;
goto lbl_61;
lbl_63:
i = i+1;
goto lbl_58;
lbl_60:
state->needf = ae_false;
goto lbl_57;
lbl_56:
/*
* Jacobian is calculated with user-provided analytic gradient
*/
lsfit_lsfitclearrequestfields(state, _state);
state->needfg = ae_true;
i = 0;
lbl_64:
if( i>n-1 )
{
goto lbl_66;
}
ae_v_move(&state->x.ptr.p_double[0], 1, &state->taskx.ptr.pp_double[i][0], 1, ae_v_len(0,m-1));
state->pointindex = i;
state->rstate.stage = 13;
goto lbl_rcomm;
lbl_13:
state->tmpf.ptr.p_double[i] = state->f;
for(j=0; j<=k-1; j++)
{
state->tmpjac.ptr.pp_double[i][j] = state->g.ptr.p_double[j];
}
i = i+1;
goto lbl_64;
lbl_66:
state->needfg = ae_false;
lbl_57:
for(i=0; i<=k-1; i++)
{
state->tmp.ptr.p_double[i] = 0.0;
}
lsfit_estimateerrors(&state->tmpjac, &state->tmpf, &state->tasky, &state->wcur, &state->tmp, &state->s, n, k, &state->rep, &state->tmpjacw, 0, _state);
lbl_51:
result = ae_false;
return result;
/*
* Saving state
*/
lbl_rcomm:
result = ae_true;
state->rstate.ia.ptr.p_int[0] = n;
state->rstate.ia.ptr.p_int[1] = m;
state->rstate.ia.ptr.p_int[2] = k;
state->rstate.ia.ptr.p_int[3] = i;
state->rstate.ia.ptr.p_int[4] = j;
state->rstate.ia.ptr.p_int[5] = j1;
state->rstate.ia.ptr.p_int[6] = info;
state->rstate.ra.ptr.p_double[0] = lx;
state->rstate.ra.ptr.p_double[1] = lf;
state->rstate.ra.ptr.p_double[2] = ld;
state->rstate.ra.ptr.p_double[3] = rx;
state->rstate.ra.ptr.p_double[4] = rf;
state->rstate.ra.ptr.p_double[5] = rd;
state->rstate.ra.ptr.p_double[6] = v;
state->rstate.ra.ptr.p_double[7] = vv;
state->rstate.ra.ptr.p_double[8] = relcnt;
return result;
}
/*************************************************************************
Nonlinear least squares fitting results.
Called after return from LSFitFit().
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
Info - completion code:
* -8 optimizer detected NAN/INF in the target
function and/or gradient
* -7 gradient verification failed.
See LSFitSetGradientCheck() for more information.
* -3 inconsistent constraints
* 2 relative step is no more than EpsX.
* 5 MaxIts steps was taken
* 7 stopping conditions are too stringent,
further improvement is impossible
C - array[0..K-1], solution
Rep - optimization report. On success following fields are set:
* R2 non-adjusted coefficient of determination
(non-weighted)
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
* WRMSError weighted rms error on the (X,Y).
ERRORS IN PARAMETERS
This solver also calculates different kinds of errors in parameters and
fills corresponding fields of report:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(J*CovPar*J')),
where J is Jacobian matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
IMPORTANT: errors in parameters are calculated without taking into
account boundary/linear constraints! Presence of constraints
changes distribution of errors, but there is no easy way to
account for constraints when you calculate covariance matrix.
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
NOTE: covariance matrix is estimated using correction for degrees
of freedom (covariances are divided by N-M instead of dividing
by N).
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
void lsfitresults(lsfitstate* state,
ae_int_t* info,
/* Real */ ae_vector* c,
lsfitreport* rep,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
*info = 0;
ae_vector_clear(c);
_lsfitreport_clear(rep);
lsfit_clearreport(rep, _state);
*info = state->repterminationtype;
rep->varidx = state->repvaridx;
if( *info>0 )
{
ae_vector_set_length(c, state->k, _state);
ae_v_move(&c->ptr.p_double[0], 1, &state->c1.ptr.p_double[0], 1, ae_v_len(0,state->k-1));
rep->rmserror = state->reprmserror;
rep->wrmserror = state->repwrmserror;
rep->avgerror = state->repavgerror;
rep->avgrelerror = state->repavgrelerror;
rep->maxerror = state->repmaxerror;
rep->iterationscount = state->repiterationscount;
ae_matrix_set_length(&rep->covpar, state->k, state->k, _state);
ae_vector_set_length(&rep->errpar, state->k, _state);
ae_vector_set_length(&rep->errcurve, state->npoints, _state);
ae_vector_set_length(&rep->noise, state->npoints, _state);
rep->r2 = state->rep.r2;
for(i=0; i<=state->k-1; i++)
{
for(j=0; j<=state->k-1; j++)
{
rep->covpar.ptr.pp_double[i][j] = state->rep.covpar.ptr.pp_double[i][j];
}
rep->errpar.ptr.p_double[i] = state->rep.errpar.ptr.p_double[i];
}
for(i=0; i<=state->npoints-1; i++)
{
rep->errcurve.ptr.p_double[i] = state->rep.errcurve.ptr.p_double[i];
rep->noise.ptr.p_double[i] = state->rep.noise.ptr.p_double[i];
}
}
}
/*************************************************************************
This subroutine turns on verification of the user-supplied analytic
gradient:
* user calls this subroutine before fitting begins
* LSFitFit() is called
* prior to actual fitting, for each point in data set X_i and each
component of parameters being fited C_j algorithm performs following
steps:
* two trial steps are made to C_j-TestStep*S[j] and C_j+TestStep*S[j],
where C_j is j-th parameter and S[j] is a scale of j-th parameter
* if needed, steps are bounded with respect to constraints on C[]
* F(X_i|C) is evaluated at these trial points
* we perform one more evaluation in the middle point of the interval
* we build cubic model using function values and derivatives at trial
points and we compare its prediction with actual value in the middle
point
* in case difference between prediction and actual value is higher than
some predetermined threshold, algorithm stops with completion code -7;
Rep.VarIdx is set to index of the parameter with incorrect derivative.
* after verification is over, algorithm proceeds to the actual optimization.
NOTE 1: verification needs N*K (points count * parameters count) gradient
evaluations. It is very costly and you should use it only for low
dimensional problems, when you want to be sure that you've
correctly calculated analytic derivatives. You should not use it
in the production code (unless you want to check derivatives
provided by some third party).
NOTE 2: you should carefully choose TestStep. Value which is too large
(so large that function behaviour is significantly non-cubic) will
lead to false alarms. You may use different step for different
parameters by means of setting scale with LSFitSetScale().
NOTE 3: this function may lead to false positives. In case it reports that
I-th derivative was calculated incorrectly, you may decrease test
step and try one more time - maybe your function changes too
sharply and your step is too large for such rapidly chanding
function.
NOTE 4: this function works only for optimizers created with LSFitCreateWFG()
or LSFitCreateFG() constructors.
INPUT PARAMETERS:
State - structure used to store algorithm state
TestStep - verification step:
* TestStep=0 turns verification off
* TestStep>0 activates verification
-- ALGLIB --
Copyright 15.06.2012 by Bochkanov Sergey
*************************************************************************/
void lsfitsetgradientcheck(lsfitstate* state,
double teststep,
ae_state *_state)
{
ae_assert(ae_isfinite(teststep, _state), "LSFitSetGradientCheck: TestStep contains NaN or Infinite", _state);
ae_assert(ae_fp_greater_eq(teststep,(double)(0)), "LSFitSetGradientCheck: invalid argument TestStep(TestStep<0)", _state);
state->teststep = teststep;
}
/*************************************************************************
This function analyzes section of curve for processing by RDP algorithm:
given set of points X,Y with indexes [I0,I1] it returns point with
worst deviation from linear model (non-parametric version which sees curve
as Y(x)).
Input parameters:
X, Y - SORTED arrays.
I0,I1 - interval (boundaries included) to process
Eps - desired precision
OUTPUT PARAMETERS:
WorstIdx - index of worst point
WorstError - error at worst point
NOTE: this function guarantees that it returns exactly zero for a section
with less than 3 points.
-- ALGLIB PROJECT --
Copyright 02.10.2014 by Bochkanov Sergey
*************************************************************************/
static void lsfit_rdpanalyzesection(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t i0,
ae_int_t i1,
ae_int_t* worstidx,
double* worsterror,
ae_state *_state)
{
ae_int_t i;
double xleft;
double xright;
double vx;
double ve;
double a;
double b;
*worstidx = 0;
*worsterror = 0;
xleft = x->ptr.p_double[i0];
xright = x->ptr.p_double[i1];
if( i1-i0+1<3||ae_fp_eq(xright,xleft) )
{
*worstidx = i0;
*worsterror = 0.0;
return;
}
a = (y->ptr.p_double[i1]-y->ptr.p_double[i0])/(xright-xleft);
b = (y->ptr.p_double[i0]*xright-y->ptr.p_double[i1]*xleft)/(xright-xleft);
*worstidx = -1;
*worsterror = (double)(0);
for(i=i0+1; i<=i1-1; i++)
{
vx = x->ptr.p_double[i];
ve = ae_fabs(a*vx+b-y->ptr.p_double[i], _state);
if( (ae_fp_greater(vx,xleft)&&ae_fp_less(vx,xright))&&ae_fp_greater(ve,*worsterror) )
{
*worsterror = ve;
*worstidx = i;
}
}
}
/*************************************************************************
Recursive splitting of interval [I0,I1] (right boundary included) with RDP
algorithm (non-parametric version which sees curve as Y(x)).
Input parameters:
X, Y - SORTED arrays.
I0,I1 - interval (boundaries included) to process
Eps - desired precision
XOut,YOut - preallocated output arrays large enough to store result;
XOut[0..1], YOut[0..1] contain first and last points of
curve
NOut - must contain 2 on input
OUTPUT PARAMETERS:
XOut, YOut - curve generated by RDP algorithm, UNSORTED
NOut - number of points in curve
-- ALGLIB PROJECT --
Copyright 02.10.2014 by Bochkanov Sergey
*************************************************************************/
static void lsfit_rdprecursive(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t i0,
ae_int_t i1,
double eps,
/* Real */ ae_vector* xout,
/* Real */ ae_vector* yout,
ae_int_t* nout,
ae_state *_state)
{
ae_int_t worstidx;
double worsterror;
ae_assert(ae_fp_greater(eps,(double)(0)), "RDPRecursive: internal error, Eps<0", _state);
lsfit_rdpanalyzesection(x, y, i0, i1, &worstidx, &worsterror, _state);
if( ae_fp_less_eq(worsterror,eps) )
{
return;
}
xout->ptr.p_double[*nout] = x->ptr.p_double[worstidx];
yout->ptr.p_double[*nout] = y->ptr.p_double[worstidx];
*nout = *nout+1;
if( worstidx-i0<i1-worstidx )
{
lsfit_rdprecursive(x, y, i0, worstidx, eps, xout, yout, nout, _state);
lsfit_rdprecursive(x, y, worstidx, i1, eps, xout, yout, nout, _state);
}
else
{
lsfit_rdprecursive(x, y, worstidx, i1, eps, xout, yout, nout, _state);
lsfit_rdprecursive(x, y, i0, worstidx, eps, xout, yout, nout, _state);
}
}
/*************************************************************************
Internal 4PL/5PL fitting function.
Accepts X, Y and already initialized and prepared MinLMState structure.
On input P1 contains initial guess, on output it contains solution. FLast
stores function value at P1.
*************************************************************************/
static void lsfit_logisticfitinternal(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_bool is4pl,
double lambdav,
minlmstate* state,
minlmreport* replm,
/* Real */ ae_vector* p1,
double* flast,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
double ta;
double tb;
double tc;
double td;
double tg;
double vp0;
double vp1;
*flast = 0;
minlmrestartfrom(state, p1, _state);
while(minlmiteration(state, _state))
{
ta = state->x.ptr.p_double[0];
tb = state->x.ptr.p_double[1];
tc = state->x.ptr.p_double[2];
td = state->x.ptr.p_double[3];
tg = state->x.ptr.p_double[4];
if( state->xupdated )
{
/*
* Save best function value obtained so far.
*/
*flast = state->f;
continue;
}
if( state->needfi||state->needfij )
{
/*
* Function vector and Jacobian
*/
for(i=0; i<=n-1; i++)
{
ae_assert(ae_fp_greater_eq(x->ptr.p_double[i],(double)(0)), "LogisticFitInternal: integrity error", _state);
/*
* Handle zero X
*/
if( ae_fp_eq(x->ptr.p_double[i],(double)(0)) )
{
if( ae_fp_greater_eq(tb,(double)(0)) )
{
/*
* Positive or zero TB, limit X^TB subject to X->+0 is equal to zero.
*/
state->fi.ptr.p_double[i] = ta-y->ptr.p_double[i];
if( state->needfij )
{
state->j.ptr.pp_double[i][0] = (double)(1);
state->j.ptr.pp_double[i][1] = (double)(0);
state->j.ptr.pp_double[i][2] = (double)(0);
state->j.ptr.pp_double[i][3] = (double)(0);
state->j.ptr.pp_double[i][4] = (double)(0);
}
}
else
{
/*
* Negative TB, limit X^TB subject to X->+0 is equal to +INF.
*/
state->fi.ptr.p_double[i] = td-y->ptr.p_double[i];
if( state->needfij )
{
state->j.ptr.pp_double[i][0] = (double)(0);
state->j.ptr.pp_double[i][1] = (double)(0);
state->j.ptr.pp_double[i][2] = (double)(0);
state->j.ptr.pp_double[i][3] = (double)(1);
state->j.ptr.pp_double[i][4] = (double)(0);
}
}
continue;
}
/*
* Positive X.
* Prepare VP0/VP1, it may become infinite or nearly overflow in some rare cases,
* handle these cases
*/
vp0 = ae_pow(x->ptr.p_double[i]/tc, tb, _state);
if( is4pl )
{
vp1 = 1+vp0;
}
else
{
vp1 = ae_pow(1+vp0, tg, _state);
}
if( (!ae_isfinite(vp1, _state)||ae_fp_greater(vp0,1.0E50))||ae_fp_greater(vp1,1.0E50) )
{
/*
* VP0/VP1 are not finite, assume that it is +INF or -INF
*/
state->fi.ptr.p_double[i] = td-y->ptr.p_double[i];
if( state->needfij )
{
state->j.ptr.pp_double[i][0] = (double)(0);
state->j.ptr.pp_double[i][1] = (double)(0);
state->j.ptr.pp_double[i][2] = (double)(0);
state->j.ptr.pp_double[i][3] = (double)(1);
state->j.ptr.pp_double[i][4] = (double)(0);
}
continue;
}
/*
* VP0/VP1 are finite, normal processing
*/
if( is4pl )
{
state->fi.ptr.p_double[i] = td+(ta-td)/vp1-y->ptr.p_double[i];
if( state->needfij )
{
state->j.ptr.pp_double[i][0] = 1/vp1;
state->j.ptr.pp_double[i][1] = -(ta-td)*vp0*ae_log(x->ptr.p_double[i]/tc, _state)/ae_sqr(vp1, _state);
state->j.ptr.pp_double[i][2] = (ta-td)*(tb/tc)*vp0/ae_sqr(vp1, _state);
state->j.ptr.pp_double[i][3] = 1-1/vp1;
state->j.ptr.pp_double[i][4] = (double)(0);
}
}
else
{
state->fi.ptr.p_double[i] = td+(ta-td)/vp1-y->ptr.p_double[i];
if( state->needfij )
{
state->j.ptr.pp_double[i][0] = 1/vp1;
state->j.ptr.pp_double[i][1] = (ta-td)*(-tg)*ae_pow(1+vp0, -tg-1, _state)*vp0*ae_log(x->ptr.p_double[i]/tc, _state);
state->j.ptr.pp_double[i][2] = (ta-td)*(-tg)*ae_pow(1+vp0, -tg-1, _state)*vp0*(-tb/tc);
state->j.ptr.pp_double[i][3] = 1-1/vp1;
state->j.ptr.pp_double[i][4] = -(ta-td)/vp1*ae_log(1+vp0, _state);
}
}
}
/*
* Add regularizer
*/
for(i=0; i<=4; i++)
{
state->fi.ptr.p_double[n+i] = lambdav*state->x.ptr.p_double[i];
if( state->needfij )
{
for(j=0; j<=4; j++)
{
state->j.ptr.pp_double[n+i][j] = 0.0;
}
state->j.ptr.pp_double[n+i][i] = lambdav;
}
}
/*
* Done
*/
continue;
}
ae_assert(ae_false, "LogisticFitX: internal error", _state);
}
minlmresultsbuf(state, p1, replm, _state);
ae_assert(replm->terminationtype>0, "LogisticFitX: internal error", _state);
}
/*************************************************************************
Calculate errors for 4PL/5PL fit.
Leaves other fields of Rep unchanged, so caller should properly initialize
it with ClearRep() call.
-- ALGLIB PROJECT --
Copyright 28.04.2017 by Bochkanov Sergey
*************************************************************************/
static void lsfit_logisticfit45errors(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
double a,
double b,
double c,
double d,
double g,
lsfitreport* rep,
ae_state *_state)
{
ae_int_t i;
ae_int_t k;
double v;
double rss;
double tss;
double meany;
/*
* Calculate errors
*/
rep->rmserror = (double)(0);
rep->avgerror = (double)(0);
rep->avgrelerror = (double)(0);
rep->maxerror = (double)(0);
k = 0;
rss = 0.0;
tss = 0.0;
meany = 0.0;
for(i=0; i<=n-1; i++)
{
meany = meany+y->ptr.p_double[i];
}
meany = meany/n;
for(i=0; i<=n-1; i++)
{
/*
* Calculate residual from regression
*/
if( ae_fp_greater(x->ptr.p_double[i],(double)(0)) )
{
v = d+(a-d)/ae_pow(1.0+ae_pow(x->ptr.p_double[i]/c, b, _state), g, _state)-y->ptr.p_double[i];
}
else
{
if( ae_fp_greater_eq(b,(double)(0)) )
{
v = a-y->ptr.p_double[i];
}
else
{
v = d-y->ptr.p_double[i];
}
}
/*
* Update RSS (residual sum of squares) and TSS (total sum of squares)
* which are used to calculate coefficient of determination.
*
* NOTE: we use formula R2 = 1-RSS/TSS because it has nice property of
* being equal to 0.0 if and only if model perfectly fits data.
*
* When we fit nonlinear models, there are exist multiple ways of
* determining R2, each of them giving different results. Formula
* above is the most intuitive one.
*/
rss = rss+v*v;
tss = tss+ae_sqr(y->ptr.p_double[i]-meany, _state);
/*
* Update errors
*/
rep->rmserror = rep->rmserror+ae_sqr(v, _state);
rep->avgerror = rep->avgerror+ae_fabs(v, _state);
if( ae_fp_neq(y->ptr.p_double[i],(double)(0)) )
{
rep->avgrelerror = rep->avgrelerror+ae_fabs(v/y->ptr.p_double[i], _state);
k = k+1;
}
rep->maxerror = ae_maxreal(rep->maxerror, ae_fabs(v, _state), _state);
}
rep->rmserror = ae_sqrt(rep->rmserror/n, _state);
rep->avgerror = rep->avgerror/n;
if( k>0 )
{
rep->avgrelerror = rep->avgrelerror/k;
}
rep->r2 = 1.0-rss/tss;
}
/*************************************************************************
Internal spline fitting subroutine
-- ALGLIB PROJECT --
Copyright 08.09.2009 by Bochkanov Sergey
*************************************************************************/
static void lsfit_spline1dfitinternal(ae_int_t st,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
ae_int_t n,
/* Real */ ae_vector* xc,
/* Real */ ae_vector* yc,
/* Integer */ ae_vector* dc,
ae_int_t k,
ae_int_t m,
ae_int_t* info,
spline1dinterpolant* s,
spline1dfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_vector _w;
ae_vector _xc;
ae_vector _yc;
ae_matrix fmatrix;
ae_matrix cmatrix;
ae_vector y2;
ae_vector w2;
ae_vector sx;
ae_vector sy;
ae_vector sd;
ae_vector tmp;
ae_vector xoriginal;
ae_vector yoriginal;
lsfitreport lrep;
double v0;
double v1;
double v2;
double mx;
spline1dinterpolant s2;
ae_int_t i;
ae_int_t j;
ae_int_t relcnt;
double xa;
double xb;
double sa;
double sb;
double bl;
double br;
double decay;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&_w, 0, sizeof(_w));
memset(&_xc, 0, sizeof(_xc));
memset(&_yc, 0, sizeof(_yc));
memset(&fmatrix, 0, sizeof(fmatrix));
memset(&cmatrix, 0, sizeof(cmatrix));
memset(&y2, 0, sizeof(y2));
memset(&w2, 0, sizeof(w2));
memset(&sx, 0, sizeof(sx));
memset(&sy, 0, sizeof(sy));
memset(&sd, 0, sizeof(sd));
memset(&tmp, 0, sizeof(tmp));
memset(&xoriginal, 0, sizeof(xoriginal));
memset(&yoriginal, 0, sizeof(yoriginal));
memset(&lrep, 0, sizeof(lrep));
memset(&s2, 0, sizeof(s2));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
ae_vector_init_copy(&_w, w, _state, ae_true);
w = &_w;
ae_vector_init_copy(&_xc, xc, _state, ae_true);
xc = &_xc;
ae_vector_init_copy(&_yc, yc, _state, ae_true);
yc = &_yc;
*info = 0;
_spline1dinterpolant_clear(s);
_spline1dfitreport_clear(rep);
ae_matrix_init(&fmatrix, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&cmatrix, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&y2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&w2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sy, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sd, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp, 0, DT_REAL, _state, ae_true);
ae_vector_init(&xoriginal, 0, DT_REAL, _state, ae_true);
ae_vector_init(&yoriginal, 0, DT_REAL, _state, ae_true);
_lsfitreport_init(&lrep, _state, ae_true);
_spline1dinterpolant_init(&s2, _state, ae_true);
ae_assert(st==0||st==1, "Spline1DFit: internal error!", _state);
if( st==0&&m<4 )
{
*info = -1;
ae_frame_leave(_state);
return;
}
if( st==1&&m<4 )
{
*info = -1;
ae_frame_leave(_state);
return;
}
if( (n<1||k<0)||k>=m )
{
*info = -1;
ae_frame_leave(_state);
return;
}
for(i=0; i<=k-1; i++)
{
*info = 0;
if( dc->ptr.p_int[i]<0 )
{
*info = -1;
}
if( dc->ptr.p_int[i]>1 )
{
*info = -1;
}
if( *info<0 )
{
ae_frame_leave(_state);
return;
}
}
if( st==1&&m%2!=0 )
{
/*
* Hermite fitter must have even number of basis functions
*/
*info = -2;
ae_frame_leave(_state);
return;
}
/*
* weight decay for correct handling of task which becomes
* degenerate after constraints are applied
*/
decay = 10000*ae_machineepsilon;
/*
* Scale X, Y, XC, YC
*/
lsfitscalexy(x, y, w, n, xc, yc, dc, k, &xa, &xb, &sa, &sb, &xoriginal, &yoriginal, _state);
/*
* allocate space, initialize:
* * SX - grid for basis functions
* * SY - values of basis functions at grid points
* * FMatrix- values of basis functions at X[]
* * CMatrix- values (derivatives) of basis functions at XC[]
*/
ae_vector_set_length(&y2, n+m, _state);
ae_vector_set_length(&w2, n+m, _state);
ae_matrix_set_length(&fmatrix, n+m, m, _state);
if( k>0 )
{
ae_matrix_set_length(&cmatrix, k, m+1, _state);
}
if( st==0 )
{
/*
* allocate space for cubic spline
*/
ae_vector_set_length(&sx, m-2, _state);
ae_vector_set_length(&sy, m-2, _state);
for(j=0; j<=m-2-1; j++)
{
sx.ptr.p_double[j] = (double)(2*j)/(double)(m-2-1)-1;
}
}
if( st==1 )
{
/*
* allocate space for Hermite spline
*/
ae_vector_set_length(&sx, m/2, _state);
ae_vector_set_length(&sy, m/2, _state);
ae_vector_set_length(&sd, m/2, _state);
for(j=0; j<=m/2-1; j++)
{
sx.ptr.p_double[j] = (double)(2*j)/(double)(m/2-1)-1;
}
}
/*
* Prepare design and constraints matrices:
* * fill constraints matrix
* * fill first N rows of design matrix with values
* * fill next M rows of design matrix with regularizing term
* * append M zeros to Y
* * append M elements, mean(abs(W)) each, to W
*/
for(j=0; j<=m-1; j++)
{
/*
* prepare Jth basis function
*/
if( st==0 )
{
/*
* cubic spline basis
*/
for(i=0; i<=m-2-1; i++)
{
sy.ptr.p_double[i] = (double)(0);
}
bl = (double)(0);
br = (double)(0);
if( j<m-2 )
{
sy.ptr.p_double[j] = (double)(1);
}
if( j==m-2 )
{
bl = (double)(1);
}
if( j==m-1 )
{
br = (double)(1);
}
spline1dbuildcubic(&sx, &sy, m-2, 1, bl, 1, br, &s2, _state);
}
if( st==1 )
{
/*
* Hermite basis
*/
for(i=0; i<=m/2-1; i++)
{
sy.ptr.p_double[i] = (double)(0);
sd.ptr.p_double[i] = (double)(0);
}
if( j%2==0 )
{
sy.ptr.p_double[j/2] = (double)(1);
}
else
{
sd.ptr.p_double[j/2] = (double)(1);
}
spline1dbuildhermite(&sx, &sy, &sd, m/2, &s2, _state);
}
/*
* values at X[], XC[]
*/
for(i=0; i<=n-1; i++)
{
fmatrix.ptr.pp_double[i][j] = spline1dcalc(&s2, x->ptr.p_double[i], _state);
}
for(i=0; i<=k-1; i++)
{
ae_assert(dc->ptr.p_int[i]>=0&&dc->ptr.p_int[i]<=2, "Spline1DFit: internal error!", _state);
spline1ddiff(&s2, xc->ptr.p_double[i], &v0, &v1, &v2, _state);
if( dc->ptr.p_int[i]==0 )
{
cmatrix.ptr.pp_double[i][j] = v0;
}
if( dc->ptr.p_int[i]==1 )
{
cmatrix.ptr.pp_double[i][j] = v1;
}
if( dc->ptr.p_int[i]==2 )
{
cmatrix.ptr.pp_double[i][j] = v2;
}
}
}
for(i=0; i<=k-1; i++)
{
cmatrix.ptr.pp_double[i][m] = yc->ptr.p_double[i];
}
for(i=0; i<=m-1; i++)
{
for(j=0; j<=m-1; j++)
{
if( i==j )
{
fmatrix.ptr.pp_double[n+i][j] = decay;
}
else
{
fmatrix.ptr.pp_double[n+i][j] = (double)(0);
}
}
}
ae_vector_set_length(&y2, n+m, _state);
ae_vector_set_length(&w2, n+m, _state);
ae_v_move(&y2.ptr.p_double[0], 1, &y->ptr.p_double[0], 1, ae_v_len(0,n-1));
ae_v_move(&w2.ptr.p_double[0], 1, &w->ptr.p_double[0], 1, ae_v_len(0,n-1));
mx = (double)(0);
for(i=0; i<=n-1; i++)
{
mx = mx+ae_fabs(w->ptr.p_double[i], _state);
}
mx = mx/n;
for(i=0; i<=m-1; i++)
{
y2.ptr.p_double[n+i] = (double)(0);
w2.ptr.p_double[n+i] = mx;
}
/*
* Solve constrained task
*/
if( k>0 )
{
/*
* solve using regularization
*/
lsfitlinearwc(&y2, &w2, &fmatrix, &cmatrix, n+m, m, k, info, &tmp, &lrep, _state);
}
else
{
/*
* no constraints, no regularization needed
*/
lsfitlinearwc(y, w, &fmatrix, &cmatrix, n, m, k, info, &tmp, &lrep, _state);
}
if( *info<0 )
{
ae_frame_leave(_state);
return;
}
/*
* Generate spline and scale it
*/
if( st==0 )
{
/*
* cubic spline basis
*/
ae_v_move(&sy.ptr.p_double[0], 1, &tmp.ptr.p_double[0], 1, ae_v_len(0,m-2-1));
spline1dbuildcubic(&sx, &sy, m-2, 1, tmp.ptr.p_double[m-2], 1, tmp.ptr.p_double[m-1], s, _state);
}
if( st==1 )
{
/*
* Hermite basis
*/
for(i=0; i<=m/2-1; i++)
{
sy.ptr.p_double[i] = tmp.ptr.p_double[2*i];
sd.ptr.p_double[i] = tmp.ptr.p_double[2*i+1];
}
spline1dbuildhermite(&sx, &sy, &sd, m/2, s, _state);
}
spline1dlintransx(s, 2/(xb-xa), -(xa+xb)/(xb-xa), _state);
spline1dlintransy(s, sb-sa, sa, _state);
/*
* Scale absolute errors obtained from LSFitLinearW.
* Relative error should be calculated separately
* (because of shifting/scaling of the task)
*/
rep->taskrcond = lrep.taskrcond;
rep->rmserror = lrep.rmserror*(sb-sa);
rep->avgerror = lrep.avgerror*(sb-sa);
rep->maxerror = lrep.maxerror*(sb-sa);
rep->avgrelerror = (double)(0);
relcnt = 0;
for(i=0; i<=n-1; i++)
{
if( ae_fp_neq(yoriginal.ptr.p_double[i],(double)(0)) )
{
rep->avgrelerror = rep->avgrelerror+ae_fabs(spline1dcalc(s, xoriginal.ptr.p_double[i], _state)-yoriginal.ptr.p_double[i], _state)/ae_fabs(yoriginal.ptr.p_double[i], _state);
relcnt = relcnt+1;
}
}
if( relcnt!=0 )
{
rep->avgrelerror = rep->avgrelerror/relcnt;
}
ae_frame_leave(_state);
}
/*************************************************************************
Internal fitting subroutine
*************************************************************************/
static void lsfit_lsfitlinearinternal(/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
/* Real */ ae_matrix* fmatrix,
ae_int_t n,
ae_int_t m,
ae_int_t* info,
/* Real */ ae_vector* c,
lsfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
double threshold;
ae_matrix ft;
ae_matrix q;
ae_matrix l;
ae_matrix r;
ae_vector b;
ae_vector wmod;
ae_vector tau;
ae_vector nzeros;
ae_vector s;
ae_int_t i;
ae_int_t j;
double v;
ae_vector sv;
ae_matrix u;
ae_matrix vt;
ae_vector tmp;
ae_vector utb;
ae_vector sutb;
ae_int_t relcnt;
ae_frame_make(_state, &_frame_block);
memset(&ft, 0, sizeof(ft));
memset(&q, 0, sizeof(q));
memset(&l, 0, sizeof(l));
memset(&r, 0, sizeof(r));
memset(&b, 0, sizeof(b));
memset(&wmod, 0, sizeof(wmod));
memset(&tau, 0, sizeof(tau));
memset(&nzeros, 0, sizeof(nzeros));
memset(&s, 0, sizeof(s));
memset(&sv, 0, sizeof(sv));
memset(&u, 0, sizeof(u));
memset(&vt, 0, sizeof(vt));
memset(&tmp, 0, sizeof(tmp));
memset(&utb, 0, sizeof(utb));
memset(&sutb, 0, sizeof(sutb));
*info = 0;
ae_vector_clear(c);
_lsfitreport_clear(rep);
ae_matrix_init(&ft, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&q, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&l, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&r, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&b, 0, DT_REAL, _state, ae_true);
ae_vector_init(&wmod, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tau, 0, DT_REAL, _state, ae_true);
ae_vector_init(&nzeros, 0, DT_REAL, _state, ae_true);
ae_vector_init(&s, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sv, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&u, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&vt, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp, 0, DT_REAL, _state, ae_true);
ae_vector_init(&utb, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sutb, 0, DT_REAL, _state, ae_true);
lsfit_clearreport(rep, _state);
if( n<1||m<1 )
{
*info = -1;
ae_frame_leave(_state);
return;
}
*info = 1;
threshold = ae_sqrt(ae_machineepsilon, _state);
/*
* Degenerate case, needs special handling
*/
if( n<m )
{
/*
* Create design matrix.
*/
ae_matrix_set_length(&ft, n, m, _state);
ae_vector_set_length(&b, n, _state);
ae_vector_set_length(&wmod, n, _state);
for(j=0; j<=n-1; j++)
{
v = w->ptr.p_double[j];
ae_v_moved(&ft.ptr.pp_double[j][0], 1, &fmatrix->ptr.pp_double[j][0], 1, ae_v_len(0,m-1), v);
b.ptr.p_double[j] = w->ptr.p_double[j]*y->ptr.p_double[j];
wmod.ptr.p_double[j] = (double)(1);
}
/*
* LQ decomposition and reduction to M=N
*/
ae_vector_set_length(c, m, _state);
for(i=0; i<=m-1; i++)
{
c->ptr.p_double[i] = (double)(0);
}
rep->taskrcond = (double)(0);
rmatrixlq(&ft, n, m, &tau, _state);
rmatrixlqunpackq(&ft, n, m, &tau, n, &q, _state);
rmatrixlqunpackl(&ft, n, m, &l, _state);
lsfit_lsfitlinearinternal(&b, &wmod, &l, n, n, info, &tmp, rep, _state);
if( *info<=0 )
{
ae_frame_leave(_state);
return;
}
for(i=0; i<=n-1; i++)
{
v = tmp.ptr.p_double[i];
ae_v_addd(&c->ptr.p_double[0], 1, &q.ptr.pp_double[i][0], 1, ae_v_len(0,m-1), v);
}
ae_frame_leave(_state);
return;
}
/*
* N>=M. Generate design matrix and reduce to N=M using
* QR decomposition.
*/
ae_matrix_set_length(&ft, n, m, _state);
ae_vector_set_length(&b, n, _state);
for(j=0; j<=n-1; j++)
{
v = w->ptr.p_double[j];
ae_v_moved(&ft.ptr.pp_double[j][0], 1, &fmatrix->ptr.pp_double[j][0], 1, ae_v_len(0,m-1), v);
b.ptr.p_double[j] = w->ptr.p_double[j]*y->ptr.p_double[j];
}
rmatrixqr(&ft, n, m, &tau, _state);
rmatrixqrunpackq(&ft, n, m, &tau, m, &q, _state);
rmatrixqrunpackr(&ft, n, m, &r, _state);
ae_vector_set_length(&tmp, m, _state);
for(i=0; i<=m-1; i++)
{
tmp.ptr.p_double[i] = (double)(0);
}
for(i=0; i<=n-1; i++)
{
v = b.ptr.p_double[i];
ae_v_addd(&tmp.ptr.p_double[0], 1, &q.ptr.pp_double[i][0], 1, ae_v_len(0,m-1), v);
}
ae_vector_set_length(&b, m, _state);
ae_v_move(&b.ptr.p_double[0], 1, &tmp.ptr.p_double[0], 1, ae_v_len(0,m-1));
/*
* R contains reduced MxM design upper triangular matrix,
* B contains reduced Mx1 right part.
*
* Determine system condition number and decide
* should we use triangular solver (faster) or
* SVD-based solver (more stable).
*
* We can use LU-based RCond estimator for this task.
*/
rep->taskrcond = rmatrixlurcondinf(&r, m, _state);
if( ae_fp_greater(rep->taskrcond,threshold) )
{
/*
* use QR-based solver
*/
ae_vector_set_length(c, m, _state);
c->ptr.p_double[m-1] = b.ptr.p_double[m-1]/r.ptr.pp_double[m-1][m-1];
for(i=m-2; i>=0; i--)
{
v = ae_v_dotproduct(&r.ptr.pp_double[i][i+1], 1, &c->ptr.p_double[i+1], 1, ae_v_len(i+1,m-1));
c->ptr.p_double[i] = (b.ptr.p_double[i]-v)/r.ptr.pp_double[i][i];
}
}
else
{
/*
* use SVD-based solver
*/
if( !rmatrixsvd(&r, m, m, 1, 1, 2, &sv, &u, &vt, _state) )
{
*info = -4;
ae_frame_leave(_state);
return;
}
ae_vector_set_length(&utb, m, _state);
ae_vector_set_length(&sutb, m, _state);
for(i=0; i<=m-1; i++)
{
utb.ptr.p_double[i] = (double)(0);
}
for(i=0; i<=m-1; i++)
{
v = b.ptr.p_double[i];
ae_v_addd(&utb.ptr.p_double[0], 1, &u.ptr.pp_double[i][0], 1, ae_v_len(0,m-1), v);
}
if( ae_fp_greater(sv.ptr.p_double[0],(double)(0)) )
{
rep->taskrcond = sv.ptr.p_double[m-1]/sv.ptr.p_double[0];
for(i=0; i<=m-1; i++)
{
if( ae_fp_greater(sv.ptr.p_double[i],threshold*sv.ptr.p_double[0]) )
{
sutb.ptr.p_double[i] = utb.ptr.p_double[i]/sv.ptr.p_double[i];
}
else
{
sutb.ptr.p_double[i] = (double)(0);
}
}
}
else
{
rep->taskrcond = (double)(0);
for(i=0; i<=m-1; i++)
{
sutb.ptr.p_double[i] = (double)(0);
}
}
ae_vector_set_length(c, m, _state);
for(i=0; i<=m-1; i++)
{
c->ptr.p_double[i] = (double)(0);
}
for(i=0; i<=m-1; i++)
{
v = sutb.ptr.p_double[i];
ae_v_addd(&c->ptr.p_double[0], 1, &vt.ptr.pp_double[i][0], 1, ae_v_len(0,m-1), v);
}
}
/*
* calculate errors
*/
rep->rmserror = (double)(0);
rep->avgerror = (double)(0);
rep->avgrelerror = (double)(0);
rep->maxerror = (double)(0);
relcnt = 0;
for(i=0; i<=n-1; i++)
{
v = ae_v_dotproduct(&fmatrix->ptr.pp_double[i][0], 1, &c->ptr.p_double[0], 1, ae_v_len(0,m-1));
rep->rmserror = rep->rmserror+ae_sqr(v-y->ptr.p_double[i], _state);
rep->avgerror = rep->avgerror+ae_fabs(v-y->ptr.p_double[i], _state);
if( ae_fp_neq(y->ptr.p_double[i],(double)(0)) )
{
rep->avgrelerror = rep->avgrelerror+ae_fabs(v-y->ptr.p_double[i], _state)/ae_fabs(y->ptr.p_double[i], _state);
relcnt = relcnt+1;
}
rep->maxerror = ae_maxreal(rep->maxerror, ae_fabs(v-y->ptr.p_double[i], _state), _state);
}
rep->rmserror = ae_sqrt(rep->rmserror/n, _state);
rep->avgerror = rep->avgerror/n;
if( relcnt!=0 )
{
rep->avgrelerror = rep->avgrelerror/relcnt;
}
ae_vector_set_length(&nzeros, n, _state);
ae_vector_set_length(&s, m, _state);
for(i=0; i<=m-1; i++)
{
s.ptr.p_double[i] = (double)(0);
}
for(i=0; i<=n-1; i++)
{
for(j=0; j<=m-1; j++)
{
s.ptr.p_double[j] = s.ptr.p_double[j]+ae_sqr(fmatrix->ptr.pp_double[i][j], _state);
}
nzeros.ptr.p_double[i] = (double)(0);
}
for(i=0; i<=m-1; i++)
{
if( ae_fp_neq(s.ptr.p_double[i],(double)(0)) )
{
s.ptr.p_double[i] = ae_sqrt(1/s.ptr.p_double[i], _state);
}
else
{
s.ptr.p_double[i] = (double)(1);
}
}
lsfit_estimateerrors(fmatrix, &nzeros, y, w, c, &s, n, m, rep, &r, 1, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Internal subroutine
*************************************************************************/
static void lsfit_lsfitclearrequestfields(lsfitstate* state,
ae_state *_state)
{
state->needf = ae_false;
state->needfg = ae_false;
state->needfgh = ae_false;
state->xupdated = ae_false;
}
/*************************************************************************
Internal subroutine, calculates barycentric basis functions.
Used for efficient simultaneous calculation of N basis functions.
-- ALGLIB --
Copyright 17.08.2009 by Bochkanov Sergey
*************************************************************************/
static void lsfit_barycentriccalcbasis(barycentricinterpolant* b,
double t,
/* Real */ ae_vector* y,
ae_state *_state)
{
double s2;
double s;
double v;
ae_int_t i;
ae_int_t j;
/*
* special case: N=1
*/
if( b->n==1 )
{
y->ptr.p_double[0] = (double)(1);
return;
}
/*
* Here we assume that task is normalized, i.e.:
* 1. abs(Y[i])<=1
* 2. abs(W[i])<=1
* 3. X[] is ordered
*
* First, we decide: should we use "safe" formula (guarded
* against overflow) or fast one?
*/
s = ae_fabs(t-b->x.ptr.p_double[0], _state);
for(i=0; i<=b->n-1; i++)
{
v = b->x.ptr.p_double[i];
if( ae_fp_eq(v,t) )
{
for(j=0; j<=b->n-1; j++)
{
y->ptr.p_double[j] = (double)(0);
}
y->ptr.p_double[i] = (double)(1);
return;
}
v = ae_fabs(t-v, _state);
if( ae_fp_less(v,s) )
{
s = v;
}
}
s2 = (double)(0);
for(i=0; i<=b->n-1; i++)
{
v = s/(t-b->x.ptr.p_double[i]);
v = v*b->w.ptr.p_double[i];
y->ptr.p_double[i] = v;
s2 = s2+v;
}
v = 1/s2;
ae_v_muld(&y->ptr.p_double[0], 1, ae_v_len(0,b->n-1), v);
}
/*************************************************************************
This is internal function for Chebyshev fitting.
It assumes that input data are normalized:
* X/XC belong to [-1,+1],
* mean(Y)=0, stddev(Y)=1.
It does not checks inputs for errors.
This function is used to fit general (shifted) Chebyshev models, power
basis models or barycentric models.
INPUT PARAMETERS:
X - points, array[0..N-1].
Y - function values, array[0..N-1].
W - weights, array[0..N-1]
N - number of points, N>0.
XC - points where polynomial values/derivatives are constrained,
array[0..K-1].
YC - values of constraints, array[0..K-1]
DC - array[0..K-1], types of constraints:
* DC[i]=0 means that P(XC[i])=YC[i]
* DC[i]=1 means that P'(XC[i])=YC[i]
K - number of constraints, 0<=K<M.
K=0 means no constraints (XC/YC/DC are not used in such cases)
M - number of basis functions (= polynomial_degree + 1), M>=1
OUTPUT PARAMETERS:
Info- same format as in LSFitLinearW() subroutine:
* Info>0 task is solved
* Info<=0 an error occured:
-4 means inconvergence of internal SVD
-3 means inconsistent constraints
C - interpolant in Chebyshev form; [-1,+1] is used as base interval
Rep - report, same format as in LSFitLinearW() subroutine.
Following fields are set:
* RMSError rms error on the (X,Y).
* AvgError average error on the (X,Y).
* AvgRelError average relative error on the non-zero Y
* MaxError maximum error
NON-WEIGHTED ERRORS ARE CALCULATED
IMPORTANT:
this subroitine doesn't calculate task's condition number for K<>0.
-- ALGLIB PROJECT --
Copyright 10.12.2009 by Bochkanov Sergey
*************************************************************************/
static void lsfit_internalchebyshevfit(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
ae_int_t n,
/* Real */ ae_vector* xc,
/* Real */ ae_vector* yc,
/* Integer */ ae_vector* dc,
ae_int_t k,
ae_int_t m,
ae_int_t* info,
/* Real */ ae_vector* c,
lsfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _xc;
ae_vector _yc;
ae_vector y2;
ae_vector w2;
ae_vector tmp;
ae_vector tmp2;
ae_vector tmpdiff;
ae_vector bx;
ae_vector by;
ae_vector bw;
ae_matrix fmatrix;
ae_matrix cmatrix;
ae_int_t i;
ae_int_t j;
double mx;
double decay;
ae_frame_make(_state, &_frame_block);
memset(&_xc, 0, sizeof(_xc));
memset(&_yc, 0, sizeof(_yc));
memset(&y2, 0, sizeof(y2));
memset(&w2, 0, sizeof(w2));
memset(&tmp, 0, sizeof(tmp));
memset(&tmp2, 0, sizeof(tmp2));
memset(&tmpdiff, 0, sizeof(tmpdiff));
memset(&bx, 0, sizeof(bx));
memset(&by, 0, sizeof(by));
memset(&bw, 0, sizeof(bw));
memset(&fmatrix, 0, sizeof(fmatrix));
memset(&cmatrix, 0, sizeof(cmatrix));
ae_vector_init_copy(&_xc, xc, _state, ae_true);
xc = &_xc;
ae_vector_init_copy(&_yc, yc, _state, ae_true);
yc = &_yc;
*info = 0;
ae_vector_clear(c);
_lsfitreport_clear(rep);
ae_vector_init(&y2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&w2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmpdiff, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&by, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bw, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&fmatrix, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&cmatrix, 0, 0, DT_REAL, _state, ae_true);
lsfit_clearreport(rep, _state);
/*
* weight decay for correct handling of task which becomes
* degenerate after constraints are applied
*/
decay = 10000*ae_machineepsilon;
/*
* allocate space, initialize/fill:
* * FMatrix- values of basis functions at X[]
* * CMatrix- values (derivatives) of basis functions at XC[]
* * fill constraints matrix
* * fill first N rows of design matrix with values
* * fill next M rows of design matrix with regularizing term
* * append M zeros to Y
* * append M elements, mean(abs(W)) each, to W
*/
ae_vector_set_length(&y2, n+m, _state);
ae_vector_set_length(&w2, n+m, _state);
ae_vector_set_length(&tmp, m, _state);
ae_vector_set_length(&tmpdiff, m, _state);
ae_matrix_set_length(&fmatrix, n+m, m, _state);
if( k>0 )
{
ae_matrix_set_length(&cmatrix, k, m+1, _state);
}
/*
* Fill design matrix, Y2, W2:
* * first N rows with basis functions for original points
* * next M rows with decay terms
*/
for(i=0; i<=n-1; i++)
{
/*
* prepare Ith row
* use Tmp for calculations to avoid multidimensional arrays overhead
*/
for(j=0; j<=m-1; j++)
{
if( j==0 )
{
tmp.ptr.p_double[j] = (double)(1);
}
else
{
if( j==1 )
{
tmp.ptr.p_double[j] = x->ptr.p_double[i];
}
else
{
tmp.ptr.p_double[j] = 2*x->ptr.p_double[i]*tmp.ptr.p_double[j-1]-tmp.ptr.p_double[j-2];
}
}
}
ae_v_move(&fmatrix.ptr.pp_double[i][0], 1, &tmp.ptr.p_double[0], 1, ae_v_len(0,m-1));
}
for(i=0; i<=m-1; i++)
{
for(j=0; j<=m-1; j++)
{
if( i==j )
{
fmatrix.ptr.pp_double[n+i][j] = decay;
}
else
{
fmatrix.ptr.pp_double[n+i][j] = (double)(0);
}
}
}
ae_v_move(&y2.ptr.p_double[0], 1, &y->ptr.p_double[0], 1, ae_v_len(0,n-1));
ae_v_move(&w2.ptr.p_double[0], 1, &w->ptr.p_double[0], 1, ae_v_len(0,n-1));
mx = (double)(0);
for(i=0; i<=n-1; i++)
{
mx = mx+ae_fabs(w->ptr.p_double[i], _state);
}
mx = mx/n;
for(i=0; i<=m-1; i++)
{
y2.ptr.p_double[n+i] = (double)(0);
w2.ptr.p_double[n+i] = mx;
}
/*
* fill constraints matrix
*/
for(i=0; i<=k-1; i++)
{
/*
* prepare Ith row
* use Tmp for basis function values,
* TmpDiff for basos function derivatives
*/
for(j=0; j<=m-1; j++)
{
if( j==0 )
{
tmp.ptr.p_double[j] = (double)(1);
tmpdiff.ptr.p_double[j] = (double)(0);
}
else
{
if( j==1 )
{
tmp.ptr.p_double[j] = xc->ptr.p_double[i];
tmpdiff.ptr.p_double[j] = (double)(1);
}
else
{
tmp.ptr.p_double[j] = 2*xc->ptr.p_double[i]*tmp.ptr.p_double[j-1]-tmp.ptr.p_double[j-2];
tmpdiff.ptr.p_double[j] = 2*(tmp.ptr.p_double[j-1]+xc->ptr.p_double[i]*tmpdiff.ptr.p_double[j-1])-tmpdiff.ptr.p_double[j-2];
}
}
}
if( dc->ptr.p_int[i]==0 )
{
ae_v_move(&cmatrix.ptr.pp_double[i][0], 1, &tmp.ptr.p_double[0], 1, ae_v_len(0,m-1));
}
if( dc->ptr.p_int[i]==1 )
{
ae_v_move(&cmatrix.ptr.pp_double[i][0], 1, &tmpdiff.ptr.p_double[0], 1, ae_v_len(0,m-1));
}
cmatrix.ptr.pp_double[i][m] = yc->ptr.p_double[i];
}
/*
* Solve constrained task
*/
if( k>0 )
{
/*
* solve using regularization
*/
lsfitlinearwc(&y2, &w2, &fmatrix, &cmatrix, n+m, m, k, info, c, rep, _state);
}
else
{
/*
* no constraints, no regularization needed
*/
lsfitlinearwc(y, w, &fmatrix, &cmatrix, n, m, 0, info, c, rep, _state);
}
if( *info<0 )
{
ae_frame_leave(_state);
return;
}
ae_frame_leave(_state);
}
/*************************************************************************
Internal Floater-Hormann fitting subroutine for fixed D
*************************************************************************/
static void lsfit_barycentricfitwcfixedd(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
ae_int_t n,
/* Real */ ae_vector* xc,
/* Real */ ae_vector* yc,
/* Integer */ ae_vector* dc,
ae_int_t k,
ae_int_t m,
ae_int_t d,
ae_int_t* info,
barycentricinterpolant* b,
barycentricfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_vector _w;
ae_vector _xc;
ae_vector _yc;
ae_matrix fmatrix;
ae_matrix cmatrix;
ae_vector y2;
ae_vector w2;
ae_vector sx;
ae_vector sy;
ae_vector sbf;
ae_vector xoriginal;
ae_vector yoriginal;
ae_vector tmp;
lsfitreport lrep;
double v0;
double v1;
double mx;
barycentricinterpolant b2;
ae_int_t i;
ae_int_t j;
ae_int_t relcnt;
double xa;
double xb;
double sa;
double sb;
double decay;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&_w, 0, sizeof(_w));
memset(&_xc, 0, sizeof(_xc));
memset(&_yc, 0, sizeof(_yc));
memset(&fmatrix, 0, sizeof(fmatrix));
memset(&cmatrix, 0, sizeof(cmatrix));
memset(&y2, 0, sizeof(y2));
memset(&w2, 0, sizeof(w2));
memset(&sx, 0, sizeof(sx));
memset(&sy, 0, sizeof(sy));
memset(&sbf, 0, sizeof(sbf));
memset(&xoriginal, 0, sizeof(xoriginal));
memset(&yoriginal, 0, sizeof(yoriginal));
memset(&tmp, 0, sizeof(tmp));
memset(&lrep, 0, sizeof(lrep));
memset(&b2, 0, sizeof(b2));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
ae_vector_init_copy(&_w, w, _state, ae_true);
w = &_w;
ae_vector_init_copy(&_xc, xc, _state, ae_true);
xc = &_xc;
ae_vector_init_copy(&_yc, yc, _state, ae_true);
yc = &_yc;
*info = 0;
_barycentricinterpolant_clear(b);
_barycentricfitreport_clear(rep);
ae_matrix_init(&fmatrix, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&cmatrix, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&y2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&w2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sy, 0, DT_REAL, _state, ae_true);
ae_vector_init(&sbf, 0, DT_REAL, _state, ae_true);
ae_vector_init(&xoriginal, 0, DT_REAL, _state, ae_true);
ae_vector_init(&yoriginal, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp, 0, DT_REAL, _state, ae_true);
_lsfitreport_init(&lrep, _state, ae_true);
_barycentricinterpolant_init(&b2, _state, ae_true);
if( ((n<1||m<2)||k<0)||k>=m )
{
*info = -1;
ae_frame_leave(_state);
return;
}
for(i=0; i<=k-1; i++)
{
*info = 0;
if( dc->ptr.p_int[i]<0 )
{
*info = -1;
}
if( dc->ptr.p_int[i]>1 )
{
*info = -1;
}
if( *info<0 )
{
ae_frame_leave(_state);
return;
}
}
/*
* weight decay for correct handling of task which becomes
* degenerate after constraints are applied
*/
decay = 10000*ae_machineepsilon;
/*
* Scale X, Y, XC, YC
*/
lsfitscalexy(x, y, w, n, xc, yc, dc, k, &xa, &xb, &sa, &sb, &xoriginal, &yoriginal, _state);
/*
* allocate space, initialize:
* * FMatrix- values of basis functions at X[]
* * CMatrix- values (derivatives) of basis functions at XC[]
*/
ae_vector_set_length(&y2, n+m, _state);
ae_vector_set_length(&w2, n+m, _state);
ae_matrix_set_length(&fmatrix, n+m, m, _state);
if( k>0 )
{
ae_matrix_set_length(&cmatrix, k, m+1, _state);
}
ae_vector_set_length(&y2, n+m, _state);
ae_vector_set_length(&w2, n+m, _state);
/*
* Prepare design and constraints matrices:
* * fill constraints matrix
* * fill first N rows of design matrix with values
* * fill next M rows of design matrix with regularizing term
* * append M zeros to Y
* * append M elements, mean(abs(W)) each, to W
*/
ae_vector_set_length(&sx, m, _state);
ae_vector_set_length(&sy, m, _state);
ae_vector_set_length(&sbf, m, _state);
for(j=0; j<=m-1; j++)
{
sx.ptr.p_double[j] = (double)(2*j)/(double)(m-1)-1;
}
for(i=0; i<=m-1; i++)
{
sy.ptr.p_double[i] = (double)(1);
}
barycentricbuildfloaterhormann(&sx, &sy, m, d, &b2, _state);
mx = (double)(0);
for(i=0; i<=n-1; i++)
{
lsfit_barycentriccalcbasis(&b2, x->ptr.p_double[i], &sbf, _state);
ae_v_move(&fmatrix.ptr.pp_double[i][0], 1, &sbf.ptr.p_double[0], 1, ae_v_len(0,m-1));
y2.ptr.p_double[i] = y->ptr.p_double[i];
w2.ptr.p_double[i] = w->ptr.p_double[i];
mx = mx+ae_fabs(w->ptr.p_double[i], _state)/n;
}
for(i=0; i<=m-1; i++)
{
for(j=0; j<=m-1; j++)
{
if( i==j )
{
fmatrix.ptr.pp_double[n+i][j] = decay;
}
else
{
fmatrix.ptr.pp_double[n+i][j] = (double)(0);
}
}
y2.ptr.p_double[n+i] = (double)(0);
w2.ptr.p_double[n+i] = mx;
}
if( k>0 )
{
for(j=0; j<=m-1; j++)
{
for(i=0; i<=m-1; i++)
{
sy.ptr.p_double[i] = (double)(0);
}
sy.ptr.p_double[j] = (double)(1);
barycentricbuildfloaterhormann(&sx, &sy, m, d, &b2, _state);
for(i=0; i<=k-1; i++)
{
ae_assert(dc->ptr.p_int[i]>=0&&dc->ptr.p_int[i]<=1, "BarycentricFit: internal error!", _state);
barycentricdiff1(&b2, xc->ptr.p_double[i], &v0, &v1, _state);
if( dc->ptr.p_int[i]==0 )
{
cmatrix.ptr.pp_double[i][j] = v0;
}
if( dc->ptr.p_int[i]==1 )
{
cmatrix.ptr.pp_double[i][j] = v1;
}
}
}
for(i=0; i<=k-1; i++)
{
cmatrix.ptr.pp_double[i][m] = yc->ptr.p_double[i];
}
}
/*
* Solve constrained task
*/
if( k>0 )
{
/*
* solve using regularization
*/
lsfitlinearwc(&y2, &w2, &fmatrix, &cmatrix, n+m, m, k, info, &tmp, &lrep, _state);
}
else
{
/*
* no constraints, no regularization needed
*/
lsfitlinearwc(y, w, &fmatrix, &cmatrix, n, m, k, info, &tmp, &lrep, _state);
}
if( *info<0 )
{
ae_frame_leave(_state);
return;
}
/*
* Generate interpolant and scale it
*/
ae_v_move(&sy.ptr.p_double[0], 1, &tmp.ptr.p_double[0], 1, ae_v_len(0,m-1));
barycentricbuildfloaterhormann(&sx, &sy, m, d, b, _state);
barycentriclintransx(b, 2/(xb-xa), -(xa+xb)/(xb-xa), _state);
barycentriclintransy(b, sb-sa, sa, _state);
/*
* Scale absolute errors obtained from LSFitLinearW.
* Relative error should be calculated separately
* (because of shifting/scaling of the task)
*/
rep->taskrcond = lrep.taskrcond;
rep->rmserror = lrep.rmserror*(sb-sa);
rep->avgerror = lrep.avgerror*(sb-sa);
rep->maxerror = lrep.maxerror*(sb-sa);
rep->avgrelerror = (double)(0);
relcnt = 0;
for(i=0; i<=n-1; i++)
{
if( ae_fp_neq(yoriginal.ptr.p_double[i],(double)(0)) )
{
rep->avgrelerror = rep->avgrelerror+ae_fabs(barycentriccalc(b, xoriginal.ptr.p_double[i], _state)-yoriginal.ptr.p_double[i], _state)/ae_fabs(yoriginal.ptr.p_double[i], _state);
relcnt = relcnt+1;
}
}
if( relcnt!=0 )
{
rep->avgrelerror = rep->avgrelerror/relcnt;
}
ae_frame_leave(_state);
}
static void lsfit_clearreport(lsfitreport* rep, ae_state *_state)
{
rep->taskrcond = (double)(0);
rep->iterationscount = 0;
rep->varidx = -1;
rep->rmserror = (double)(0);
rep->avgerror = (double)(0);
rep->avgrelerror = (double)(0);
rep->maxerror = (double)(0);
rep->wrmserror = (double)(0);
rep->r2 = (double)(0);
ae_matrix_set_length(&rep->covpar, 0, 0, _state);
ae_vector_set_length(&rep->errpar, 0, _state);
ae_vector_set_length(&rep->errcurve, 0, _state);
ae_vector_set_length(&rep->noise, 0, _state);
}
/*************************************************************************
This internal function estimates covariance matrix and other error-related
information for linear/nonlinear least squares model.
It has a bit awkward interface, but it can be used for both linear and
nonlinear problems.
INPUT PARAMETERS:
F1 - array[0..N-1,0..K-1]:
* for linear problems - matrix of function values
* for nonlinear problems - Jacobian matrix
F0 - array[0..N-1]:
* for linear problems - must be filled with zeros
* for nonlinear problems - must store values of function being
fitted
Y - array[0..N-1]:
* for linear and nonlinear problems - must store target values
W - weights, array[0..N-1]:
* for linear and nonlinear problems - weights
X - array[0..K-1]:
* for linear and nonlinear problems - current solution
S - array[0..K-1]:
* its components should be strictly positive
* squared inverse of this diagonal matrix is used as damping
factor for covariance matrix (linear and nonlinear problems)
* for nonlinear problems, when scale of the variables is usually
explicitly given by user, you may use scale vector for this
parameter
* for linear problems you may set this parameter to
S=sqrt(1/diag(F'*F))
* this parameter is automatically rescaled by this function,
only relative magnitudes of its components (with respect to
each other) matter.
N - number of points, N>0.
K - number of dimensions
Rep - structure which is used to store results
Z - additional matrix which, depending on ZKind, may contain some
information used to accelerate calculations - or just can be
temporary buffer:
* for ZKind=0 Z contains no information, just temporary
buffer which can be resized and used as needed
* for ZKind=1 Z contains triangular matrix from QR
decomposition of W*F1. This matrix can be used
to speedup calculation of covariance matrix.
It should not be changed by algorithm.
ZKind- contents of Z
OUTPUT PARAMETERS:
* Rep.CovPar covariance matrix for parameters, array[K,K].
* Rep.ErrPar errors in parameters, array[K],
errpar = sqrt(diag(CovPar))
* Rep.ErrCurve vector of fit errors - standard deviations of empirical
best-fit curve from "ideal" best-fit curve built with
infinite number of samples, array[N].
errcurve = sqrt(diag(J*CovPar*J')),
where J is Jacobian matrix.
* Rep.Noise vector of per-point estimates of noise, array[N]
* Rep.R2 coefficient of determination (non-weighted)
Other fields of Rep are not changed.
IMPORTANT: errors in parameters are calculated without taking into
account boundary/linear constraints! Presence of constraints
changes distribution of errors, but there is no easy way to
account for constraints when you calculate covariance matrix.
NOTE: noise in the data is estimated as follows:
* for fitting without user-supplied weights all points are
assumed to have same level of noise, which is estimated from
the data
* for fitting with user-supplied weights we assume that noise
level in I-th point is inversely proportional to Ith weight.
Coefficient of proportionality is estimated from the data.
NOTE: we apply small amount of regularization when we invert squared
Jacobian and calculate covariance matrix. It guarantees that
algorithm won't divide by zero during inversion, but skews
error estimates a bit (fractional error is about 10^-9).
However, we believe that this difference is insignificant for
all practical purposes except for the situation when you want
to compare ALGLIB results with "reference" implementation up
to the last significant digit.
-- ALGLIB PROJECT --
Copyright 10.12.2009 by Bochkanov Sergey
*************************************************************************/
static void lsfit_estimateerrors(/* Real */ ae_matrix* f1,
/* Real */ ae_vector* f0,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
/* Real */ ae_vector* x,
/* Real */ ae_vector* s,
ae_int_t n,
ae_int_t k,
lsfitreport* rep,
/* Real */ ae_matrix* z,
ae_int_t zkind,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _s;
ae_int_t i;
ae_int_t j;
ae_int_t j1;
double v;
double noisec;
ae_int_t info;
matinvreport invrep;
ae_int_t nzcnt;
double avg;
double rss;
double tss;
double sz;
double ss;
ae_frame_make(_state, &_frame_block);
memset(&_s, 0, sizeof(_s));
memset(&invrep, 0, sizeof(invrep));
ae_vector_init_copy(&_s, s, _state, ae_true);
s = &_s;
_matinvreport_init(&invrep, _state, ae_true);
/*
* Compute NZCnt - count of non-zero weights
*/
nzcnt = 0;
for(i=0; i<=n-1; i++)
{
if( ae_fp_neq(w->ptr.p_double[i],(double)(0)) )
{
nzcnt = nzcnt+1;
}
}
/*
* Compute R2
*/
if( nzcnt>0 )
{
avg = 0.0;
for(i=0; i<=n-1; i++)
{
if( ae_fp_neq(w->ptr.p_double[i],(double)(0)) )
{
avg = avg+y->ptr.p_double[i];
}
}
avg = avg/nzcnt;
rss = 0.0;
tss = 0.0;
for(i=0; i<=n-1; i++)
{
if( ae_fp_neq(w->ptr.p_double[i],(double)(0)) )
{
v = ae_v_dotproduct(&f1->ptr.pp_double[i][0], 1, &x->ptr.p_double[0], 1, ae_v_len(0,k-1));
v = v+f0->ptr.p_double[i];
rss = rss+ae_sqr(v-y->ptr.p_double[i], _state);
tss = tss+ae_sqr(y->ptr.p_double[i]-avg, _state);
}
}
if( ae_fp_neq(tss,(double)(0)) )
{
rep->r2 = ae_maxreal(1.0-rss/tss, 0.0, _state);
}
else
{
rep->r2 = 1.0;
}
}
else
{
rep->r2 = (double)(0);
}
/*
* Compute estimate of proportionality between noise in the data and weights:
* NoiseC = mean(per-point-noise*per-point-weight)
* Noise level (standard deviation) at each point is equal to NoiseC/W[I].
*/
if( nzcnt>k )
{
noisec = 0.0;
for(i=0; i<=n-1; i++)
{
if( ae_fp_neq(w->ptr.p_double[i],(double)(0)) )
{
v = ae_v_dotproduct(&f1->ptr.pp_double[i][0], 1, &x->ptr.p_double[0], 1, ae_v_len(0,k-1));
v = v+f0->ptr.p_double[i];
noisec = noisec+ae_sqr((v-y->ptr.p_double[i])*w->ptr.p_double[i], _state);
}
}
noisec = ae_sqrt(noisec/(nzcnt-k), _state);
}
else
{
noisec = 0.0;
}
/*
* Two branches on noise level:
* * NoiseC>0 normal situation
* * NoiseC=0 degenerate case CovPar is filled by zeros
*/
rmatrixsetlengthatleast(&rep->covpar, k, k, _state);
if( ae_fp_greater(noisec,(double)(0)) )
{
/*
* Normal situation: non-zero noise level
*/
ae_assert(zkind==0||zkind==1, "LSFit: internal error in EstimateErrors() function", _state);
if( zkind==0 )
{
/*
* Z contains no additional information which can be used to speed up
* calculations. We have to calculate covariance matrix on our own:
* * Compute scaled Jacobian N*J, where N[i,i]=WCur[I]/NoiseC, store in Z
* * Compute Z'*Z, store in CovPar
* * Apply moderate regularization to CovPar and compute matrix inverse.
* In case inverse failed, increase regularization parameter and try
* again.
*/
rmatrixsetlengthatleast(z, n, k, _state);
for(i=0; i<=n-1; i++)
{
v = w->ptr.p_double[i]/noisec;
ae_v_moved(&z->ptr.pp_double[i][0], 1, &f1->ptr.pp_double[i][0], 1, ae_v_len(0,k-1), v);
}
/*
* Convert S to automatically scaled damped matrix:
* * calculate SZ - sum of diagonal elements of Z'*Z
* * calculate SS - sum of diagonal elements of S^(-2)
* * overwrite S by (SZ/SS)*S^(-2)
* * now S has approximately same magnitude as giagonal of Z'*Z
*/
sz = (double)(0);
for(i=0; i<=n-1; i++)
{
for(j=0; j<=k-1; j++)
{
sz = sz+z->ptr.pp_double[i][j]*z->ptr.pp_double[i][j];
}
}
if( ae_fp_eq(sz,(double)(0)) )
{
sz = (double)(1);
}
ss = (double)(0);
for(j=0; j<=k-1; j++)
{
ss = ss+1/ae_sqr(s->ptr.p_double[j], _state);
}
for(j=0; j<=k-1; j++)
{
s->ptr.p_double[j] = sz/ss/ae_sqr(s->ptr.p_double[j], _state);
}
/*
* Calculate damped inverse inv(Z'*Z+S).
* We increase damping factor V until Z'*Z become well-conditioned.
*/
v = 1.0E3*ae_machineepsilon;
do
{
rmatrixsyrk(k, n, 1.0, z, 0, 0, 2, 0.0, &rep->covpar, 0, 0, ae_true, _state);
for(i=0; i<=k-1; i++)
{
rep->covpar.ptr.pp_double[i][i] = rep->covpar.ptr.pp_double[i][i]+v*s->ptr.p_double[i];
}
spdmatrixinverse(&rep->covpar, k, ae_true, &info, &invrep, _state);
v = 10*v;
}
while(info<=0);
for(i=0; i<=k-1; i++)
{
for(j=i+1; j<=k-1; j++)
{
rep->covpar.ptr.pp_double[j][i] = rep->covpar.ptr.pp_double[i][j];
}
}
}
if( zkind==1 )
{
/*
* We can reuse additional information:
* * Z contains R matrix from QR decomposition of W*F1
* * After multiplication by 1/NoiseC we get Z_mod = N*F1, where diag(N)=w[i]/NoiseC
* * Such triangular Z_mod is a Cholesky factor from decomposition of J'*N'*N*J.
* Thus, we can calculate covariance matrix as inverse of the matrix given by
* its Cholesky decomposition. It allow us to avoid time-consuming calculation
* of J'*N'*N*J in CovPar - complexity is reduced from O(N*K^2) to O(K^3), which
* is quite good because K is usually orders of magnitude smaller than N.
*
* First, convert S to automatically scaled damped matrix:
* * calculate SZ - sum of magnitudes of diagonal elements of Z/NoiseC
* * calculate SS - sum of diagonal elements of S^(-1)
* * overwrite S by (SZ/SS)*S^(-1)
* * now S has approximately same magnitude as giagonal of Z'*Z
*/
sz = (double)(0);
for(j=0; j<=k-1; j++)
{
sz = sz+ae_fabs(z->ptr.pp_double[j][j]/noisec, _state);
}
if( ae_fp_eq(sz,(double)(0)) )
{
sz = (double)(1);
}
ss = (double)(0);
for(j=0; j<=k-1; j++)
{
ss = ss+1/s->ptr.p_double[j];
}
for(j=0; j<=k-1; j++)
{
s->ptr.p_double[j] = sz/ss/s->ptr.p_double[j];
}
/*
* Calculate damped inverse of inv((Z+v*S)'*(Z+v*S))
* We increase damping factor V until matrix become well-conditioned.
*/
v = 1.0E3*ae_machineepsilon;
do
{
for(i=0; i<=k-1; i++)
{
for(j=i; j<=k-1; j++)
{
rep->covpar.ptr.pp_double[i][j] = z->ptr.pp_double[i][j]/noisec;
}
rep->covpar.ptr.pp_double[i][i] = rep->covpar.ptr.pp_double[i][i]+v*s->ptr.p_double[i];
}
spdmatrixcholeskyinverse(&rep->covpar, k, ae_true, &info, &invrep, _state);
v = 10*v;
}
while(info<=0);
for(i=0; i<=k-1; i++)
{
for(j=i+1; j<=k-1; j++)
{
rep->covpar.ptr.pp_double[j][i] = rep->covpar.ptr.pp_double[i][j];
}
}
}
}
else
{
/*
* Degenerate situation: zero noise level, covariance matrix is zero.
*/
for(i=0; i<=k-1; i++)
{
for(j=0; j<=k-1; j++)
{
rep->covpar.ptr.pp_double[j][i] = (double)(0);
}
}
}
/*
* Estimate erorrs in parameters, curve and per-point noise
*/
rvectorsetlengthatleast(&rep->errpar, k, _state);
rvectorsetlengthatleast(&rep->errcurve, n, _state);
rvectorsetlengthatleast(&rep->noise, n, _state);
for(i=0; i<=k-1; i++)
{
rep->errpar.ptr.p_double[i] = ae_sqrt(rep->covpar.ptr.pp_double[i][i], _state);
}
for(i=0; i<=n-1; i++)
{
/*
* ErrCurve[I] is sqrt(P[i,i]) where P=J*CovPar*J'
*/
v = 0.0;
for(j=0; j<=k-1; j++)
{
for(j1=0; j1<=k-1; j1++)
{
v = v+f1->ptr.pp_double[i][j]*rep->covpar.ptr.pp_double[j][j1]*f1->ptr.pp_double[i][j1];
}
}
rep->errcurve.ptr.p_double[i] = ae_sqrt(v, _state);
/*
* Noise[i] is filled using weights and current estimate of noise level
*/
if( ae_fp_neq(w->ptr.p_double[i],(double)(0)) )
{
rep->noise.ptr.p_double[i] = noisec/w->ptr.p_double[i];
}
else
{
rep->noise.ptr.p_double[i] = (double)(0);
}
}
ae_frame_leave(_state);
}
void _polynomialfitreport_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
polynomialfitreport *p = (polynomialfitreport*)_p;
ae_touch_ptr((void*)p);
}
void _polynomialfitreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
polynomialfitreport *dst = (polynomialfitreport*)_dst;
polynomialfitreport *src = (polynomialfitreport*)_src;
dst->taskrcond = src->taskrcond;
dst->rmserror = src->rmserror;
dst->avgerror = src->avgerror;
dst->avgrelerror = src->avgrelerror;
dst->maxerror = src->maxerror;
}
void _polynomialfitreport_clear(void* _p)
{
polynomialfitreport *p = (polynomialfitreport*)_p;
ae_touch_ptr((void*)p);
}
void _polynomialfitreport_destroy(void* _p)
{
polynomialfitreport *p = (polynomialfitreport*)_p;
ae_touch_ptr((void*)p);
}
void _barycentricfitreport_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
barycentricfitreport *p = (barycentricfitreport*)_p;
ae_touch_ptr((void*)p);
}
void _barycentricfitreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
barycentricfitreport *dst = (barycentricfitreport*)_dst;
barycentricfitreport *src = (barycentricfitreport*)_src;
dst->taskrcond = src->taskrcond;
dst->dbest = src->dbest;
dst->rmserror = src->rmserror;
dst->avgerror = src->avgerror;
dst->avgrelerror = src->avgrelerror;
dst->maxerror = src->maxerror;
}
void _barycentricfitreport_clear(void* _p)
{
barycentricfitreport *p = (barycentricfitreport*)_p;
ae_touch_ptr((void*)p);
}
void _barycentricfitreport_destroy(void* _p)
{
barycentricfitreport *p = (barycentricfitreport*)_p;
ae_touch_ptr((void*)p);
}
void _lsfitreport_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
lsfitreport *p = (lsfitreport*)_p;
ae_touch_ptr((void*)p);
ae_matrix_init(&p->covpar, 0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->errpar, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->errcurve, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->noise, 0, DT_REAL, _state, make_automatic);
}
void _lsfitreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
lsfitreport *dst = (lsfitreport*)_dst;
lsfitreport *src = (lsfitreport*)_src;
dst->taskrcond = src->taskrcond;
dst->iterationscount = src->iterationscount;
dst->varidx = src->varidx;
dst->rmserror = src->rmserror;
dst->avgerror = src->avgerror;
dst->avgrelerror = src->avgrelerror;
dst->maxerror = src->maxerror;
dst->wrmserror = src->wrmserror;
ae_matrix_init_copy(&dst->covpar, &src->covpar, _state, make_automatic);
ae_vector_init_copy(&dst->errpar, &src->errpar, _state, make_automatic);
ae_vector_init_copy(&dst->errcurve, &src->errcurve, _state, make_automatic);
ae_vector_init_copy(&dst->noise, &src->noise, _state, make_automatic);
dst->r2 = src->r2;
}
void _lsfitreport_clear(void* _p)
{
lsfitreport *p = (lsfitreport*)_p;
ae_touch_ptr((void*)p);
ae_matrix_clear(&p->covpar);
ae_vector_clear(&p->errpar);
ae_vector_clear(&p->errcurve);
ae_vector_clear(&p->noise);
}
void _lsfitreport_destroy(void* _p)
{
lsfitreport *p = (lsfitreport*)_p;
ae_touch_ptr((void*)p);
ae_matrix_destroy(&p->covpar);
ae_vector_destroy(&p->errpar);
ae_vector_destroy(&p->errcurve);
ae_vector_destroy(&p->noise);
}
void _lsfitstate_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
lsfitstate *p = (lsfitstate*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->c0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->c1, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->s, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->bndl, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->bndu, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->taskx, 0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tasky, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->taskw, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->cleic, 0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->x, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->c, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->g, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->h, 0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->wcur, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tmpct, 0, DT_INT, _state, make_automatic);
ae_vector_init(&p->tmp, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tmpf, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->tmpjac, 0, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->tmpjacw, 0, 0, DT_REAL, _state, make_automatic);
_matinvreport_init(&p->invrep, _state, make_automatic);
_lsfitreport_init(&p->rep, _state, make_automatic);
_minlmstate_init(&p->optstate, _state, make_automatic);
_minlmreport_init(&p->optrep, _state, make_automatic);
_rcommstate_init(&p->rstate, _state, make_automatic);
}
void _lsfitstate_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
lsfitstate *dst = (lsfitstate*)_dst;
lsfitstate *src = (lsfitstate*)_src;
dst->optalgo = src->optalgo;
dst->m = src->m;
dst->k = src->k;
dst->epsx = src->epsx;
dst->maxits = src->maxits;
dst->stpmax = src->stpmax;
dst->xrep = src->xrep;
ae_vector_init_copy(&dst->c0, &src->c0, _state, make_automatic);
ae_vector_init_copy(&dst->c1, &src->c1, _state, make_automatic);
ae_vector_init_copy(&dst->s, &src->s, _state, make_automatic);
ae_vector_init_copy(&dst->bndl, &src->bndl, _state, make_automatic);
ae_vector_init_copy(&dst->bndu, &src->bndu, _state, make_automatic);
ae_matrix_init_copy(&dst->taskx, &src->taskx, _state, make_automatic);
ae_vector_init_copy(&dst->tasky, &src->tasky, _state, make_automatic);
dst->npoints = src->npoints;
ae_vector_init_copy(&dst->taskw, &src->taskw, _state, make_automatic);
dst->nweights = src->nweights;
dst->wkind = src->wkind;
dst->wits = src->wits;
dst->diffstep = src->diffstep;
dst->teststep = src->teststep;
ae_matrix_init_copy(&dst->cleic, &src->cleic, _state, make_automatic);
dst->nec = src->nec;
dst->nic = src->nic;
dst->xupdated = src->xupdated;
dst->needf = src->needf;
dst->needfg = src->needfg;
dst->needfgh = src->needfgh;
dst->pointindex = src->pointindex;
ae_vector_init_copy(&dst->x, &src->x, _state, make_automatic);
ae_vector_init_copy(&dst->c, &src->c, _state, make_automatic);
dst->f = src->f;
ae_vector_init_copy(&dst->g, &src->g, _state, make_automatic);
ae_matrix_init_copy(&dst->h, &src->h, _state, make_automatic);
ae_vector_init_copy(&dst->wcur, &src->wcur, _state, make_automatic);
ae_vector_init_copy(&dst->tmpct, &src->tmpct, _state, make_automatic);
ae_vector_init_copy(&dst->tmp, &src->tmp, _state, make_automatic);
ae_vector_init_copy(&dst->tmpf, &src->tmpf, _state, make_automatic);
ae_matrix_init_copy(&dst->tmpjac, &src->tmpjac, _state, make_automatic);
ae_matrix_init_copy(&dst->tmpjacw, &src->tmpjacw, _state, make_automatic);
dst->tmpnoise = src->tmpnoise;
_matinvreport_init_copy(&dst->invrep, &src->invrep, _state, make_automatic);
dst->repiterationscount = src->repiterationscount;
dst->repterminationtype = src->repterminationtype;
dst->repvaridx = src->repvaridx;
dst->reprmserror = src->reprmserror;
dst->repavgerror = src->repavgerror;
dst->repavgrelerror = src->repavgrelerror;
dst->repmaxerror = src->repmaxerror;
dst->repwrmserror = src->repwrmserror;
_lsfitreport_init_copy(&dst->rep, &src->rep, _state, make_automatic);
_minlmstate_init_copy(&dst->optstate, &src->optstate, _state, make_automatic);
_minlmreport_init_copy(&dst->optrep, &src->optrep, _state, make_automatic);
dst->prevnpt = src->prevnpt;
dst->prevalgo = src->prevalgo;
_rcommstate_init_copy(&dst->rstate, &src->rstate, _state, make_automatic);
}
void _lsfitstate_clear(void* _p)
{
lsfitstate *p = (lsfitstate*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->c0);
ae_vector_clear(&p->c1);
ae_vector_clear(&p->s);
ae_vector_clear(&p->bndl);
ae_vector_clear(&p->bndu);
ae_matrix_clear(&p->taskx);
ae_vector_clear(&p->tasky);
ae_vector_clear(&p->taskw);
ae_matrix_clear(&p->cleic);
ae_vector_clear(&p->x);
ae_vector_clear(&p->c);
ae_vector_clear(&p->g);
ae_matrix_clear(&p->h);
ae_vector_clear(&p->wcur);
ae_vector_clear(&p->tmpct);
ae_vector_clear(&p->tmp);
ae_vector_clear(&p->tmpf);
ae_matrix_clear(&p->tmpjac);
ae_matrix_clear(&p->tmpjacw);
_matinvreport_clear(&p->invrep);
_lsfitreport_clear(&p->rep);
_minlmstate_clear(&p->optstate);
_minlmreport_clear(&p->optrep);
_rcommstate_clear(&p->rstate);
}
void _lsfitstate_destroy(void* _p)
{
lsfitstate *p = (lsfitstate*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->c0);
ae_vector_destroy(&p->c1);
ae_vector_destroy(&p->s);
ae_vector_destroy(&p->bndl);
ae_vector_destroy(&p->bndu);
ae_matrix_destroy(&p->taskx);
ae_vector_destroy(&p->tasky);
ae_vector_destroy(&p->taskw);
ae_matrix_destroy(&p->cleic);
ae_vector_destroy(&p->x);
ae_vector_destroy(&p->c);
ae_vector_destroy(&p->g);
ae_matrix_destroy(&p->h);
ae_vector_destroy(&p->wcur);
ae_vector_destroy(&p->tmpct);
ae_vector_destroy(&p->tmp);
ae_vector_destroy(&p->tmpf);
ae_matrix_destroy(&p->tmpjac);
ae_matrix_destroy(&p->tmpjacw);
_matinvreport_destroy(&p->invrep);
_lsfitreport_destroy(&p->rep);
_minlmstate_destroy(&p->optstate);
_minlmreport_destroy(&p->optrep);
_rcommstate_destroy(&p->rstate);
}
#endif
#if defined(AE_COMPILE_RBFV2) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This function creates RBF model for a scalar (NY=1) or vector (NY>1)
function in a NX-dimensional space (NX=2 or NX=3).
INPUT PARAMETERS:
NX - dimension of the space, NX=2 or NX=3
NY - function dimension, NY>=1
OUTPUT PARAMETERS:
S - RBF model (initially equals to zero)
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfv2create(ae_int_t nx,
ae_int_t ny,
rbfv2model* s,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
_rbfv2model_clear(s);
ae_assert(nx>=1, "RBFCreate: NX<1", _state);
ae_assert(ny>=1, "RBFCreate: NY<1", _state);
/*
* Serializable parameters
*/
s->nx = nx;
s->ny = ny;
s->bf = 0;
s->nh = 0;
ae_matrix_set_length(&s->v, ny, nx+1, _state);
for(i=0; i<=ny-1; i++)
{
for(j=0; j<=nx; j++)
{
s->v.ptr.pp_double[i][j] = (double)(0);
}
}
/*
* Non-serializable parameters
*/
s->lambdareg = rbfv2_defaultlambdareg;
s->maxits = rbfv2_defaultmaxits;
s->supportr = rbfv2_defaultsupportr;
s->basisfunction = rbfv2_defaultbf;
}
/*************************************************************************
This function creates buffer structure which can be used to perform
parallel RBF model evaluations (with one RBF model instance being
used from multiple threads, as long as different threads use different
instances of buffer).
This buffer object can be used with rbftscalcbuf() function (here "ts"
stands for "thread-safe", "buf" is a suffix which denotes function which
reuses previously allocated output space).
How to use it:
* create RBF model structure with rbfcreate()
* load data, tune parameters
* call rbfbuildmodel()
* call rbfcreatecalcbuffer(), once per thread working with RBF model (you
should call this function only AFTER call to rbfbuildmodel(), see below
for more information)
* call rbftscalcbuf() from different threads, with each thread working
with its own copy of buffer object.
INPUT PARAMETERS
S - RBF model
OUTPUT PARAMETERS
Buf - external buffer.
IMPORTANT: buffer object should be used only with RBF model object which
was used to initialize buffer. Any attempt to use buffer with
different object is dangerous - you may get memory violation
error because sizes of internal arrays do not fit to dimensions
of RBF structure.
IMPORTANT: you should call this function only for model which was built
with rbfbuildmodel() function, after successful invocation of
rbfbuildmodel(). Sizes of some internal structures are
determined only after model is built, so buffer object created
before model construction stage will be useless (and any
attempt to use it will result in exception).
-- ALGLIB --
Copyright 02.04.2016 by Sergey Bochkanov
*************************************************************************/
void rbfv2createcalcbuffer(rbfv2model* s,
rbfv2calcbuffer* buf,
ae_state *_state)
{
_rbfv2calcbuffer_clear(buf);
rbfv2_allocatecalcbuffer(s, buf, _state);
}
/*************************************************************************
This function builds hierarchical RBF model.
INPUT PARAMETERS:
X - array[N,S.NX], X-values
Y - array[N,S.NY], Y-values
ScaleVec- array[S.NX], vector of per-dimension scales
N - points count
ATerm - linear term type, 1 for linear, 2 for constant, 3 for zero.
NH - hierarchy height
RBase - base RBF radius
BF - basis function type: 0 for Gaussian, 1 for compact
LambdaNS- non-smoothness penalty coefficient. Exactly zero value means
that no penalty is applied, and even system matrix does not
contain penalty-related rows. Value of 1 means
S - RBF model, initialized by RBFCreate() call.
progress10000- variable used for progress reports, it is regularly set
to the current progress multiplied by 10000, in order to
get value in [0,10000] range. The rationale for such scaling
is that it allows us to use integer type to store progress,
which has less potential for non-atomic corruption on unprotected
reads from another threads.
You can read this variable from some other thread to get
estimate of the current progress.
Initial value of this variable is ignored, it is written by
this function, but not read.
terminationrequest - variable used for termination requests; its initial
value must be False, and you can set it to True from some
other thread. This routine regularly checks this variable
and will terminate model construction shortly upon discovering
that termination was requested.
OUTPUT PARAMETERS:
S - updated model (for rep.terminationtype>0, unchanged otherwise)
Rep - report:
* Rep.TerminationType:
* -5 - non-distinct basis function centers were detected,
interpolation aborted
* -4 - nonconvergence of the internal SVD solver
* 1 - successful termination
* 8 terminated by user via rbfrequesttermination()
Fields are used for debugging purposes:
* Rep.IterationsCount - iterations count of the LSQR solver
* Rep.NMV - number of matrix-vector products
* Rep.ARows - rows count for the system matrix
* Rep.ACols - columns count for the system matrix
* Rep.ANNZ - number of significantly non-zero elements
(elements above some algorithm-determined threshold)
NOTE: failure to build model will leave current state of the structure
unchanged.
-- ALGLIB --
Copyright 20.06.2016 by Bochkanov Sergey
*************************************************************************/
void rbfv2buildhierarchical(/* Real */ ae_matrix* x,
/* Real */ ae_matrix* y,
ae_int_t n,
/* Real */ ae_vector* scalevec,
ae_int_t aterm,
ae_int_t nh,
double rbase,
double lambdans,
rbfv2model* s,
ae_int_t* progress10000,
ae_bool* terminationrequest,
rbfv2report* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t nx;
ae_int_t ny;
ae_int_t bf;
ae_matrix rhs;
ae_matrix residualy;
ae_matrix v;
ae_int_t rowsperpoint;
ae_vector hidx;
ae_vector xr;
ae_vector ri;
ae_vector kdroots;
ae_vector kdnodes;
ae_vector kdsplits;
ae_vector kdboxmin;
ae_vector kdboxmax;
ae_vector cw;
ae_vector cwrange;
ae_matrix curxy;
ae_int_t curn;
ae_int_t nbasis;
kdtree curtree;
kdtree globaltree;
ae_vector x0;
ae_vector x1;
ae_vector tags;
ae_vector dist;
ae_vector nncnt;
ae_vector rowsizes;
ae_vector diagata;
ae_vector prec;
ae_vector tmpx;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t k2;
ae_int_t levelidx;
ae_int_t offsi;
ae_int_t offsj;
double val;
double criticalr;
ae_int_t cnt;
double avgdiagata;
ae_vector avgrowsize;
double sumrowsize;
double rprogress;
ae_int_t maxits;
linlsqrstate linstate;
linlsqrreport lsqrrep;
sparsematrix sparseacrs;
ae_vector densew1;
ae_vector denseb1;
rbfv2calcbuffer calcbuf;
ae_vector vr2;
ae_vector voffs;
ae_vector rowindexes;
ae_vector rowvals;
double penalty;
ae_frame_make(_state, &_frame_block);
memset(&rhs, 0, sizeof(rhs));
memset(&residualy, 0, sizeof(residualy));
memset(&v, 0, sizeof(v));
memset(&hidx, 0, sizeof(hidx));
memset(&xr, 0, sizeof(xr));
memset(&ri, 0, sizeof(ri));
memset(&kdroots, 0, sizeof(kdroots));
memset(&kdnodes, 0, sizeof(kdnodes));
memset(&kdsplits, 0, sizeof(kdsplits));
memset(&kdboxmin, 0, sizeof(kdboxmin));
memset(&kdboxmax, 0, sizeof(kdboxmax));
memset(&cw, 0, sizeof(cw));
memset(&cwrange, 0, sizeof(cwrange));
memset(&curxy, 0, sizeof(curxy));
memset(&curtree, 0, sizeof(curtree));
memset(&globaltree, 0, sizeof(globaltree));
memset(&x0, 0, sizeof(x0));
memset(&x1, 0, sizeof(x1));
memset(&tags, 0, sizeof(tags));
memset(&dist, 0, sizeof(dist));
memset(&nncnt, 0, sizeof(nncnt));
memset(&rowsizes, 0, sizeof(rowsizes));
memset(&diagata, 0, sizeof(diagata));
memset(&prec, 0, sizeof(prec));
memset(&tmpx, 0, sizeof(tmpx));
memset(&avgrowsize, 0, sizeof(avgrowsize));
memset(&linstate, 0, sizeof(linstate));
memset(&lsqrrep, 0, sizeof(lsqrrep));
memset(&sparseacrs, 0, sizeof(sparseacrs));
memset(&densew1, 0, sizeof(densew1));
memset(&denseb1, 0, sizeof(denseb1));
memset(&calcbuf, 0, sizeof(calcbuf));
memset(&vr2, 0, sizeof(vr2));
memset(&voffs, 0, sizeof(voffs));
memset(&rowindexes, 0, sizeof(rowindexes));
memset(&rowvals, 0, sizeof(rowvals));
_rbfv2report_clear(rep);
ae_matrix_init(&rhs, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&residualy, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&v, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&hidx, 0, DT_INT, _state, ae_true);
ae_vector_init(&xr, 0, DT_REAL, _state, ae_true);
ae_vector_init(&ri, 0, DT_REAL, _state, ae_true);
ae_vector_init(&kdroots, 0, DT_INT, _state, ae_true);
ae_vector_init(&kdnodes, 0, DT_INT, _state, ae_true);
ae_vector_init(&kdsplits, 0, DT_REAL, _state, ae_true);
ae_vector_init(&kdboxmin, 0, DT_REAL, _state, ae_true);
ae_vector_init(&kdboxmax, 0, DT_REAL, _state, ae_true);
ae_vector_init(&cw, 0, DT_REAL, _state, ae_true);
ae_vector_init(&cwrange, 0, DT_INT, _state, ae_true);
ae_matrix_init(&curxy, 0, 0, DT_REAL, _state, ae_true);
_kdtree_init(&curtree, _state, ae_true);
_kdtree_init(&globaltree, _state, ae_true);
ae_vector_init(&x0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&x1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tags, 0, DT_INT, _state, ae_true);
ae_vector_init(&dist, 0, DT_REAL, _state, ae_true);
ae_vector_init(&nncnt, 0, DT_INT, _state, ae_true);
ae_vector_init(&rowsizes, 0, DT_INT, _state, ae_true);
ae_vector_init(&diagata, 0, DT_REAL, _state, ae_true);
ae_vector_init(&prec, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmpx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&avgrowsize, 0, DT_REAL, _state, ae_true);
_linlsqrstate_init(&linstate, _state, ae_true);
_linlsqrreport_init(&lsqrrep, _state, ae_true);
_sparsematrix_init(&sparseacrs, _state, ae_true);
ae_vector_init(&densew1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&denseb1, 0, DT_REAL, _state, ae_true);
_rbfv2calcbuffer_init(&calcbuf, _state, ae_true);
ae_vector_init(&vr2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&voffs, 0, DT_INT, _state, ae_true);
ae_vector_init(&rowindexes, 0, DT_INT, _state, ae_true);
ae_vector_init(&rowvals, 0, DT_REAL, _state, ae_true);
ae_assert(s->nx>0, "RBFV2BuildHierarchical: incorrect NX", _state);
ae_assert(s->ny>0, "RBFV2BuildHierarchical: incorrect NY", _state);
ae_assert(ae_fp_greater_eq(lambdans,(double)(0)), "RBFV2BuildHierarchical: incorrect LambdaNS", _state);
for(j=0; j<=s->nx-1; j++)
{
ae_assert(ae_fp_greater(scalevec->ptr.p_double[j],(double)(0)), "RBFV2BuildHierarchical: incorrect ScaleVec", _state);
}
nx = s->nx;
ny = s->ny;
bf = s->basisfunction;
ae_assert(bf==0||bf==1, "RBFV2BuildHierarchical: incorrect BF", _state);
/*
* Clean up communication and report fields
*/
*progress10000 = 0;
rep->maxerror = (double)(0);
rep->rmserror = (double)(0);
/*
* Quick exit when we have no points
*/
if( n==0 )
{
rbfv2_zerofill(s, nx, ny, bf, _state);
rep->terminationtype = 1;
*progress10000 = 10000;
ae_frame_leave(_state);
return;
}
/*
* First model in a sequence - linear model.
* Residuals from linear regression are stored in the ResidualY variable
* (used later to build RBF models).
*/
ae_matrix_set_length(&residualy, n, ny, _state);
for(i=0; i<=n-1; i++)
{
for(j=0; j<=ny-1; j++)
{
residualy.ptr.pp_double[i][j] = y->ptr.pp_double[i][j];
}
}
if( !rbfv2_rbfv2buildlinearmodel(x, &residualy, n, nx, ny, aterm, &v, _state) )
{
rbfv2_zerofill(s, nx, ny, bf, _state);
rep->terminationtype = -5;
*progress10000 = 10000;
ae_frame_leave(_state);
return;
}
/*
* Handle special case: multilayer model with NLayers=0.
* Quick exit.
*/
if( nh==0 )
{
rep->terminationtype = 1;
rbfv2_zerofill(s, nx, ny, bf, _state);
for(i=0; i<=ny-1; i++)
{
for(j=0; j<=nx; j++)
{
s->v.ptr.pp_double[i][j] = v.ptr.pp_double[i][j];
}
}
rep->maxerror = (double)(0);
rep->rmserror = (double)(0);
for(i=0; i<=n-1; i++)
{
for(j=0; j<=ny-1; j++)
{
rep->maxerror = ae_maxreal(rep->maxerror, ae_fabs(residualy.ptr.pp_double[i][j], _state), _state);
rep->rmserror = rep->rmserror+ae_sqr(residualy.ptr.pp_double[i][j], _state);
}
}
rep->rmserror = ae_sqrt(rep->rmserror/(n*ny), _state);
*progress10000 = 10000;
ae_frame_leave(_state);
return;
}
/*
* Penalty coefficient is set to LambdaNS*RBase^2.
*
* We use such normalization because VALUES of radial basis
* functions have roughly unit magnitude, but their DERIVATIVES
* are (roughly) inversely proportional to the radius. Thus,
* without additional scaling, regularization coefficient
* looses invariancy w.r.t. scaling of variables.
*/
if( ae_fp_eq(lambdans,(double)(0)) )
{
rowsperpoint = 1;
}
else
{
/*
* NOTE: simplified penalty function is used, which does not provide rotation invariance
*/
rowsperpoint = 1+nx;
}
penalty = lambdans*ae_sqr(rbase, _state);
/*
* Prepare temporary structures
*/
ae_matrix_set_length(&rhs, n*rowsperpoint, ny, _state);
ae_matrix_set_length(&curxy, n, nx+ny, _state);
ae_vector_set_length(&x0, nx, _state);
ae_vector_set_length(&x1, nx, _state);
ae_vector_set_length(&tags, n, _state);
ae_vector_set_length(&dist, n, _state);
ae_vector_set_length(&vr2, n, _state);
ae_vector_set_length(&voffs, n, _state);
ae_vector_set_length(&nncnt, n, _state);
ae_vector_set_length(&rowsizes, n*rowsperpoint, _state);
ae_vector_set_length(&denseb1, n*rowsperpoint, _state);
for(i=0; i<=n*rowsperpoint-1; i++)
{
for(j=0; j<=ny-1; j++)
{
rhs.ptr.pp_double[i][j] = (double)(0);
}
}
for(i=0; i<=n-1; i++)
{
for(j=0; j<=nx-1; j++)
{
curxy.ptr.pp_double[i][j] = x->ptr.pp_double[i][j]/scalevec->ptr.p_double[j];
}
for(j=0; j<=ny-1; j++)
{
rhs.ptr.pp_double[i*rowsperpoint][j] = residualy.ptr.pp_double[i][j];
}
tags.ptr.p_int[i] = i;
}
kdtreebuildtagged(&curxy, &tags, n, nx, 0, 2, &globaltree, _state);
/*
* Generate sequence of layer radii.
* Prepare assignment of different levels to points.
*/
ae_assert(n>0, "RBFV2BuildHierarchical: integrity check failed", _state);
ae_vector_set_length(&ri, nh, _state);
for(levelidx=0; levelidx<=nh-1; levelidx++)
{
ri.ptr.p_double[levelidx] = rbase*ae_pow((double)(2), (double)(-levelidx), _state);
}
ae_vector_set_length(&hidx, n, _state);
ae_vector_set_length(&xr, n, _state);
for(i=0; i<=n-1; i++)
{
hidx.ptr.p_int[i] = nh;
xr.ptr.p_double[i] = ae_maxrealnumber;
ae_assert(ae_fp_greater(xr.ptr.p_double[i],ri.ptr.p_double[0]), "RBFV2BuildHierarchical: integrity check failed", _state);
}
for(levelidx=0; levelidx<=nh-1; levelidx++)
{
/*
* Scan dataset points, for each such point that distance to nearest
* "support" point is larger than SupportR*Ri[LevelIdx] we:
* * set distance of current point to 0 (it is support now) and update HIdx
* * perform R-NN request with radius SupportR*Ri[LevelIdx]
* * for each point in request update its distance
*/
criticalr = s->supportr*ri.ptr.p_double[levelidx];
for(i=0; i<=n-1; i++)
{
if( ae_fp_greater(xr.ptr.p_double[i],criticalr) )
{
/*
* Mark point as support
*/
ae_assert(hidx.ptr.p_int[i]==nh, "RBFV2BuildHierarchical: integrity check failed", _state);
hidx.ptr.p_int[i] = levelidx;
xr.ptr.p_double[i] = (double)(0);
/*
* Update neighbors
*/
for(j=0; j<=nx-1; j++)
{
x0.ptr.p_double[j] = x->ptr.pp_double[i][j]/scalevec->ptr.p_double[j];
}
k = kdtreequeryrnn(&globaltree, &x0, criticalr, ae_true, _state);
kdtreequeryresultstags(&globaltree, &tags, _state);
kdtreequeryresultsdistances(&globaltree, &dist, _state);
for(j=0; j<=k-1; j++)
{
xr.ptr.p_double[tags.ptr.p_int[j]] = ae_minreal(xr.ptr.p_double[tags.ptr.p_int[j]], dist.ptr.p_double[j], _state);
}
}
}
}
/*
* Build multitree (with zero weights) according to hierarchy.
*
* NOTE: this code assumes that during every iteration kdNodes,
* kdSplits and CW have size which EXACTLY fits their
* contents, and that these variables are resized at each
* iteration when we add new hierarchical model.
*/
ae_vector_set_length(&kdroots, nh+1, _state);
ae_vector_set_length(&kdnodes, 0, _state);
ae_vector_set_length(&kdsplits, 0, _state);
ae_vector_set_length(&kdboxmin, nx, _state);
ae_vector_set_length(&kdboxmax, nx, _state);
ae_vector_set_length(&cw, 0, _state);
ae_vector_set_length(&cwrange, nh+1, _state);
kdtreeexplorebox(&globaltree, &kdboxmin, &kdboxmax, _state);
cwrange.ptr.p_int[0] = 0;
for(levelidx=0; levelidx<=nh-1; levelidx++)
{
/*
* Prepare radius and root offset
*/
kdroots.ptr.p_int[levelidx] = kdnodes.cnt;
/*
* Generate LevelIdx-th tree and append to multi-tree
*/
curn = 0;
for(i=0; i<=n-1; i++)
{
if( hidx.ptr.p_int[i]<=levelidx )
{
for(j=0; j<=nx-1; j++)
{
curxy.ptr.pp_double[curn][j] = x->ptr.pp_double[i][j]/scalevec->ptr.p_double[j];
}
for(j=0; j<=ny-1; j++)
{
curxy.ptr.pp_double[curn][nx+j] = (double)(0);
}
inc(&curn, _state);
}
}
ae_assert(curn>0, "RBFV2BuildHierarchical: integrity check failed", _state);
kdtreebuild(&curxy, curn, nx, ny, 2, &curtree, _state);
rbfv2_convertandappendtree(&curtree, curn, nx, ny, &kdnodes, &kdsplits, &cw, _state);
/*
* Fill entry of CWRange (we assume that length of CW exactly fits its actual size)
*/
cwrange.ptr.p_int[levelidx+1] = cw.cnt;
}
kdroots.ptr.p_int[nh] = kdnodes.cnt;
/*
* Prepare buffer and scaled dataset
*/
rbfv2_allocatecalcbuffer(s, &calcbuf, _state);
for(i=0; i<=n-1; i++)
{
for(j=0; j<=nx-1; j++)
{
curxy.ptr.pp_double[i][j] = x->ptr.pp_double[i][j]/scalevec->ptr.p_double[j];
}
}
/*
* Calculate average row sizes for each layer; these values are used
* for smooth progress reporting (it adds some overhead, but in most
* cases - insignificant one).
*/
rvectorsetlengthatleast(&avgrowsize, nh, _state);
sumrowsize = (double)(0);
for(levelidx=0; levelidx<=nh-1; levelidx++)
{
cnt = 0;
for(i=0; i<=n-1; i++)
{
for(j=0; j<=nx-1; j++)
{
x0.ptr.p_double[j] = curxy.ptr.pp_double[i][j];
}
cnt = cnt+rbfv2_designmatrixrowsize(&kdnodes, &kdsplits, &cw, &ri, &kdroots, &kdboxmin, &kdboxmax, nx, ny, nh, levelidx, rbfv2nearradius(bf, _state), &x0, &calcbuf, _state);
}
avgrowsize.ptr.p_double[levelidx] = coalesce((double)(cnt), (double)(1), _state)/coalesce((double)(n), (double)(1), _state);
sumrowsize = sumrowsize+avgrowsize.ptr.p_double[levelidx];
}
/*
* Build unconstrained model with LSQR solver, applied layer by layer
*/
for(levelidx=0; levelidx<=nh-1; levelidx++)
{
/*
* Generate A - matrix of basis functions (near radius is used)
*
* NOTE: AvgDiagATA is average value of diagonal element of A^T*A.
* It is used to calculate value of Tikhonov regularization
* coefficient.
*/
nbasis = (cwrange.ptr.p_int[levelidx+1]-cwrange.ptr.p_int[levelidx])/(nx+ny);
ae_assert(cwrange.ptr.p_int[levelidx+1]-cwrange.ptr.p_int[levelidx]==nbasis*(nx+ny), "Assertion failed", _state);
for(i=0; i<=n-1; i++)
{
for(j=0; j<=nx-1; j++)
{
x0.ptr.p_double[j] = curxy.ptr.pp_double[i][j];
}
cnt = rbfv2_designmatrixrowsize(&kdnodes, &kdsplits, &cw, &ri, &kdroots, &kdboxmin, &kdboxmax, nx, ny, nh, levelidx, rbfv2nearradius(bf, _state), &x0, &calcbuf, _state);
nncnt.ptr.p_int[i] = cnt;
for(j=0; j<=rowsperpoint-1; j++)
{
rowsizes.ptr.p_int[i*rowsperpoint+j] = cnt;
}
}
ivectorsetlengthatleast(&rowindexes, nbasis, _state);
rvectorsetlengthatleast(&rowvals, nbasis*rowsperpoint, _state);
rvectorsetlengthatleast(&diagata, nbasis, _state);
sparsecreatecrsbuf(n*rowsperpoint, nbasis, &rowsizes, &sparseacrs, _state);
avgdiagata = 0.0;
for(j=0; j<=nbasis-1; j++)
{
diagata.ptr.p_double[j] = (double)(0);
}
for(i=0; i<=n-1; i++)
{
/*
* Fill design matrix row, diagonal of A^T*A
*/
for(j=0; j<=nx-1; j++)
{
x0.ptr.p_double[j] = curxy.ptr.pp_double[i][j];
}
rbfv2_designmatrixgeneraterow(&kdnodes, &kdsplits, &cw, &ri, &kdroots, &kdboxmin, &kdboxmax, &cwrange, nx, ny, nh, levelidx, bf, rbfv2nearradius(bf, _state), rowsperpoint, penalty, &x0, &calcbuf, &vr2, &voffs, &rowindexes, &rowvals, &cnt, _state);
ae_assert(cnt==nncnt.ptr.p_int[i], "RBFV2BuildHierarchical: integrity check failed", _state);
for(k=0; k<=rowsperpoint-1; k++)
{
for(j=0; j<=cnt-1; j++)
{
val = rowvals.ptr.p_double[j*rowsperpoint+k];
sparseset(&sparseacrs, i*rowsperpoint+k, rowindexes.ptr.p_int[j], val, _state);
avgdiagata = avgdiagata+ae_sqr(val, _state);
diagata.ptr.p_double[rowindexes.ptr.p_int[j]] = diagata.ptr.p_double[rowindexes.ptr.p_int[j]]+ae_sqr(val, _state);
}
}
/*
* Handle possible termination requests
*/
if( *terminationrequest )
{
/*
* Request for termination was submitted, terminate immediately
*/
rbfv2_zerofill(s, nx, ny, bf, _state);
rep->terminationtype = 8;
*progress10000 = 10000;
ae_frame_leave(_state);
return;
}
}
avgdiagata = avgdiagata/nbasis;
rvectorsetlengthatleast(&prec, nbasis, _state);
for(j=0; j<=nbasis-1; j++)
{
prec.ptr.p_double[j] = 1/coalesce(ae_sqrt(diagata.ptr.p_double[j], _state), (double)(1), _state);
}
/*
* solve
*/
maxits = coalescei(s->maxits, rbfv2_defaultmaxits, _state);
rvectorsetlengthatleast(&tmpx, nbasis, _state);
linlsqrcreate(n*rowsperpoint, nbasis, &linstate, _state);
linlsqrsetcond(&linstate, 0.0, 0.0, maxits, _state);
linlsqrsetlambdai(&linstate, ae_sqrt(s->lambdareg*avgdiagata, _state), _state);
for(j=0; j<=ny-1; j++)
{
for(i=0; i<=n*rowsperpoint-1; i++)
{
denseb1.ptr.p_double[i] = rhs.ptr.pp_double[i][j];
}
linlsqrsetb(&linstate, &denseb1, _state);
linlsqrrestart(&linstate, _state);
linlsqrsetxrep(&linstate, ae_true, _state);
while(linlsqriteration(&linstate, _state))
{
if( *terminationrequest )
{
/*
* Request for termination was submitted, terminate immediately
*/
rbfv2_zerofill(s, nx, ny, bf, _state);
rep->terminationtype = 8;
*progress10000 = 10000;
ae_frame_leave(_state);
return;
}
if( linstate.needmv )
{
for(i=0; i<=nbasis-1; i++)
{
tmpx.ptr.p_double[i] = prec.ptr.p_double[i]*linstate.x.ptr.p_double[i];
}
sparsemv(&sparseacrs, &tmpx, &linstate.mv, _state);
continue;
}
if( linstate.needmtv )
{
sparsemtv(&sparseacrs, &linstate.x, &linstate.mtv, _state);
for(i=0; i<=nbasis-1; i++)
{
linstate.mtv.ptr.p_double[i] = prec.ptr.p_double[i]*linstate.mtv.ptr.p_double[i];
}
continue;
}
if( linstate.xupdated )
{
rprogress = (double)(0);
for(i=0; i<=levelidx-1; i++)
{
rprogress = rprogress+maxits*ny*avgrowsize.ptr.p_double[i];
}
rprogress = rprogress+(linlsqrpeekiterationscount(&linstate, _state)+j*maxits)*avgrowsize.ptr.p_double[levelidx];
rprogress = rprogress/(sumrowsize*maxits*ny);
rprogress = 10000*rprogress;
rprogress = ae_maxreal(rprogress, (double)(0), _state);
rprogress = ae_minreal(rprogress, (double)(10000), _state);
ae_assert(*progress10000<=ae_round(rprogress, _state)+1, "HRBF: integrity check failed (progress indicator) even after +1 safeguard correction", _state);
*progress10000 = ae_round(rprogress, _state);
continue;
}
ae_assert(ae_false, "HRBF: unexpected request from LSQR solver", _state);
}
linlsqrresults(&linstate, &densew1, &lsqrrep, _state);
ae_assert(lsqrrep.terminationtype>0, "RBFV2BuildHierarchical: integrity check failed", _state);
for(i=0; i<=nbasis-1; i++)
{
densew1.ptr.p_double[i] = prec.ptr.p_double[i]*densew1.ptr.p_double[i];
}
for(i=0; i<=nbasis-1; i++)
{
offsi = cwrange.ptr.p_int[levelidx]+(nx+ny)*i;
cw.ptr.p_double[offsi+nx+j] = densew1.ptr.p_double[i];
}
}
/*
* Update residuals (far radius is used)
*/
for(i=0; i<=n-1; i++)
{
for(j=0; j<=nx-1; j++)
{
x0.ptr.p_double[j] = curxy.ptr.pp_double[i][j];
}
rbfv2_designmatrixgeneraterow(&kdnodes, &kdsplits, &cw, &ri, &kdroots, &kdboxmin, &kdboxmax, &cwrange, nx, ny, nh, levelidx, bf, rbfv2farradius(bf, _state), rowsperpoint, penalty, &x0, &calcbuf, &vr2, &voffs, &rowindexes, &rowvals, &cnt, _state);
for(j=0; j<=cnt-1; j++)
{
offsj = cwrange.ptr.p_int[levelidx]+(nx+ny)*rowindexes.ptr.p_int[j]+nx;
for(k=0; k<=rowsperpoint-1; k++)
{
val = rowvals.ptr.p_double[j*rowsperpoint+k];
for(k2=0; k2<=ny-1; k2++)
{
rhs.ptr.pp_double[i*rowsperpoint+k][k2] = rhs.ptr.pp_double[i*rowsperpoint+k][k2]-val*cw.ptr.p_double[offsj+k2];
}
}
}
}
}
/*
* Model is built.
*
* Copy local variables by swapping, global ones (ScaleVec) are copied
* explicitly.
*/
s->bf = bf;
s->nh = nh;
ae_swap_vectors(&s->ri, &ri);
ae_swap_vectors(&s->kdroots, &kdroots);
ae_swap_vectors(&s->kdnodes, &kdnodes);
ae_swap_vectors(&s->kdsplits, &kdsplits);
ae_swap_vectors(&s->kdboxmin, &kdboxmin);
ae_swap_vectors(&s->kdboxmax, &kdboxmax);
ae_swap_vectors(&s->cw, &cw);
ae_swap_matrices(&s->v, &v);
ae_vector_set_length(&s->s, nx, _state);
for(i=0; i<=nx-1; i++)
{
s->s.ptr.p_double[i] = scalevec->ptr.p_double[i];
}
rep->terminationtype = 1;
/*
* Calculate maximum and RMS errors
*/
rep->maxerror = (double)(0);
rep->rmserror = (double)(0);
for(i=0; i<=n-1; i++)
{
for(j=0; j<=ny-1; j++)
{
rep->maxerror = ae_maxreal(rep->maxerror, ae_fabs(rhs.ptr.pp_double[i*rowsperpoint][j], _state), _state);
rep->rmserror = rep->rmserror+ae_sqr(rhs.ptr.pp_double[i*rowsperpoint][j], _state);
}
}
rep->rmserror = ae_sqrt(rep->rmserror/(n*ny), _state);
/*
* Update progress reports
*/
*progress10000 = 10000;
ae_frame_leave(_state);
}
/*************************************************************************
Serializer: allocation
-- ALGLIB --
Copyright 02.02.2012 by Bochkanov Sergey
*************************************************************************/
void rbfv2alloc(ae_serializer* s, rbfv2model* model, ae_state *_state)
{
/*
* Data
*/
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
allocrealarray(s, &model->ri, -1, _state);
allocrealarray(s, &model->s, -1, _state);
allocintegerarray(s, &model->kdroots, -1, _state);
allocintegerarray(s, &model->kdnodes, -1, _state);
allocrealarray(s, &model->kdsplits, -1, _state);
allocrealarray(s, &model->kdboxmin, -1, _state);
allocrealarray(s, &model->kdboxmax, -1, _state);
allocrealarray(s, &model->cw, -1, _state);
allocrealmatrix(s, &model->v, -1, -1, _state);
}
/*************************************************************************
Serializer: serialization
-- ALGLIB --
Copyright 02.02.2012 by Bochkanov Sergey
*************************************************************************/
void rbfv2serialize(ae_serializer* s, rbfv2model* model, ae_state *_state)
{
/*
* Data
*/
ae_serializer_serialize_int(s, model->nx, _state);
ae_serializer_serialize_int(s, model->ny, _state);
ae_serializer_serialize_int(s, model->nh, _state);
ae_serializer_serialize_int(s, model->bf, _state);
serializerealarray(s, &model->ri, -1, _state);
serializerealarray(s, &model->s, -1, _state);
serializeintegerarray(s, &model->kdroots, -1, _state);
serializeintegerarray(s, &model->kdnodes, -1, _state);
serializerealarray(s, &model->kdsplits, -1, _state);
serializerealarray(s, &model->kdboxmin, -1, _state);
serializerealarray(s, &model->kdboxmax, -1, _state);
serializerealarray(s, &model->cw, -1, _state);
serializerealmatrix(s, &model->v, -1, -1, _state);
}
/*************************************************************************
Serializer: unserialization
-- ALGLIB --
Copyright 02.02.2012 by Bochkanov Sergey
*************************************************************************/
void rbfv2unserialize(ae_serializer* s,
rbfv2model* model,
ae_state *_state)
{
ae_int_t nx;
ae_int_t ny;
_rbfv2model_clear(model);
/*
* Unserialize primary model parameters, initialize model.
*
* It is necessary to call RBFCreate() because some internal fields
* which are NOT unserialized will need initialization.
*/
ae_serializer_unserialize_int(s, &nx, _state);
ae_serializer_unserialize_int(s, &ny, _state);
rbfv2create(nx, ny, model, _state);
ae_serializer_unserialize_int(s, &model->nh, _state);
ae_serializer_unserialize_int(s, &model->bf, _state);
unserializerealarray(s, &model->ri, _state);
unserializerealarray(s, &model->s, _state);
unserializeintegerarray(s, &model->kdroots, _state);
unserializeintegerarray(s, &model->kdnodes, _state);
unserializerealarray(s, &model->kdsplits, _state);
unserializerealarray(s, &model->kdboxmin, _state);
unserializerealarray(s, &model->kdboxmax, _state);
unserializerealarray(s, &model->cw, _state);
unserializerealmatrix(s, &model->v, _state);
}
/*************************************************************************
Returns far radius for basis function type
*************************************************************************/
double rbfv2farradius(ae_int_t bf, ae_state *_state)
{
double result;
result = (double)(1);
if( bf==0 )
{
result = 5.0;
}
if( bf==1 )
{
result = (double)(3);
}
return result;
}
/*************************************************************************
Returns near radius for basis function type
*************************************************************************/
double rbfv2nearradius(ae_int_t bf, ae_state *_state)
{
double result;
result = (double)(1);
if( bf==0 )
{
result = 3.0;
}
if( bf==1 )
{
result = (double)(3);
}
return result;
}
/*************************************************************************
Returns basis function value.
Assumes that D2>=0
*************************************************************************/
double rbfv2basisfunc(ae_int_t bf, double d2, ae_state *_state)
{
double v;
double result;
result = (double)(0);
if( bf==0 )
{
result = ae_exp(-d2, _state);
return result;
}
if( bf==1 )
{
/*
* if D2<3:
* Exp(1)*Exp(-D2)*Exp(-1/(1-D2/9))
* else:
* 0
*/
v = 1-d2/9;
if( ae_fp_less_eq(v,(double)(0)) )
{
result = (double)(0);
return result;
}
result = 2.718281828459045*ae_exp(-d2, _state)*ae_exp(-1/v, _state);
return result;
}
ae_assert(ae_false, "RBFV2BasisFunc: unknown BF type", _state);
return result;
}
/*************************************************************************
Returns basis function value, first and second derivatives
Assumes that D2>=0
*************************************************************************/
void rbfv2basisfuncdiff2(ae_int_t bf,
double d2,
double* f,
double* df,
double* d2f,
ae_state *_state)
{
double v;
*f = 0;
*df = 0;
*d2f = 0;
if( bf==0 )
{
*f = ae_exp(-d2, _state);
*df = -*f;
*d2f = *f;
return;
}
if( bf==1 )
{
/*
* if D2<3:
* F = Exp(1)*Exp(-D2)*Exp(-1/(1-D2/9))
* dF = -F * [pow(D2/9-1,-2)/9 + 1]
* d2F = -dF * [pow(D2/9-1,-2)/9 + 1] + F*(2/81)*pow(D2/9-1,-3)
* else:
* 0
*/
v = 1-d2/9;
if( ae_fp_less_eq(v,(double)(0)) )
{
*f = (double)(0);
*df = (double)(0);
*d2f = (double)(0);
return;
}
*f = ae_exp((double)(1), _state)*ae_exp(-d2, _state)*ae_exp(-1/v, _state);
*df = -*f*(1/(9*v*v)+1);
*d2f = -*df*(1/(9*v*v)+1)+*f*((double)2/(double)81)/(v*v*v);
return;
}
ae_assert(ae_false, "RBFV2BasisFuncDiff2: unknown BF type", _state);
}
/*************************************************************************
This function calculates values of the RBF model in the given point.
This function should be used when we have NY=1 (scalar function) and NX=1
(1-dimensional space).
This function returns 0.0 when:
* model is not initialized
* NX<>1
*NY<>1
INPUT PARAMETERS:
S - RBF model
X0 - X-coordinate, finite number
RESULT:
value of the model or 0.0 (as defined above)
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
double rbfv2calc1(rbfv2model* s, double x0, ae_state *_state)
{
double result;
ae_assert(ae_isfinite(x0, _state), "RBFCalc1: invalid value for X0 (X0 is Inf)!", _state);
if( s->ny!=1||s->nx!=1 )
{
result = (double)(0);
return result;
}
result = s->v.ptr.pp_double[0][0]*x0-s->v.ptr.pp_double[0][1];
if( s->nh==0 )
{
return result;
}
rbfv2_allocatecalcbuffer(s, &s->calcbuf, _state);
s->calcbuf.x123.ptr.p_double[0] = x0;
rbfv2tscalcbuf(s, &s->calcbuf, &s->calcbuf.x123, &s->calcbuf.y123, _state);
result = s->calcbuf.y123.ptr.p_double[0];
return result;
}
/*************************************************************************
This function calculates values of the RBF model in the given point.
This function should be used when we have NY=1 (scalar function) and NX=2
(2-dimensional space). If you have 3-dimensional space, use RBFCalc3(). If
you have general situation (NX-dimensional space, NY-dimensional function)
you should use general, less efficient implementation RBFCalc().
If you want to calculate function values many times, consider using
RBFGridCalc2(), which is far more efficient than many subsequent calls to
RBFCalc2().
This function returns 0.0 when:
* model is not initialized
* NX<>2
*NY<>1
INPUT PARAMETERS:
S - RBF model
X0 - first coordinate, finite number
X1 - second coordinate, finite number
RESULT:
value of the model or 0.0 (as defined above)
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
double rbfv2calc2(rbfv2model* s, double x0, double x1, ae_state *_state)
{
double result;
ae_assert(ae_isfinite(x0, _state), "RBFCalc2: invalid value for X0 (X0 is Inf)!", _state);
ae_assert(ae_isfinite(x1, _state), "RBFCalc2: invalid value for X1 (X1 is Inf)!", _state);
if( s->ny!=1||s->nx!=2 )
{
result = (double)(0);
return result;
}
result = s->v.ptr.pp_double[0][0]*x0+s->v.ptr.pp_double[0][1]*x1+s->v.ptr.pp_double[0][2];
if( s->nh==0 )
{
return result;
}
rbfv2_allocatecalcbuffer(s, &s->calcbuf, _state);
s->calcbuf.x123.ptr.p_double[0] = x0;
s->calcbuf.x123.ptr.p_double[1] = x1;
rbfv2tscalcbuf(s, &s->calcbuf, &s->calcbuf.x123, &s->calcbuf.y123, _state);
result = s->calcbuf.y123.ptr.p_double[0];
return result;
}
/*************************************************************************
This function calculates values of the RBF model in the given point.
This function should be used when we have NY=1 (scalar function) and NX=3
(3-dimensional space). If you have 2-dimensional space, use RBFCalc2(). If
you have general situation (NX-dimensional space, NY-dimensional function)
you should use general, less efficient implementation RBFCalc().
This function returns 0.0 when:
* model is not initialized
* NX<>3
*NY<>1
INPUT PARAMETERS:
S - RBF model
X0 - first coordinate, finite number
X1 - second coordinate, finite number
X2 - third coordinate, finite number
RESULT:
value of the model or 0.0 (as defined above)
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
double rbfv2calc3(rbfv2model* s,
double x0,
double x1,
double x2,
ae_state *_state)
{
double result;
ae_assert(ae_isfinite(x0, _state), "RBFCalc3: invalid value for X0 (X0 is Inf or NaN)!", _state);
ae_assert(ae_isfinite(x1, _state), "RBFCalc3: invalid value for X1 (X1 is Inf or NaN)!", _state);
ae_assert(ae_isfinite(x2, _state), "RBFCalc3: invalid value for X2 (X2 is Inf or NaN)!", _state);
if( s->ny!=1||s->nx!=3 )
{
result = (double)(0);
return result;
}
result = s->v.ptr.pp_double[0][0]*x0+s->v.ptr.pp_double[0][1]*x1+s->v.ptr.pp_double[0][2]*x2+s->v.ptr.pp_double[0][3];
if( s->nh==0 )
{
return result;
}
rbfv2_allocatecalcbuffer(s, &s->calcbuf, _state);
s->calcbuf.x123.ptr.p_double[0] = x0;
s->calcbuf.x123.ptr.p_double[1] = x1;
s->calcbuf.x123.ptr.p_double[2] = x2;
rbfv2tscalcbuf(s, &s->calcbuf, &s->calcbuf.x123, &s->calcbuf.y123, _state);
result = s->calcbuf.y123.ptr.p_double[0];
return result;
}
/*************************************************************************
This function calculates values of the RBF model at the given point.
Same as RBFCalc(), but does not reallocate Y when in is large enough to
store function values.
INPUT PARAMETERS:
S - RBF model
X - coordinates, array[NX].
X may have more than NX elements, in this case only
leading NX will be used.
Y - possibly preallocated array
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is not reallocated when it
is larger than NY.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfv2calcbuf(rbfv2model* s,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state)
{
rbfv2tscalcbuf(s, &s->calcbuf, x, y, _state);
}
/*************************************************************************
This function calculates values of the RBF model at the given point, using
external buffer object (internal temporaries of RBF model are not
modified).
This function allows to use same RBF model object in different threads,
assuming that different threads use different instances of buffer
structure.
INPUT PARAMETERS:
S - RBF model, may be shared between different threads
Buf - buffer object created for this particular instance of RBF
model with rbfcreatecalcbuffer().
X - coordinates, array[NX].
X may have more than NX elements, in this case only
leading NX will be used.
Y - possibly preallocated array
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is not reallocated when it
is larger than NY.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfv2tscalcbuf(rbfv2model* s,
rbfv2calcbuffer* buf,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
ae_int_t levelidx;
double rcur;
double rquery2;
double invrc2;
ae_int_t nx;
ae_int_t ny;
ae_assert(x->cnt>=s->nx, "RBFCalcBuf: Length(X)<NX", _state);
ae_assert(isfinitevector(x, s->nx, _state), "RBFCalcBuf: X contains infinite or NaN values", _state);
nx = s->nx;
ny = s->ny;
/*
* Handle linear term
*/
if( y->cnt<ny )
{
ae_vector_set_length(y, ny, _state);
}
for(i=0; i<=ny-1; i++)
{
y->ptr.p_double[i] = s->v.ptr.pp_double[i][nx];
for(j=0; j<=nx-1; j++)
{
y->ptr.p_double[i] = y->ptr.p_double[i]+s->v.ptr.pp_double[i][j]*x->ptr.p_double[j];
}
}
if( s->nh==0 )
{
return;
}
/*
* Handle nonlinear term
*/
rbfv2_allocatecalcbuffer(s, buf, _state);
for(j=0; j<=nx-1; j++)
{
buf->x.ptr.p_double[j] = x->ptr.p_double[j]/s->s.ptr.p_double[j];
}
for(levelidx=0; levelidx<=s->nh-1; levelidx++)
{
/*
* Prepare fields of Buf required by PartialCalcRec()
*/
buf->curdist2 = (double)(0);
for(j=0; j<=nx-1; j++)
{
buf->curboxmin.ptr.p_double[j] = s->kdboxmin.ptr.p_double[j];
buf->curboxmax.ptr.p_double[j] = s->kdboxmax.ptr.p_double[j];
if( ae_fp_less(buf->x.ptr.p_double[j],buf->curboxmin.ptr.p_double[j]) )
{
buf->curdist2 = buf->curdist2+ae_sqr(buf->curboxmin.ptr.p_double[j]-buf->x.ptr.p_double[j], _state);
}
else
{
if( ae_fp_greater(buf->x.ptr.p_double[j],buf->curboxmax.ptr.p_double[j]) )
{
buf->curdist2 = buf->curdist2+ae_sqr(buf->x.ptr.p_double[j]-buf->curboxmax.ptr.p_double[j], _state);
}
}
}
/*
* Call PartialCalcRec()
*/
rcur = s->ri.ptr.p_double[levelidx];
invrc2 = 1/(rcur*rcur);
rquery2 = ae_sqr(rcur*rbfv2farradius(s->bf, _state), _state);
rbfv2_partialcalcrec(s, buf, s->kdroots.ptr.p_int[levelidx], invrc2, rquery2, &buf->x, y, _state);
}
}
/*************************************************************************
This function calculates values of the RBF model at the regular grid.
Grid have N0*N1 points, with Point[I,J] = (X0[I], X1[J])
This function returns 0.0 when:
* model is not initialized
* NX<>2
*NY<>1
INPUT PARAMETERS:
S - RBF model
X0 - array of grid nodes, first coordinates, array[N0]
N0 - grid size (number of nodes) in the first dimension
X1 - array of grid nodes, second coordinates, array[N1]
N1 - grid size (number of nodes) in the second dimension
OUTPUT PARAMETERS:
Y - function values, array[N0,N1]. Y is out-variable and
is reallocated by this function.
NOTE: as a special exception, this function supports unordered arrays X0
and X1. However, future versions may be more efficient for X0/X1
ordered by ascending.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfv2gridcalc2(rbfv2model* s,
/* Real */ ae_vector* x0,
ae_int_t n0,
/* Real */ ae_vector* x1,
ae_int_t n1,
/* Real */ ae_matrix* y,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector cpx0;
ae_vector cpx1;
ae_vector dummyx2;
ae_vector dummyx3;
ae_vector dummyflag;
ae_vector p01;
ae_vector p11;
ae_vector p2;
ae_vector vy;
ae_int_t i;
ae_int_t j;
ae_frame_make(_state, &_frame_block);
memset(&cpx0, 0, sizeof(cpx0));
memset(&cpx1, 0, sizeof(cpx1));
memset(&dummyx2, 0, sizeof(dummyx2));
memset(&dummyx3, 0, sizeof(dummyx3));
memset(&dummyflag, 0, sizeof(dummyflag));
memset(&p01, 0, sizeof(p01));
memset(&p11, 0, sizeof(p11));
memset(&p2, 0, sizeof(p2));
memset(&vy, 0, sizeof(vy));
ae_matrix_clear(y);
ae_vector_init(&cpx0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&cpx1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dummyx2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dummyx3, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dummyflag, 0, DT_BOOL, _state, ae_true);
ae_vector_init(&p01, 0, DT_INT, _state, ae_true);
ae_vector_init(&p11, 0, DT_INT, _state, ae_true);
ae_vector_init(&p2, 0, DT_INT, _state, ae_true);
ae_vector_init(&vy, 0, DT_REAL, _state, ae_true);
ae_assert(n0>0, "RBFGridCalc2: invalid value for N0 (N0<=0)!", _state);
ae_assert(n1>0, "RBFGridCalc2: invalid value for N1 (N1<=0)!", _state);
ae_assert(x0->cnt>=n0, "RBFGridCalc2: Length(X0)<N0", _state);
ae_assert(x1->cnt>=n1, "RBFGridCalc2: Length(X1)<N1", _state);
ae_assert(isfinitevector(x0, n0, _state), "RBFGridCalc2: X0 contains infinite or NaN values!", _state);
ae_assert(isfinitevector(x1, n1, _state), "RBFGridCalc2: X1 contains infinite or NaN values!", _state);
ae_matrix_set_length(y, n0, n1, _state);
for(i=0; i<=n0-1; i++)
{
for(j=0; j<=n1-1; j++)
{
y->ptr.pp_double[i][j] = (double)(0);
}
}
if( s->ny!=1||s->nx!=2 )
{
ae_frame_leave(_state);
return;
}
/*
*create and sort arrays
*/
ae_vector_set_length(&cpx0, n0, _state);
for(i=0; i<=n0-1; i++)
{
cpx0.ptr.p_double[i] = x0->ptr.p_double[i];
}
tagsort(&cpx0, n0, &p01, &p2, _state);
ae_vector_set_length(&cpx1, n1, _state);
for(i=0; i<=n1-1; i++)
{
cpx1.ptr.p_double[i] = x1->ptr.p_double[i];
}
tagsort(&cpx1, n1, &p11, &p2, _state);
ae_vector_set_length(&dummyx2, 1, _state);
dummyx2.ptr.p_double[0] = (double)(0);
ae_vector_set_length(&dummyx3, 1, _state);
dummyx3.ptr.p_double[0] = (double)(0);
ae_vector_set_length(&vy, n0*n1, _state);
rbfv2gridcalcvx(s, &cpx0, n0, &cpx1, n1, &dummyx2, 1, &dummyx3, 1, &dummyflag, ae_false, &vy, _state);
for(i=0; i<=n0-1; i++)
{
for(j=0; j<=n1-1; j++)
{
y->ptr.pp_double[i][j] = vy.ptr.p_double[i+j*n0];
}
}
ae_frame_leave(_state);
}
/*************************************************************************
This function is used to perform gridded calculation for 2D, 3D or 4D
problems. It accepts parameters X0...X3 and counters N0...N3. If RBF model
has dimensionality less than 4, corresponding arrays should contain just
one element equal to zero, and corresponding N's should be equal to 1.
NOTE: array Y should be preallocated by caller.
-- ALGLIB --
Copyright 12.07.2016 by Bochkanov Sergey
*************************************************************************/
void rbfv2gridcalcvx(rbfv2model* s,
/* Real */ ae_vector* x0,
ae_int_t n0,
/* Real */ ae_vector* x1,
ae_int_t n1,
/* Real */ ae_vector* x2,
ae_int_t n2,
/* Real */ ae_vector* x3,
ae_int_t n3,
/* Boolean */ ae_vector* flagy,
ae_bool sparsey,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t nx;
ae_int_t ny;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_vector tx;
ae_vector ty;
ae_vector z;
ae_int_t dstoffs;
ae_int_t dummy;
rbfv2gridcalcbuffer bufseedv2;
ae_shared_pool bufpool;
ae_int_t rowidx;
ae_int_t rowcnt;
double v;
double rcur;
ae_int_t levelidx;
double searchradius2;
ae_int_t ntrials;
double avgfuncpernode;
hqrndstate rs;
ae_vector blocks0;
ae_vector blocks1;
ae_vector blocks2;
ae_vector blocks3;
ae_int_t blockscnt0;
ae_int_t blockscnt1;
ae_int_t blockscnt2;
ae_int_t blockscnt3;
double blockwidth0;
double blockwidth1;
double blockwidth2;
double blockwidth3;
ae_int_t maxblocksize;
ae_frame_make(_state, &_frame_block);
memset(&tx, 0, sizeof(tx));
memset(&ty, 0, sizeof(ty));
memset(&z, 0, sizeof(z));
memset(&bufseedv2, 0, sizeof(bufseedv2));
memset(&bufpool, 0, sizeof(bufpool));
memset(&rs, 0, sizeof(rs));
memset(&blocks0, 0, sizeof(blocks0));
memset(&blocks1, 0, sizeof(blocks1));
memset(&blocks2, 0, sizeof(blocks2));
memset(&blocks3, 0, sizeof(blocks3));
ae_vector_init(&tx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&ty, 0, DT_REAL, _state, ae_true);
ae_vector_init(&z, 0, DT_REAL, _state, ae_true);
_rbfv2gridcalcbuffer_init(&bufseedv2, _state, ae_true);
ae_shared_pool_init(&bufpool, _state, ae_true);
_hqrndstate_init(&rs, _state, ae_true);
ae_vector_init(&blocks0, 0, DT_INT, _state, ae_true);
ae_vector_init(&blocks1, 0, DT_INT, _state, ae_true);
ae_vector_init(&blocks2, 0, DT_INT, _state, ae_true);
ae_vector_init(&blocks3, 0, DT_INT, _state, ae_true);
nx = s->nx;
ny = s->ny;
hqrndseed(532, 54734, &rs, _state);
/*
* Perform integrity checks
*/
ae_assert(s->nx==2||s->nx==3, "RBFGridCalcVX: integrity check failed", _state);
ae_assert(s->nx>=4||((x3->cnt>=1&&ae_fp_eq(x3->ptr.p_double[0],(double)(0)))&&n3==1), "RBFGridCalcVX: integrity check failed", _state);
ae_assert(s->nx>=3||((x2->cnt>=1&&ae_fp_eq(x2->ptr.p_double[0],(double)(0)))&&n2==1), "RBFGridCalcVX: integrity check failed", _state);
ae_assert(s->nx>=2||((x1->cnt>=1&&ae_fp_eq(x1->ptr.p_double[0],(double)(0)))&&n1==1), "RBFGridCalcVX: integrity check failed", _state);
/*
* Allocate arrays
*/
ae_assert(s->nx<=4, "RBFGridCalcVX: integrity check failed", _state);
ae_vector_set_length(&z, ny, _state);
ae_vector_set_length(&tx, 4, _state);
ae_vector_set_length(&ty, ny, _state);
/*
* Calculate linear term
*/
rowcnt = n1*n2*n3;
for(rowidx=0; rowidx<=rowcnt-1; rowidx++)
{
/*
* Calculate TX - current position
*/
k = rowidx;
tx.ptr.p_double[0] = (double)(0);
tx.ptr.p_double[1] = x1->ptr.p_double[k%n1];
k = k/n1;
tx.ptr.p_double[2] = x2->ptr.p_double[k%n2];
k = k/n2;
tx.ptr.p_double[3] = x3->ptr.p_double[k%n3];
k = k/n3;
ae_assert(k==0, "RBFGridCalcVX: integrity check failed", _state);
for(j=0; j<=ny-1; j++)
{
v = s->v.ptr.pp_double[j][nx];
for(k=1; k<=nx-1; k++)
{
v = v+tx.ptr.p_double[k]*s->v.ptr.pp_double[j][k];
}
z.ptr.p_double[j] = v;
}
for(i=0; i<=n0-1; i++)
{
dstoffs = ny*(rowidx*n0+i);
if( sparsey&&!flagy->ptr.p_bool[rowidx*n0+i] )
{
for(j=0; j<=ny-1; j++)
{
y->ptr.p_double[j+dstoffs] = (double)(0);
}
continue;
}
v = x0->ptr.p_double[i];
for(j=0; j<=ny-1; j++)
{
y->ptr.p_double[j+dstoffs] = z.ptr.p_double[j]+v*s->v.ptr.pp_double[j][0];
}
}
}
if( s->nh==0 )
{
ae_frame_leave(_state);
return;
}
/*
* Process RBF terms, layer by layer
*/
for(levelidx=0; levelidx<=s->nh-1; levelidx++)
{
rcur = s->ri.ptr.p_double[levelidx];
blockwidth0 = (double)(1);
blockwidth1 = (double)(1);
blockwidth2 = (double)(1);
blockwidth3 = (double)(1);
if( nx>=1 )
{
blockwidth0 = rcur*s->s.ptr.p_double[0];
}
if( nx>=2 )
{
blockwidth1 = rcur*s->s.ptr.p_double[1];
}
if( nx>=3 )
{
blockwidth2 = rcur*s->s.ptr.p_double[2];
}
if( nx>=4 )
{
blockwidth3 = rcur*s->s.ptr.p_double[3];
}
maxblocksize = 8;
/*
* Group grid nodes into blocks according to current radius
*/
ae_vector_set_length(&blocks0, n0+1, _state);
blockscnt0 = 0;
blocks0.ptr.p_int[0] = 0;
for(i=1; i<=n0-1; i++)
{
if( ae_fp_greater(x0->ptr.p_double[i]-x0->ptr.p_double[blocks0.ptr.p_int[blockscnt0]],blockwidth0)||i-blocks0.ptr.p_int[blockscnt0]>=maxblocksize )
{
inc(&blockscnt0, _state);
blocks0.ptr.p_int[blockscnt0] = i;
}
}
inc(&blockscnt0, _state);
blocks0.ptr.p_int[blockscnt0] = n0;
ae_vector_set_length(&blocks1, n1+1, _state);
blockscnt1 = 0;
blocks1.ptr.p_int[0] = 0;
for(i=1; i<=n1-1; i++)
{
if( ae_fp_greater(x1->ptr.p_double[i]-x1->ptr.p_double[blocks1.ptr.p_int[blockscnt1]],blockwidth1)||i-blocks1.ptr.p_int[blockscnt1]>=maxblocksize )
{
inc(&blockscnt1, _state);
blocks1.ptr.p_int[blockscnt1] = i;
}
}
inc(&blockscnt1, _state);
blocks1.ptr.p_int[blockscnt1] = n1;
ae_vector_set_length(&blocks2, n2+1, _state);
blockscnt2 = 0;
blocks2.ptr.p_int[0] = 0;
for(i=1; i<=n2-1; i++)
{
if( ae_fp_greater(x2->ptr.p_double[i]-x2->ptr.p_double[blocks2.ptr.p_int[blockscnt2]],blockwidth2)||i-blocks2.ptr.p_int[blockscnt2]>=maxblocksize )
{
inc(&blockscnt2, _state);
blocks2.ptr.p_int[blockscnt2] = i;
}
}
inc(&blockscnt2, _state);
blocks2.ptr.p_int[blockscnt2] = n2;
ae_vector_set_length(&blocks3, n3+1, _state);
blockscnt3 = 0;
blocks3.ptr.p_int[0] = 0;
for(i=1; i<=n3-1; i++)
{
if( ae_fp_greater(x3->ptr.p_double[i]-x3->ptr.p_double[blocks3.ptr.p_int[blockscnt3]],blockwidth3)||i-blocks3.ptr.p_int[blockscnt3]>=maxblocksize )
{
inc(&blockscnt3, _state);
blocks3.ptr.p_int[blockscnt3] = i;
}
}
inc(&blockscnt3, _state);
blocks3.ptr.p_int[blockscnt3] = n3;
/*
* Prepare seed for shared pool
*/
rbfv2_allocatecalcbuffer(s, &bufseedv2.calcbuf, _state);
ae_shared_pool_set_seed(&bufpool, &bufseedv2, sizeof(bufseedv2), _rbfv2gridcalcbuffer_init, _rbfv2gridcalcbuffer_init_copy, _rbfv2gridcalcbuffer_destroy, _state);
/*
* Determine average number of neighbor per node
*/
searchradius2 = ae_sqr(rcur*rbfv2farradius(s->bf, _state), _state);
ntrials = 100;
avgfuncpernode = 0.0;
for(i=0; i<=ntrials-1; i++)
{
tx.ptr.p_double[0] = x0->ptr.p_double[hqrnduniformi(&rs, n0, _state)];
tx.ptr.p_double[1] = x1->ptr.p_double[hqrnduniformi(&rs, n1, _state)];
tx.ptr.p_double[2] = x2->ptr.p_double[hqrnduniformi(&rs, n2, _state)];
tx.ptr.p_double[3] = x3->ptr.p_double[hqrnduniformi(&rs, n3, _state)];
rbfv2_preparepartialquery(&tx, &s->kdboxmin, &s->kdboxmax, nx, &bufseedv2.calcbuf, &dummy, _state);
avgfuncpernode = avgfuncpernode+(double)rbfv2_partialcountrec(&s->kdnodes, &s->kdsplits, &s->cw, nx, ny, &bufseedv2.calcbuf, s->kdroots.ptr.p_int[levelidx], searchradius2, &tx, _state)/(double)ntrials;
}
/*
* Perform calculation in multithreaded mode
*/
rbfv2partialgridcalcrec(s, x0, n0, x1, n1, x2, n2, x3, n3, &blocks0, 0, blockscnt0, &blocks1, 0, blockscnt1, &blocks2, 0, blockscnt2, &blocks3, 0, blockscnt3, flagy, sparsey, levelidx, avgfuncpernode, &bufpool, y, _state);
}
ae_frame_leave(_state);
}
void rbfv2partialgridcalcrec(rbfv2model* s,
/* Real */ ae_vector* x0,
ae_int_t n0,
/* Real */ ae_vector* x1,
ae_int_t n1,
/* Real */ ae_vector* x2,
ae_int_t n2,
/* Real */ ae_vector* x3,
ae_int_t n3,
/* Integer */ ae_vector* blocks0,
ae_int_t block0a,
ae_int_t block0b,
/* Integer */ ae_vector* blocks1,
ae_int_t block1a,
ae_int_t block1b,
/* Integer */ ae_vector* blocks2,
ae_int_t block2a,
ae_int_t block2b,
/* Integer */ ae_vector* blocks3,
ae_int_t block3a,
ae_int_t block3b,
/* Boolean */ ae_vector* flagy,
ae_bool sparsey,
ae_int_t levelidx,
double avgfuncpernode,
ae_shared_pool* bufpool,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t nx;
ae_int_t ny;
ae_int_t k;
ae_int_t l;
ae_int_t blkidx;
ae_int_t blkcnt;
ae_int_t nodeidx;
ae_int_t nodescnt;
ae_int_t rowidx;
ae_int_t rowscnt;
ae_int_t i0;
ae_int_t i1;
ae_int_t i2;
ae_int_t i3;
ae_int_t j0;
ae_int_t j1;
ae_int_t j2;
ae_int_t j3;
double rcur;
double invrc2;
double rquery2;
double rfar2;
ae_int_t dstoffs;
ae_int_t srcoffs;
ae_int_t dummy;
double rowwidth;
double maxrowwidth;
double problemcost;
ae_int_t maxbs;
ae_int_t midpoint;
ae_bool emptyrow;
rbfv2gridcalcbuffer *buf;
ae_smart_ptr _buf;
ae_frame_make(_state, &_frame_block);
memset(&_buf, 0, sizeof(_buf));
ae_smart_ptr_init(&_buf, (void**)&buf, _state, ae_true);
nx = s->nx;
ny = s->ny;
/*
* Integrity checks
*/
ae_assert(s->nx==2||s->nx==3, "RBFV2PartialGridCalcRec: integrity check failed", _state);
/*
* Try to split large problem
*/
problemcost = s->ny*2*(avgfuncpernode+1);
problemcost = problemcost*(blocks0->ptr.p_int[block0b]-blocks0->ptr.p_int[block0a]);
problemcost = problemcost*(blocks1->ptr.p_int[block1b]-blocks1->ptr.p_int[block1a]);
problemcost = problemcost*(blocks2->ptr.p_int[block2b]-blocks2->ptr.p_int[block2a]);
problemcost = problemcost*(blocks3->ptr.p_int[block3b]-blocks3->ptr.p_int[block3a]);
maxbs = 0;
maxbs = ae_maxint(maxbs, block0b-block0a, _state);
maxbs = ae_maxint(maxbs, block1b-block1a, _state);
maxbs = ae_maxint(maxbs, block2b-block2a, _state);
maxbs = ae_maxint(maxbs, block3b-block3a, _state);
if( ae_fp_greater_eq(problemcost*rbfv2_complexitymultiplier,smpactivationlevel(_state)) )
{
if( _trypexec_rbfv2partialgridcalcrec(s,x0,n0,x1,n1,x2,n2,x3,n3,blocks0,block0a,block0b,blocks1,block1a,block1b,blocks2,block2a,block2b,blocks3,block3a,block3b,flagy,sparsey,levelidx,avgfuncpernode,bufpool,y, _state) )
{
ae_frame_leave(_state);
return;
}
}
if( ae_fp_greater_eq(problemcost*rbfv2_complexitymultiplier,spawnlevel(_state))&&maxbs>=2 )
{
if( block0b-block0a==maxbs )
{
midpoint = block0a+maxbs/2;
rbfv2partialgridcalcrec(s, x0, n0, x1, n1, x2, n2, x3, n3, blocks0, block0a, midpoint, blocks1, block1a, block1b, blocks2, block2a, block2b, blocks3, block3a, block3b, flagy, sparsey, levelidx, avgfuncpernode, bufpool, y, _state);
rbfv2partialgridcalcrec(s, x0, n0, x1, n1, x2, n2, x3, n3, blocks0, midpoint, block0b, blocks1, block1a, block1b, blocks2, block2a, block2b, blocks3, block3a, block3b, flagy, sparsey, levelidx, avgfuncpernode, bufpool, y, _state);
ae_frame_leave(_state);
return;
}
if( block1b-block1a==maxbs )
{
midpoint = block1a+maxbs/2;
rbfv2partialgridcalcrec(s, x0, n0, x1, n1, x2, n2, x3, n3, blocks0, block0a, block0b, blocks1, block1a, midpoint, blocks2, block2a, block2b, blocks3, block3a, block3b, flagy, sparsey, levelidx, avgfuncpernode, bufpool, y, _state);
rbfv2partialgridcalcrec(s, x0, n0, x1, n1, x2, n2, x3, n3, blocks0, block0a, block0b, blocks1, midpoint, block1b, blocks2, block2a, block2b, blocks3, block3a, block3b, flagy, sparsey, levelidx, avgfuncpernode, bufpool, y, _state);
ae_frame_leave(_state);
return;
}
if( block2b-block2a==maxbs )
{
midpoint = block2a+maxbs/2;
rbfv2partialgridcalcrec(s, x0, n0, x1, n1, x2, n2, x3, n3, blocks0, block0a, block0b, blocks1, block1a, block1b, blocks2, block2a, midpoint, blocks3, block3a, block3b, flagy, sparsey, levelidx, avgfuncpernode, bufpool, y, _state);
rbfv2partialgridcalcrec(s, x0, n0, x1, n1, x2, n2, x3, n3, blocks0, block0a, block0b, blocks1, block1a, block1b, blocks2, midpoint, block2b, blocks3, block3a, block3b, flagy, sparsey, levelidx, avgfuncpernode, bufpool, y, _state);
ae_frame_leave(_state);
return;
}
if( block3b-block3a==maxbs )
{
midpoint = block3a+maxbs/2;
rbfv2partialgridcalcrec(s, x0, n0, x1, n1, x2, n2, x3, n3, blocks0, block0a, block0b, blocks1, block1a, block1b, blocks2, block2a, block2b, blocks3, block3a, midpoint, flagy, sparsey, levelidx, avgfuncpernode, bufpool, y, _state);
rbfv2partialgridcalcrec(s, x0, n0, x1, n1, x2, n2, x3, n3, blocks0, block0a, block0b, blocks1, block1a, block1b, blocks2, block2a, block2b, blocks3, midpoint, block3b, flagy, sparsey, levelidx, avgfuncpernode, bufpool, y, _state);
ae_frame_leave(_state);
return;
}
ae_assert(ae_false, "RBFV2PartialGridCalcRec: integrity check failed", _state);
}
/*
* Retrieve buffer object from pool (it will be returned later)
*/
ae_shared_pool_retrieve(bufpool, &_buf, _state);
/*
* Calculate RBF model
*/
ae_assert(nx<=4, "RBFV2PartialGridCalcRec: integrity check failed", _state);
ae_vector_set_length(&buf->tx, 4, _state);
ae_vector_set_length(&buf->cx, 4, _state);
ae_vector_set_length(&buf->ty, ny, _state);
rcur = s->ri.ptr.p_double[levelidx];
invrc2 = 1/(rcur*rcur);
blkcnt = (block3b-block3a)*(block2b-block2a)*(block1b-block1a)*(block0b-block0a);
for(blkidx=0; blkidx<=blkcnt-1; blkidx++)
{
/*
* Select block (I0,I1,I2,I3).
*
* NOTE: for problems with NX<4 corresponding I_? are zero.
*/
k = blkidx;
i0 = block0a+k%(block0b-block0a);
k = k/(block0b-block0a);
i1 = block1a+k%(block1b-block1a);
k = k/(block1b-block1a);
i2 = block2a+k%(block2b-block2a);
k = k/(block2b-block2a);
i3 = block3a+k%(block3b-block3a);
k = k/(block3b-block3a);
ae_assert(k==0, "RBFV2PartialGridCalcRec: integrity check failed", _state);
/*
* We partitioned grid into blocks and selected block with
* index (I0,I1,I2,I3). This block is a 4D cube (some dimensions
* may be zero) of nodes with indexes (J0,J1,J2,J3), which is
* further partitioned into a set of rows, each row corresponding
* to indexes J1...J3 being fixed.
*
* We process block row by row, and each row may be handled
* by either "generic" (nodes are processed separately) or
* batch algorithm (that's the reason to use rows, after all).
*
*
* Process nodes of the block
*/
rowscnt = (blocks3->ptr.p_int[i3+1]-blocks3->ptr.p_int[i3])*(blocks2->ptr.p_int[i2+1]-blocks2->ptr.p_int[i2])*(blocks1->ptr.p_int[i1+1]-blocks1->ptr.p_int[i1]);
for(rowidx=0; rowidx<=rowscnt-1; rowidx++)
{
/*
* Find out node indexes (*,J1,J2,J3).
*
* NOTE: for problems with NX<4 corresponding J_? are zero.
*/
k = rowidx;
j1 = blocks1->ptr.p_int[i1]+k%(blocks1->ptr.p_int[i1+1]-blocks1->ptr.p_int[i1]);
k = k/(blocks1->ptr.p_int[i1+1]-blocks1->ptr.p_int[i1]);
j2 = blocks2->ptr.p_int[i2]+k%(blocks2->ptr.p_int[i2+1]-blocks2->ptr.p_int[i2]);
k = k/(blocks2->ptr.p_int[i2+1]-blocks2->ptr.p_int[i2]);
j3 = blocks3->ptr.p_int[i3]+k%(blocks3->ptr.p_int[i3+1]-blocks3->ptr.p_int[i3]);
k = k/(blocks3->ptr.p_int[i3+1]-blocks3->ptr.p_int[i3]);
ae_assert(k==0, "RBFV2PartialGridCalcRec: integrity check failed", _state);
/*
* Analyze row, skip completely empty rows
*/
nodescnt = blocks0->ptr.p_int[i0+1]-blocks0->ptr.p_int[i0];
srcoffs = blocks0->ptr.p_int[i0]+(j1+(j2+j3*n2)*n1)*n0;
emptyrow = ae_true;
for(nodeidx=0; nodeidx<=nodescnt-1; nodeidx++)
{
emptyrow = emptyrow&&(sparsey&&!flagy->ptr.p_bool[srcoffs+nodeidx]);
}
if( emptyrow )
{
continue;
}
/*
* Process row - use either "batch" (rowsize>1) or "generic"
* (row size is 1) algorithm.
*
* NOTE: "generic" version may also be used as fallback code for
* situations when we do not want to use batch code.
*/
maxrowwidth = 0.5*rbfv2nearradius(s->bf, _state)*rcur*s->s.ptr.p_double[0];
rowwidth = x0->ptr.p_double[blocks0->ptr.p_int[i0+1]-1]-x0->ptr.p_double[blocks0->ptr.p_int[i0]];
if( nodescnt>1&&ae_fp_less_eq(rowwidth,maxrowwidth) )
{
/*
* "Batch" code which processes entire row at once, saving
* some time in kd-tree search code.
*/
rquery2 = ae_sqr(rcur*rbfv2farradius(s->bf, _state)+0.5*rowwidth/s->s.ptr.p_double[0], _state);
rfar2 = ae_sqr(rcur*rbfv2farradius(s->bf, _state), _state);
j0 = blocks0->ptr.p_int[i0];
if( nx>0 )
{
buf->cx.ptr.p_double[0] = (x0->ptr.p_double[j0]+0.5*rowwidth)/s->s.ptr.p_double[0];
}
if( nx>1 )
{
buf->cx.ptr.p_double[1] = x1->ptr.p_double[j1]/s->s.ptr.p_double[1];
}
if( nx>2 )
{
buf->cx.ptr.p_double[2] = x2->ptr.p_double[j2]/s->s.ptr.p_double[2];
}
if( nx>3 )
{
buf->cx.ptr.p_double[3] = x3->ptr.p_double[j3]/s->s.ptr.p_double[3];
}
srcoffs = j0+(j1+(j2+j3*n2)*n1)*n0;
dstoffs = ny*srcoffs;
rvectorsetlengthatleast(&buf->rx, nodescnt, _state);
bvectorsetlengthatleast(&buf->rf, nodescnt, _state);
rvectorsetlengthatleast(&buf->ry, nodescnt*ny, _state);
for(nodeidx=0; nodeidx<=nodescnt-1; nodeidx++)
{
buf->rx.ptr.p_double[nodeidx] = x0->ptr.p_double[j0+nodeidx]/s->s.ptr.p_double[0];
buf->rf.ptr.p_bool[nodeidx] = !sparsey||flagy->ptr.p_bool[srcoffs+nodeidx];
}
for(k=0; k<=nodescnt*ny-1; k++)
{
buf->ry.ptr.p_double[k] = (double)(0);
}
rbfv2_preparepartialquery(&buf->cx, &s->kdboxmin, &s->kdboxmax, nx, &buf->calcbuf, &dummy, _state);
rbfv2_partialrowcalcrec(s, &buf->calcbuf, s->kdroots.ptr.p_int[levelidx], invrc2, rquery2, rfar2, &buf->cx, &buf->rx, &buf->rf, nodescnt, &buf->ry, _state);
for(k=0; k<=nodescnt*ny-1; k++)
{
y->ptr.p_double[dstoffs+k] = y->ptr.p_double[dstoffs+k]+buf->ry.ptr.p_double[k];
}
}
else
{
/*
* "Generic" code. Although we usually move here
* only when NodesCnt=1, we still use a loop on
* NodeIdx just to be able to use this branch as
* fallback code without any modifications.
*/
rquery2 = ae_sqr(rcur*rbfv2farradius(s->bf, _state), _state);
for(nodeidx=0; nodeidx<=nodescnt-1; nodeidx++)
{
/*
* Prepare TX - current point
*/
j0 = blocks0->ptr.p_int[i0]+nodeidx;
if( nx>0 )
{
buf->tx.ptr.p_double[0] = x0->ptr.p_double[j0]/s->s.ptr.p_double[0];
}
if( nx>1 )
{
buf->tx.ptr.p_double[1] = x1->ptr.p_double[j1]/s->s.ptr.p_double[1];
}
if( nx>2 )
{
buf->tx.ptr.p_double[2] = x2->ptr.p_double[j2]/s->s.ptr.p_double[2];
}
if( nx>3 )
{
buf->tx.ptr.p_double[3] = x3->ptr.p_double[j3]/s->s.ptr.p_double[3];
}
/*
* Evaluate and add to Y
*/
srcoffs = j0+(j1+(j2+j3*n2)*n1)*n0;
dstoffs = ny*srcoffs;
for(l=0; l<=ny-1; l++)
{
buf->ty.ptr.p_double[l] = (double)(0);
}
if( !sparsey||flagy->ptr.p_bool[srcoffs] )
{
rbfv2_preparepartialquery(&buf->tx, &s->kdboxmin, &s->kdboxmax, nx, &buf->calcbuf, &dummy, _state);
rbfv2_partialcalcrec(s, &buf->calcbuf, s->kdroots.ptr.p_int[levelidx], invrc2, rquery2, &buf->tx, &buf->ty, _state);
}
for(l=0; l<=ny-1; l++)
{
y->ptr.p_double[dstoffs+l] = y->ptr.p_double[dstoffs+l]+buf->ty.ptr.p_double[l];
}
}
}
}
}
/*
* Recycle buffer object back to pool
*/
ae_shared_pool_recycle(bufpool, &_buf, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Serial stub for GPL edition.
*************************************************************************/
ae_bool _trypexec_rbfv2partialgridcalcrec(rbfv2model* s,
/* Real */ ae_vector* x0,
ae_int_t n0,
/* Real */ ae_vector* x1,
ae_int_t n1,
/* Real */ ae_vector* x2,
ae_int_t n2,
/* Real */ ae_vector* x3,
ae_int_t n3,
/* Integer */ ae_vector* blocks0,
ae_int_t block0a,
ae_int_t block0b,
/* Integer */ ae_vector* blocks1,
ae_int_t block1a,
ae_int_t block1b,
/* Integer */ ae_vector* blocks2,
ae_int_t block2a,
ae_int_t block2b,
/* Integer */ ae_vector* blocks3,
ae_int_t block3a,
ae_int_t block3b,
/* Boolean */ ae_vector* flagy,
ae_bool sparsey,
ae_int_t levelidx,
double avgfuncpernode,
ae_shared_pool* bufpool,
/* Real */ ae_vector* y,
ae_state *_state)
{
return ae_false;
}
/*************************************************************************
This function "unpacks" RBF model by extracting its coefficients.
INPUT PARAMETERS:
S - RBF model
OUTPUT PARAMETERS:
NX - dimensionality of argument
NY - dimensionality of the target function
XWR - model information, array[NC,NX+NY+1].
One row of the array corresponds to one basis function:
* first NX columns - coordinates of the center
* next NY columns - weights, one per dimension of the
function being modelled
* last NX columns - radii, per dimension
NC - number of the centers
V - polynomial term , array[NY,NX+1]. One row per one
dimension of the function being modelled. First NX
elements are linear coefficients, V[NX] is equal to the
constant part.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfv2unpack(rbfv2model* s,
ae_int_t* nx,
ae_int_t* ny,
/* Real */ ae_matrix* xwr,
ae_int_t* nc,
/* Real */ ae_matrix* v,
ae_state *_state)
{
ae_int_t i;
ae_int_t ncactual;
*nx = 0;
*ny = 0;
ae_matrix_clear(xwr);
*nc = 0;
ae_matrix_clear(v);
*nx = s->nx;
*ny = s->ny;
*nc = 0;
/*
* Fill V
*/
ae_matrix_set_length(v, s->ny, s->nx+1, _state);
for(i=0; i<=s->ny-1; i++)
{
ae_v_move(&v->ptr.pp_double[i][0], 1, &s->v.ptr.pp_double[i][0], 1, ae_v_len(0,s->nx));
}
/*
* Fill XWR
*/
ae_assert(s->cw.cnt%(s->nx+s->ny)==0, "RBFV2Unpack: integrity error", _state);
*nc = s->cw.cnt/(s->nx+s->ny);
ncactual = 0;
if( *nc>0 )
{
ae_matrix_set_length(xwr, *nc, s->nx+s->ny+s->nx, _state);
for(i=0; i<=s->nh-1; i++)
{
rbfv2_partialunpackrec(&s->kdnodes, &s->kdsplits, &s->cw, &s->s, s->nx, s->ny, s->kdroots.ptr.p_int[i], s->ri.ptr.p_double[i], xwr, &ncactual, _state);
}
}
ae_assert(*nc==ncactual, "RBFV2Unpack: integrity error", _state);
}
static ae_bool rbfv2_rbfv2buildlinearmodel(/* Real */ ae_matrix* x,
/* Real */ ae_matrix* y,
ae_int_t n,
ae_int_t nx,
ae_int_t ny,
ae_int_t modeltype,
/* Real */ ae_matrix* v,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector tmpy;
ae_matrix a;
double scaling;
ae_vector shifting;
double mn;
double mx;
ae_vector c;
lsfitreport rep;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t info;
ae_bool result;
ae_frame_make(_state, &_frame_block);
memset(&tmpy, 0, sizeof(tmpy));
memset(&a, 0, sizeof(a));
memset(&shifting, 0, sizeof(shifting));
memset(&c, 0, sizeof(c));
memset(&rep, 0, sizeof(rep));
ae_matrix_clear(v);
ae_vector_init(&tmpy, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&a, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&shifting, 0, DT_REAL, _state, ae_true);
ae_vector_init(&c, 0, DT_REAL, _state, ae_true);
_lsfitreport_init(&rep, _state, ae_true);
ae_assert(n>=0, "BuildLinearModel: N<0", _state);
ae_assert(nx>0, "BuildLinearModel: NX<=0", _state);
ae_assert(ny>0, "BuildLinearModel: NY<=0", _state);
/*
* Handle degenerate case (N=0)
*/
result = ae_true;
ae_matrix_set_length(v, ny, nx+1, _state);
if( n==0 )
{
for(j=0; j<=nx; j++)
{
for(i=0; i<=ny-1; i++)
{
v->ptr.pp_double[i][j] = (double)(0);
}
}
ae_frame_leave(_state);
return result;
}
/*
* Allocate temporaries
*/
ae_vector_set_length(&tmpy, n, _state);
/*
* General linear model.
*/
if( modeltype==1 )
{
/*
* Calculate scaling/shifting, transform variables, prepare LLS problem
*/
ae_matrix_set_length(&a, n, nx+1, _state);
ae_vector_set_length(&shifting, nx, _state);
scaling = (double)(0);
for(i=0; i<=nx-1; i++)
{
mn = x->ptr.pp_double[0][i];
mx = mn;
for(j=1; j<=n-1; j++)
{
if( ae_fp_greater(mn,x->ptr.pp_double[j][i]) )
{
mn = x->ptr.pp_double[j][i];
}
if( ae_fp_less(mx,x->ptr.pp_double[j][i]) )
{
mx = x->ptr.pp_double[j][i];
}
}
scaling = ae_maxreal(scaling, mx-mn, _state);
shifting.ptr.p_double[i] = 0.5*(mx+mn);
}
if( ae_fp_eq(scaling,(double)(0)) )
{
scaling = (double)(1);
}
else
{
scaling = 0.5*scaling;
}
for(i=0; i<=n-1; i++)
{
for(j=0; j<=nx-1; j++)
{
a.ptr.pp_double[i][j] = (x->ptr.pp_double[i][j]-shifting.ptr.p_double[j])/scaling;
}
}
for(i=0; i<=n-1; i++)
{
a.ptr.pp_double[i][nx] = (double)(1);
}
/*
* Solve linear system in transformed variables, make backward
*/
for(i=0; i<=ny-1; i++)
{
for(j=0; j<=n-1; j++)
{
tmpy.ptr.p_double[j] = y->ptr.pp_double[j][i];
}
lsfitlinear(&tmpy, &a, n, nx+1, &info, &c, &rep, _state);
if( info<=0 )
{
result = ae_false;
ae_frame_leave(_state);
return result;
}
for(j=0; j<=nx-1; j++)
{
v->ptr.pp_double[i][j] = c.ptr.p_double[j]/scaling;
}
v->ptr.pp_double[i][nx] = c.ptr.p_double[nx];
for(j=0; j<=nx-1; j++)
{
v->ptr.pp_double[i][nx] = v->ptr.pp_double[i][nx]-shifting.ptr.p_double[j]*v->ptr.pp_double[i][j];
}
for(j=0; j<=n-1; j++)
{
for(k=0; k<=nx-1; k++)
{
y->ptr.pp_double[j][i] = y->ptr.pp_double[j][i]-x->ptr.pp_double[j][k]*v->ptr.pp_double[i][k];
}
y->ptr.pp_double[j][i] = y->ptr.pp_double[j][i]-v->ptr.pp_double[i][nx];
}
}
ae_frame_leave(_state);
return result;
}
/*
* Constant model, very simple
*/
if( modeltype==2 )
{
for(i=0; i<=ny-1; i++)
{
for(j=0; j<=nx; j++)
{
v->ptr.pp_double[i][j] = (double)(0);
}
for(j=0; j<=n-1; j++)
{
v->ptr.pp_double[i][nx] = v->ptr.pp_double[i][nx]+y->ptr.pp_double[j][i];
}
if( n>0 )
{
v->ptr.pp_double[i][nx] = v->ptr.pp_double[i][nx]/n;
}
for(j=0; j<=n-1; j++)
{
y->ptr.pp_double[j][i] = y->ptr.pp_double[j][i]-v->ptr.pp_double[i][nx];
}
}
ae_frame_leave(_state);
return result;
}
/*
* Zero model
*/
ae_assert(modeltype==3, "BuildLinearModel: unknown model type", _state);
for(i=0; i<=ny-1; i++)
{
for(j=0; j<=nx; j++)
{
v->ptr.pp_double[i][j] = (double)(0);
}
}
ae_frame_leave(_state);
return result;
}
/*************************************************************************
Reallocates calcBuf if necessary, reuses previously allocated space if
possible.
-- ALGLIB --
Copyright 20.06.2016 by Sergey Bochkanov
*************************************************************************/
static void rbfv2_allocatecalcbuffer(rbfv2model* s,
rbfv2calcbuffer* buf,
ae_state *_state)
{
if( buf->x.cnt<s->nx )
{
ae_vector_set_length(&buf->x, s->nx, _state);
}
if( buf->curboxmin.cnt<s->nx )
{
ae_vector_set_length(&buf->curboxmin, s->nx, _state);
}
if( buf->curboxmax.cnt<s->nx )
{
ae_vector_set_length(&buf->curboxmax, s->nx, _state);
}
if( buf->x123.cnt<s->nx )
{
ae_vector_set_length(&buf->x123, s->nx, _state);
}
if( buf->y123.cnt<s->ny )
{
ae_vector_set_length(&buf->y123, s->ny, _state);
}
}
/*************************************************************************
Extracts structure (and XY-values too) from kd-tree built for a small
subset of points and appends it to multi-tree.
-- ALGLIB --
Copyright 20.06.2016 by Sergey Bochkanov
*************************************************************************/
static void rbfv2_convertandappendtree(kdtree* curtree,
ae_int_t n,
ae_int_t nx,
ae_int_t ny,
/* Integer */ ae_vector* kdnodes,
/* Real */ ae_vector* kdsplits,
/* Real */ ae_vector* cw,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t nodesbase;
ae_int_t splitsbase;
ae_int_t cwbase;
ae_vector localnodes;
ae_vector localsplits;
ae_vector localcw;
ae_matrix xybuf;
ae_int_t localnodessize;
ae_int_t localsplitssize;
ae_int_t localcwsize;
ae_int_t i;
ae_frame_make(_state, &_frame_block);
memset(&localnodes, 0, sizeof(localnodes));
memset(&localsplits, 0, sizeof(localsplits));
memset(&localcw, 0, sizeof(localcw));
memset(&xybuf, 0, sizeof(xybuf));
ae_vector_init(&localnodes, 0, DT_INT, _state, ae_true);
ae_vector_init(&localsplits, 0, DT_REAL, _state, ae_true);
ae_vector_init(&localcw, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&xybuf, 0, 0, DT_REAL, _state, ae_true);
/*
* Calculate base offsets
*/
nodesbase = kdnodes->cnt;
splitsbase = kdsplits->cnt;
cwbase = cw->cnt;
/*
* Prepare local copy of tree
*/
ae_vector_set_length(&localnodes, n*rbfv2_maxnodesize, _state);
ae_vector_set_length(&localsplits, n, _state);
ae_vector_set_length(&localcw, (nx+ny)*n, _state);
localnodessize = 0;
localsplitssize = 0;
localcwsize = 0;
rbfv2_converttreerec(curtree, n, nx, ny, 0, nodesbase, splitsbase, cwbase, &localnodes, &localnodessize, &localsplits, &localsplitssize, &localcw, &localcwsize, &xybuf, _state);
/*
* Append to multi-tree
*/
ivectorresize(kdnodes, kdnodes->cnt+localnodessize, _state);
rvectorresize(kdsplits, kdsplits->cnt+localsplitssize, _state);
rvectorresize(cw, cw->cnt+localcwsize, _state);
for(i=0; i<=localnodessize-1; i++)
{
kdnodes->ptr.p_int[nodesbase+i] = localnodes.ptr.p_int[i];
}
for(i=0; i<=localsplitssize-1; i++)
{
kdsplits->ptr.p_double[splitsbase+i] = localsplits.ptr.p_double[i];
}
for(i=0; i<=localcwsize-1; i++)
{
cw->ptr.p_double[cwbase+i] = localcw.ptr.p_double[i];
}
ae_frame_leave(_state);
}
/*************************************************************************
Recurrent tree conversion
CurTree - tree to convert
N, NX, NY - dataset metrics
NodeOffset - offset of current tree node, 0 for root
NodesBase - a value which is added to intra-tree node indexes;
although this tree is stored in separate array, it
is intended to be stored in the larger tree, with
localNodes being moved to offset NodesBase.
SplitsBase - similarly, offset of localSplits in the final tree
CWBase - similarly, offset of localCW in the final tree
*************************************************************************/
static void rbfv2_converttreerec(kdtree* curtree,
ae_int_t n,
ae_int_t nx,
ae_int_t ny,
ae_int_t nodeoffset,
ae_int_t nodesbase,
ae_int_t splitsbase,
ae_int_t cwbase,
/* Integer */ ae_vector* localnodes,
ae_int_t* localnodessize,
/* Real */ ae_vector* localsplits,
ae_int_t* localsplitssize,
/* Real */ ae_vector* localcw,
ae_int_t* localcwsize,
/* Real */ ae_matrix* xybuf,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
ae_int_t nodetype;
ae_int_t cnt;
ae_int_t d;
double s;
ae_int_t nodele;
ae_int_t nodege;
ae_int_t oldnodessize;
kdtreeexplorenodetype(curtree, nodeoffset, &nodetype, _state);
/*
* Leaf node
*/
if( nodetype==0 )
{
kdtreeexploreleaf(curtree, nodeoffset, xybuf, &cnt, _state);
ae_assert(localnodes->cnt>=*localnodessize+2, "ConvertTreeRec: integrity check failed", _state);
ae_assert(localcw->cnt>=*localcwsize+cnt*(nx+ny), "ConvertTreeRec: integrity check failed", _state);
localnodes->ptr.p_int[*localnodessize+0] = cnt;
localnodes->ptr.p_int[*localnodessize+1] = cwbase+(*localcwsize);
*localnodessize = *localnodessize+2;
for(i=0; i<=cnt-1; i++)
{
for(j=0; j<=nx+ny-1; j++)
{
localcw->ptr.p_double[*localcwsize+i*(nx+ny)+j] = xybuf->ptr.pp_double[i][j];
}
}
*localcwsize = *localcwsize+cnt*(nx+ny);
return;
}
/*
* Split node
*/
if( nodetype==1 )
{
kdtreeexploresplit(curtree, nodeoffset, &d, &s, &nodele, &nodege, _state);
ae_assert(localnodes->cnt>=*localnodessize+rbfv2_maxnodesize, "ConvertTreeRec: integrity check failed", _state);
ae_assert(localsplits->cnt>=*localsplitssize+1, "ConvertTreeRec: integrity check failed", _state);
oldnodessize = *localnodessize;
localnodes->ptr.p_int[*localnodessize+0] = 0;
localnodes->ptr.p_int[*localnodessize+1] = d;
localnodes->ptr.p_int[*localnodessize+2] = splitsbase+(*localsplitssize);
localnodes->ptr.p_int[*localnodessize+3] = -1;
localnodes->ptr.p_int[*localnodessize+4] = -1;
*localnodessize = *localnodessize+5;
localsplits->ptr.p_double[*localsplitssize+0] = s;
*localsplitssize = *localsplitssize+1;
localnodes->ptr.p_int[oldnodessize+3] = nodesbase+(*localnodessize);
rbfv2_converttreerec(curtree, n, nx, ny, nodele, nodesbase, splitsbase, cwbase, localnodes, localnodessize, localsplits, localsplitssize, localcw, localcwsize, xybuf, _state);
localnodes->ptr.p_int[oldnodessize+4] = nodesbase+(*localnodessize);
rbfv2_converttreerec(curtree, n, nx, ny, nodege, nodesbase, splitsbase, cwbase, localnodes, localnodessize, localsplits, localsplitssize, localcw, localcwsize, xybuf, _state);
return;
}
/*
* Integrity error
*/
ae_assert(ae_false, "ConvertTreeRec: integrity check failed", _state);
}
/*************************************************************************
This function performs partial calculation of hierarchical model: given
evaluation point X and partially computed value Y, it updates Y by values
computed using part of multi-tree given by RootIdx.
INPUT PARAMETERS:
S - V2 model
Buf - calc-buffer, this function uses following fields:
* Buf.CurBoxMin - should be set by caller
* Buf.CurBoxMax - should be set by caller
* Buf.CurDist2 - squared distance from X to current bounding box,
should be set by caller
RootIdx - offset of partial kd-tree
InvR2 - 1/R^2, where R is basis function radius
QueryR2 - squared query radius, usually it is (R*FarRadius(BasisFunction))^2
X - evaluation point, array[NX]
Y - partial value, array[NY]
OUTPUT PARAMETERS
Y - updated partial value
-- ALGLIB --
Copyright 20.06.2016 by Bochkanov Sergey
*************************************************************************/
static void rbfv2_partialcalcrec(rbfv2model* s,
rbfv2calcbuffer* buf,
ae_int_t rootidx,
double invr2,
double queryr2,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
double ptdist2;
double v;
double v0;
double v1;
ae_int_t cwoffs;
ae_int_t cwcnt;
ae_int_t itemoffs;
double arg;
double val;
ae_int_t d;
double split;
ae_int_t childle;
ae_int_t childge;
ae_int_t childoffs;
ae_bool updatemin;
double prevdist2;
double t1;
ae_int_t nx;
ae_int_t ny;
nx = s->nx;
ny = s->ny;
/*
* Helps to avoid spurious warnings
*/
val = (double)(0);
/*
* Leaf node.
*/
if( s->kdnodes.ptr.p_int[rootidx]>0 )
{
cwcnt = s->kdnodes.ptr.p_int[rootidx+0];
cwoffs = s->kdnodes.ptr.p_int[rootidx+1];
for(i=0; i<=cwcnt-1; i++)
{
/*
* Calculate distance
*/
itemoffs = cwoffs+i*(nx+ny);
ptdist2 = (double)(0);
for(j=0; j<=nx-1; j++)
{
v = s->cw.ptr.p_double[itemoffs+j]-x->ptr.p_double[j];
ptdist2 = ptdist2+v*v;
}
/*
* Skip points if distance too large
*/
if( ptdist2>=queryr2 )
{
continue;
}
/*
* Update Y
*/
arg = ptdist2*invr2;
if( s->bf==0 )
{
val = ae_exp(-arg, _state);
}
else
{
if( s->bf==1 )
{
val = rbfv2basisfunc(s->bf, arg, _state);
}
else
{
ae_assert(ae_false, "PartialCalcRec: integrity check failed", _state);
}
}
itemoffs = itemoffs+nx;
for(j=0; j<=ny-1; j++)
{
y->ptr.p_double[j] = y->ptr.p_double[j]+val*s->cw.ptr.p_double[itemoffs+j];
}
}
return;
}
/*
* Simple split
*/
if( s->kdnodes.ptr.p_int[rootidx]==0 )
{
/*
* Load:
* * D dimension to split
* * Split split position
* * ChildLE, ChildGE - indexes of childs
*/
d = s->kdnodes.ptr.p_int[rootidx+1];
split = s->kdsplits.ptr.p_double[s->kdnodes.ptr.p_int[rootidx+2]];
childle = s->kdnodes.ptr.p_int[rootidx+3];
childge = s->kdnodes.ptr.p_int[rootidx+4];
/*
* Navigate through childs
*/
for(i=0; i<=1; i++)
{
/*
* Select child to process:
* * ChildOffs current child offset in Nodes[]
* * UpdateMin whether minimum or maximum value
* of bounding box is changed on update
*/
updatemin = i!=0;
if( i==0 )
{
childoffs = childle;
}
else
{
childoffs = childge;
}
/*
* Update bounding box and current distance
*/
prevdist2 = buf->curdist2;
t1 = x->ptr.p_double[d];
if( updatemin )
{
v = buf->curboxmin.ptr.p_double[d];
if( t1<=split )
{
v0 = v-t1;
if( v0<0 )
{
v0 = (double)(0);
}
v1 = split-t1;
buf->curdist2 = buf->curdist2-v0*v0+v1*v1;
}
buf->curboxmin.ptr.p_double[d] = split;
}
else
{
v = buf->curboxmax.ptr.p_double[d];
if( t1>=split )
{
v0 = t1-v;
if( v0<0 )
{
v0 = (double)(0);
}
v1 = t1-split;
buf->curdist2 = buf->curdist2-v0*v0+v1*v1;
}
buf->curboxmax.ptr.p_double[d] = split;
}
/*
* Decide: to dive into cell or not to dive
*/
if( buf->curdist2<queryr2 )
{
rbfv2_partialcalcrec(s, buf, childoffs, invr2, queryr2, x, y, _state);
}
/*
* Restore bounding box and distance
*/
if( updatemin )
{
buf->curboxmin.ptr.p_double[d] = v;
}
else
{
buf->curboxmax.ptr.p_double[d] = v;
}
buf->curdist2 = prevdist2;
}
return;
}
/*
* Integrity failure
*/
ae_assert(ae_false, "PartialCalcRec: integrity check failed", _state);
}
/*************************************************************************
This function performs same operation as partialcalcrec(), but for entire
row of the grid. "Row" is a set of nodes (x0,x1,x2,x3) which share x1..x3,
but have different x0's. (note: for 2D/3D problems x2..x3 are zero).
Row is given by:
* central point XC, which is located at the center of the row, and used to
perform kd-tree requests
* set of x0 coordinates stored in RX array (array may be unordered, but it
is expected that spread of x0 is no more than R; function may be
inefficient for larger spreads).
* set of YFlag values stored in RF
INPUT PARAMETERS:
S - V2 model
Buf - calc-buffer, this function uses following fields:
* Buf.CurBoxMin - should be set by caller
* Buf.CurBoxMax - should be set by caller
* Buf.CurDist2 - squared distance from X to current bounding box,
should be set by caller
RootIdx - offset of partial kd-tree
InvR2 - 1/R^2, where R is basis function radius
RQuery2 - squared query radius, usually it is (R*FarRadius(BasisFunction)+0.5*RowWidth)^2,
where RowWidth is its spatial extent (after scaling of
variables). This radius is used to perform initial query
for neighbors of CX.
RFar2 - squared far radius; far radius is used to perform actual
filtering of results of query made with RQuery2.
CX - central point, array[NX], used for queries
RX - x0 coordinates, array[RowSize]
RF - sparsity flags, array[RowSize]
RowSize - row size in elements
RY - input partial value, array[NY]
OUTPUT PARAMETERS
RY - updated partial value (function adds its results to RY)
-- ALGLIB --
Copyright 20.06.2016 by Bochkanov Sergey
*************************************************************************/
static void rbfv2_partialrowcalcrec(rbfv2model* s,
rbfv2calcbuffer* buf,
ae_int_t rootidx,
double invr2,
double rquery2,
double rfar2,
/* Real */ ae_vector* cx,
/* Real */ ae_vector* rx,
/* Boolean */ ae_vector* rf,
ae_int_t rowsize,
/* Real */ ae_vector* ry,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
ae_int_t i0;
ae_int_t i1;
double partialptdist2;
double ptdist2;
double v;
double v0;
double v1;
ae_int_t cwoffs;
ae_int_t cwcnt;
ae_int_t itemoffs;
ae_int_t woffs;
double val;
ae_int_t d;
double split;
ae_int_t childle;
ae_int_t childge;
ae_int_t childoffs;
ae_bool updatemin;
double prevdist2;
double t1;
ae_int_t nx;
ae_int_t ny;
nx = s->nx;
ny = s->ny;
/*
* Leaf node.
*/
if( s->kdnodes.ptr.p_int[rootidx]>0 )
{
cwcnt = s->kdnodes.ptr.p_int[rootidx+0];
cwoffs = s->kdnodes.ptr.p_int[rootidx+1];
for(i0=0; i0<=cwcnt-1; i0++)
{
/*
* Calculate partial distance (components from 1 to NX-1)
*/
itemoffs = cwoffs+i0*(nx+ny);
partialptdist2 = (double)(0);
for(j=1; j<=nx-1; j++)
{
v = s->cw.ptr.p_double[itemoffs+j]-cx->ptr.p_double[j];
partialptdist2 = partialptdist2+v*v;
}
/*
* Process each element of the row
*/
for(i1=0; i1<=rowsize-1; i1++)
{
if( rf->ptr.p_bool[i1] )
{
/*
* Calculate distance
*/
v = s->cw.ptr.p_double[itemoffs]-rx->ptr.p_double[i1];
ptdist2 = partialptdist2+v*v;
/*
* Skip points if distance too large
*/
if( ptdist2>=rfar2 )
{
continue;
}
/*
* Update Y
*/
val = rbfv2basisfunc(s->bf, ptdist2*invr2, _state);
woffs = itemoffs+nx;
for(j=0; j<=ny-1; j++)
{
ry->ptr.p_double[j+i1*ny] = ry->ptr.p_double[j+i1*ny]+val*s->cw.ptr.p_double[woffs+j];
}
}
}
}
return;
}
/*
* Simple split
*/
if( s->kdnodes.ptr.p_int[rootidx]==0 )
{
/*
* Load:
* * D dimension to split
* * Split split position
* * ChildLE, ChildGE - indexes of childs
*/
d = s->kdnodes.ptr.p_int[rootidx+1];
split = s->kdsplits.ptr.p_double[s->kdnodes.ptr.p_int[rootidx+2]];
childle = s->kdnodes.ptr.p_int[rootidx+3];
childge = s->kdnodes.ptr.p_int[rootidx+4];
/*
* Navigate through childs
*/
for(i=0; i<=1; i++)
{
/*
* Select child to process:
* * ChildOffs current child offset in Nodes[]
* * UpdateMin whether minimum or maximum value
* of bounding box is changed on update
*/
updatemin = i!=0;
if( i==0 )
{
childoffs = childle;
}
else
{
childoffs = childge;
}
/*
* Update bounding box and current distance
*/
prevdist2 = buf->curdist2;
t1 = cx->ptr.p_double[d];
if( updatemin )
{
v = buf->curboxmin.ptr.p_double[d];
if( t1<=split )
{
v0 = v-t1;
if( v0<0 )
{
v0 = (double)(0);
}
v1 = split-t1;
buf->curdist2 = buf->curdist2-v0*v0+v1*v1;
}
buf->curboxmin.ptr.p_double[d] = split;
}
else
{
v = buf->curboxmax.ptr.p_double[d];
if( t1>=split )
{
v0 = t1-v;
if( v0<0 )
{
v0 = (double)(0);
}
v1 = t1-split;
buf->curdist2 = buf->curdist2-v0*v0+v1*v1;
}
buf->curboxmax.ptr.p_double[d] = split;
}
/*
* Decide: to dive into cell or not to dive
*/
if( buf->curdist2<rquery2 )
{
rbfv2_partialrowcalcrec(s, buf, childoffs, invr2, rquery2, rfar2, cx, rx, rf, rowsize, ry, _state);
}
/*
* Restore bounding box and distance
*/
if( updatemin )
{
buf->curboxmin.ptr.p_double[d] = v;
}
else
{
buf->curboxmax.ptr.p_double[d] = v;
}
buf->curdist2 = prevdist2;
}
return;
}
/*
* Integrity failure
*/
ae_assert(ae_false, "PartialCalcRec: integrity check failed", _state);
}
/*************************************************************************
This function prepares partial query
INPUT PARAMETERS:
X - query point
kdBoxMin, kdBoxMax - current bounding box
NX - problem size
Buf - preallocated buffer; this function just loads data, but
does not allocate place for them.
Cnt - counter variable which is set to zery by this function, as
convenience, and to remember about necessity to zero counter
prior to calling partialqueryrec().
OUTPUT PARAMETERS
Buf - calc-buffer:
* Buf.CurBoxMin - current box
* Buf.CurBoxMax - current box
* Buf.CurDist2 - squared distance from X to current box
Cnt - set to zero
-- ALGLIB --
Copyright 20.06.2016 by Bochkanov Sergey
*************************************************************************/
static void rbfv2_preparepartialquery(/* Real */ ae_vector* x,
/* Real */ ae_vector* kdboxmin,
/* Real */ ae_vector* kdboxmax,
ae_int_t nx,
rbfv2calcbuffer* buf,
ae_int_t* cnt,
ae_state *_state)
{
ae_int_t j;
*cnt = 0;
buf->curdist2 = (double)(0);
for(j=0; j<=nx-1; j++)
{
buf->curboxmin.ptr.p_double[j] = kdboxmin->ptr.p_double[j];
buf->curboxmax.ptr.p_double[j] = kdboxmax->ptr.p_double[j];
if( ae_fp_less(x->ptr.p_double[j],buf->curboxmin.ptr.p_double[j]) )
{
buf->curdist2 = buf->curdist2+ae_sqr(buf->curboxmin.ptr.p_double[j]-x->ptr.p_double[j], _state);
}
else
{
if( ae_fp_greater(x->ptr.p_double[j],buf->curboxmax.ptr.p_double[j]) )
{
buf->curdist2 = buf->curdist2+ae_sqr(x->ptr.p_double[j]-buf->curboxmax.ptr.p_double[j], _state);
}
}
}
}
/*************************************************************************
This function performs partial (for just one subtree of multi-tree) query
for neighbors located in R-sphere around X. It returns squared distances
from X to points and offsets in S.CW[] array for points being found.
INPUT PARAMETERS:
kdNodes, kdSplits, CW, NX, NY - corresponding fields of V2 model
Buf - calc-buffer, this function uses following fields:
* Buf.CurBoxMin - should be set by caller
* Buf.CurBoxMax - should be set by caller
* Buf.CurDist2 - squared distance from X to current
bounding box, should be set by caller
You may use preparepartialquery() function to initialize
these fields.
RootIdx - offset of partial kd-tree
QueryR2 - squared query radius
X - array[NX], point being queried
R2 - preallocated output buffer; it is caller's responsibility
to make sure that R2 has enough space.
Offs - preallocated output buffer; it is caller's responsibility
to make sure that Offs has enough space.
K - MUST BE ZERO ON INITIAL CALL. This variable is incremented,
not set. So, any no-zero value will result in the incorrect
points count being returned.
OUTPUT PARAMETERS
R2 - squared distances in first K elements
Offs - offsets in S.CW in first K elements
K - points count
-- ALGLIB --
Copyright 20.06.2016 by Bochkanov Sergey
*************************************************************************/
static void rbfv2_partialqueryrec(/* Integer */ ae_vector* kdnodes,
/* Real */ ae_vector* kdsplits,
/* Real */ ae_vector* cw,
ae_int_t nx,
ae_int_t ny,
rbfv2calcbuffer* buf,
ae_int_t rootidx,
double queryr2,
/* Real */ ae_vector* x,
/* Real */ ae_vector* r2,
/* Integer */ ae_vector* offs,
ae_int_t* k,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
double ptdist2;
double v;
ae_int_t cwoffs;
ae_int_t cwcnt;
ae_int_t itemoffs;
ae_int_t d;
double split;
ae_int_t childle;
ae_int_t childge;
ae_int_t childoffs;
ae_bool updatemin;
double prevdist2;
double t1;
/*
* Leaf node.
*/
if( kdnodes->ptr.p_int[rootidx]>0 )
{
cwcnt = kdnodes->ptr.p_int[rootidx+0];
cwoffs = kdnodes->ptr.p_int[rootidx+1];
for(i=0; i<=cwcnt-1; i++)
{
/*
* Calculate distance
*/
itemoffs = cwoffs+i*(nx+ny);
ptdist2 = (double)(0);
for(j=0; j<=nx-1; j++)
{
v = cw->ptr.p_double[itemoffs+j]-x->ptr.p_double[j];
ptdist2 = ptdist2+v*v;
}
/*
* Skip points if distance too large
*/
if( ae_fp_greater_eq(ptdist2,queryr2) )
{
continue;
}
/*
* Output
*/
r2->ptr.p_double[*k] = ptdist2;
offs->ptr.p_int[*k] = itemoffs;
*k = *k+1;
}
return;
}
/*
* Simple split
*/
if( kdnodes->ptr.p_int[rootidx]==0 )
{
/*
* Load:
* * D dimension to split
* * Split split position
* * ChildLE, ChildGE - indexes of childs
*/
d = kdnodes->ptr.p_int[rootidx+1];
split = kdsplits->ptr.p_double[kdnodes->ptr.p_int[rootidx+2]];
childle = kdnodes->ptr.p_int[rootidx+3];
childge = kdnodes->ptr.p_int[rootidx+4];
/*
* Navigate through childs
*/
for(i=0; i<=1; i++)
{
/*
* Select child to process:
* * ChildOffs current child offset in Nodes[]
* * UpdateMin whether minimum or maximum value
* of bounding box is changed on update
*/
updatemin = i!=0;
if( i==0 )
{
childoffs = childle;
}
else
{
childoffs = childge;
}
/*
* Update bounding box and current distance
*/
prevdist2 = buf->curdist2;
t1 = x->ptr.p_double[d];
if( updatemin )
{
v = buf->curboxmin.ptr.p_double[d];
if( ae_fp_less_eq(t1,split) )
{
buf->curdist2 = buf->curdist2-ae_sqr(ae_maxreal(v-t1, (double)(0), _state), _state)+ae_sqr(split-t1, _state);
}
buf->curboxmin.ptr.p_double[d] = split;
}
else
{
v = buf->curboxmax.ptr.p_double[d];
if( ae_fp_greater_eq(t1,split) )
{
buf->curdist2 = buf->curdist2-ae_sqr(ae_maxreal(t1-v, (double)(0), _state), _state)+ae_sqr(t1-split, _state);
}
buf->curboxmax.ptr.p_double[d] = split;
}
/*
* Decide: to dive into cell or not to dive
*/
if( ae_fp_less(buf->curdist2,queryr2) )
{
rbfv2_partialqueryrec(kdnodes, kdsplits, cw, nx, ny, buf, childoffs, queryr2, x, r2, offs, k, _state);
}
/*
* Restore bounding box and distance
*/
if( updatemin )
{
buf->curboxmin.ptr.p_double[d] = v;
}
else
{
buf->curboxmax.ptr.p_double[d] = v;
}
buf->curdist2 = prevdist2;
}
return;
}
/*
* Integrity failure
*/
ae_assert(ae_false, "PartialQueryRec: integrity check failed", _state);
}
/*************************************************************************
This function performs partial (for just one subtree of multi-tree)
counting of neighbors located in R-sphere around X.
This function does not guarantee consistency of results with other partial
queries, it should be used only to get approximate estimates (well, we do
not use approximate algorithms, but rounding errors may give us
inconsistent results in just-at-the-boundary cases).
INPUT PARAMETERS:
kdNodes, kdSplits, CW, NX, NY - corresponding fields of V2 model
Buf - calc-buffer, this function uses following fields:
* Buf.CurBoxMin - should be set by caller
* Buf.CurBoxMax - should be set by caller
* Buf.CurDist2 - squared distance from X to current
bounding box, should be set by caller
You may use preparepartialquery() function to initialize
these fields.
RootIdx - offset of partial kd-tree
QueryR2 - squared query radius
X - array[NX], point being queried
RESULT:
points count
-- ALGLIB --
Copyright 20.06.2016 by Bochkanov Sergey
*************************************************************************/
static ae_int_t rbfv2_partialcountrec(/* Integer */ ae_vector* kdnodes,
/* Real */ ae_vector* kdsplits,
/* Real */ ae_vector* cw,
ae_int_t nx,
ae_int_t ny,
rbfv2calcbuffer* buf,
ae_int_t rootidx,
double queryr2,
/* Real */ ae_vector* x,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
double ptdist2;
double v;
ae_int_t cwoffs;
ae_int_t cwcnt;
ae_int_t itemoffs;
ae_int_t d;
double split;
ae_int_t childle;
ae_int_t childge;
ae_int_t childoffs;
ae_bool updatemin;
double prevdist2;
double t1;
ae_int_t result;
result = 0;
/*
* Leaf node.
*/
if( kdnodes->ptr.p_int[rootidx]>0 )
{
cwcnt = kdnodes->ptr.p_int[rootidx+0];
cwoffs = kdnodes->ptr.p_int[rootidx+1];
for(i=0; i<=cwcnt-1; i++)
{
/*
* Calculate distance
*/
itemoffs = cwoffs+i*(nx+ny);
ptdist2 = (double)(0);
for(j=0; j<=nx-1; j++)
{
v = cw->ptr.p_double[itemoffs+j]-x->ptr.p_double[j];
ptdist2 = ptdist2+v*v;
}
/*
* Skip points if distance too large
*/
if( ae_fp_greater_eq(ptdist2,queryr2) )
{
continue;
}
/*
* Output
*/
result = result+1;
}
return result;
}
/*
* Simple split
*/
if( kdnodes->ptr.p_int[rootidx]==0 )
{
/*
* Load:
* * D dimension to split
* * Split split position
* * ChildLE, ChildGE - indexes of childs
*/
d = kdnodes->ptr.p_int[rootidx+1];
split = kdsplits->ptr.p_double[kdnodes->ptr.p_int[rootidx+2]];
childle = kdnodes->ptr.p_int[rootidx+3];
childge = kdnodes->ptr.p_int[rootidx+4];
/*
* Navigate through childs
*/
for(i=0; i<=1; i++)
{
/*
* Select child to process:
* * ChildOffs current child offset in Nodes[]
* * UpdateMin whether minimum or maximum value
* of bounding box is changed on update
*/
updatemin = i!=0;
if( i==0 )
{
childoffs = childle;
}
else
{
childoffs = childge;
}
/*
* Update bounding box and current distance
*/
prevdist2 = buf->curdist2;
t1 = x->ptr.p_double[d];
if( updatemin )
{
v = buf->curboxmin.ptr.p_double[d];
if( ae_fp_less_eq(t1,split) )
{
buf->curdist2 = buf->curdist2-ae_sqr(ae_maxreal(v-t1, (double)(0), _state), _state)+ae_sqr(split-t1, _state);
}
buf->curboxmin.ptr.p_double[d] = split;
}
else
{
v = buf->curboxmax.ptr.p_double[d];
if( ae_fp_greater_eq(t1,split) )
{
buf->curdist2 = buf->curdist2-ae_sqr(ae_maxreal(t1-v, (double)(0), _state), _state)+ae_sqr(t1-split, _state);
}
buf->curboxmax.ptr.p_double[d] = split;
}
/*
* Decide: to dive into cell or not to dive
*/
if( ae_fp_less(buf->curdist2,queryr2) )
{
result = result+rbfv2_partialcountrec(kdnodes, kdsplits, cw, nx, ny, buf, childoffs, queryr2, x, _state);
}
/*
* Restore bounding box and distance
*/
if( updatemin )
{
buf->curboxmin.ptr.p_double[d] = v;
}
else
{
buf->curboxmax.ptr.p_double[d] = v;
}
buf->curdist2 = prevdist2;
}
return result;
}
/*
* Integrity failure
*/
ae_assert(ae_false, "PartialCountRec: integrity check failed", _state);
return result;
}
/*************************************************************************
This function performs partial (for just one subtree of multi-tree) unpack
for RBF model. It appends center coordinates, weights and per-dimension
radii (according to current scaling) to preallocated output array.
INPUT PARAMETERS:
kdNodes, kdSplits, CW, S, NX, NY - corresponding fields of V2 model
RootIdx - offset of partial kd-tree
R - radius for current partial tree
XWR - preallocated output buffer; it is caller's responsibility
to make sure that XWR has enough space. First K rows are
already occupied.
K - number of already occupied rows in XWR.
OUTPUT PARAMETERS
XWR - updated XWR
K - updated rows count
-- ALGLIB --
Copyright 20.06.2016 by Bochkanov Sergey
*************************************************************************/
static void rbfv2_partialunpackrec(/* Integer */ ae_vector* kdnodes,
/* Real */ ae_vector* kdsplits,
/* Real */ ae_vector* cw,
/* Real */ ae_vector* s,
ae_int_t nx,
ae_int_t ny,
ae_int_t rootidx,
double r,
/* Real */ ae_matrix* xwr,
ae_int_t* k,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
ae_int_t childle;
ae_int_t childge;
ae_int_t itemoffs;
ae_int_t cwoffs;
ae_int_t cwcnt;
/*
* Leaf node.
*/
if( kdnodes->ptr.p_int[rootidx]>0 )
{
cwcnt = kdnodes->ptr.p_int[rootidx+0];
cwoffs = kdnodes->ptr.p_int[rootidx+1];
for(i=0; i<=cwcnt-1; i++)
{
itemoffs = cwoffs+i*(nx+ny);
for(j=0; j<=nx+ny-1; j++)
{
xwr->ptr.pp_double[*k][j] = cw->ptr.p_double[itemoffs+j];
}
for(j=0; j<=nx-1; j++)
{
xwr->ptr.pp_double[*k][j] = xwr->ptr.pp_double[*k][j]*s->ptr.p_double[j];
}
for(j=0; j<=nx-1; j++)
{
xwr->ptr.pp_double[*k][nx+ny+j] = r*s->ptr.p_double[j];
}
*k = *k+1;
}
return;
}
/*
* Simple split
*/
if( kdnodes->ptr.p_int[rootidx]==0 )
{
/*
* Load:
* * ChildLE, ChildGE - indexes of childs
*/
childle = kdnodes->ptr.p_int[rootidx+3];
childge = kdnodes->ptr.p_int[rootidx+4];
/*
* Process both parts of split
*/
rbfv2_partialunpackrec(kdnodes, kdsplits, cw, s, nx, ny, childle, r, xwr, k, _state);
rbfv2_partialunpackrec(kdnodes, kdsplits, cw, s, nx, ny, childge, r, xwr, k, _state);
return;
}
/*
* Integrity failure
*/
ae_assert(ae_false, "PartialUnpackRec: integrity check failed", _state);
}
/*************************************************************************
This function returns size of design matrix row for evaluation point X0,
given:
* query radius multiplier (either RBFV2NearRadius() or RBFV2FarRadius())
* hierarchy level: value in [0,NH) for single-level model, or negative
value for multilevel model (all levels of hierarchy in single matrix,
like one used by nonnegative RBF)
INPUT PARAMETERS:
kdNodes, kdSplits, CW, Ri, kdRoots, kdBoxMin, kdBoxMax, NX, NY, NH - corresponding fields of V2 model
Level - value in [0,NH) for single-level design matrix, negative
value for multilevel design matrix
RCoeff - radius coefficient, either RBFV2NearRadius() or RBFV2FarRadius()
X0 - query point
CalcBuf - buffer for PreparePartialQuery(), allocated by caller
RESULT:
row size
-- ALGLIB --
Copyright 28.09.2016 by Bochkanov Sergey
*************************************************************************/
static ae_int_t rbfv2_designmatrixrowsize(/* Integer */ ae_vector* kdnodes,
/* Real */ ae_vector* kdsplits,
/* Real */ ae_vector* cw,
/* Real */ ae_vector* ri,
/* Integer */ ae_vector* kdroots,
/* Real */ ae_vector* kdboxmin,
/* Real */ ae_vector* kdboxmax,
ae_int_t nx,
ae_int_t ny,
ae_int_t nh,
ae_int_t level,
double rcoeff,
/* Real */ ae_vector* x0,
rbfv2calcbuffer* calcbuf,
ae_state *_state)
{
ae_int_t dummy;
ae_int_t levelidx;
ae_int_t level0;
ae_int_t level1;
double curradius2;
ae_int_t result;
ae_assert(nh>0, "DesignMatrixRowSize: integrity failure", _state);
if( level>=0 )
{
level0 = level;
level1 = level;
}
else
{
level0 = 0;
level1 = nh-1;
}
result = 0;
for(levelidx=level0; levelidx<=level1; levelidx++)
{
curradius2 = ae_sqr(ri->ptr.p_double[levelidx]*rcoeff, _state);
rbfv2_preparepartialquery(x0, kdboxmin, kdboxmax, nx, calcbuf, &dummy, _state);
result = result+rbfv2_partialcountrec(kdnodes, kdsplits, cw, nx, ny, calcbuf, kdroots->ptr.p_int[levelidx], curradius2, x0, _state);
}
return result;
}
/*************************************************************************
This function generates design matrix row for evaluation point X0, given:
* query radius multiplier (either RBFV2NearRadius() or RBFV2FarRadius())
* hierarchy level: value in [0,NH) for single-level model, or negative
value for multilevel model (all levels of hierarchy in single matrix,
like one used by nonnegative RBF)
INPUT PARAMETERS:
kdNodes, kdSplits, CW, Ri, kdRoots, kdBoxMin, kdBoxMax, NX, NY, NH - corresponding fields of V2 model
CWRange - internal array[NH+1] used by RBF construction function,
stores ranges of CW occupied by NH trees.
Level - value in [0,NH) for single-level design matrix, negative
value for multilevel design matrix
BF - basis function type
RCoeff - radius coefficient, either RBFV2NearRadius() or RBFV2FarRadius()
RowsPerPoint-equal to:
* 1 for unpenalized regression model
* 1+NX for basic form of nonsmoothness penalty
Penalty - nonsmoothness penalty coefficient
X0 - query point
CalcBuf - buffer for PreparePartialQuery(), allocated by caller
R2 - preallocated temporary buffer, size is at least NPoints;
it is caller's responsibility to make sure that R2 has enough space.
Offs - preallocated temporary buffer; size is at least NPoints;
it is caller's responsibility to make sure that Offs has enough space.
K - MUST BE ZERO ON INITIAL CALL. This variable is incremented,
not set. So, any no-zero value will result in the incorrect
points count being returned.
RowIdx - preallocated array, at least RowSize elements
RowVal - preallocated array, at least RowSize*RowsPerPoint elements
RESULT:
RowIdx - RowSize elements are filled with column indexes of non-zero
design matrix entries
RowVal - RowSize*RowsPerPoint elements are filled with design matrix
values, with column RowIdx[0] being stored in first RowsPerPoint
elements of RowVal, column RowIdx[1] being stored in next
RowsPerPoint elements, and so on.
First element in contiguous set of RowsPerPoint elements
corresponds to
RowSize - number of columns per row
-- ALGLIB --
Copyright 28.09.2016 by Bochkanov Sergey
*************************************************************************/
static void rbfv2_designmatrixgeneraterow(/* Integer */ ae_vector* kdnodes,
/* Real */ ae_vector* kdsplits,
/* Real */ ae_vector* cw,
/* Real */ ae_vector* ri,
/* Integer */ ae_vector* kdroots,
/* Real */ ae_vector* kdboxmin,
/* Real */ ae_vector* kdboxmax,
/* Integer */ ae_vector* cwrange,
ae_int_t nx,
ae_int_t ny,
ae_int_t nh,
ae_int_t level,
ae_int_t bf,
double rcoeff,
ae_int_t rowsperpoint,
double penalty,
/* Real */ ae_vector* x0,
rbfv2calcbuffer* calcbuf,
/* Real */ ae_vector* tmpr2,
/* Integer */ ae_vector* tmpoffs,
/* Integer */ ae_vector* rowidx,
/* Real */ ae_vector* rowval,
ae_int_t* rowsize,
ae_state *_state)
{
ae_int_t j;
ae_int_t k;
ae_int_t cnt;
ae_int_t levelidx;
ae_int_t level0;
ae_int_t level1;
double invri2;
double curradius2;
double val;
double dval;
double d2val;
*rowsize = 0;
ae_assert(nh>0, "DesignMatrixGenerateRow: integrity failure (a)", _state);
ae_assert(rowsperpoint==1||rowsperpoint==1+nx, "DesignMatrixGenerateRow: integrity failure (b)", _state);
if( level>=0 )
{
level0 = level;
level1 = level;
}
else
{
level0 = 0;
level1 = nh-1;
}
*rowsize = 0;
for(levelidx=level0; levelidx<=level1; levelidx++)
{
curradius2 = ae_sqr(ri->ptr.p_double[levelidx]*rcoeff, _state);
invri2 = 1/ae_sqr(ri->ptr.p_double[levelidx], _state);
rbfv2_preparepartialquery(x0, kdboxmin, kdboxmax, nx, calcbuf, &cnt, _state);
rbfv2_partialqueryrec(kdnodes, kdsplits, cw, nx, ny, calcbuf, kdroots->ptr.p_int[levelidx], curradius2, x0, tmpr2, tmpoffs, &cnt, _state);
ae_assert(tmpr2->cnt>=cnt, "DesignMatrixRowSize: integrity failure (c)", _state);
ae_assert(tmpoffs->cnt>=cnt, "DesignMatrixRowSize: integrity failure (d)", _state);
ae_assert(rowidx->cnt>=*rowsize+cnt, "DesignMatrixRowSize: integrity failure (e)", _state);
ae_assert(rowval->cnt>=rowsperpoint*(*rowsize+cnt), "DesignMatrixRowSize: integrity failure (f)", _state);
for(j=0; j<=cnt-1; j++)
{
/*
* Generate element corresponding to fitting error.
* Store derivative information which may be required later.
*/
ae_assert((tmpoffs->ptr.p_int[j]-cwrange->ptr.p_int[level0])%(nx+ny)==0, "DesignMatrixRowSize: integrity failure (g)", _state);
rbfv2basisfuncdiff2(bf, tmpr2->ptr.p_double[j]*invri2, &val, &dval, &d2val, _state);
rowidx->ptr.p_int[*rowsize+j] = (tmpoffs->ptr.p_int[j]-cwrange->ptr.p_int[level0])/(nx+ny);
rowval->ptr.p_double[(*rowsize+j)*rowsperpoint+0] = val;
if( rowsperpoint==1 )
{
continue;
}
/*
* Generate elements corresponding to nonsmoothness penalty
*/
ae_assert(rowsperpoint==1+nx, "DesignMatrixRowSize: integrity failure (h)", _state);
for(k=0; k<=nx-1; k++)
{
rowval->ptr.p_double[(*rowsize+j)*rowsperpoint+1+k] = penalty*(dval*2*invri2+d2val*ae_sqr(2*(x0->ptr.p_double[k]-cw->ptr.p_double[tmpoffs->ptr.p_int[j]+k])*invri2, _state));
}
}
/*
* Update columns counter
*/
*rowsize = *rowsize+cnt;
}
}
/*************************************************************************
This function fills RBF model by zeros.
-- ALGLIB --
Copyright 17.11.2018 by Bochkanov Sergey
*************************************************************************/
static void rbfv2_zerofill(rbfv2model* s,
ae_int_t nx,
ae_int_t ny,
ae_int_t bf,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
s->bf = bf;
s->nh = 0;
ae_vector_set_length(&s->ri, 0, _state);
ae_vector_set_length(&s->s, 0, _state);
ae_vector_set_length(&s->kdroots, 0, _state);
ae_vector_set_length(&s->kdnodes, 0, _state);
ae_vector_set_length(&s->kdsplits, 0, _state);
ae_vector_set_length(&s->kdboxmin, 0, _state);
ae_vector_set_length(&s->kdboxmax, 0, _state);
ae_vector_set_length(&s->cw, 0, _state);
ae_matrix_set_length(&s->v, ny, nx+1, _state);
for(i=0; i<=ny-1; i++)
{
for(j=0; j<=nx; j++)
{
s->v.ptr.pp_double[i][j] = (double)(0);
}
}
}
void _rbfv2calcbuffer_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
rbfv2calcbuffer *p = (rbfv2calcbuffer*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->x, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->curboxmin, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->curboxmax, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->x123, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->y123, 0, DT_REAL, _state, make_automatic);
}
void _rbfv2calcbuffer_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
rbfv2calcbuffer *dst = (rbfv2calcbuffer*)_dst;
rbfv2calcbuffer *src = (rbfv2calcbuffer*)_src;
ae_vector_init_copy(&dst->x, &src->x, _state, make_automatic);
ae_vector_init_copy(&dst->curboxmin, &src->curboxmin, _state, make_automatic);
ae_vector_init_copy(&dst->curboxmax, &src->curboxmax, _state, make_automatic);
dst->curdist2 = src->curdist2;
ae_vector_init_copy(&dst->x123, &src->x123, _state, make_automatic);
ae_vector_init_copy(&dst->y123, &src->y123, _state, make_automatic);
}
void _rbfv2calcbuffer_clear(void* _p)
{
rbfv2calcbuffer *p = (rbfv2calcbuffer*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->x);
ae_vector_clear(&p->curboxmin);
ae_vector_clear(&p->curboxmax);
ae_vector_clear(&p->x123);
ae_vector_clear(&p->y123);
}
void _rbfv2calcbuffer_destroy(void* _p)
{
rbfv2calcbuffer *p = (rbfv2calcbuffer*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->x);
ae_vector_destroy(&p->curboxmin);
ae_vector_destroy(&p->curboxmax);
ae_vector_destroy(&p->x123);
ae_vector_destroy(&p->y123);
}
void _rbfv2model_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
rbfv2model *p = (rbfv2model*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->ri, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->s, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->kdroots, 0, DT_INT, _state, make_automatic);
ae_vector_init(&p->kdnodes, 0, DT_INT, _state, make_automatic);
ae_vector_init(&p->kdsplits, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->kdboxmin, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->kdboxmax, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->cw, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->v, 0, 0, DT_REAL, _state, make_automatic);
_rbfv2calcbuffer_init(&p->calcbuf, _state, make_automatic);
}
void _rbfv2model_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
rbfv2model *dst = (rbfv2model*)_dst;
rbfv2model *src = (rbfv2model*)_src;
dst->ny = src->ny;
dst->nx = src->nx;
dst->bf = src->bf;
dst->nh = src->nh;
ae_vector_init_copy(&dst->ri, &src->ri, _state, make_automatic);
ae_vector_init_copy(&dst->s, &src->s, _state, make_automatic);
ae_vector_init_copy(&dst->kdroots, &src->kdroots, _state, make_automatic);
ae_vector_init_copy(&dst->kdnodes, &src->kdnodes, _state, make_automatic);
ae_vector_init_copy(&dst->kdsplits, &src->kdsplits, _state, make_automatic);
ae_vector_init_copy(&dst->kdboxmin, &src->kdboxmin, _state, make_automatic);
ae_vector_init_copy(&dst->kdboxmax, &src->kdboxmax, _state, make_automatic);
ae_vector_init_copy(&dst->cw, &src->cw, _state, make_automatic);
ae_matrix_init_copy(&dst->v, &src->v, _state, make_automatic);
dst->lambdareg = src->lambdareg;
dst->maxits = src->maxits;
dst->supportr = src->supportr;
dst->basisfunction = src->basisfunction;
_rbfv2calcbuffer_init_copy(&dst->calcbuf, &src->calcbuf, _state, make_automatic);
}
void _rbfv2model_clear(void* _p)
{
rbfv2model *p = (rbfv2model*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->ri);
ae_vector_clear(&p->s);
ae_vector_clear(&p->kdroots);
ae_vector_clear(&p->kdnodes);
ae_vector_clear(&p->kdsplits);
ae_vector_clear(&p->kdboxmin);
ae_vector_clear(&p->kdboxmax);
ae_vector_clear(&p->cw);
ae_matrix_clear(&p->v);
_rbfv2calcbuffer_clear(&p->calcbuf);
}
void _rbfv2model_destroy(void* _p)
{
rbfv2model *p = (rbfv2model*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->ri);
ae_vector_destroy(&p->s);
ae_vector_destroy(&p->kdroots);
ae_vector_destroy(&p->kdnodes);
ae_vector_destroy(&p->kdsplits);
ae_vector_destroy(&p->kdboxmin);
ae_vector_destroy(&p->kdboxmax);
ae_vector_destroy(&p->cw);
ae_matrix_destroy(&p->v);
_rbfv2calcbuffer_destroy(&p->calcbuf);
}
void _rbfv2gridcalcbuffer_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
rbfv2gridcalcbuffer *p = (rbfv2gridcalcbuffer*)_p;
ae_touch_ptr((void*)p);
_rbfv2calcbuffer_init(&p->calcbuf, _state, make_automatic);
ae_vector_init(&p->cx, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->rx, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->ry, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tx, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->ty, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->rf, 0, DT_BOOL, _state, make_automatic);
}
void _rbfv2gridcalcbuffer_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
rbfv2gridcalcbuffer *dst = (rbfv2gridcalcbuffer*)_dst;
rbfv2gridcalcbuffer *src = (rbfv2gridcalcbuffer*)_src;
_rbfv2calcbuffer_init_copy(&dst->calcbuf, &src->calcbuf, _state, make_automatic);
ae_vector_init_copy(&dst->cx, &src->cx, _state, make_automatic);
ae_vector_init_copy(&dst->rx, &src->rx, _state, make_automatic);
ae_vector_init_copy(&dst->ry, &src->ry, _state, make_automatic);
ae_vector_init_copy(&dst->tx, &src->tx, _state, make_automatic);
ae_vector_init_copy(&dst->ty, &src->ty, _state, make_automatic);
ae_vector_init_copy(&dst->rf, &src->rf, _state, make_automatic);
}
void _rbfv2gridcalcbuffer_clear(void* _p)
{
rbfv2gridcalcbuffer *p = (rbfv2gridcalcbuffer*)_p;
ae_touch_ptr((void*)p);
_rbfv2calcbuffer_clear(&p->calcbuf);
ae_vector_clear(&p->cx);
ae_vector_clear(&p->rx);
ae_vector_clear(&p->ry);
ae_vector_clear(&p->tx);
ae_vector_clear(&p->ty);
ae_vector_clear(&p->rf);
}
void _rbfv2gridcalcbuffer_destroy(void* _p)
{
rbfv2gridcalcbuffer *p = (rbfv2gridcalcbuffer*)_p;
ae_touch_ptr((void*)p);
_rbfv2calcbuffer_destroy(&p->calcbuf);
ae_vector_destroy(&p->cx);
ae_vector_destroy(&p->rx);
ae_vector_destroy(&p->ry);
ae_vector_destroy(&p->tx);
ae_vector_destroy(&p->ty);
ae_vector_destroy(&p->rf);
}
void _rbfv2report_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
rbfv2report *p = (rbfv2report*)_p;
ae_touch_ptr((void*)p);
}
void _rbfv2report_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
rbfv2report *dst = (rbfv2report*)_dst;
rbfv2report *src = (rbfv2report*)_src;
dst->terminationtype = src->terminationtype;
dst->maxerror = src->maxerror;
dst->rmserror = src->rmserror;
}
void _rbfv2report_clear(void* _p)
{
rbfv2report *p = (rbfv2report*)_p;
ae_touch_ptr((void*)p);
}
void _rbfv2report_destroy(void* _p)
{
rbfv2report *p = (rbfv2report*)_p;
ae_touch_ptr((void*)p);
}
#endif
#if defined(AE_COMPILE_SPLINE2D) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This subroutine calculates the value of the bilinear or bicubic spline at
the given point X.
Input parameters:
C - 2D spline object.
Built by spline2dbuildbilinearv or spline2dbuildbicubicv.
X, Y- point
Result:
S(x,y)
-- ALGLIB PROJECT --
Copyright 05.07.2007 by Bochkanov Sergey
*************************************************************************/
double spline2dcalc(spline2dinterpolant* c,
double x,
double y,
ae_state *_state)
{
ae_int_t ix;
ae_int_t iy;
ae_int_t l;
ae_int_t r;
ae_int_t h;
double t;
double dt;
double u;
double du;
double y1;
double y2;
double y3;
double y4;
ae_int_t s1;
ae_int_t s2;
ae_int_t s3;
ae_int_t s4;
ae_int_t sfx;
ae_int_t sfy;
ae_int_t sfxy;
double t2;
double t3;
double u2;
double u3;
double ht00;
double ht01;
double ht10;
double ht11;
double hu00;
double hu01;
double hu10;
double hu11;
double result;
ae_assert(c->stype==-1||c->stype==-3, "Spline2DCalc: incorrect C (incorrect parameter C.SType)", _state);
ae_assert(ae_isfinite(x, _state)&&ae_isfinite(y, _state), "Spline2DCalc: X or Y contains NaN or Infinite value", _state);
if( c->d!=1 )
{
result = (double)(0);
return result;
}
/*
* Determine evaluation interval
*/
l = 0;
r = c->n-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->x.ptr.p_double[h],x) )
{
r = h;
}
else
{
l = h;
}
}
dt = 1.0/(c->x.ptr.p_double[l+1]-c->x.ptr.p_double[l]);
t = (x-c->x.ptr.p_double[l])*dt;
ix = l;
l = 0;
r = c->m-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->y.ptr.p_double[h],y) )
{
r = h;
}
else
{
l = h;
}
}
du = 1.0/(c->y.ptr.p_double[l+1]-c->y.ptr.p_double[l]);
u = (y-c->y.ptr.p_double[l])*du;
iy = l;
/*
* Bilinear interpolation
*/
if( c->stype==-1 )
{
y1 = c->f.ptr.p_double[c->n*iy+ix];
y2 = c->f.ptr.p_double[c->n*iy+(ix+1)];
y3 = c->f.ptr.p_double[c->n*(iy+1)+(ix+1)];
y4 = c->f.ptr.p_double[c->n*(iy+1)+ix];
result = (1-t)*(1-u)*y1+t*(1-u)*y2+t*u*y3+(1-t)*u*y4;
return result;
}
/*
* Bicubic interpolation:
* * calculate Hermite basis for dimensions X and Y (variables T and U),
* here HTij means basis function whose I-th derivative has value 1 at T=J.
* Same for HUij.
* * after initial calculation, apply scaling by DT/DU to the basis
* * calculate using stored table of second derivatives
*/
ae_assert(c->stype==-3, "Spline2DCalc: integrity check failed", _state);
sfx = c->n*c->m;
sfy = 2*c->n*c->m;
sfxy = 3*c->n*c->m;
s1 = c->n*iy+ix;
s2 = c->n*iy+(ix+1);
s3 = c->n*(iy+1)+ix;
s4 = c->n*(iy+1)+(ix+1);
t2 = t*t;
t3 = t*t2;
u2 = u*u;
u3 = u*u2;
ht00 = 2*t3-3*t2+1;
ht10 = t3-2*t2+t;
ht01 = -2*t3+3*t2;
ht11 = t3-t2;
hu00 = 2*u3-3*u2+1;
hu10 = u3-2*u2+u;
hu01 = -2*u3+3*u2;
hu11 = u3-u2;
ht10 = ht10/dt;
ht11 = ht11/dt;
hu10 = hu10/du;
hu11 = hu11/du;
result = (double)(0);
result = result+c->f.ptr.p_double[s1]*ht00*hu00+c->f.ptr.p_double[s2]*ht01*hu00+c->f.ptr.p_double[s3]*ht00*hu01+c->f.ptr.p_double[s4]*ht01*hu01;
result = result+c->f.ptr.p_double[sfx+s1]*ht10*hu00+c->f.ptr.p_double[sfx+s2]*ht11*hu00+c->f.ptr.p_double[sfx+s3]*ht10*hu01+c->f.ptr.p_double[sfx+s4]*ht11*hu01;
result = result+c->f.ptr.p_double[sfy+s1]*ht00*hu10+c->f.ptr.p_double[sfy+s2]*ht01*hu10+c->f.ptr.p_double[sfy+s3]*ht00*hu11+c->f.ptr.p_double[sfy+s4]*ht01*hu11;
result = result+c->f.ptr.p_double[sfxy+s1]*ht10*hu10+c->f.ptr.p_double[sfxy+s2]*ht11*hu10+c->f.ptr.p_double[sfxy+s3]*ht10*hu11+c->f.ptr.p_double[sfxy+s4]*ht11*hu11;
return result;
}
/*************************************************************************
This subroutine calculates the value of the bilinear or bicubic spline at
the given point X and its derivatives.
Input parameters:
C - spline interpolant.
X, Y- point
Output parameters:
F - S(x,y)
FX - dS(x,y)/dX
FY - dS(x,y)/dY
FXY - d2S(x,y)/dXdY
-- ALGLIB PROJECT --
Copyright 05.07.2007 by Bochkanov Sergey
*************************************************************************/
void spline2ddiff(spline2dinterpolant* c,
double x,
double y,
double* f,
double* fx,
double* fy,
double* fxy,
ae_state *_state)
{
double t;
double dt;
double u;
double du;
ae_int_t ix;
ae_int_t iy;
ae_int_t l;
ae_int_t r;
ae_int_t h;
ae_int_t s1;
ae_int_t s2;
ae_int_t s3;
ae_int_t s4;
ae_int_t sfx;
ae_int_t sfy;
ae_int_t sfxy;
double y1;
double y2;
double y3;
double y4;
double v0;
double v1;
double v2;
double v3;
double t2;
double t3;
double u2;
double u3;
double ht00;
double ht01;
double ht10;
double ht11;
double hu00;
double hu01;
double hu10;
double hu11;
double dht00;
double dht01;
double dht10;
double dht11;
double dhu00;
double dhu01;
double dhu10;
double dhu11;
*f = 0;
*fx = 0;
*fy = 0;
*fxy = 0;
ae_assert(c->stype==-1||c->stype==-3, "Spline2DDiff: incorrect C (incorrect parameter C.SType)", _state);
ae_assert(ae_isfinite(x, _state)&&ae_isfinite(y, _state), "Spline2DDiff: X or Y contains NaN or Infinite value", _state);
/*
* Prepare F, dF/dX, dF/dY, d2F/dXdY
*/
*f = (double)(0);
*fx = (double)(0);
*fy = (double)(0);
*fxy = (double)(0);
if( c->d!=1 )
{
return;
}
/*
* Binary search in the [ x[0], ..., x[n-2] ] (x[n-1] is not included)
*/
l = 0;
r = c->n-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->x.ptr.p_double[h],x) )
{
r = h;
}
else
{
l = h;
}
}
t = (x-c->x.ptr.p_double[l])/(c->x.ptr.p_double[l+1]-c->x.ptr.p_double[l]);
dt = 1.0/(c->x.ptr.p_double[l+1]-c->x.ptr.p_double[l]);
ix = l;
/*
* Binary search in the [ y[0], ..., y[m-2] ] (y[m-1] is not included)
*/
l = 0;
r = c->m-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->y.ptr.p_double[h],y) )
{
r = h;
}
else
{
l = h;
}
}
u = (y-c->y.ptr.p_double[l])/(c->y.ptr.p_double[l+1]-c->y.ptr.p_double[l]);
du = 1.0/(c->y.ptr.p_double[l+1]-c->y.ptr.p_double[l]);
iy = l;
/*
* Bilinear interpolation
*/
if( c->stype==-1 )
{
y1 = c->f.ptr.p_double[c->n*iy+ix];
y2 = c->f.ptr.p_double[c->n*iy+(ix+1)];
y3 = c->f.ptr.p_double[c->n*(iy+1)+(ix+1)];
y4 = c->f.ptr.p_double[c->n*(iy+1)+ix];
*f = (1-t)*(1-u)*y1+t*(1-u)*y2+t*u*y3+(1-t)*u*y4;
*fx = (-(1-u)*y1+(1-u)*y2+u*y3-u*y4)*dt;
*fy = (-(1-t)*y1-t*y2+t*y3+(1-t)*y4)*du;
*fxy = (y1-y2+y3-y4)*du*dt;
return;
}
/*
* Bicubic interpolation
*/
if( c->stype==-3 )
{
sfx = c->n*c->m;
sfy = 2*c->n*c->m;
sfxy = 3*c->n*c->m;
s1 = c->n*iy+ix;
s2 = c->n*iy+(ix+1);
s3 = c->n*(iy+1)+ix;
s4 = c->n*(iy+1)+(ix+1);
t2 = t*t;
t3 = t*t2;
u2 = u*u;
u3 = u*u2;
ht00 = 2*t3-3*t2+1;
ht10 = t3-2*t2+t;
ht01 = -2*t3+3*t2;
ht11 = t3-t2;
hu00 = 2*u3-3*u2+1;
hu10 = u3-2*u2+u;
hu01 = -2*u3+3*u2;
hu11 = u3-u2;
ht10 = ht10/dt;
ht11 = ht11/dt;
hu10 = hu10/du;
hu11 = hu11/du;
dht00 = 6*t2-6*t;
dht10 = 3*t2-4*t+1;
dht01 = -6*t2+6*t;
dht11 = 3*t2-2*t;
dhu00 = 6*u2-6*u;
dhu10 = 3*u2-4*u+1;
dhu01 = -6*u2+6*u;
dhu11 = 3*u2-2*u;
dht00 = dht00*dt;
dht01 = dht01*dt;
dhu00 = dhu00*du;
dhu01 = dhu01*du;
*f = (double)(0);
*fx = (double)(0);
*fy = (double)(0);
*fxy = (double)(0);
v0 = c->f.ptr.p_double[s1];
v1 = c->f.ptr.p_double[s2];
v2 = c->f.ptr.p_double[s3];
v3 = c->f.ptr.p_double[s4];
*f = *f+v0*ht00*hu00+v1*ht01*hu00+v2*ht00*hu01+v3*ht01*hu01;
*fx = *fx+v0*dht00*hu00+v1*dht01*hu00+v2*dht00*hu01+v3*dht01*hu01;
*fy = *fy+v0*ht00*dhu00+v1*ht01*dhu00+v2*ht00*dhu01+v3*ht01*dhu01;
*fxy = *fxy+v0*dht00*dhu00+v1*dht01*dhu00+v2*dht00*dhu01+v3*dht01*dhu01;
v0 = c->f.ptr.p_double[sfx+s1];
v1 = c->f.ptr.p_double[sfx+s2];
v2 = c->f.ptr.p_double[sfx+s3];
v3 = c->f.ptr.p_double[sfx+s4];
*f = *f+v0*ht10*hu00+v1*ht11*hu00+v2*ht10*hu01+v3*ht11*hu01;
*fx = *fx+v0*dht10*hu00+v1*dht11*hu00+v2*dht10*hu01+v3*dht11*hu01;
*fy = *fy+v0*ht10*dhu00+v1*ht11*dhu00+v2*ht10*dhu01+v3*ht11*dhu01;
*fxy = *fxy+v0*dht10*dhu00+v1*dht11*dhu00+v2*dht10*dhu01+v3*dht11*dhu01;
v0 = c->f.ptr.p_double[sfy+s1];
v1 = c->f.ptr.p_double[sfy+s2];
v2 = c->f.ptr.p_double[sfy+s3];
v3 = c->f.ptr.p_double[sfy+s4];
*f = *f+v0*ht00*hu10+v1*ht01*hu10+v2*ht00*hu11+v3*ht01*hu11;
*fx = *fx+v0*dht00*hu10+v1*dht01*hu10+v2*dht00*hu11+v3*dht01*hu11;
*fy = *fy+v0*ht00*dhu10+v1*ht01*dhu10+v2*ht00*dhu11+v3*ht01*dhu11;
*fxy = *fxy+v0*dht00*dhu10+v1*dht01*dhu10+v2*dht00*dhu11+v3*dht01*dhu11;
v0 = c->f.ptr.p_double[sfxy+s1];
v1 = c->f.ptr.p_double[sfxy+s2];
v2 = c->f.ptr.p_double[sfxy+s3];
v3 = c->f.ptr.p_double[sfxy+s4];
*f = *f+v0*ht10*hu10+v1*ht11*hu10+v2*ht10*hu11+v3*ht11*hu11;
*fx = *fx+v0*dht10*hu10+v1*dht11*hu10+v2*dht10*hu11+v3*dht11*hu11;
*fy = *fy+v0*ht10*dhu10+v1*ht11*dhu10+v2*ht10*dhu11+v3*ht11*dhu11;
*fxy = *fxy+v0*dht10*dhu10+v1*dht11*dhu10+v2*dht10*dhu11+v3*dht11*dhu11;
return;
}
}
/*************************************************************************
This subroutine calculates bilinear or bicubic vector-valued spline at the
given point (X,Y).
If you need just some specific component of vector-valued spline, you can
use spline2dcalcvi() function.
INPUT PARAMETERS:
C - spline interpolant.
X, Y- point
F - output buffer, possibly preallocated array. In case array size
is large enough to store result, it is not reallocated. Array
which is too short will be reallocated
OUTPUT PARAMETERS:
F - array[D] (or larger) which stores function values
-- ALGLIB PROJECT --
Copyright 01.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dcalcvbuf(spline2dinterpolant* c,
double x,
double y,
/* Real */ ae_vector* f,
ae_state *_state)
{
ae_int_t ix;
ae_int_t iy;
ae_int_t l;
ae_int_t r;
ae_int_t h;
ae_int_t i;
double t;
double dt;
double u;
double du;
double y1;
double y2;
double y3;
double y4;
ae_int_t s1;
ae_int_t s2;
ae_int_t s3;
ae_int_t s4;
ae_int_t sfx;
ae_int_t sfy;
ae_int_t sfxy;
double t2;
double t3;
double u2;
double u3;
double ht00;
double ht01;
double ht10;
double ht11;
double hu00;
double hu01;
double hu10;
double hu11;
ae_assert(c->stype==-1||c->stype==-3, "Spline2DCalcVBuf: incorrect C (incorrect parameter C.SType)", _state);
ae_assert(ae_isfinite(x, _state)&&ae_isfinite(y, _state), "Spline2DCalcVBuf: X or Y contains NaN or Infinite value", _state);
/*
* Allocate place for output
*/
rvectorsetlengthatleast(f, c->d, _state);
/*
* Determine evaluation interval
*/
l = 0;
r = c->n-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->x.ptr.p_double[h],x) )
{
r = h;
}
else
{
l = h;
}
}
dt = 1.0/(c->x.ptr.p_double[l+1]-c->x.ptr.p_double[l]);
t = (x-c->x.ptr.p_double[l])*dt;
ix = l;
l = 0;
r = c->m-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->y.ptr.p_double[h],y) )
{
r = h;
}
else
{
l = h;
}
}
du = 1.0/(c->y.ptr.p_double[l+1]-c->y.ptr.p_double[l]);
u = (y-c->y.ptr.p_double[l])*du;
iy = l;
/*
* Bilinear interpolation
*/
if( c->stype==-1 )
{
for(i=0; i<=c->d-1; i++)
{
y1 = c->f.ptr.p_double[c->d*(c->n*iy+ix)+i];
y2 = c->f.ptr.p_double[c->d*(c->n*iy+(ix+1))+i];
y3 = c->f.ptr.p_double[c->d*(c->n*(iy+1)+(ix+1))+i];
y4 = c->f.ptr.p_double[c->d*(c->n*(iy+1)+ix)+i];
f->ptr.p_double[i] = (1-t)*(1-u)*y1+t*(1-u)*y2+t*u*y3+(1-t)*u*y4;
}
return;
}
/*
* Bicubic interpolation:
* * calculate Hermite basis for dimensions X and Y (variables T and U),
* here HTij means basis function whose I-th derivative has value 1 at T=J.
* Same for HUij.
* * after initial calculation, apply scaling by DT/DU to the basis
* * calculate using stored table of second derivatives
*/
ae_assert(c->stype==-3, "Spline2DCalc: integrity check failed", _state);
sfx = c->n*c->m*c->d;
sfy = 2*c->n*c->m*c->d;
sfxy = 3*c->n*c->m*c->d;
s1 = (c->n*iy+ix)*c->d;
s2 = (c->n*iy+(ix+1))*c->d;
s3 = (c->n*(iy+1)+ix)*c->d;
s4 = (c->n*(iy+1)+(ix+1))*c->d;
t2 = t*t;
t3 = t*t2;
u2 = u*u;
u3 = u*u2;
ht00 = 2*t3-3*t2+1;
ht10 = t3-2*t2+t;
ht01 = -2*t3+3*t2;
ht11 = t3-t2;
hu00 = 2*u3-3*u2+1;
hu10 = u3-2*u2+u;
hu01 = -2*u3+3*u2;
hu11 = u3-u2;
ht10 = ht10/dt;
ht11 = ht11/dt;
hu10 = hu10/du;
hu11 = hu11/du;
for(i=0; i<=c->d-1; i++)
{
/*
* Calculate I-th component
*/
f->ptr.p_double[i] = (double)(0);
f->ptr.p_double[i] = f->ptr.p_double[i]+c->f.ptr.p_double[s1]*ht00*hu00+c->f.ptr.p_double[s2]*ht01*hu00+c->f.ptr.p_double[s3]*ht00*hu01+c->f.ptr.p_double[s4]*ht01*hu01;
f->ptr.p_double[i] = f->ptr.p_double[i]+c->f.ptr.p_double[sfx+s1]*ht10*hu00+c->f.ptr.p_double[sfx+s2]*ht11*hu00+c->f.ptr.p_double[sfx+s3]*ht10*hu01+c->f.ptr.p_double[sfx+s4]*ht11*hu01;
f->ptr.p_double[i] = f->ptr.p_double[i]+c->f.ptr.p_double[sfy+s1]*ht00*hu10+c->f.ptr.p_double[sfy+s2]*ht01*hu10+c->f.ptr.p_double[sfy+s3]*ht00*hu11+c->f.ptr.p_double[sfy+s4]*ht01*hu11;
f->ptr.p_double[i] = f->ptr.p_double[i]+c->f.ptr.p_double[sfxy+s1]*ht10*hu10+c->f.ptr.p_double[sfxy+s2]*ht11*hu10+c->f.ptr.p_double[sfxy+s3]*ht10*hu11+c->f.ptr.p_double[sfxy+s4]*ht11*hu11;
/*
* Advance source indexes
*/
s1 = s1+1;
s2 = s2+1;
s3 = s3+1;
s4 = s4+1;
}
}
/*************************************************************************
This subroutine calculates specific component of vector-valued bilinear or
bicubic spline at the given point (X,Y).
INPUT PARAMETERS:
C - spline interpolant.
X, Y- point
I - component index, in [0,D). An exception is generated for out
of range values.
RESULT:
value of I-th component
-- ALGLIB PROJECT --
Copyright 01.02.2018 by Bochkanov Sergey
*************************************************************************/
double spline2dcalcvi(spline2dinterpolant* c,
double x,
double y,
ae_int_t i,
ae_state *_state)
{
ae_int_t ix;
ae_int_t iy;
ae_int_t l;
ae_int_t r;
ae_int_t h;
double t;
double dt;
double u;
double du;
double y1;
double y2;
double y3;
double y4;
ae_int_t s1;
ae_int_t s2;
ae_int_t s3;
ae_int_t s4;
ae_int_t sfx;
ae_int_t sfy;
ae_int_t sfxy;
double t2;
double t3;
double u2;
double u3;
double ht00;
double ht01;
double ht10;
double ht11;
double hu00;
double hu01;
double hu10;
double hu11;
double result;
ae_assert(c->stype==-1||c->stype==-3, "Spline2DCalcVi: incorrect C (incorrect parameter C.SType)", _state);
ae_assert(ae_isfinite(x, _state)&&ae_isfinite(y, _state), "Spline2DCalcVi: X or Y contains NaN or Infinite value", _state);
ae_assert(i>=0&&i<c->d, "Spline2DCalcVi: incorrect I (I<0 or I>=D)", _state);
/*
* Determine evaluation interval
*/
l = 0;
r = c->n-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->x.ptr.p_double[h],x) )
{
r = h;
}
else
{
l = h;
}
}
dt = 1.0/(c->x.ptr.p_double[l+1]-c->x.ptr.p_double[l]);
t = (x-c->x.ptr.p_double[l])*dt;
ix = l;
l = 0;
r = c->m-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->y.ptr.p_double[h],y) )
{
r = h;
}
else
{
l = h;
}
}
du = 1.0/(c->y.ptr.p_double[l+1]-c->y.ptr.p_double[l]);
u = (y-c->y.ptr.p_double[l])*du;
iy = l;
/*
* Bilinear interpolation
*/
if( c->stype==-1 )
{
y1 = c->f.ptr.p_double[c->d*(c->n*iy+ix)+i];
y2 = c->f.ptr.p_double[c->d*(c->n*iy+(ix+1))+i];
y3 = c->f.ptr.p_double[c->d*(c->n*(iy+1)+(ix+1))+i];
y4 = c->f.ptr.p_double[c->d*(c->n*(iy+1)+ix)+i];
result = (1-t)*(1-u)*y1+t*(1-u)*y2+t*u*y3+(1-t)*u*y4;
return result;
}
/*
* Bicubic interpolation:
* * calculate Hermite basis for dimensions X and Y (variables T and U),
* here HTij means basis function whose I-th derivative has value 1 at T=J.
* Same for HUij.
* * after initial calculation, apply scaling by DT/DU to the basis
* * calculate using stored table of second derivatives
*/
ae_assert(c->stype==-3, "Spline2DCalc: integrity check failed", _state);
sfx = c->n*c->m*c->d;
sfy = 2*c->n*c->m*c->d;
sfxy = 3*c->n*c->m*c->d;
s1 = (c->n*iy+ix)*c->d;
s2 = (c->n*iy+(ix+1))*c->d;
s3 = (c->n*(iy+1)+ix)*c->d;
s4 = (c->n*(iy+1)+(ix+1))*c->d;
t2 = t*t;
t3 = t*t2;
u2 = u*u;
u3 = u*u2;
ht00 = 2*t3-3*t2+1;
ht10 = t3-2*t2+t;
ht01 = -2*t3+3*t2;
ht11 = t3-t2;
hu00 = 2*u3-3*u2+1;
hu10 = u3-2*u2+u;
hu01 = -2*u3+3*u2;
hu11 = u3-u2;
ht10 = ht10/dt;
ht11 = ht11/dt;
hu10 = hu10/du;
hu11 = hu11/du;
/*
* Advance source indexes to I-th position
*/
s1 = s1+i;
s2 = s2+i;
s3 = s3+i;
s4 = s4+i;
/*
* Calculate I-th component
*/
result = (double)(0);
result = result+c->f.ptr.p_double[s1]*ht00*hu00+c->f.ptr.p_double[s2]*ht01*hu00+c->f.ptr.p_double[s3]*ht00*hu01+c->f.ptr.p_double[s4]*ht01*hu01;
result = result+c->f.ptr.p_double[sfx+s1]*ht10*hu00+c->f.ptr.p_double[sfx+s2]*ht11*hu00+c->f.ptr.p_double[sfx+s3]*ht10*hu01+c->f.ptr.p_double[sfx+s4]*ht11*hu01;
result = result+c->f.ptr.p_double[sfy+s1]*ht00*hu10+c->f.ptr.p_double[sfy+s2]*ht01*hu10+c->f.ptr.p_double[sfy+s3]*ht00*hu11+c->f.ptr.p_double[sfy+s4]*ht01*hu11;
result = result+c->f.ptr.p_double[sfxy+s1]*ht10*hu10+c->f.ptr.p_double[sfxy+s2]*ht11*hu10+c->f.ptr.p_double[sfxy+s3]*ht10*hu11+c->f.ptr.p_double[sfxy+s4]*ht11*hu11;
return result;
}
/*************************************************************************
This subroutine calculates bilinear or bicubic vector-valued spline at the
given point (X,Y).
INPUT PARAMETERS:
C - spline interpolant.
X, Y- point
OUTPUT PARAMETERS:
F - array[D] which stores function values. F is out-parameter and
it is reallocated after call to this function. In case you
want to reuse previously allocated F, you may use
Spline2DCalcVBuf(), which reallocates F only when it is too
small.
-- ALGLIB PROJECT --
Copyright 16.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline2dcalcv(spline2dinterpolant* c,
double x,
double y,
/* Real */ ae_vector* f,
ae_state *_state)
{
ae_vector_clear(f);
ae_assert(c->stype==-1||c->stype==-3, "Spline2DCalcV: incorrect C (incorrect parameter C.SType)", _state);
ae_assert(ae_isfinite(x, _state)&&ae_isfinite(y, _state), "Spline2DCalcV: either X=NaN/Infinite or Y=NaN/Infinite", _state);
spline2dcalcvbuf(c, x, y, f, _state);
}
/*************************************************************************
This subroutine calculates value of specific component of bilinear or
bicubic vector-valued spline and its derivatives.
Input parameters:
C - spline interpolant.
X, Y- point
I - component index, in [0,D)
Output parameters:
F - S(x,y)
FX - dS(x,y)/dX
FY - dS(x,y)/dY
FXY - d2S(x,y)/dXdY
-- ALGLIB PROJECT --
Copyright 05.07.2007 by Bochkanov Sergey
*************************************************************************/
void spline2ddiffvi(spline2dinterpolant* c,
double x,
double y,
ae_int_t i,
double* f,
double* fx,
double* fy,
double* fxy,
ae_state *_state)
{
ae_int_t d;
double t;
double dt;
double u;
double du;
ae_int_t ix;
ae_int_t iy;
ae_int_t l;
ae_int_t r;
ae_int_t h;
ae_int_t s1;
ae_int_t s2;
ae_int_t s3;
ae_int_t s4;
ae_int_t sfx;
ae_int_t sfy;
ae_int_t sfxy;
double y1;
double y2;
double y3;
double y4;
double v0;
double v1;
double v2;
double v3;
double t2;
double t3;
double u2;
double u3;
double ht00;
double ht01;
double ht10;
double ht11;
double hu00;
double hu01;
double hu10;
double hu11;
double dht00;
double dht01;
double dht10;
double dht11;
double dhu00;
double dhu01;
double dhu10;
double dhu11;
*f = 0;
*fx = 0;
*fy = 0;
*fxy = 0;
ae_assert(c->stype==-1||c->stype==-3, "Spline2DDiffVI: incorrect C (incorrect parameter C.SType)", _state);
ae_assert(ae_isfinite(x, _state)&&ae_isfinite(y, _state), "Spline2DDiffVI: X or Y contains NaN or Infinite value", _state);
ae_assert(i>=0&&i<c->d, "Spline2DDiffVI: I<0 or I>=D", _state);
/*
* Prepare F, dF/dX, dF/dY, d2F/dXdY
*/
*f = (double)(0);
*fx = (double)(0);
*fy = (double)(0);
*fxy = (double)(0);
d = c->d;
/*
* Binary search in the [ x[0], ..., x[n-2] ] (x[n-1] is not included)
*/
l = 0;
r = c->n-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->x.ptr.p_double[h],x) )
{
r = h;
}
else
{
l = h;
}
}
t = (x-c->x.ptr.p_double[l])/(c->x.ptr.p_double[l+1]-c->x.ptr.p_double[l]);
dt = 1.0/(c->x.ptr.p_double[l+1]-c->x.ptr.p_double[l]);
ix = l;
/*
* Binary search in the [ y[0], ..., y[m-2] ] (y[m-1] is not included)
*/
l = 0;
r = c->m-1;
while(l!=r-1)
{
h = (l+r)/2;
if( ae_fp_greater_eq(c->y.ptr.p_double[h],y) )
{
r = h;
}
else
{
l = h;
}
}
u = (y-c->y.ptr.p_double[l])/(c->y.ptr.p_double[l+1]-c->y.ptr.p_double[l]);
du = 1.0/(c->y.ptr.p_double[l+1]-c->y.ptr.p_double[l]);
iy = l;
/*
* Bilinear interpolation
*/
if( c->stype==-1 )
{
y1 = c->f.ptr.p_double[d*(c->n*iy+ix)+i];
y2 = c->f.ptr.p_double[d*(c->n*iy+(ix+1))+i];
y3 = c->f.ptr.p_double[d*(c->n*(iy+1)+(ix+1))+i];
y4 = c->f.ptr.p_double[d*(c->n*(iy+1)+ix)+i];
*f = (1-t)*(1-u)*y1+t*(1-u)*y2+t*u*y3+(1-t)*u*y4;
*fx = (-(1-u)*y1+(1-u)*y2+u*y3-u*y4)*dt;
*fy = (-(1-t)*y1-t*y2+t*y3+(1-t)*y4)*du;
*fxy = (y1-y2+y3-y4)*du*dt;
return;
}
/*
* Bicubic interpolation
*/
if( c->stype==-3 )
{
sfx = c->n*c->m*d;
sfy = 2*c->n*c->m*d;
sfxy = 3*c->n*c->m*d;
s1 = d*(c->n*iy+ix)+i;
s2 = d*(c->n*iy+(ix+1))+i;
s3 = d*(c->n*(iy+1)+ix)+i;
s4 = d*(c->n*(iy+1)+(ix+1))+i;
t2 = t*t;
t3 = t*t2;
u2 = u*u;
u3 = u*u2;
ht00 = 2*t3-3*t2+1;
ht10 = t3-2*t2+t;
ht01 = -2*t3+3*t2;
ht11 = t3-t2;
hu00 = 2*u3-3*u2+1;
hu10 = u3-2*u2+u;
hu01 = -2*u3+3*u2;
hu11 = u3-u2;
ht10 = ht10/dt;
ht11 = ht11/dt;
hu10 = hu10/du;
hu11 = hu11/du;
dht00 = 6*t2-6*t;
dht10 = 3*t2-4*t+1;
dht01 = -6*t2+6*t;
dht11 = 3*t2-2*t;
dhu00 = 6*u2-6*u;
dhu10 = 3*u2-4*u+1;
dhu01 = -6*u2+6*u;
dhu11 = 3*u2-2*u;
dht00 = dht00*dt;
dht01 = dht01*dt;
dhu00 = dhu00*du;
dhu01 = dhu01*du;
*f = (double)(0);
*fx = (double)(0);
*fy = (double)(0);
*fxy = (double)(0);
v0 = c->f.ptr.p_double[s1];
v1 = c->f.ptr.p_double[s2];
v2 = c->f.ptr.p_double[s3];
v3 = c->f.ptr.p_double[s4];
*f = *f+v0*ht00*hu00+v1*ht01*hu00+v2*ht00*hu01+v3*ht01*hu01;
*fx = *fx+v0*dht00*hu00+v1*dht01*hu00+v2*dht00*hu01+v3*dht01*hu01;
*fy = *fy+v0*ht00*dhu00+v1*ht01*dhu00+v2*ht00*dhu01+v3*ht01*dhu01;
*fxy = *fxy+v0*dht00*dhu00+v1*dht01*dhu00+v2*dht00*dhu01+v3*dht01*dhu01;
v0 = c->f.ptr.p_double[sfx+s1];
v1 = c->f.ptr.p_double[sfx+s2];
v2 = c->f.ptr.p_double[sfx+s3];
v3 = c->f.ptr.p_double[sfx+s4];
*f = *f+v0*ht10*hu00+v1*ht11*hu00+v2*ht10*hu01+v3*ht11*hu01;
*fx = *fx+v0*dht10*hu00+v1*dht11*hu00+v2*dht10*hu01+v3*dht11*hu01;
*fy = *fy+v0*ht10*dhu00+v1*ht11*dhu00+v2*ht10*dhu01+v3*ht11*dhu01;
*fxy = *fxy+v0*dht10*dhu00+v1*dht11*dhu00+v2*dht10*dhu01+v3*dht11*dhu01;
v0 = c->f.ptr.p_double[sfy+s1];
v1 = c->f.ptr.p_double[sfy+s2];
v2 = c->f.ptr.p_double[sfy+s3];
v3 = c->f.ptr.p_double[sfy+s4];
*f = *f+v0*ht00*hu10+v1*ht01*hu10+v2*ht00*hu11+v3*ht01*hu11;
*fx = *fx+v0*dht00*hu10+v1*dht01*hu10+v2*dht00*hu11+v3*dht01*hu11;
*fy = *fy+v0*ht00*dhu10+v1*ht01*dhu10+v2*ht00*dhu11+v3*ht01*dhu11;
*fxy = *fxy+v0*dht00*dhu10+v1*dht01*dhu10+v2*dht00*dhu11+v3*dht01*dhu11;
v0 = c->f.ptr.p_double[sfxy+s1];
v1 = c->f.ptr.p_double[sfxy+s2];
v2 = c->f.ptr.p_double[sfxy+s3];
v3 = c->f.ptr.p_double[sfxy+s4];
*f = *f+v0*ht10*hu10+v1*ht11*hu10+v2*ht10*hu11+v3*ht11*hu11;
*fx = *fx+v0*dht10*hu10+v1*dht11*hu10+v2*dht10*hu11+v3*dht11*hu11;
*fy = *fy+v0*ht10*dhu10+v1*ht11*dhu10+v2*ht10*dhu11+v3*ht11*dhu11;
*fxy = *fxy+v0*dht10*dhu10+v1*dht11*dhu10+v2*dht10*dhu11+v3*dht11*dhu11;
return;
}
}
/*************************************************************************
This subroutine performs linear transformation of the spline argument.
Input parameters:
C - spline interpolant
AX, BX - transformation coefficients: x = A*t + B
AY, BY - transformation coefficients: y = A*u + B
Result:
C - transformed spline
-- ALGLIB PROJECT --
Copyright 30.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline2dlintransxy(spline2dinterpolant* c,
double ax,
double bx,
double ay,
double by,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector x;
ae_vector y;
ae_vector f;
ae_vector v;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_frame_make(_state, &_frame_block);
memset(&x, 0, sizeof(x));
memset(&y, 0, sizeof(y));
memset(&f, 0, sizeof(f));
memset(&v, 0, sizeof(v));
ae_vector_init(&x, 0, DT_REAL, _state, ae_true);
ae_vector_init(&y, 0, DT_REAL, _state, ae_true);
ae_vector_init(&f, 0, DT_REAL, _state, ae_true);
ae_vector_init(&v, 0, DT_REAL, _state, ae_true);
ae_assert(c->stype==-3||c->stype==-1, "Spline2DLinTransXY: incorrect C (incorrect parameter C.SType)", _state);
ae_assert(ae_isfinite(ax, _state), "Spline2DLinTransXY: AX is infinite or NaN", _state);
ae_assert(ae_isfinite(bx, _state), "Spline2DLinTransXY: BX is infinite or NaN", _state);
ae_assert(ae_isfinite(ay, _state), "Spline2DLinTransXY: AY is infinite or NaN", _state);
ae_assert(ae_isfinite(by, _state), "Spline2DLinTransXY: BY is infinite or NaN", _state);
ae_vector_set_length(&x, c->n, _state);
ae_vector_set_length(&y, c->m, _state);
ae_vector_set_length(&f, c->m*c->n*c->d, _state);
for(j=0; j<=c->n-1; j++)
{
x.ptr.p_double[j] = c->x.ptr.p_double[j];
}
for(i=0; i<=c->m-1; i++)
{
y.ptr.p_double[i] = c->y.ptr.p_double[i];
}
for(i=0; i<=c->m-1; i++)
{
for(j=0; j<=c->n-1; j++)
{
for(k=0; k<=c->d-1; k++)
{
f.ptr.p_double[c->d*(i*c->n+j)+k] = c->f.ptr.p_double[c->d*(i*c->n+j)+k];
}
}
}
/*
* Handle different combinations of AX/AY
*/
if( ae_fp_eq(ax,(double)(0))&&ae_fp_neq(ay,(double)(0)) )
{
for(i=0; i<=c->m-1; i++)
{
spline2dcalcvbuf(c, bx, y.ptr.p_double[i], &v, _state);
y.ptr.p_double[i] = (y.ptr.p_double[i]-by)/ay;
for(j=0; j<=c->n-1; j++)
{
for(k=0; k<=c->d-1; k++)
{
f.ptr.p_double[c->d*(i*c->n+j)+k] = v.ptr.p_double[k];
}
}
}
}
if( ae_fp_neq(ax,(double)(0))&&ae_fp_eq(ay,(double)(0)) )
{
for(j=0; j<=c->n-1; j++)
{
spline2dcalcvbuf(c, x.ptr.p_double[j], by, &v, _state);
x.ptr.p_double[j] = (x.ptr.p_double[j]-bx)/ax;
for(i=0; i<=c->m-1; i++)
{
for(k=0; k<=c->d-1; k++)
{
f.ptr.p_double[c->d*(i*c->n+j)+k] = v.ptr.p_double[k];
}
}
}
}
if( ae_fp_neq(ax,(double)(0))&&ae_fp_neq(ay,(double)(0)) )
{
for(j=0; j<=c->n-1; j++)
{
x.ptr.p_double[j] = (x.ptr.p_double[j]-bx)/ax;
}
for(i=0; i<=c->m-1; i++)
{
y.ptr.p_double[i] = (y.ptr.p_double[i]-by)/ay;
}
}
if( ae_fp_eq(ax,(double)(0))&&ae_fp_eq(ay,(double)(0)) )
{
spline2dcalcvbuf(c, bx, by, &v, _state);
for(i=0; i<=c->m-1; i++)
{
for(j=0; j<=c->n-1; j++)
{
for(k=0; k<=c->d-1; k++)
{
f.ptr.p_double[c->d*(i*c->n+j)+k] = v.ptr.p_double[k];
}
}
}
}
/*
* Rebuild spline
*/
if( c->stype==-3 )
{
spline2dbuildbicubicv(&x, c->n, &y, c->m, &f, c->d, c, _state);
}
if( c->stype==-1 )
{
spline2dbuildbilinearv(&x, c->n, &y, c->m, &f, c->d, c, _state);
}
ae_frame_leave(_state);
}
/*************************************************************************
This subroutine performs linear transformation of the spline.
Input parameters:
C - spline interpolant.
A, B- transformation coefficients: S2(x,y) = A*S(x,y) + B
Output parameters:
C - transformed spline
-- ALGLIB PROJECT --
Copyright 30.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline2dlintransf(spline2dinterpolant* c,
double a,
double b,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector x;
ae_vector y;
ae_vector f;
ae_int_t i;
ae_int_t j;
ae_frame_make(_state, &_frame_block);
memset(&x, 0, sizeof(x));
memset(&y, 0, sizeof(y));
memset(&f, 0, sizeof(f));
ae_vector_init(&x, 0, DT_REAL, _state, ae_true);
ae_vector_init(&y, 0, DT_REAL, _state, ae_true);
ae_vector_init(&f, 0, DT_REAL, _state, ae_true);
ae_assert(c->stype==-3||c->stype==-1, "Spline2DLinTransF: incorrect C (incorrect parameter C.SType)", _state);
ae_vector_set_length(&x, c->n, _state);
ae_vector_set_length(&y, c->m, _state);
ae_vector_set_length(&f, c->m*c->n*c->d, _state);
for(j=0; j<=c->n-1; j++)
{
x.ptr.p_double[j] = c->x.ptr.p_double[j];
}
for(i=0; i<=c->m-1; i++)
{
y.ptr.p_double[i] = c->y.ptr.p_double[i];
}
for(i=0; i<=c->m*c->n*c->d-1; i++)
{
f.ptr.p_double[i] = a*c->f.ptr.p_double[i]+b;
}
if( c->stype==-3 )
{
spline2dbuildbicubicv(&x, c->n, &y, c->m, &f, c->d, c, _state);
}
if( c->stype==-1 )
{
spline2dbuildbilinearv(&x, c->n, &y, c->m, &f, c->d, c, _state);
}
ae_frame_leave(_state);
}
/*************************************************************************
This subroutine makes the copy of the spline model.
Input parameters:
C - spline interpolant
Output parameters:
CC - spline copy
-- ALGLIB PROJECT --
Copyright 29.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline2dcopy(spline2dinterpolant* c,
spline2dinterpolant* cc,
ae_state *_state)
{
ae_int_t tblsize;
_spline2dinterpolant_clear(cc);
ae_assert(c->stype==-1||c->stype==-3, "Spline2DCopy: incorrect C (incorrect parameter C.SType)", _state);
cc->n = c->n;
cc->m = c->m;
cc->d = c->d;
cc->stype = c->stype;
tblsize = -1;
if( c->stype==-3 )
{
tblsize = 4*c->n*c->m*c->d;
}
if( c->stype==-1 )
{
tblsize = c->n*c->m*c->d;
}
ae_assert(tblsize>0, "Spline2DCopy: internal error", _state);
ae_vector_set_length(&cc->x, cc->n, _state);
ae_vector_set_length(&cc->y, cc->m, _state);
ae_vector_set_length(&cc->f, tblsize, _state);
ae_v_move(&cc->x.ptr.p_double[0], 1, &c->x.ptr.p_double[0], 1, ae_v_len(0,cc->n-1));
ae_v_move(&cc->y.ptr.p_double[0], 1, &c->y.ptr.p_double[0], 1, ae_v_len(0,cc->m-1));
ae_v_move(&cc->f.ptr.p_double[0], 1, &c->f.ptr.p_double[0], 1, ae_v_len(0,tblsize-1));
}
/*************************************************************************
Bicubic spline resampling
Input parameters:
A - function values at the old grid,
array[0..OldHeight-1, 0..OldWidth-1]
OldHeight - old grid height, OldHeight>1
OldWidth - old grid width, OldWidth>1
NewHeight - new grid height, NewHeight>1
NewWidth - new grid width, NewWidth>1
Output parameters:
B - function values at the new grid,
array[0..NewHeight-1, 0..NewWidth-1]
-- ALGLIB routine --
15 May, 2007
Copyright by Bochkanov Sergey
*************************************************************************/
void spline2dresamplebicubic(/* Real */ ae_matrix* a,
ae_int_t oldheight,
ae_int_t oldwidth,
/* Real */ ae_matrix* b,
ae_int_t newheight,
ae_int_t newwidth,
ae_state *_state)
{
ae_frame _frame_block;
ae_matrix buf;
ae_vector x;
ae_vector y;
spline1dinterpolant c;
ae_int_t mw;
ae_int_t mh;
ae_int_t i;
ae_int_t j;
ae_frame_make(_state, &_frame_block);
memset(&buf, 0, sizeof(buf));
memset(&x, 0, sizeof(x));
memset(&y, 0, sizeof(y));
memset(&c, 0, sizeof(c));
ae_matrix_clear(b);
ae_matrix_init(&buf, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&x, 0, DT_REAL, _state, ae_true);
ae_vector_init(&y, 0, DT_REAL, _state, ae_true);
_spline1dinterpolant_init(&c, _state, ae_true);
ae_assert(oldwidth>1&&oldheight>1, "Spline2DResampleBicubic: width/height less than 1", _state);
ae_assert(newwidth>1&&newheight>1, "Spline2DResampleBicubic: width/height less than 1", _state);
/*
* Prepare
*/
mw = ae_maxint(oldwidth, newwidth, _state);
mh = ae_maxint(oldheight, newheight, _state);
ae_matrix_set_length(b, newheight, newwidth, _state);
ae_matrix_set_length(&buf, oldheight, newwidth, _state);
ae_vector_set_length(&x, ae_maxint(mw, mh, _state), _state);
ae_vector_set_length(&y, ae_maxint(mw, mh, _state), _state);
/*
* Horizontal interpolation
*/
for(i=0; i<=oldheight-1; i++)
{
/*
* Fill X, Y
*/
for(j=0; j<=oldwidth-1; j++)
{
x.ptr.p_double[j] = (double)j/(double)(oldwidth-1);
y.ptr.p_double[j] = a->ptr.pp_double[i][j];
}
/*
* Interpolate and place result into temporary matrix
*/
spline1dbuildcubic(&x, &y, oldwidth, 0, 0.0, 0, 0.0, &c, _state);
for(j=0; j<=newwidth-1; j++)
{
buf.ptr.pp_double[i][j] = spline1dcalc(&c, (double)j/(double)(newwidth-1), _state);
}
}
/*
* Vertical interpolation
*/
for(j=0; j<=newwidth-1; j++)
{
/*
* Fill X, Y
*/
for(i=0; i<=oldheight-1; i++)
{
x.ptr.p_double[i] = (double)i/(double)(oldheight-1);
y.ptr.p_double[i] = buf.ptr.pp_double[i][j];
}
/*
* Interpolate and place result into B
*/
spline1dbuildcubic(&x, &y, oldheight, 0, 0.0, 0, 0.0, &c, _state);
for(i=0; i<=newheight-1; i++)
{
b->ptr.pp_double[i][j] = spline1dcalc(&c, (double)i/(double)(newheight-1), _state);
}
}
ae_frame_leave(_state);
}
/*************************************************************************
Bilinear spline resampling
Input parameters:
A - function values at the old grid,
array[0..OldHeight-1, 0..OldWidth-1]
OldHeight - old grid height, OldHeight>1
OldWidth - old grid width, OldWidth>1
NewHeight - new grid height, NewHeight>1
NewWidth - new grid width, NewWidth>1
Output parameters:
B - function values at the new grid,
array[0..NewHeight-1, 0..NewWidth-1]
-- ALGLIB routine --
09.07.2007
Copyright by Bochkanov Sergey
*************************************************************************/
void spline2dresamplebilinear(/* Real */ ae_matrix* a,
ae_int_t oldheight,
ae_int_t oldwidth,
/* Real */ ae_matrix* b,
ae_int_t newheight,
ae_int_t newwidth,
ae_state *_state)
{
ae_int_t l;
ae_int_t c;
double t;
double u;
ae_int_t i;
ae_int_t j;
ae_matrix_clear(b);
ae_assert(oldwidth>1&&oldheight>1, "Spline2DResampleBilinear: width/height less than 1", _state);
ae_assert(newwidth>1&&newheight>1, "Spline2DResampleBilinear: width/height less than 1", _state);
ae_matrix_set_length(b, newheight, newwidth, _state);
for(i=0; i<=newheight-1; i++)
{
for(j=0; j<=newwidth-1; j++)
{
l = i*(oldheight-1)/(newheight-1);
if( l==oldheight-1 )
{
l = oldheight-2;
}
u = (double)i/(double)(newheight-1)*(oldheight-1)-l;
c = j*(oldwidth-1)/(newwidth-1);
if( c==oldwidth-1 )
{
c = oldwidth-2;
}
t = (double)(j*(oldwidth-1))/(double)(newwidth-1)-c;
b->ptr.pp_double[i][j] = (1-t)*(1-u)*a->ptr.pp_double[l][c]+t*(1-u)*a->ptr.pp_double[l][c+1]+t*u*a->ptr.pp_double[l+1][c+1]+(1-t)*u*a->ptr.pp_double[l+1][c];
}
}
}
/*************************************************************************
This subroutine builds bilinear vector-valued spline.
Input parameters:
X - spline abscissas, array[0..N-1]
Y - spline ordinates, array[0..M-1]
F - function values, array[0..M*N*D-1]:
* first D elements store D values at (X[0],Y[0])
* next D elements store D values at (X[1],Y[0])
* general form - D function values at (X[i],Y[j]) are stored
at F[D*(J*N+I)...D*(J*N+I)+D-1].
M,N - grid size, M>=2, N>=2
D - vector dimension, D>=1
Output parameters:
C - spline interpolant
-- ALGLIB PROJECT --
Copyright 16.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildbilinearv(/* Real */ ae_vector* x,
ae_int_t n,
/* Real */ ae_vector* y,
ae_int_t m,
/* Real */ ae_vector* f,
ae_int_t d,
spline2dinterpolant* c,
ae_state *_state)
{
double t;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t i0;
_spline2dinterpolant_clear(c);
ae_assert(n>=2, "Spline2DBuildBilinearV: N is less then 2", _state);
ae_assert(m>=2, "Spline2DBuildBilinearV: M is less then 2", _state);
ae_assert(d>=1, "Spline2DBuildBilinearV: invalid argument D (D<1)", _state);
ae_assert(x->cnt>=n&&y->cnt>=m, "Spline2DBuildBilinearV: length of X or Y is too short (Length(X/Y)<N/M)", _state);
ae_assert(isfinitevector(x, n, _state)&&isfinitevector(y, m, _state), "Spline2DBuildBilinearV: X or Y contains NaN or Infinite value", _state);
k = n*m*d;
ae_assert(f->cnt>=k, "Spline2DBuildBilinearV: length of F is too short (Length(F)<N*M*D)", _state);
ae_assert(isfinitevector(f, k, _state), "Spline2DBuildBilinearV: F contains NaN or Infinite value", _state);
/*
* Fill interpolant
*/
c->n = n;
c->m = m;
c->d = d;
c->stype = -1;
ae_vector_set_length(&c->x, c->n, _state);
ae_vector_set_length(&c->y, c->m, _state);
ae_vector_set_length(&c->f, k, _state);
for(i=0; i<=c->n-1; i++)
{
c->x.ptr.p_double[i] = x->ptr.p_double[i];
}
for(i=0; i<=c->m-1; i++)
{
c->y.ptr.p_double[i] = y->ptr.p_double[i];
}
for(i=0; i<=k-1; i++)
{
c->f.ptr.p_double[i] = f->ptr.p_double[i];
}
/*
* Sort points
*/
for(j=0; j<=c->n-1; j++)
{
k = j;
for(i=j+1; i<=c->n-1; i++)
{
if( ae_fp_less(c->x.ptr.p_double[i],c->x.ptr.p_double[k]) )
{
k = i;
}
}
if( k!=j )
{
for(i=0; i<=c->m-1; i++)
{
for(i0=0; i0<=c->d-1; i0++)
{
t = c->f.ptr.p_double[c->d*(i*c->n+j)+i0];
c->f.ptr.p_double[c->d*(i*c->n+j)+i0] = c->f.ptr.p_double[c->d*(i*c->n+k)+i0];
c->f.ptr.p_double[c->d*(i*c->n+k)+i0] = t;
}
}
t = c->x.ptr.p_double[j];
c->x.ptr.p_double[j] = c->x.ptr.p_double[k];
c->x.ptr.p_double[k] = t;
}
}
for(i=0; i<=c->m-1; i++)
{
k = i;
for(j=i+1; j<=c->m-1; j++)
{
if( ae_fp_less(c->y.ptr.p_double[j],c->y.ptr.p_double[k]) )
{
k = j;
}
}
if( k!=i )
{
for(j=0; j<=c->n-1; j++)
{
for(i0=0; i0<=c->d-1; i0++)
{
t = c->f.ptr.p_double[c->d*(i*c->n+j)+i0];
c->f.ptr.p_double[c->d*(i*c->n+j)+i0] = c->f.ptr.p_double[c->d*(k*c->n+j)+i0];
c->f.ptr.p_double[c->d*(k*c->n+j)+i0] = t;
}
}
t = c->y.ptr.p_double[i];
c->y.ptr.p_double[i] = c->y.ptr.p_double[k];
c->y.ptr.p_double[k] = t;
}
}
}
/*************************************************************************
This subroutine builds bicubic vector-valued spline.
Input parameters:
X - spline abscissas, array[0..N-1]
Y - spline ordinates, array[0..M-1]
F - function values, array[0..M*N*D-1]:
* first D elements store D values at (X[0],Y[0])
* next D elements store D values at (X[1],Y[0])
* general form - D function values at (X[i],Y[j]) are stored
at F[D*(J*N+I)...D*(J*N+I)+D-1].
M,N - grid size, M>=2, N>=2
D - vector dimension, D>=1
Output parameters:
C - spline interpolant
-- ALGLIB PROJECT --
Copyright 16.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildbicubicv(/* Real */ ae_vector* x,
ae_int_t n,
/* Real */ ae_vector* y,
ae_int_t m,
/* Real */ ae_vector* f,
ae_int_t d,
spline2dinterpolant* c,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _f;
ae_matrix tf;
ae_matrix dx;
ae_matrix dy;
ae_matrix dxy;
double t;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t di;
ae_frame_make(_state, &_frame_block);
memset(&_f, 0, sizeof(_f));
memset(&tf, 0, sizeof(tf));
memset(&dx, 0, sizeof(dx));
memset(&dy, 0, sizeof(dy));
memset(&dxy, 0, sizeof(dxy));
ae_vector_init_copy(&_f, f, _state, ae_true);
f = &_f;
_spline2dinterpolant_clear(c);
ae_matrix_init(&tf, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&dx, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&dy, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&dxy, 0, 0, DT_REAL, _state, ae_true);
ae_assert(n>=2, "Spline2DBuildBicubicV: N is less than 2", _state);
ae_assert(m>=2, "Spline2DBuildBicubicV: M is less than 2", _state);
ae_assert(d>=1, "Spline2DBuildBicubicV: invalid argument D (D<1)", _state);
ae_assert(x->cnt>=n&&y->cnt>=m, "Spline2DBuildBicubicV: length of X or Y is too short (Length(X/Y)<N/M)", _state);
ae_assert(isfinitevector(x, n, _state)&&isfinitevector(y, m, _state), "Spline2DBuildBicubicV: X or Y contains NaN or Infinite value", _state);
k = n*m*d;
ae_assert(f->cnt>=k, "Spline2DBuildBicubicV: length of F is too short (Length(F)<N*M*D)", _state);
ae_assert(isfinitevector(f, k, _state), "Spline2DBuildBicubicV: F contains NaN or Infinite value", _state);
/*
* Fill interpolant:
* F[0]...F[N*M*D-1]:
* f(i,j) table. f(0,0), f(0, 1), f(0,2) and so on...
* F[N*M*D]...F[2*N*M*D-1]:
* df(i,j)/dx table.
* F[2*N*M*D]...F[3*N*M*D-1]:
* df(i,j)/dy table.
* F[3*N*M*D]...F[4*N*M*D-1]:
* d2f(i,j)/dxdy table.
*/
c->d = d;
c->n = n;
c->m = m;
c->stype = -3;
k = 4*k;
ae_vector_set_length(&c->x, c->n, _state);
ae_vector_set_length(&c->y, c->m, _state);
ae_vector_set_length(&c->f, k, _state);
ae_matrix_set_length(&tf, c->m, c->n, _state);
for(i=0; i<=c->n-1; i++)
{
c->x.ptr.p_double[i] = x->ptr.p_double[i];
}
for(i=0; i<=c->m-1; i++)
{
c->y.ptr.p_double[i] = y->ptr.p_double[i];
}
/*
* Sort points
*/
for(j=0; j<=c->n-1; j++)
{
k = j;
for(i=j+1; i<=c->n-1; i++)
{
if( ae_fp_less(c->x.ptr.p_double[i],c->x.ptr.p_double[k]) )
{
k = i;
}
}
if( k!=j )
{
for(i=0; i<=c->m-1; i++)
{
for(di=0; di<=c->d-1; di++)
{
t = f->ptr.p_double[c->d*(i*c->n+j)+di];
f->ptr.p_double[c->d*(i*c->n+j)+di] = f->ptr.p_double[c->d*(i*c->n+k)+di];
f->ptr.p_double[c->d*(i*c->n+k)+di] = t;
}
}
t = c->x.ptr.p_double[j];
c->x.ptr.p_double[j] = c->x.ptr.p_double[k];
c->x.ptr.p_double[k] = t;
}
}
for(i=0; i<=c->m-1; i++)
{
k = i;
for(j=i+1; j<=c->m-1; j++)
{
if( ae_fp_less(c->y.ptr.p_double[j],c->y.ptr.p_double[k]) )
{
k = j;
}
}
if( k!=i )
{
for(j=0; j<=c->n-1; j++)
{
for(di=0; di<=c->d-1; di++)
{
t = f->ptr.p_double[c->d*(i*c->n+j)+di];
f->ptr.p_double[c->d*(i*c->n+j)+di] = f->ptr.p_double[c->d*(k*c->n+j)+di];
f->ptr.p_double[c->d*(k*c->n+j)+di] = t;
}
}
t = c->y.ptr.p_double[i];
c->y.ptr.p_double[i] = c->y.ptr.p_double[k];
c->y.ptr.p_double[k] = t;
}
}
for(di=0; di<=c->d-1; di++)
{
for(i=0; i<=c->m-1; i++)
{
for(j=0; j<=c->n-1; j++)
{
tf.ptr.pp_double[i][j] = f->ptr.p_double[c->d*(i*c->n+j)+di];
}
}
spline2d_bicubiccalcderivatives(&tf, &c->x, &c->y, c->m, c->n, &dx, &dy, &dxy, _state);
for(i=0; i<=c->m-1; i++)
{
for(j=0; j<=c->n-1; j++)
{
k = c->d*(i*c->n+j)+di;
c->f.ptr.p_double[k] = tf.ptr.pp_double[i][j];
c->f.ptr.p_double[c->n*c->m*c->d+k] = dx.ptr.pp_double[i][j];
c->f.ptr.p_double[2*c->n*c->m*c->d+k] = dy.ptr.pp_double[i][j];
c->f.ptr.p_double[3*c->n*c->m*c->d+k] = dxy.ptr.pp_double[i][j];
}
}
}
ae_frame_leave(_state);
}
/*************************************************************************
This subroutine unpacks two-dimensional spline into the coefficients table
Input parameters:
C - spline interpolant.
Result:
M, N- grid size (x-axis and y-axis)
D - number of components
Tbl - coefficients table, unpacked format,
D - components: [0..(N-1)*(M-1)*D-1, 0..19].
For T=0..D-1 (component index), I = 0...N-2 (x index),
J=0..M-2 (y index):
K := T + I*D + J*D*(N-1)
K-th row stores decomposition for T-th component of the
vector-valued function
Tbl[K,0] = X[i]
Tbl[K,1] = X[i+1]
Tbl[K,2] = Y[j]
Tbl[K,3] = Y[j+1]
Tbl[K,4] = C00
Tbl[K,5] = C01
Tbl[K,6] = C02
Tbl[K,7] = C03
Tbl[K,8] = C10
Tbl[K,9] = C11
...
Tbl[K,19] = C33
On each grid square spline is equals to:
S(x) = SUM(c[i,j]*(t^i)*(u^j), i=0..3, j=0..3)
t = x-x[j]
u = y-y[i]
-- ALGLIB PROJECT --
Copyright 16.04.2012 by Bochkanov Sergey
*************************************************************************/
void spline2dunpackv(spline2dinterpolant* c,
ae_int_t* m,
ae_int_t* n,
ae_int_t* d,
/* Real */ ae_matrix* tbl,
ae_state *_state)
{
ae_int_t k;
ae_int_t p;
ae_int_t ci;
ae_int_t cj;
ae_int_t s1;
ae_int_t s2;
ae_int_t s3;
ae_int_t s4;
ae_int_t sfx;
ae_int_t sfy;
ae_int_t sfxy;
double y1;
double y2;
double y3;
double y4;
double dt;
double du;
ae_int_t i;
ae_int_t j;
ae_int_t k0;
*m = 0;
*n = 0;
*d = 0;
ae_matrix_clear(tbl);
ae_assert(c->stype==-3||c->stype==-1, "Spline2DUnpackV: incorrect C (incorrect parameter C.SType)", _state);
*n = c->n;
*m = c->m;
*d = c->d;
ae_matrix_set_length(tbl, (*n-1)*(*m-1)*(*d), 20, _state);
sfx = *n*(*m)*(*d);
sfy = 2*(*n)*(*m)*(*d);
sfxy = 3*(*n)*(*m)*(*d);
for(i=0; i<=*m-2; i++)
{
for(j=0; j<=*n-2; j++)
{
for(k=0; k<=*d-1; k++)
{
p = *d*(i*(*n-1)+j)+k;
tbl->ptr.pp_double[p][0] = c->x.ptr.p_double[j];
tbl->ptr.pp_double[p][1] = c->x.ptr.p_double[j+1];
tbl->ptr.pp_double[p][2] = c->y.ptr.p_double[i];
tbl->ptr.pp_double[p][3] = c->y.ptr.p_double[i+1];
dt = 1/(tbl->ptr.pp_double[p][1]-tbl->ptr.pp_double[p][0]);
du = 1/(tbl->ptr.pp_double[p][3]-tbl->ptr.pp_double[p][2]);
/*
* Bilinear interpolation
*/
if( c->stype==-1 )
{
for(k0=4; k0<=19; k0++)
{
tbl->ptr.pp_double[p][k0] = (double)(0);
}
y1 = c->f.ptr.p_double[*d*(*n*i+j)+k];
y2 = c->f.ptr.p_double[*d*(*n*i+(j+1))+k];
y3 = c->f.ptr.p_double[*d*(*n*(i+1)+(j+1))+k];
y4 = c->f.ptr.p_double[*d*(*n*(i+1)+j)+k];
tbl->ptr.pp_double[p][4] = y1;
tbl->ptr.pp_double[p][4+1*4+0] = y2-y1;
tbl->ptr.pp_double[p][4+0*4+1] = y4-y1;
tbl->ptr.pp_double[p][4+1*4+1] = y3-y2-y4+y1;
}
/*
* Bicubic interpolation
*/
if( c->stype==-3 )
{
s1 = *d*(*n*i+j)+k;
s2 = *d*(*n*i+(j+1))+k;
s3 = *d*(*n*(i+1)+(j+1))+k;
s4 = *d*(*n*(i+1)+j)+k;
tbl->ptr.pp_double[p][4+0*4+0] = c->f.ptr.p_double[s1];
tbl->ptr.pp_double[p][4+0*4+1] = c->f.ptr.p_double[sfy+s1]/du;
tbl->ptr.pp_double[p][4+0*4+2] = -3*c->f.ptr.p_double[s1]+3*c->f.ptr.p_double[s4]-2*c->f.ptr.p_double[sfy+s1]/du-c->f.ptr.p_double[sfy+s4]/du;
tbl->ptr.pp_double[p][4+0*4+3] = 2*c->f.ptr.p_double[s1]-2*c->f.ptr.p_double[s4]+c->f.ptr.p_double[sfy+s1]/du+c->f.ptr.p_double[sfy+s4]/du;
tbl->ptr.pp_double[p][4+1*4+0] = c->f.ptr.p_double[sfx+s1]/dt;
tbl->ptr.pp_double[p][4+1*4+1] = c->f.ptr.p_double[sfxy+s1]/(dt*du);
tbl->ptr.pp_double[p][4+1*4+2] = -3*c->f.ptr.p_double[sfx+s1]/dt+3*c->f.ptr.p_double[sfx+s4]/dt-2*c->f.ptr.p_double[sfxy+s1]/(dt*du)-c->f.ptr.p_double[sfxy+s4]/(dt*du);
tbl->ptr.pp_double[p][4+1*4+3] = 2*c->f.ptr.p_double[sfx+s1]/dt-2*c->f.ptr.p_double[sfx+s4]/dt+c->f.ptr.p_double[sfxy+s1]/(dt*du)+c->f.ptr.p_double[sfxy+s4]/(dt*du);
tbl->ptr.pp_double[p][4+2*4+0] = -3*c->f.ptr.p_double[s1]+3*c->f.ptr.p_double[s2]-2*c->f.ptr.p_double[sfx+s1]/dt-c->f.ptr.p_double[sfx+s2]/dt;
tbl->ptr.pp_double[p][4+2*4+1] = -3*c->f.ptr.p_double[sfy+s1]/du+3*c->f.ptr.p_double[sfy+s2]/du-2*c->f.ptr.p_double[sfxy+s1]/(dt*du)-c->f.ptr.p_double[sfxy+s2]/(dt*du);
tbl->ptr.pp_double[p][4+2*4+2] = 9*c->f.ptr.p_double[s1]-9*c->f.ptr.p_double[s2]+9*c->f.ptr.p_double[s3]-9*c->f.ptr.p_double[s4]+6*c->f.ptr.p_double[sfx+s1]/dt+3*c->f.ptr.p_double[sfx+s2]/dt-3*c->f.ptr.p_double[sfx+s3]/dt-6*c->f.ptr.p_double[sfx+s4]/dt+6*c->f.ptr.p_double[sfy+s1]/du-6*c->f.ptr.p_double[sfy+s2]/du-3*c->f.ptr.p_double[sfy+s3]/du+3*c->f.ptr.p_double[sfy+s4]/du+4*c->f.ptr.p_double[sfxy+s1]/(dt*du)+2*c->f.ptr.p_double[sfxy+s2]/(dt*du)+c->f.ptr.p_double[sfxy+s3]/(dt*du)+2*c->f.ptr.p_double[sfxy+s4]/(dt*du);
tbl->ptr.pp_double[p][4+2*4+3] = -6*c->f.ptr.p_double[s1]+6*c->f.ptr.p_double[s2]-6*c->f.ptr.p_double[s3]+6*c->f.ptr.p_double[s4]-4*c->f.ptr.p_double[sfx+s1]/dt-2*c->f.ptr.p_double[sfx+s2]/dt+2*c->f.ptr.p_double[sfx+s3]/dt+4*c->f.ptr.p_double[sfx+s4]/dt-3*c->f.ptr.p_double[sfy+s1]/du+3*c->f.ptr.p_double[sfy+s2]/du+3*c->f.ptr.p_double[sfy+s3]/du-3*c->f.ptr.p_double[sfy+s4]/du-2*c->f.ptr.p_double[sfxy+s1]/(dt*du)-c->f.ptr.p_double[sfxy+s2]/(dt*du)-c->f.ptr.p_double[sfxy+s3]/(dt*du)-2*c->f.ptr.p_double[sfxy+s4]/(dt*du);
tbl->ptr.pp_double[p][4+3*4+0] = 2*c->f.ptr.p_double[s1]-2*c->f.ptr.p_double[s2]+c->f.ptr.p_double[sfx+s1]/dt+c->f.ptr.p_double[sfx+s2]/dt;
tbl->ptr.pp_double[p][4+3*4+1] = 2*c->f.ptr.p_double[sfy+s1]/du-2*c->f.ptr.p_double[sfy+s2]/du+c->f.ptr.p_double[sfxy+s1]/(dt*du)+c->f.ptr.p_double[sfxy+s2]/(dt*du);
tbl->ptr.pp_double[p][4+3*4+2] = -6*c->f.ptr.p_double[s1]+6*c->f.ptr.p_double[s2]-6*c->f.ptr.p_double[s3]+6*c->f.ptr.p_double[s4]-3*c->f.ptr.p_double[sfx+s1]/dt-3*c->f.ptr.p_double[sfx+s2]/dt+3*c->f.ptr.p_double[sfx+s3]/dt+3*c->f.ptr.p_double[sfx+s4]/dt-4*c->f.ptr.p_double[sfy+s1]/du+4*c->f.ptr.p_double[sfy+s2]/du+2*c->f.ptr.p_double[sfy+s3]/du-2*c->f.ptr.p_double[sfy+s4]/du-2*c->f.ptr.p_double[sfxy+s1]/(dt*du)-2*c->f.ptr.p_double[sfxy+s2]/(dt*du)-c->f.ptr.p_double[sfxy+s3]/(dt*du)-c->f.ptr.p_double[sfxy+s4]/(dt*du);
tbl->ptr.pp_double[p][4+3*4+3] = 4*c->f.ptr.p_double[s1]-4*c->f.ptr.p_double[s2]+4*c->f.ptr.p_double[s3]-4*c->f.ptr.p_double[s4]+2*c->f.ptr.p_double[sfx+s1]/dt+2*c->f.ptr.p_double[sfx+s2]/dt-2*c->f.ptr.p_double[sfx+s3]/dt-2*c->f.ptr.p_double[sfx+s4]/dt+2*c->f.ptr.p_double[sfy+s1]/du-2*c->f.ptr.p_double[sfy+s2]/du-2*c->f.ptr.p_double[sfy+s3]/du+2*c->f.ptr.p_double[sfy+s4]/du+c->f.ptr.p_double[sfxy+s1]/(dt*du)+c->f.ptr.p_double[sfxy+s2]/(dt*du)+c->f.ptr.p_double[sfxy+s3]/(dt*du)+c->f.ptr.p_double[sfxy+s4]/(dt*du);
}
/*
* Rescale Cij
*/
for(ci=0; ci<=3; ci++)
{
for(cj=0; cj<=3; cj++)
{
tbl->ptr.pp_double[p][4+ci*4+cj] = tbl->ptr.pp_double[p][4+ci*4+cj]*ae_pow(dt, (double)(ci), _state)*ae_pow(du, (double)(cj), _state);
}
}
}
}
}
}
/*************************************************************************
This subroutine was deprecated in ALGLIB 3.6.0
We recommend you to switch to Spline2DBuildBilinearV(), which is more
flexible and accepts its arguments in more convenient order.
-- ALGLIB PROJECT --
Copyright 05.07.2007 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildbilinear(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_matrix* f,
ae_int_t m,
ae_int_t n,
spline2dinterpolant* c,
ae_state *_state)
{
double t;
ae_int_t i;
ae_int_t j;
ae_int_t k;
_spline2dinterpolant_clear(c);
ae_assert(n>=2, "Spline2DBuildBilinear: N<2", _state);
ae_assert(m>=2, "Spline2DBuildBilinear: M<2", _state);
ae_assert(x->cnt>=n&&y->cnt>=m, "Spline2DBuildBilinear: length of X or Y is too short (Length(X/Y)<N/M)", _state);
ae_assert(isfinitevector(x, n, _state)&&isfinitevector(y, m, _state), "Spline2DBuildBilinear: X or Y contains NaN or Infinite value", _state);
ae_assert(f->rows>=m&&f->cols>=n, "Spline2DBuildBilinear: size of F is too small (rows(F)<M or cols(F)<N)", _state);
ae_assert(apservisfinitematrix(f, m, n, _state), "Spline2DBuildBilinear: F contains NaN or Infinite value", _state);
/*
* Fill interpolant
*/
c->n = n;
c->m = m;
c->d = 1;
c->stype = -1;
ae_vector_set_length(&c->x, c->n, _state);
ae_vector_set_length(&c->y, c->m, _state);
ae_vector_set_length(&c->f, c->n*c->m, _state);
for(i=0; i<=c->n-1; i++)
{
c->x.ptr.p_double[i] = x->ptr.p_double[i];
}
for(i=0; i<=c->m-1; i++)
{
c->y.ptr.p_double[i] = y->ptr.p_double[i];
}
for(i=0; i<=c->m-1; i++)
{
for(j=0; j<=c->n-1; j++)
{
c->f.ptr.p_double[i*c->n+j] = f->ptr.pp_double[i][j];
}
}
/*
* Sort points
*/
for(j=0; j<=c->n-1; j++)
{
k = j;
for(i=j+1; i<=c->n-1; i++)
{
if( ae_fp_less(c->x.ptr.p_double[i],c->x.ptr.p_double[k]) )
{
k = i;
}
}
if( k!=j )
{
for(i=0; i<=c->m-1; i++)
{
t = c->f.ptr.p_double[i*c->n+j];
c->f.ptr.p_double[i*c->n+j] = c->f.ptr.p_double[i*c->n+k];
c->f.ptr.p_double[i*c->n+k] = t;
}
t = c->x.ptr.p_double[j];
c->x.ptr.p_double[j] = c->x.ptr.p_double[k];
c->x.ptr.p_double[k] = t;
}
}
for(i=0; i<=c->m-1; i++)
{
k = i;
for(j=i+1; j<=c->m-1; j++)
{
if( ae_fp_less(c->y.ptr.p_double[j],c->y.ptr.p_double[k]) )
{
k = j;
}
}
if( k!=i )
{
for(j=0; j<=c->n-1; j++)
{
t = c->f.ptr.p_double[i*c->n+j];
c->f.ptr.p_double[i*c->n+j] = c->f.ptr.p_double[k*c->n+j];
c->f.ptr.p_double[k*c->n+j] = t;
}
t = c->y.ptr.p_double[i];
c->y.ptr.p_double[i] = c->y.ptr.p_double[k];
c->y.ptr.p_double[k] = t;
}
}
}
/*************************************************************************
This subroutine was deprecated in ALGLIB 3.6.0
We recommend you to switch to Spline2DBuildBicubicV(), which is more
flexible and accepts its arguments in more convenient order.
-- ALGLIB PROJECT --
Copyright 05.07.2007 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildbicubic(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_matrix* f,
ae_int_t m,
ae_int_t n,
spline2dinterpolant* c,
ae_state *_state)
{
ae_frame _frame_block;
ae_matrix _f;
ae_int_t sfx;
ae_int_t sfy;
ae_int_t sfxy;
ae_matrix dx;
ae_matrix dy;
ae_matrix dxy;
double t;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_frame_make(_state, &_frame_block);
memset(&_f, 0, sizeof(_f));
memset(&dx, 0, sizeof(dx));
memset(&dy, 0, sizeof(dy));
memset(&dxy, 0, sizeof(dxy));
ae_matrix_init_copy(&_f, f, _state, ae_true);
f = &_f;
_spline2dinterpolant_clear(c);
ae_matrix_init(&dx, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&dy, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&dxy, 0, 0, DT_REAL, _state, ae_true);
ae_assert(n>=2, "Spline2DBuildBicubicSpline: N<2", _state);
ae_assert(m>=2, "Spline2DBuildBicubicSpline: M<2", _state);
ae_assert(x->cnt>=n&&y->cnt>=m, "Spline2DBuildBicubic: length of X or Y is too short (Length(X/Y)<N/M)", _state);
ae_assert(isfinitevector(x, n, _state)&&isfinitevector(y, m, _state), "Spline2DBuildBicubic: X or Y contains NaN or Infinite value", _state);
ae_assert(f->rows>=m&&f->cols>=n, "Spline2DBuildBicubic: size of F is too small (rows(F)<M or cols(F)<N)", _state);
ae_assert(apservisfinitematrix(f, m, n, _state), "Spline2DBuildBicubic: F contains NaN or Infinite value", _state);
/*
* Fill interpolant:
* F[0]...F[N*M-1]:
* f(i,j) table. f(0,0), f(0, 1), f(0,2) and so on...
* F[N*M]...F[2*N*M-1]:
* df(i,j)/dx table.
* F[2*N*M]...F[3*N*M-1]:
* df(i,j)/dy table.
* F[3*N*M]...F[4*N*M-1]:
* d2f(i,j)/dxdy table.
*/
c->d = 1;
c->n = n;
c->m = m;
c->stype = -3;
sfx = c->n*c->m;
sfy = 2*c->n*c->m;
sfxy = 3*c->n*c->m;
ae_vector_set_length(&c->x, c->n, _state);
ae_vector_set_length(&c->y, c->m, _state);
ae_vector_set_length(&c->f, 4*c->n*c->m, _state);
for(i=0; i<=c->n-1; i++)
{
c->x.ptr.p_double[i] = x->ptr.p_double[i];
}
for(i=0; i<=c->m-1; i++)
{
c->y.ptr.p_double[i] = y->ptr.p_double[i];
}
/*
* Sort points
*/
for(j=0; j<=c->n-1; j++)
{
k = j;
for(i=j+1; i<=c->n-1; i++)
{
if( ae_fp_less(c->x.ptr.p_double[i],c->x.ptr.p_double[k]) )
{
k = i;
}
}
if( k!=j )
{
for(i=0; i<=c->m-1; i++)
{
t = f->ptr.pp_double[i][j];
f->ptr.pp_double[i][j] = f->ptr.pp_double[i][k];
f->ptr.pp_double[i][k] = t;
}
t = c->x.ptr.p_double[j];
c->x.ptr.p_double[j] = c->x.ptr.p_double[k];
c->x.ptr.p_double[k] = t;
}
}
for(i=0; i<=c->m-1; i++)
{
k = i;
for(j=i+1; j<=c->m-1; j++)
{
if( ae_fp_less(c->y.ptr.p_double[j],c->y.ptr.p_double[k]) )
{
k = j;
}
}
if( k!=i )
{
for(j=0; j<=c->n-1; j++)
{
t = f->ptr.pp_double[i][j];
f->ptr.pp_double[i][j] = f->ptr.pp_double[k][j];
f->ptr.pp_double[k][j] = t;
}
t = c->y.ptr.p_double[i];
c->y.ptr.p_double[i] = c->y.ptr.p_double[k];
c->y.ptr.p_double[k] = t;
}
}
spline2d_bicubiccalcderivatives(f, &c->x, &c->y, c->m, c->n, &dx, &dy, &dxy, _state);
for(i=0; i<=c->m-1; i++)
{
for(j=0; j<=c->n-1; j++)
{
k = i*c->n+j;
c->f.ptr.p_double[k] = f->ptr.pp_double[i][j];
c->f.ptr.p_double[sfx+k] = dx.ptr.pp_double[i][j];
c->f.ptr.p_double[sfy+k] = dy.ptr.pp_double[i][j];
c->f.ptr.p_double[sfxy+k] = dxy.ptr.pp_double[i][j];
}
}
ae_frame_leave(_state);
}
/*************************************************************************
This subroutine was deprecated in ALGLIB 3.6.0
We recommend you to switch to Spline2DUnpackV(), which is more flexible
and accepts its arguments in more convenient order.
-- ALGLIB PROJECT --
Copyright 29.06.2007 by Bochkanov Sergey
*************************************************************************/
void spline2dunpack(spline2dinterpolant* c,
ae_int_t* m,
ae_int_t* n,
/* Real */ ae_matrix* tbl,
ae_state *_state)
{
ae_int_t k;
ae_int_t p;
ae_int_t ci;
ae_int_t cj;
ae_int_t s1;
ae_int_t s2;
ae_int_t s3;
ae_int_t s4;
ae_int_t sfx;
ae_int_t sfy;
ae_int_t sfxy;
double y1;
double y2;
double y3;
double y4;
double dt;
double du;
ae_int_t i;
ae_int_t j;
*m = 0;
*n = 0;
ae_matrix_clear(tbl);
ae_assert(c->stype==-3||c->stype==-1, "Spline2DUnpack: incorrect C (incorrect parameter C.SType)", _state);
if( c->d!=1 )
{
*n = 0;
*m = 0;
return;
}
*n = c->n;
*m = c->m;
ae_matrix_set_length(tbl, (*n-1)*(*m-1), 20, _state);
sfx = *n*(*m);
sfy = 2*(*n)*(*m);
sfxy = 3*(*n)*(*m);
/*
* Fill
*/
for(i=0; i<=*m-2; i++)
{
for(j=0; j<=*n-2; j++)
{
p = i*(*n-1)+j;
tbl->ptr.pp_double[p][0] = c->x.ptr.p_double[j];
tbl->ptr.pp_double[p][1] = c->x.ptr.p_double[j+1];
tbl->ptr.pp_double[p][2] = c->y.ptr.p_double[i];
tbl->ptr.pp_double[p][3] = c->y.ptr.p_double[i+1];
dt = 1/(tbl->ptr.pp_double[p][1]-tbl->ptr.pp_double[p][0]);
du = 1/(tbl->ptr.pp_double[p][3]-tbl->ptr.pp_double[p][2]);
/*
* Bilinear interpolation
*/
if( c->stype==-1 )
{
for(k=4; k<=19; k++)
{
tbl->ptr.pp_double[p][k] = (double)(0);
}
y1 = c->f.ptr.p_double[*n*i+j];
y2 = c->f.ptr.p_double[*n*i+(j+1)];
y3 = c->f.ptr.p_double[*n*(i+1)+(j+1)];
y4 = c->f.ptr.p_double[*n*(i+1)+j];
tbl->ptr.pp_double[p][4] = y1;
tbl->ptr.pp_double[p][4+1*4+0] = y2-y1;
tbl->ptr.pp_double[p][4+0*4+1] = y4-y1;
tbl->ptr.pp_double[p][4+1*4+1] = y3-y2-y4+y1;
}
/*
* Bicubic interpolation
*/
if( c->stype==-3 )
{
s1 = *n*i+j;
s2 = *n*i+(j+1);
s3 = *n*(i+1)+(j+1);
s4 = *n*(i+1)+j;
tbl->ptr.pp_double[p][4+0*4+0] = c->f.ptr.p_double[s1];
tbl->ptr.pp_double[p][4+0*4+1] = c->f.ptr.p_double[sfy+s1]/du;
tbl->ptr.pp_double[p][4+0*4+2] = -3*c->f.ptr.p_double[s1]+3*c->f.ptr.p_double[s4]-2*c->f.ptr.p_double[sfy+s1]/du-c->f.ptr.p_double[sfy+s4]/du;
tbl->ptr.pp_double[p][4+0*4+3] = 2*c->f.ptr.p_double[s1]-2*c->f.ptr.p_double[s4]+c->f.ptr.p_double[sfy+s1]/du+c->f.ptr.p_double[sfy+s4]/du;
tbl->ptr.pp_double[p][4+1*4+0] = c->f.ptr.p_double[sfx+s1]/dt;
tbl->ptr.pp_double[p][4+1*4+1] = c->f.ptr.p_double[sfxy+s1]/(dt*du);
tbl->ptr.pp_double[p][4+1*4+2] = -3*c->f.ptr.p_double[sfx+s1]/dt+3*c->f.ptr.p_double[sfx+s4]/dt-2*c->f.ptr.p_double[sfxy+s1]/(dt*du)-c->f.ptr.p_double[sfxy+s4]/(dt*du);
tbl->ptr.pp_double[p][4+1*4+3] = 2*c->f.ptr.p_double[sfx+s1]/dt-2*c->f.ptr.p_double[sfx+s4]/dt+c->f.ptr.p_double[sfxy+s1]/(dt*du)+c->f.ptr.p_double[sfxy+s4]/(dt*du);
tbl->ptr.pp_double[p][4+2*4+0] = -3*c->f.ptr.p_double[s1]+3*c->f.ptr.p_double[s2]-2*c->f.ptr.p_double[sfx+s1]/dt-c->f.ptr.p_double[sfx+s2]/dt;
tbl->ptr.pp_double[p][4+2*4+1] = -3*c->f.ptr.p_double[sfy+s1]/du+3*c->f.ptr.p_double[sfy+s2]/du-2*c->f.ptr.p_double[sfxy+s1]/(dt*du)-c->f.ptr.p_double[sfxy+s2]/(dt*du);
tbl->ptr.pp_double[p][4+2*4+2] = 9*c->f.ptr.p_double[s1]-9*c->f.ptr.p_double[s2]+9*c->f.ptr.p_double[s3]-9*c->f.ptr.p_double[s4]+6*c->f.ptr.p_double[sfx+s1]/dt+3*c->f.ptr.p_double[sfx+s2]/dt-3*c->f.ptr.p_double[sfx+s3]/dt-6*c->f.ptr.p_double[sfx+s4]/dt+6*c->f.ptr.p_double[sfy+s1]/du-6*c->f.ptr.p_double[sfy+s2]/du-3*c->f.ptr.p_double[sfy+s3]/du+3*c->f.ptr.p_double[sfy+s4]/du+4*c->f.ptr.p_double[sfxy+s1]/(dt*du)+2*c->f.ptr.p_double[sfxy+s2]/(dt*du)+c->f.ptr.p_double[sfxy+s3]/(dt*du)+2*c->f.ptr.p_double[sfxy+s4]/(dt*du);
tbl->ptr.pp_double[p][4+2*4+3] = -6*c->f.ptr.p_double[s1]+6*c->f.ptr.p_double[s2]-6*c->f.ptr.p_double[s3]+6*c->f.ptr.p_double[s4]-4*c->f.ptr.p_double[sfx+s1]/dt-2*c->f.ptr.p_double[sfx+s2]/dt+2*c->f.ptr.p_double[sfx+s3]/dt+4*c->f.ptr.p_double[sfx+s4]/dt-3*c->f.ptr.p_double[sfy+s1]/du+3*c->f.ptr.p_double[sfy+s2]/du+3*c->f.ptr.p_double[sfy+s3]/du-3*c->f.ptr.p_double[sfy+s4]/du-2*c->f.ptr.p_double[sfxy+s1]/(dt*du)-c->f.ptr.p_double[sfxy+s2]/(dt*du)-c->f.ptr.p_double[sfxy+s3]/(dt*du)-2*c->f.ptr.p_double[sfxy+s4]/(dt*du);
tbl->ptr.pp_double[p][4+3*4+0] = 2*c->f.ptr.p_double[s1]-2*c->f.ptr.p_double[s2]+c->f.ptr.p_double[sfx+s1]/dt+c->f.ptr.p_double[sfx+s2]/dt;
tbl->ptr.pp_double[p][4+3*4+1] = 2*c->f.ptr.p_double[sfy+s1]/du-2*c->f.ptr.p_double[sfy+s2]/du+c->f.ptr.p_double[sfxy+s1]/(dt*du)+c->f.ptr.p_double[sfxy+s2]/(dt*du);
tbl->ptr.pp_double[p][4+3*4+2] = -6*c->f.ptr.p_double[s1]+6*c->f.ptr.p_double[s2]-6*c->f.ptr.p_double[s3]+6*c->f.ptr.p_double[s4]-3*c->f.ptr.p_double[sfx+s1]/dt-3*c->f.ptr.p_double[sfx+s2]/dt+3*c->f.ptr.p_double[sfx+s3]/dt+3*c->f.ptr.p_double[sfx+s4]/dt-4*c->f.ptr.p_double[sfy+s1]/du+4*c->f.ptr.p_double[sfy+s2]/du+2*c->f.ptr.p_double[sfy+s3]/du-2*c->f.ptr.p_double[sfy+s4]/du-2*c->f.ptr.p_double[sfxy+s1]/(dt*du)-2*c->f.ptr.p_double[sfxy+s2]/(dt*du)-c->f.ptr.p_double[sfxy+s3]/(dt*du)-c->f.ptr.p_double[sfxy+s4]/(dt*du);
tbl->ptr.pp_double[p][4+3*4+3] = 4*c->f.ptr.p_double[s1]-4*c->f.ptr.p_double[s2]+4*c->f.ptr.p_double[s3]-4*c->f.ptr.p_double[s4]+2*c->f.ptr.p_double[sfx+s1]/dt+2*c->f.ptr.p_double[sfx+s2]/dt-2*c->f.ptr.p_double[sfx+s3]/dt-2*c->f.ptr.p_double[sfx+s4]/dt+2*c->f.ptr.p_double[sfy+s1]/du-2*c->f.ptr.p_double[sfy+s2]/du-2*c->f.ptr.p_double[sfy+s3]/du+2*c->f.ptr.p_double[sfy+s4]/du+c->f.ptr.p_double[sfxy+s1]/(dt*du)+c->f.ptr.p_double[sfxy+s2]/(dt*du)+c->f.ptr.p_double[sfxy+s3]/(dt*du)+c->f.ptr.p_double[sfxy+s4]/(dt*du);
}
/*
* Rescale Cij
*/
for(ci=0; ci<=3; ci++)
{
for(cj=0; cj<=3; cj++)
{
tbl->ptr.pp_double[p][4+ci*4+cj] = tbl->ptr.pp_double[p][4+ci*4+cj]*ae_pow(dt, (double)(ci), _state)*ae_pow(du, (double)(cj), _state);
}
}
}
}
}
/*************************************************************************
This subroutine creates least squares solver used to fit 2D splines to
irregularly sampled (scattered) data.
Solver object is used to perform spline fits as follows:
* solver object is created with spline2dbuildercreate() function
* dataset is added with spline2dbuildersetpoints() function
* fit area is chosen:
* spline2dbuildersetarea() - for user-defined area
* spline2dbuildersetareaauto() - for automatically chosen area
* number of grid nodes is chosen with spline2dbuildersetgrid()
* prior term is chosen with one of the following functions:
* spline2dbuildersetlinterm() to set linear prior
* spline2dbuildersetconstterm() to set constant prior
* spline2dbuildersetzeroterm() to set zero prior
* spline2dbuildersetuserterm() to set user-defined constant prior
* solver algorithm is chosen with either:
* spline2dbuildersetalgoblocklls() - BlockLLS algorithm, medium-scale problems
* spline2dbuildersetalgofastddm() - FastDDM algorithm, large-scale problems
* finally, fitting itself is performed with spline2dfit() function.
Most of the steps above can be omitted, solver is configured with good
defaults. The minimum is to call:
* spline2dbuildercreate() to create solver object
* spline2dbuildersetpoints() to specify dataset
* spline2dbuildersetgrid() to tell how many nodes you need
* spline2dfit() to perform fit
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
D - positive number, number of Y-components: D=1 for simple scalar
fit, D>1 for vector-valued spline fitting.
OUTPUT PARAMETERS:
S - solver object
-- ALGLIB PROJECT --
Copyright 29.01.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildercreate(ae_int_t d,
spline2dbuilder* state,
ae_state *_state)
{
_spline2dbuilder_clear(state);
ae_assert(d>=1, "Spline2DBuilderCreate: D<=0", _state);
/*
* NOTES:
*
* 1. Prior term is set to linear one (good default option)
* 2. Solver is set to BlockLLS - good enough for small-scale problems.
* 3. Refinement rounds: 5; enough to get good convergence.
*/
state->priorterm = 1;
state->priortermval = (double)(0);
state->areatype = 0;
state->gridtype = 0;
state->smoothing = 0.0;
state->nlayers = 0;
state->solvertype = 1;
state->npoints = 0;
state->d = d;
state->sx = 1.0;
state->sy = 1.0;
state->lsqrcnt = 5;
/*
* Algorithm settings
*/
state->adddegreeoffreedom = ae_true;
state->maxcoresize = 16;
state->interfacesize = 5;
}
/*************************************************************************
This function sets constant prior term (model is a sum of bicubic spline
and global prior, which can be linear, constant, user-defined constant or
zero).
Constant prior term is determined by least squares fitting.
INPUT PARAMETERS:
S - spline builder
V - value for user-defined prior
-- ALGLIB --
Copyright 01.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetuserterm(spline2dbuilder* state,
double v,
ae_state *_state)
{
ae_assert(ae_isfinite(v, _state), "Spline2DBuilderSetUserTerm: infinite/NAN value passed", _state);
state->priorterm = 0;
state->priortermval = v;
}
/*************************************************************************
This function sets linear prior term (model is a sum of bicubic spline and
global prior, which can be linear, constant, user-defined constant or
zero).
Linear prior term is determined by least squares fitting.
INPUT PARAMETERS:
S - spline builder
-- ALGLIB --
Copyright 01.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetlinterm(spline2dbuilder* state, ae_state *_state)
{
state->priorterm = 1;
}
/*************************************************************************
This function sets constant prior term (model is a sum of bicubic spline
and global prior, which can be linear, constant, user-defined constant or
zero).
Constant prior term is determined by least squares fitting.
INPUT PARAMETERS:
S - spline builder
-- ALGLIB --
Copyright 01.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetconstterm(spline2dbuilder* state, ae_state *_state)
{
state->priorterm = 2;
}
/*************************************************************************
This function sets zero prior term (model is a sum of bicubic spline and
global prior, which can be linear, constant, user-defined constant or
zero).
INPUT PARAMETERS:
S - spline builder
-- ALGLIB --
Copyright 01.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetzeroterm(spline2dbuilder* state, ae_state *_state)
{
state->priorterm = 3;
}
/*************************************************************************
This function adds dataset to the builder object.
This function overrides results of the previous calls, i.e. multiple calls
of this function will result in only the last set being added.
INPUT PARAMETERS:
S - spline 2D builder object
XY - points, array[N,2+D]. One row corresponds to one point
in the dataset. First 2 elements are coordinates, next
D elements are function values. Array may be larger than
specified, in this case only leading [N,NX+NY] elements
will be used.
N - number of points in the dataset
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetpoints(spline2dbuilder* state,
/* Real */ ae_matrix* xy,
ae_int_t n,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
ae_int_t ew;
ae_assert(n>0, "Spline2DBuilderSetPoints: N<0", _state);
ae_assert(xy->rows>=n, "Spline2DBuilderSetPoints: Rows(XY)<N", _state);
ae_assert(xy->cols>=2+state->d, "Spline2DBuilderSetPoints: Cols(XY)<NX+NY", _state);
ae_assert(apservisfinitematrix(xy, n, 2+state->d, _state), "Spline2DBuilderSetPoints: XY contains infinite or NaN values!", _state);
state->npoints = n;
ew = 2+state->d;
rvectorsetlengthatleast(&state->xy, n*ew, _state);
for(i=0; i<=n-1; i++)
{
for(j=0; j<=ew-1; j++)
{
state->xy.ptr.p_double[i*ew+j] = xy->ptr.pp_double[i][j];
}
}
}
/*************************************************************************
This function sets area where 2D spline interpolant is built. "Auto" means
that area extent is determined automatically from dataset extent.
INPUT PARAMETERS:
S - spline 2D builder object
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetareaauto(spline2dbuilder* state, ae_state *_state)
{
state->areatype = 0;
}
/*************************************************************************
This function sets area where 2D spline interpolant is built to
user-defined one: [XA,XB]*[YA,YB]
INPUT PARAMETERS:
S - spline 2D builder object
XA,XB - spatial extent in the first (X) dimension, XA<XB
YA,YB - spatial extent in the second (Y) dimension, YA<YB
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetarea(spline2dbuilder* state,
double xa,
double xb,
double ya,
double yb,
ae_state *_state)
{
ae_assert(ae_isfinite(xa, _state), "Spline2DBuilderSetArea: XA is not finite", _state);
ae_assert(ae_isfinite(xb, _state), "Spline2DBuilderSetArea: XB is not finite", _state);
ae_assert(ae_isfinite(ya, _state), "Spline2DBuilderSetArea: YA is not finite", _state);
ae_assert(ae_isfinite(yb, _state), "Spline2DBuilderSetArea: YB is not finite", _state);
ae_assert(ae_fp_less(xa,xb), "Spline2DBuilderSetArea: XA>=XB", _state);
ae_assert(ae_fp_less(ya,yb), "Spline2DBuilderSetArea: YA>=YB", _state);
state->areatype = 1;
state->xa = xa;
state->xb = xb;
state->ya = ya;
state->yb = yb;
}
/*************************************************************************
This function sets nodes count for 2D spline interpolant. Fitting is
performed on area defined with one of the "setarea" functions; this one
sets number of nodes placed upon the fitting area.
INPUT PARAMETERS:
S - spline 2D builder object
KX - nodes count for the first (X) dimension; fitting interval
[XA,XB] is separated into KX-1 subintervals, with KX nodes
created at the boundaries.
KY - nodes count for the first (Y) dimension; fitting interval
[YA,YB] is separated into KY-1 subintervals, with KY nodes
created at the boundaries.
NOTE: at least 4 nodes is created in each dimension, so KX and KY are
silently increased if needed.
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetgrid(spline2dbuilder* state,
ae_int_t kx,
ae_int_t ky,
ae_state *_state)
{
ae_assert(kx>0, "Spline2DBuilderSetGridSizePrecisely: KX<=0", _state);
ae_assert(ky>0, "Spline2DBuilderSetGridSizePrecisely: KY<=0", _state);
state->gridtype = 1;
state->kx = ae_maxint(kx, 4, _state);
state->ky = ae_maxint(ky, 4, _state);
}
/*************************************************************************
This function allows you to choose least squares solver used to perform
fitting. This function sets solver algorithm to "FastDDM", which performs
fast parallel fitting by splitting problem into smaller chunks and merging
results together.
This solver is optimized for large-scale problems, starting from 256x256
grids, and up to 10000x10000 grids. Of course, it will work for smaller
grids too.
More detailed description of the algorithm is given below:
* algorithm generates hierarchy of nested grids, ranging from ~16x16
(topmost "layer" of the model) to ~KX*KY one (final layer). Upper layers
model global behavior of the function, lower layers are used to model
fine details. Moving from layer to layer doubles grid density.
* fitting is started from topmost layer, subsequent layers are fitted
using residuals from previous ones.
* user may choose to skip generation of upper layers and generate only a
few bottom ones, which will result in much better performance and
parallelization efficiency, at the cost of algorithm inability to "patch"
large holes in the dataset.
* every layer is regularized using progressively increasing regularization
coefficient; thus, increasing LambdaV penalizes fine details first,
leaving lower frequencies almost intact for a while.
* after fitting is done, all layers are merged together into one bicubic
spline
IMPORTANT: regularization coefficient used by this solver is different
from the one used by BlockLLS. Latter utilizes nonlinearity
penalty, which is global in nature (large regularization
results in global linear trend being extracted); this solver
uses another, localized form of penalty, which is suitable for
parallel processing.
Notes on memory and performance:
* memory requirements: most memory is consumed during modeling of the
higher layers; ~[512*NPoints] bytes is required for a model with full
hierarchy of grids being generated. However, if you skip a few topmost
layers, you will get nearly constant (wrt. points count and grid size)
memory consumption.
* serial running time: O(K*K)+O(NPoints) for a KxK grid
* parallelism potential: good. You may get nearly linear speed-up when
performing fitting with just a few layers. Adding more layers results in
model becoming more global, which somewhat reduces efficiency of the
parallel code.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
S - spline 2D builder object
NLayers - number of layers in the model:
* NLayers>=1 means that up to chosen number of bottom
layers is fitted
* NLayers=0 means that maximum number of layers is chosen
(according to current grid size)
* NLayers<=-1 means that up to |NLayers| topmost layers is
skipped
Recommendations:
* good "default" value is 2 layers
* you may need more layers, if your dataset is very
irregular and you want to "patch" large holes. For a
grid step H (equal to AreaWidth/GridSize) you may expect
that last layer reproduces variations at distance H (and
can patch holes that wide); that higher layers operate
at distances 2*H, 4*H, 8*H and so on.
* good value for "bullletproof" mode is NLayers=0, which
results in complete hierarchy of layers being generated.
LambdaV - regularization coefficient, chosen in such a way that it
penalizes bottom layers (fine details) first.
LambdaV>=0, zero value means that no penalty is applied.
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetalgofastddm(spline2dbuilder* state,
ae_int_t nlayers,
double lambdav,
ae_state *_state)
{
ae_assert(ae_isfinite(lambdav, _state), "Spline2DBuilderSetAlgoFastDDM: LambdaV is not finite value", _state);
ae_assert(ae_fp_greater_eq(lambdav,(double)(0)), "Spline2DBuilderSetAlgoFastDDM: LambdaV<0", _state);
state->solvertype = 3;
state->nlayers = nlayers;
state->smoothing = lambdav;
}
/*************************************************************************
This function allows you to choose least squares solver used to perform
fitting. This function sets solver algorithm to "BlockLLS", which performs
least squares fitting with fast sparse direct solver, with optional
nonsmoothness penalty being applied.
Nonlinearity penalty has the following form:
[ ]
P() ~ Lambda* integral[ (d2S/dx2)^2 + 2*(d2S/dxdy)^2 + (d2S/dy2)^2 ]dxdy
[ ]
here integral is calculated over entire grid, and "~" means "proportional"
because integral is normalized after calcilation. Extremely large values
of Lambda result in linear fit being performed.
NOTE: this algorithm is the most robust and controllable one, but it is
limited by 512x512 grids and (say) up to 1.000.000 points. However,
ALGLIB has one more spline solver: FastDDM algorithm, which is
intended for really large-scale problems (in 10M-100M range). FastDDM
algorithm also has better parallelism properties.
More information on BlockLLS solver:
* memory requirements: ~[32*K^3+256*NPoints] bytes for KxK grid with
NPoints-sized dataset
* serial running time: O(K^4+NPoints)
* parallelism potential: limited. You may get some sublinear gain when
working with large grids (K's in 256..512 range)
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
S - spline 2D builder object
LambdaNS- non-negative value:
* positive value means that some smoothing is applied
* zero value means that no smoothing is applied, and
corresponding entries of design matrix are numerically
zero and dropped from consideration.
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetalgoblocklls(spline2dbuilder* state,
double lambdans,
ae_state *_state)
{
ae_assert(ae_isfinite(lambdans, _state), "Spline2DBuilderSetAlgoBlockLLS: LambdaNS is not finite value", _state);
ae_assert(ae_fp_greater_eq(lambdans,(double)(0)), "Spline2DBuilderSetAlgoBlockLLS: LambdaNS<0", _state);
state->solvertype = 1;
state->smoothing = lambdans;
}
/*************************************************************************
This function allows you to choose least squares solver used to perform
fitting. This function sets solver algorithm to "NaiveLLS".
IMPORTANT: NaiveLLS is NOT intended to be used in real life code! This
algorithm solves problem by generated dense (K^2)x(K^2+NPoints)
matrix and solves linear least squares problem with dense
solver.
It is here just to test BlockLLS against reference solver
(and maybe for someone trying to compare well optimized solver
against straightforward approach to the LLS problem).
More information on naive LLS solver:
* memory requirements: ~[8*K^4+256*NPoints] bytes for KxK grid.
* serial running time: O(K^6+NPoints) for KxK grid
* when compared with BlockLLS, NaiveLLS has ~K larger memory demand and
~K^2 larger running time.
INPUT PARAMETERS:
S - spline 2D builder object
LambdaNS- nonsmoothness penalty
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dbuildersetalgonaivells(spline2dbuilder* state,
double lambdans,
ae_state *_state)
{
ae_assert(ae_isfinite(lambdans, _state), "Spline2DBuilderSetAlgoBlockLLS: LambdaNS is not finite value", _state);
ae_assert(ae_fp_greater_eq(lambdans,(double)(0)), "Spline2DBuilderSetAlgoBlockLLS: LambdaNS<0", _state);
state->solvertype = 2;
state->smoothing = lambdans;
}
/*************************************************************************
This function fits bicubic spline to current dataset, using current area/
grid and current LLS solver.
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
! * hardware vendor (Intel) implementations of linear algebra primitives
! (C++ and C# versions, x86/x64 platform)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
INPUT PARAMETERS:
State - spline 2D builder object
OUTPUT PARAMETERS:
S - 2D spline, fit result
Rep - fitting report, which provides some additional info about
errors, R2 coefficient and so on.
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dfit(spline2dbuilder* state,
spline2dinterpolant* s,
spline2dfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
double xa;
double xb;
double ya;
double yb;
double xaraw;
double xbraw;
double yaraw;
double ybraw;
ae_int_t kx;
ae_int_t ky;
double hx;
double hy;
double invhx;
double invhy;
ae_int_t gridexpansion;
ae_int_t nzwidth;
ae_int_t bfrad;
ae_int_t npoints;
ae_int_t d;
ae_int_t ew;
ae_int_t i;
ae_int_t j;
ae_int_t k;
double v;
ae_int_t k0;
ae_int_t k1;
double vx;
double vy;
ae_int_t arows;
ae_int_t acopied;
ae_int_t basecasex;
ae_int_t basecasey;
double eps;
ae_vector xywork;
ae_matrix vterm;
ae_vector tmpx;
ae_vector tmpy;
ae_vector tmp0;
ae_vector tmp1;
ae_vector meany;
ae_vector xyindex;
ae_vector tmpi;
spline1dinterpolant basis1;
sparsematrix av;
sparsematrix ah;
spline2dxdesignmatrix xdesignmatrix;
ae_vector z;
spline2dblockllsbuf blockllsbuf;
ae_int_t sfx;
ae_int_t sfy;
ae_int_t sfxy;
double tss;
ae_int_t dstidx;
ae_frame_make(_state, &_frame_block);
memset(&xywork, 0, sizeof(xywork));
memset(&vterm, 0, sizeof(vterm));
memset(&tmpx, 0, sizeof(tmpx));
memset(&tmpy, 0, sizeof(tmpy));
memset(&tmp0, 0, sizeof(tmp0));
memset(&tmp1, 0, sizeof(tmp1));
memset(&meany, 0, sizeof(meany));
memset(&xyindex, 0, sizeof(xyindex));
memset(&tmpi, 0, sizeof(tmpi));
memset(&basis1, 0, sizeof(basis1));
memset(&av, 0, sizeof(av));
memset(&ah, 0, sizeof(ah));
memset(&xdesignmatrix, 0, sizeof(xdesignmatrix));
memset(&z, 0, sizeof(z));
memset(&blockllsbuf, 0, sizeof(blockllsbuf));
_spline2dinterpolant_clear(s);
_spline2dfitreport_clear(rep);
ae_vector_init(&xywork, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&vterm, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmpx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmpy, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&meany, 0, DT_REAL, _state, ae_true);
ae_vector_init(&xyindex, 0, DT_INT, _state, ae_true);
ae_vector_init(&tmpi, 0, DT_INT, _state, ae_true);
_spline1dinterpolant_init(&basis1, _state, ae_true);
_sparsematrix_init(&av, _state, ae_true);
_sparsematrix_init(&ah, _state, ae_true);
_spline2dxdesignmatrix_init(&xdesignmatrix, _state, ae_true);
ae_vector_init(&z, 0, DT_REAL, _state, ae_true);
_spline2dblockllsbuf_init(&blockllsbuf, _state, ae_true);
nzwidth = 4;
bfrad = 2;
npoints = state->npoints;
d = state->d;
ew = 2+d;
/*
* Integrity checks
*/
ae_assert(ae_fp_eq(state->sx,(double)(1)), "Spline2DFit: integrity error", _state);
ae_assert(ae_fp_eq(state->sy,(double)(1)), "Spline2DFit: integrity error", _state);
/*
* Determine actual area size and grid step
*
* NOTE: initialize vars by zeros in order to avoid spurious
* compiler warnings.
*/
xa = (double)(0);
xb = (double)(0);
ya = (double)(0);
yb = (double)(0);
if( state->areatype==0 )
{
if( npoints>0 )
{
xa = state->xy.ptr.p_double[0];
xb = state->xy.ptr.p_double[0];
ya = state->xy.ptr.p_double[1];
yb = state->xy.ptr.p_double[1];
for(i=1; i<=npoints-1; i++)
{
xa = ae_minreal(xa, state->xy.ptr.p_double[i*ew+0], _state);
xb = ae_maxreal(xb, state->xy.ptr.p_double[i*ew+0], _state);
ya = ae_minreal(ya, state->xy.ptr.p_double[i*ew+1], _state);
yb = ae_maxreal(yb, state->xy.ptr.p_double[i*ew+1], _state);
}
}
else
{
xa = (double)(-1);
xb = (double)(1);
ya = (double)(-1);
yb = (double)(1);
}
}
else
{
if( state->areatype==1 )
{
xa = state->xa;
xb = state->xb;
ya = state->ya;
yb = state->yb;
}
else
{
ae_assert(ae_false, "Assertion failed", _state);
}
}
if( ae_fp_eq(xa,xb) )
{
v = xa;
if( ae_fp_greater_eq(v,(double)(0)) )
{
xa = v/2-1;
xb = v*2+1;
}
else
{
xa = v*2-1;
xb = v/2+1;
}
}
if( ae_fp_eq(ya,yb) )
{
v = ya;
if( ae_fp_greater_eq(v,(double)(0)) )
{
ya = v/2-1;
yb = v*2+1;
}
else
{
ya = v*2-1;
yb = v/2+1;
}
}
ae_assert(ae_fp_less(xa,xb), "Spline2DFit: integrity error", _state);
ae_assert(ae_fp_less(ya,yb), "Spline2DFit: integrity error", _state);
kx = 0;
ky = 0;
if( state->gridtype==0 )
{
kx = 4;
ky = 4;
}
else
{
if( state->gridtype==1 )
{
kx = state->kx;
ky = state->ky;
}
else
{
ae_assert(ae_false, "Assertion failed", _state);
}
}
ae_assert(kx>0, "Spline2DFit: integrity error", _state);
ae_assert(ky>0, "Spline2DFit: integrity error", _state);
basecasex = -1;
basecasey = -1;
if( state->solvertype==3 )
{
/*
* Large-scale solver with special requirements to grid size.
*/
kx = ae_maxint(kx, nzwidth, _state);
ky = ae_maxint(ky, nzwidth, _state);
k = 1;
while(imin2(kx, ky, _state)>state->maxcoresize+1)
{
kx = idivup(kx-1, 2, _state)+1;
ky = idivup(ky-1, 2, _state)+1;
k = k+1;
}
basecasex = kx-1;
k0 = 1;
while(kx>state->maxcoresize+1)
{
basecasex = idivup(kx-1, 2, _state);
kx = basecasex+1;
k0 = k0+1;
}
while(k0>1)
{
kx = (kx-1)*2+1;
k0 = k0-1;
}
basecasey = ky-1;
k1 = 1;
while(ky>state->maxcoresize+1)
{
basecasey = idivup(ky-1, 2, _state);
ky = basecasey+1;
k1 = k1+1;
}
while(k1>1)
{
ky = (ky-1)*2+1;
k1 = k1-1;
}
while(k>1)
{
kx = (kx-1)*2+1;
ky = (ky-1)*2+1;
k = k-1;
}
/*
* Grid is NOT expanded. We have very strict requirements on
* grid size, and we do not want to overcomplicate it by
* playing with grid size in order to add one more degree of
* freedom. It is not relevant for such large tasks.
*/
gridexpansion = 0;
}
else
{
/*
* Medium-scale solvers which are tolerant to grid size.
*/
kx = ae_maxint(kx, nzwidth, _state);
ky = ae_maxint(ky, nzwidth, _state);
/*
* Grid is expanded by 1 in order to add one more effective degree
* of freedom to the spline. Having additional nodes outside of the
* area allows us to emulate changes in the derivative at the bound
* without having specialized "boundary" version of the basis function.
*/
if( state->adddegreeoffreedom )
{
gridexpansion = 1;
}
else
{
gridexpansion = 0;
}
}
hx = coalesce(xb-xa, 1.0, _state)/(kx-1);
hy = coalesce(yb-ya, 1.0, _state)/(ky-1);
invhx = 1/hx;
invhy = 1/hy;
/*
* We determined "raw" grid size. Now perform a grid correction according
* to current grid expansion size.
*/
xaraw = xa;
yaraw = ya;
xbraw = xb;
ybraw = yb;
xa = xa-hx*gridexpansion;
ya = ya-hy*gridexpansion;
xb = xb+hx*gridexpansion;
yb = yb+hy*gridexpansion;
kx = kx+2*gridexpansion;
ky = ky+2*gridexpansion;
/*
* Create output spline using transformed (unit-scale)
* coordinates, fill by zero values
*/
s->d = d;
s->n = kx;
s->m = ky;
s->stype = -3;
sfx = s->n*s->m*d;
sfy = 2*s->n*s->m*d;
sfxy = 3*s->n*s->m*d;
ae_vector_set_length(&s->x, s->n, _state);
ae_vector_set_length(&s->y, s->m, _state);
ae_vector_set_length(&s->f, 4*s->n*s->m*d, _state);
for(i=0; i<=s->n-1; i++)
{
s->x.ptr.p_double[i] = (double)(i);
}
for(i=0; i<=s->m-1; i++)
{
s->y.ptr.p_double[i] = (double)(i);
}
for(i=0; i<=4*s->n*s->m*d-1; i++)
{
s->f.ptr.p_double[i] = 0.0;
}
/*
* Create local copy of dataset (only points in the grid are copied;
* we allow small step out of the grid, by Eps*H, in order to deal
* with numerical rounding errors).
*
* An additional copy of Y-values is created at columns beyond 2+J;
* it is preserved during all transformations. This copy is used
* to calculate error-related metrics.
*
* Calculate mean(Y), TSS
*/
ae_vector_set_length(&meany, d, _state);
for(j=0; j<=d-1; j++)
{
meany.ptr.p_double[j] = (double)(0);
}
rvectorsetlengthatleast(&xywork, npoints*ew, _state);
acopied = 0;
eps = 1.0E-6;
for(i=0; i<=npoints-1; i++)
{
vx = state->xy.ptr.p_double[i*ew+0];
vy = state->xy.ptr.p_double[i*ew+1];
if( ((ae_fp_less_eq(xaraw-eps*hx,vx)&&ae_fp_less_eq(vx,xbraw+eps*hx))&&ae_fp_less_eq(yaraw-eps*hy,vy))&&ae_fp_less_eq(vy,ybraw+eps*hy) )
{
xywork.ptr.p_double[acopied*ew+0] = (vx-xa)*invhx;
xywork.ptr.p_double[acopied*ew+1] = (vy-ya)*invhy;
for(j=0; j<=d-1; j++)
{
v = state->xy.ptr.p_double[i*ew+2+j];
xywork.ptr.p_double[acopied*ew+2+j] = v;
meany.ptr.p_double[j] = meany.ptr.p_double[j]+v;
}
acopied = acopied+1;
}
}
npoints = acopied;
for(j=0; j<=d-1; j++)
{
meany.ptr.p_double[j] = meany.ptr.p_double[j]/coalesce((double)(npoints), (double)(1), _state);
}
tss = 0.0;
for(i=0; i<=npoints-1; i++)
{
for(j=0; j<=d-1; j++)
{
tss = tss+ae_sqr(xywork.ptr.p_double[i*ew+2+j]-meany.ptr.p_double[j], _state);
}
}
tss = coalesce(tss, 1.0, _state);
/*
* Handle prior term.
* Modify output spline.
* Quick exit if dataset is empty.
*/
buildpriorterm1(&xywork, npoints, 2, d, state->priorterm, state->priortermval, &vterm, _state);
if( npoints==0 )
{
/*
* Quick exit
*/
for(k=0; k<=s->n*s->m-1; k++)
{
k0 = k%s->n;
k1 = k/s->n;
for(j=0; j<=d-1; j++)
{
dstidx = d*(k1*s->n+k0)+j;
s->f.ptr.p_double[dstidx] = s->f.ptr.p_double[dstidx]+vterm.ptr.pp_double[j][0]*s->x.ptr.p_double[k0]+vterm.ptr.pp_double[j][1]*s->y.ptr.p_double[k1]+vterm.ptr.pp_double[j][2];
s->f.ptr.p_double[sfx+dstidx] = s->f.ptr.p_double[sfx+dstidx]+vterm.ptr.pp_double[j][0];
s->f.ptr.p_double[sfy+dstidx] = s->f.ptr.p_double[sfy+dstidx]+vterm.ptr.pp_double[j][1];
}
}
for(i=0; i<=s->n-1; i++)
{
s->x.ptr.p_double[i] = s->x.ptr.p_double[i]*hx+xa;
}
for(i=0; i<=s->m-1; i++)
{
s->y.ptr.p_double[i] = s->y.ptr.p_double[i]*hy+ya;
}
for(i=0; i<=s->n*s->m*d-1; i++)
{
s->f.ptr.p_double[sfx+i] = s->f.ptr.p_double[sfx+i]*invhx;
s->f.ptr.p_double[sfy+i] = s->f.ptr.p_double[sfy+i]*invhy;
s->f.ptr.p_double[sfxy+i] = s->f.ptr.p_double[sfxy+i]*invhx*invhy;
}
rep->rmserror = (double)(0);
rep->avgerror = (double)(0);
rep->maxerror = (double)(0);
rep->r2 = 1.0;
ae_frame_leave(_state);
return;
}
/*
* Build 1D compact basis function
* Generate design matrix
*/
ae_vector_set_length(&tmpx, 7, _state);
ae_vector_set_length(&tmpy, 7, _state);
tmpx.ptr.p_double[0] = (double)(-3);
tmpx.ptr.p_double[1] = (double)(-2);
tmpx.ptr.p_double[2] = (double)(-1);
tmpx.ptr.p_double[3] = (double)(0);
tmpx.ptr.p_double[4] = (double)(1);
tmpx.ptr.p_double[5] = (double)(2);
tmpx.ptr.p_double[6] = (double)(3);
tmpy.ptr.p_double[0] = (double)(0);
tmpy.ptr.p_double[1] = (double)(0);
tmpy.ptr.p_double[2] = (double)1/(double)12;
tmpy.ptr.p_double[3] = (double)2/(double)6;
tmpy.ptr.p_double[4] = (double)1/(double)12;
tmpy.ptr.p_double[5] = (double)(0);
tmpy.ptr.p_double[6] = (double)(0);
spline1dbuildcubic(&tmpx, &tmpy, tmpx.cnt, 2, 0.0, 2, 0.0, &basis1, _state);
/*
* Solve.
* Update spline.
*/
if( state->solvertype==1 )
{
/*
* BlockLLS
*/
spline2d_reorderdatasetandbuildindex(&xywork, npoints, d, &tmp0, 0, kx, ky, &xyindex, &tmpi, _state);
spline2d_xdesigngenerate(&xywork, &xyindex, 0, kx, kx, 0, ky, ky, d, spline2d_lambdaregblocklls, state->smoothing, &basis1, &xdesignmatrix, _state);
spline2d_blockllsfit(&xdesignmatrix, state->lsqrcnt, &z, rep, tss, &blockllsbuf, _state);
spline2d_updatesplinetable(&z, kx, ky, d, &basis1, bfrad, &s->f, s->m, s->n, 1, _state);
}
else
{
if( state->solvertype==2 )
{
/*
* NaiveLLS, reference implementation
*/
spline2d_generatedesignmatrix(&xywork, npoints, d, kx, ky, state->smoothing, spline2d_lambdaregblocklls, &basis1, &av, &ah, &arows, _state);
spline2d_naivellsfit(&av, &ah, arows, &xywork, kx, ky, npoints, d, state->lsqrcnt, &z, rep, tss, _state);
spline2d_updatesplinetable(&z, kx, ky, d, &basis1, bfrad, &s->f, s->m, s->n, 1, _state);
}
else
{
if( state->solvertype==3 )
{
/*
* FastDDM method
*/
ae_assert(basecasex>0, "Spline2DFit: integrity error", _state);
ae_assert(basecasey>0, "Spline2DFit: integrity error", _state);
spline2d_fastddmfit(&xywork, npoints, d, kx, ky, basecasex, basecasey, state->maxcoresize, state->interfacesize, state->nlayers, state->smoothing, state->lsqrcnt, &basis1, s, rep, tss, _state);
}
else
{
ae_assert(ae_false, "Spline2DFit: integrity error", _state);
}
}
}
/*
* Append prior term.
* Transform spline to original coordinates
*/
for(k=0; k<=s->n*s->m-1; k++)
{
k0 = k%s->n;
k1 = k/s->n;
for(j=0; j<=d-1; j++)
{
dstidx = d*(k1*s->n+k0)+j;
s->f.ptr.p_double[dstidx] = s->f.ptr.p_double[dstidx]+vterm.ptr.pp_double[j][0]*s->x.ptr.p_double[k0]+vterm.ptr.pp_double[j][1]*s->y.ptr.p_double[k1]+vterm.ptr.pp_double[j][2];
s->f.ptr.p_double[sfx+dstidx] = s->f.ptr.p_double[sfx+dstidx]+vterm.ptr.pp_double[j][0];
s->f.ptr.p_double[sfy+dstidx] = s->f.ptr.p_double[sfy+dstidx]+vterm.ptr.pp_double[j][1];
}
}
for(i=0; i<=s->n-1; i++)
{
s->x.ptr.p_double[i] = s->x.ptr.p_double[i]*hx+xa;
}
for(i=0; i<=s->m-1; i++)
{
s->y.ptr.p_double[i] = s->y.ptr.p_double[i]*hy+ya;
}
for(i=0; i<=s->n*s->m*d-1; i++)
{
s->f.ptr.p_double[sfx+i] = s->f.ptr.p_double[sfx+i]*invhx;
s->f.ptr.p_double[sfy+i] = s->f.ptr.p_double[sfy+i]*invhy;
s->f.ptr.p_double[sfxy+i] = s->f.ptr.p_double[sfxy+i]*invhx*invhy;
}
ae_frame_leave(_state);
}
/*************************************************************************
Serializer: allocation
-- ALGLIB --
Copyright 28.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dalloc(ae_serializer* s,
spline2dinterpolant* spline,
ae_state *_state)
{
/*
* Header
*/
ae_serializer_alloc_entry(s);
/*
* Data
*/
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
allocrealarray(s, &spline->x, -1, _state);
allocrealarray(s, &spline->y, -1, _state);
allocrealarray(s, &spline->f, -1, _state);
}
/*************************************************************************
Serializer: serialization
-- ALGLIB --
Copyright 28.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dserialize(ae_serializer* s,
spline2dinterpolant* spline,
ae_state *_state)
{
/*
* Header
*/
ae_serializer_serialize_int(s, getspline2dserializationcode(_state), _state);
/*
* Data
*/
ae_serializer_serialize_int(s, spline->stype, _state);
ae_serializer_serialize_int(s, spline->n, _state);
ae_serializer_serialize_int(s, spline->m, _state);
ae_serializer_serialize_int(s, spline->d, _state);
serializerealarray(s, &spline->x, -1, _state);
serializerealarray(s, &spline->y, -1, _state);
serializerealarray(s, &spline->f, -1, _state);
}
/*************************************************************************
Serializer: unserialization
-- ALGLIB --
Copyright 28.02.2018 by Bochkanov Sergey
*************************************************************************/
void spline2dunserialize(ae_serializer* s,
spline2dinterpolant* spline,
ae_state *_state)
{
ae_int_t scode;
_spline2dinterpolant_clear(spline);
/*
* Header
*/
ae_serializer_unserialize_int(s, &scode, _state);
ae_assert(scode==getspline2dserializationcode(_state), "Spline2DUnserialize: stream header corrupted", _state);
/*
* Data
*/
ae_serializer_unserialize_int(s, &spline->stype, _state);
ae_serializer_unserialize_int(s, &spline->n, _state);
ae_serializer_unserialize_int(s, &spline->m, _state);
ae_serializer_unserialize_int(s, &spline->d, _state);
unserializerealarray(s, &spline->x, _state);
unserializerealarray(s, &spline->y, _state);
unserializerealarray(s, &spline->f, _state);
}
/*************************************************************************
Internal subroutine.
Calculation of the first derivatives and the cross-derivative.
*************************************************************************/
static void spline2d_bicubiccalcderivatives(/* Real */ ae_matrix* a,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t m,
ae_int_t n,
/* Real */ ae_matrix* dx,
/* Real */ ae_matrix* dy,
/* Real */ ae_matrix* dxy,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_int_t j;
ae_vector xt;
ae_vector ft;
double s;
double ds;
double d2s;
spline1dinterpolant c;
ae_frame_make(_state, &_frame_block);
memset(&xt, 0, sizeof(xt));
memset(&ft, 0, sizeof(ft));
memset(&c, 0, sizeof(c));
ae_matrix_clear(dx);
ae_matrix_clear(dy);
ae_matrix_clear(dxy);
ae_vector_init(&xt, 0, DT_REAL, _state, ae_true);
ae_vector_init(&ft, 0, DT_REAL, _state, ae_true);
_spline1dinterpolant_init(&c, _state, ae_true);
ae_matrix_set_length(dx, m, n, _state);
ae_matrix_set_length(dy, m, n, _state);
ae_matrix_set_length(dxy, m, n, _state);
/*
* dF/dX
*/
ae_vector_set_length(&xt, n, _state);
ae_vector_set_length(&ft, n, _state);
for(i=0; i<=m-1; i++)
{
for(j=0; j<=n-1; j++)
{
xt.ptr.p_double[j] = x->ptr.p_double[j];
ft.ptr.p_double[j] = a->ptr.pp_double[i][j];
}
spline1dbuildcubic(&xt, &ft, n, 0, 0.0, 0, 0.0, &c, _state);
for(j=0; j<=n-1; j++)
{
spline1ddiff(&c, x->ptr.p_double[j], &s, &ds, &d2s, _state);
dx->ptr.pp_double[i][j] = ds;
}
}
/*
* dF/dY
*/
ae_vector_set_length(&xt, m, _state);
ae_vector_set_length(&ft, m, _state);
for(j=0; j<=n-1; j++)
{
for(i=0; i<=m-1; i++)
{
xt.ptr.p_double[i] = y->ptr.p_double[i];
ft.ptr.p_double[i] = a->ptr.pp_double[i][j];
}
spline1dbuildcubic(&xt, &ft, m, 0, 0.0, 0, 0.0, &c, _state);
for(i=0; i<=m-1; i++)
{
spline1ddiff(&c, y->ptr.p_double[i], &s, &ds, &d2s, _state);
dy->ptr.pp_double[i][j] = ds;
}
}
/*
* d2F/dXdY
*/
ae_vector_set_length(&xt, n, _state);
ae_vector_set_length(&ft, n, _state);
for(i=0; i<=m-1; i++)
{
for(j=0; j<=n-1; j++)
{
xt.ptr.p_double[j] = x->ptr.p_double[j];
ft.ptr.p_double[j] = dy->ptr.pp_double[i][j];
}
spline1dbuildcubic(&xt, &ft, n, 0, 0.0, 0, 0.0, &c, _state);
for(j=0; j<=n-1; j++)
{
spline1ddiff(&c, x->ptr.p_double[j], &s, &ds, &d2s, _state);
dxy->ptr.pp_double[i][j] = ds;
}
}
ae_frame_leave(_state);
}
/*************************************************************************
This function generates design matrix for the problem (in fact, two design
matrices are generated: "vertical" one and transposed (horizontal) one.
INPUT PARAMETERS:
XY - array[NPoints*(2+D)]; dataset after scaling in such
way that grid step is equal to 1.0 in both dimensions.
NPoints - dataset size, NPoints>=1
KX, KY - grid size, KX,KY>=4
Smoothing - nonlinearity penalty coefficient, >=0
LambdaReg - regularization coefficient, >=0
Basis1 - basis spline, expected to be non-zero only at [-2,+2]
AV, AH - possibly preallocated buffers
OUTPUT PARAMETERS:
AV - sparse matrix[ARows,KX*KY]; design matrix
AH - transpose of AV
ARows - number of rows in design matrix
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_generatedesignmatrix(/* Real */ ae_vector* xy,
ae_int_t npoints,
ae_int_t d,
ae_int_t kx,
ae_int_t ky,
double smoothing,
double lambdareg,
spline1dinterpolant* basis1,
sparsematrix* av,
sparsematrix* ah,
ae_int_t* arows,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t nzwidth;
ae_int_t nzshift;
ae_int_t ew;
ae_int_t i;
ae_int_t j0;
ae_int_t j1;
ae_int_t k0;
ae_int_t k1;
ae_int_t dstidx;
double v;
double v0;
double v1;
double v2;
double w0;
double w1;
double w2;
ae_vector crx;
ae_vector cry;
ae_vector nrs;
ae_matrix d2x;
ae_matrix d2y;
ae_matrix dxy;
ae_frame_make(_state, &_frame_block);
memset(&crx, 0, sizeof(crx));
memset(&cry, 0, sizeof(cry));
memset(&nrs, 0, sizeof(nrs));
memset(&d2x, 0, sizeof(d2x));
memset(&d2y, 0, sizeof(d2y));
memset(&dxy, 0, sizeof(dxy));
*arows = 0;
ae_vector_init(&crx, 0, DT_INT, _state, ae_true);
ae_vector_init(&cry, 0, DT_INT, _state, ae_true);
ae_vector_init(&nrs, 0, DT_INT, _state, ae_true);
ae_matrix_init(&d2x, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&d2y, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&dxy, 0, 0, DT_REAL, _state, ae_true);
nzwidth = 4;
nzshift = 1;
ae_assert(npoints>0, "Spline2DFit: integrity check failed", _state);
ae_assert(kx>=nzwidth, "Spline2DFit: integrity check failed", _state);
ae_assert(ky>=nzwidth, "Spline2DFit: integrity check failed", _state);
ew = 2+d;
/*
* Determine canonical rectangle for every point. Every point of the dataset is
* influenced by at most NZWidth*NZWidth basis functions, which form NZWidth*NZWidth
* canonical rectangle.
*
* Thus, we have (KX-NZWidth+1)*(KY-NZWidth+1) overlapping canonical rectangles.
* Assigning every point to its rectangle simplifies creation of sparse basis
* matrix at the next steps.
*/
ae_vector_set_length(&crx, npoints, _state);
ae_vector_set_length(&cry, npoints, _state);
for(i=0; i<=npoints-1; i++)
{
crx.ptr.p_int[i] = iboundval(ae_ifloor(xy->ptr.p_double[i*ew+0], _state)-nzshift, 0, kx-nzwidth, _state);
cry.ptr.p_int[i] = iboundval(ae_ifloor(xy->ptr.p_double[i*ew+1], _state)-nzshift, 0, ky-nzwidth, _state);
}
/*
* Create vertical and horizontal design matrices
*/
*arows = npoints+kx*ky;
if( ae_fp_neq(smoothing,0.0) )
{
ae_assert(ae_fp_greater(smoothing,0.0), "Spline2DFit: integrity check failed", _state);
*arows = *arows+3*(kx-2)*(ky-2);
}
ae_vector_set_length(&nrs, *arows, _state);
dstidx = 0;
for(i=0; i<=npoints-1; i++)
{
nrs.ptr.p_int[dstidx+i] = nzwidth*nzwidth;
}
dstidx = dstidx+npoints;
for(i=0; i<=kx*ky-1; i++)
{
nrs.ptr.p_int[dstidx+i] = 1;
}
dstidx = dstidx+kx*ky;
if( ae_fp_neq(smoothing,0.0) )
{
for(i=0; i<=3*(kx-2)*(ky-2)-1; i++)
{
nrs.ptr.p_int[dstidx+i] = 3*3;
}
dstidx = dstidx+3*(kx-2)*(ky-2);
}
ae_assert(dstidx==(*arows), "Spline2DFit: integrity check failed", _state);
sparsecreatecrs(*arows, kx*ky, &nrs, av, _state);
dstidx = 0;
for(i=0; i<=npoints-1; i++)
{
for(j1=0; j1<=nzwidth-1; j1++)
{
for(j0=0; j0<=nzwidth-1; j0++)
{
v0 = spline1dcalc(basis1, xy->ptr.p_double[i*ew+0]-(crx.ptr.p_int[i]+j0), _state);
v1 = spline1dcalc(basis1, xy->ptr.p_double[i*ew+1]-(cry.ptr.p_int[i]+j1), _state);
sparseset(av, dstidx+i, (cry.ptr.p_int[i]+j1)*kx+(crx.ptr.p_int[i]+j0), v0*v1, _state);
}
}
}
dstidx = dstidx+npoints;
for(i=0; i<=kx*ky-1; i++)
{
sparseset(av, dstidx+i, i, lambdareg, _state);
}
dstidx = dstidx+kx*ky;
if( ae_fp_neq(smoothing,0.0) )
{
/*
* Smoothing is applied. Because all grid nodes are same,
* we apply same smoothing kernel, which is calculated only
* once at the beginning of design matrix generation.
*/
ae_matrix_set_length(&d2x, 3, 3, _state);
ae_matrix_set_length(&d2y, 3, 3, _state);
ae_matrix_set_length(&dxy, 3, 3, _state);
for(j1=0; j1<=2; j1++)
{
for(j0=0; j0<=2; j0++)
{
d2x.ptr.pp_double[j0][j1] = 0.0;
d2y.ptr.pp_double[j0][j1] = 0.0;
dxy.ptr.pp_double[j0][j1] = 0.0;
}
}
for(k1=0; k1<=2; k1++)
{
for(k0=0; k0<=2; k0++)
{
spline1ddiff(basis1, (double)(-(k0-1)), &v0, &v1, &v2, _state);
spline1ddiff(basis1, (double)(-(k1-1)), &w0, &w1, &w2, _state);
d2x.ptr.pp_double[k0][k1] = d2x.ptr.pp_double[k0][k1]+v2*w0;
d2y.ptr.pp_double[k0][k1] = d2y.ptr.pp_double[k0][k1]+w2*v0;
dxy.ptr.pp_double[k0][k1] = dxy.ptr.pp_double[k0][k1]+v1*w1;
}
}
/*
* Now, kernel is ready - apply it to all inner nodes of the grid.
*/
for(j1=1; j1<=ky-2; j1++)
{
for(j0=1; j0<=kx-2; j0++)
{
/*
* d2F/dx2 term
*/
v = smoothing;
for(k1=-1; k1<=1; k1++)
{
for(k0=-1; k0<=1; k0++)
{
sparseset(av, dstidx, (j1+k1)*kx+(j0+k0), v*d2x.ptr.pp_double[1+k0][1+k1], _state);
}
}
dstidx = dstidx+1;
/*
* d2F/dy2 term
*/
v = smoothing;
for(k1=-1; k1<=1; k1++)
{
for(k0=-1; k0<=1; k0++)
{
sparseset(av, dstidx, (j1+k1)*kx+(j0+k0), v*d2y.ptr.pp_double[1+k0][1+k1], _state);
}
}
dstidx = dstidx+1;
/*
* 2*d2F/dxdy term
*/
v = ae_sqrt((double)(2), _state)*smoothing;
for(k1=-1; k1<=1; k1++)
{
for(k0=-1; k0<=1; k0++)
{
sparseset(av, dstidx, (j1+k1)*kx+(j0+k0), v*dxy.ptr.pp_double[1+k0][1+k1], _state);
}
}
dstidx = dstidx+1;
}
}
}
ae_assert(dstidx==(*arows), "Spline2DFit: integrity check failed", _state);
sparsecopy(av, ah, _state);
sparsetransposecrs(ah, _state);
ae_frame_leave(_state);
}
/*************************************************************************
This function updates table of spline values/derivatives using coefficients
for a layer of basis functions.
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_updatesplinetable(/* Real */ ae_vector* z,
ae_int_t kx,
ae_int_t ky,
ae_int_t d,
spline1dinterpolant* basis1,
ae_int_t bfrad,
/* Real */ ae_vector* ftbl,
ae_int_t m,
ae_int_t n,
ae_int_t scalexy,
ae_state *_state)
{
ae_int_t k;
ae_int_t k0;
ae_int_t k1;
ae_int_t j;
ae_int_t j0;
ae_int_t j1;
ae_int_t j0a;
ae_int_t j0b;
ae_int_t j1a;
ae_int_t j1b;
double v;
double v0;
double v1;
double v01;
double v11;
double rdummy;
ae_int_t dstidx;
ae_int_t sfx;
ae_int_t sfy;
ae_int_t sfxy;
double invscalexy;
ae_assert(n==(kx-1)*scalexy+1, "Spline2DFit.UpdateSplineTable: integrity check failed", _state);
ae_assert(m==(ky-1)*scalexy+1, "Spline2DFit.UpdateSplineTable: integrity check failed", _state);
invscalexy = (double)1/(double)scalexy;
sfx = n*m*d;
sfy = 2*n*m*d;
sfxy = 3*n*m*d;
for(k=0; k<=kx*ky-1; k++)
{
k0 = k%kx;
k1 = k/kx;
j0a = iboundval(k0*scalexy-(bfrad*scalexy-1), 0, n-1, _state);
j0b = iboundval(k0*scalexy+(bfrad*scalexy-1), 0, n-1, _state);
j1a = iboundval(k1*scalexy-(bfrad*scalexy-1), 0, m-1, _state);
j1b = iboundval(k1*scalexy+(bfrad*scalexy-1), 0, m-1, _state);
for(j1=j1a; j1<=j1b; j1++)
{
spline1ddiff(basis1, (j1-k1*scalexy)*invscalexy, &v1, &v11, &rdummy, _state);
v11 = v11*invscalexy;
for(j0=j0a; j0<=j0b; j0++)
{
spline1ddiff(basis1, (j0-k0*scalexy)*invscalexy, &v0, &v01, &rdummy, _state);
v01 = v01*invscalexy;
for(j=0; j<=d-1; j++)
{
dstidx = d*(j1*n+j0)+j;
v = z->ptr.p_double[j*kx*ky+k];
ftbl->ptr.p_double[dstidx] = ftbl->ptr.p_double[dstidx]+v0*v1*v;
ftbl->ptr.p_double[sfx+dstidx] = ftbl->ptr.p_double[sfx+dstidx]+v01*v1*v;
ftbl->ptr.p_double[sfy+dstidx] = ftbl->ptr.p_double[sfy+dstidx]+v0*v11*v;
ftbl->ptr.p_double[sfxy+dstidx] = ftbl->ptr.p_double[sfxy+dstidx]+v01*v11*v;
}
}
}
}
}
/*************************************************************************
This function performs fitting with FastDDM solver.
Internal function, never use it directly.
INPUT PARAMETERS:
XY - array[NPoints*(2+D)], dataset; destroyed in process
KX, KY - grid size
TileSize - tile size
InterfaceSize- interface size
NPoints - points count
D - number of components in vector-valued spline, D>=1
LSQRCnt - number of iterations, non-zero:
* LSQRCnt>0 means that specified amount of preconditioned
LSQR iterations will be performed to solve problem;
usually we need 2..5 its. Recommended option - best
convergence and stability/quality.
* LSQRCnt<0 means that instead of LSQR we use iterative
refinement on normal equations. Again, 2..5 its is enough.
Basis1 - basis spline, expected to be non-zero only at [-2,+2]
Z - possibly preallocated buffer for solution
Residuals - possibly preallocated buffer for residuals at dataset points
Rep - report structure; fields which are not set by this function
are left intact
TSS - total sum of squares; used to calculate R2
OUTPUT PARAMETERS:
XY - destroyed in process
Z - array[KX*KY*D], filled by solution; KX*KY coefficients
corresponding to each of D dimensions are stored contiguously.
Rep - following fields are set:
* Rep.RMSError
* Rep.AvgError
* Rep.MaxError
* Rep.R2
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_fastddmfit(/* Real */ ae_vector* xy,
ae_int_t npoints,
ae_int_t d,
ae_int_t kx,
ae_int_t ky,
ae_int_t basecasex,
ae_int_t basecasey,
ae_int_t maxcoresize,
ae_int_t interfacesize,
ae_int_t nlayers,
double smoothing,
ae_int_t lsqrcnt,
spline1dinterpolant* basis1,
spline2dinterpolant* spline,
spline2dfitreport* rep,
double tss,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_int_t j;
ae_int_t nzwidth;
ae_int_t xew;
ae_int_t ntotallayers;
ae_int_t scaleidx;
ae_int_t scalexy;
double invscalexy;
ae_int_t kxcur;
ae_int_t kycur;
ae_int_t tilescount0;
ae_int_t tilescount1;
double v;
double rss;
ae_vector yraw;
ae_vector xyindex;
ae_vector tmp0;
ae_vector bufi;
spline2dfastddmbuf seed;
ae_shared_pool pool;
spline2dxdesignmatrix xdesignmatrix;
spline2dblockllsbuf blockllsbuf;
spline2dfitreport dummyrep;
ae_frame_make(_state, &_frame_block);
memset(&yraw, 0, sizeof(yraw));
memset(&xyindex, 0, sizeof(xyindex));
memset(&tmp0, 0, sizeof(tmp0));
memset(&bufi, 0, sizeof(bufi));
memset(&seed, 0, sizeof(seed));
memset(&pool, 0, sizeof(pool));
memset(&xdesignmatrix, 0, sizeof(xdesignmatrix));
memset(&blockllsbuf, 0, sizeof(blockllsbuf));
memset(&dummyrep, 0, sizeof(dummyrep));
ae_vector_init(&yraw, 0, DT_REAL, _state, ae_true);
ae_vector_init(&xyindex, 0, DT_INT, _state, ae_true);
ae_vector_init(&tmp0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bufi, 0, DT_INT, _state, ae_true);
_spline2dfastddmbuf_init(&seed, _state, ae_true);
ae_shared_pool_init(&pool, _state, ae_true);
_spline2dxdesignmatrix_init(&xdesignmatrix, _state, ae_true);
_spline2dblockllsbuf_init(&blockllsbuf, _state, ae_true);
_spline2dfitreport_init(&dummyrep, _state, ae_true);
/*
* Dataset metrics and integrity checks
*/
nzwidth = 4;
xew = 2+d;
ae_assert(maxcoresize>=2, "Spline2DFit: integrity check failed", _state);
ae_assert(interfacesize>=1, "Spline2DFit: integrity check failed", _state);
ae_assert(kx>=nzwidth, "Spline2DFit: integrity check failed", _state);
ae_assert(ky>=nzwidth, "Spline2DFit: integrity check failed", _state);
/*
* Verify consistency of the grid size (KX,KY) with basecase sizes.
* Determine full number of layers.
*/
ae_assert(basecasex<=maxcoresize, "Spline2DFit: integrity error", _state);
ae_assert(basecasey<=maxcoresize, "Spline2DFit: integrity error", _state);
ntotallayers = 1;
scalexy = 1;
kxcur = kx;
kycur = ky;
while(kxcur>basecasex+1&&kycur>basecasey+1)
{
ae_assert(kxcur%2==1, "Spline2DFit: integrity error", _state);
ae_assert(kycur%2==1, "Spline2DFit: integrity error", _state);
kxcur = (kxcur-1)/2+1;
kycur = (kycur-1)/2+1;
scalexy = scalexy*2;
inc(&ntotallayers, _state);
}
invscalexy = (double)1/(double)scalexy;
ae_assert((kxcur<=maxcoresize+1&&kxcur==basecasex+1)||kxcur%basecasex==1, "Spline2DFit: integrity error", _state);
ae_assert((kycur<=maxcoresize+1&&kycur==basecasey+1)||kycur%basecasey==1, "Spline2DFit: integrity error", _state);
ae_assert(kxcur==basecasex+1||kycur==basecasey+1, "Spline2DFit: integrity error", _state);
/*
* Initial scaling of dataset.
* Store original target values to YRaw.
*/
rvectorsetlengthatleast(&yraw, npoints*d, _state);
for(i=0; i<=npoints-1; i++)
{
xy->ptr.p_double[xew*i+0] = xy->ptr.p_double[xew*i+0]*invscalexy;
xy->ptr.p_double[xew*i+1] = xy->ptr.p_double[xew*i+1]*invscalexy;
for(j=0; j<=d-1; j++)
{
yraw.ptr.p_double[i*d+j] = xy->ptr.p_double[xew*i+2+j];
}
}
kxcur = (kx-1)/scalexy+1;
kycur = (ky-1)/scalexy+1;
/*
* Build initial dataset index; area is divided into (KXCur-1)*(KYCur-1)
* cells, with contiguous storage of points in the same cell.
* Iterate over different scales
*/
ae_shared_pool_set_seed(&pool, &seed, sizeof(seed), _spline2dfastddmbuf_init, _spline2dfastddmbuf_init_copy, _spline2dfastddmbuf_destroy, _state);
spline2d_reorderdatasetandbuildindex(xy, npoints, d, &yraw, d, kxcur, kycur, &xyindex, &bufi, _state);
for(scaleidx=ntotallayers-1; scaleidx>=0; scaleidx--)
{
if( (nlayers>0&&scaleidx<nlayers)||(nlayers<=0&&scaleidx<imax2(ntotallayers+nlayers, 1, _state)) )
{
/*
* Fit current layer
*/
ae_assert(kxcur%basecasex==1, "Spline2DFit: integrity error", _state);
ae_assert(kycur%basecasey==1, "Spline2DFit: integrity error", _state);
tilescount0 = kxcur/basecasex;
tilescount1 = kycur/basecasey;
spline2d_fastddmfitlayer(xy, d, scalexy, &xyindex, basecasex, 0, tilescount0, tilescount0, basecasey, 0, tilescount1, tilescount1, maxcoresize, interfacesize, lsqrcnt, spline2d_lambdaregfastddm+smoothing*ae_pow(spline2d_lambdadecay, (double)(scaleidx), _state), basis1, &pool, spline, _state);
/*
* Compute residuals and update XY
*/
spline2d_computeresidualsfromscratch(xy, &yraw, npoints, d, scalexy, spline, _state);
}
/*
* Move to the next level
*/
if( scaleidx!=0 )
{
/*
* Transform dataset (multply everything by 2.0) and refine grid.
*/
kxcur = 2*kxcur-1;
kycur = 2*kycur-1;
scalexy = scalexy/2;
invscalexy = (double)1/(double)scalexy;
spline2d_rescaledatasetandrefineindex(xy, npoints, d, &yraw, d, kxcur, kycur, &xyindex, &bufi, _state);
/*
* Clear temporaries from previous round.
*
* We have to do it because upper layer of the multilevel spline
* needs more memory then subsequent layers, and we want to free
* this memory as soon as possible.
*/
ae_shared_pool_clear_recycled(&pool, _state);
}
}
/*
* Post-check
*/
ae_assert(kxcur==kx, "Spline2DFit: integrity check failed", _state);
ae_assert(kycur==ky, "Spline2DFit: integrity check failed", _state);
ae_assert(scalexy==1, "Spline2DFit: integrity check failed", _state);
/*
* Report
*/
rep->rmserror = (double)(0);
rep->avgerror = (double)(0);
rep->maxerror = (double)(0);
rss = 0.0;
for(i=0; i<=npoints-1; i++)
{
for(j=0; j<=d-1; j++)
{
v = xy->ptr.p_double[i*xew+2+j];
rss = rss+v*v;
rep->rmserror = rep->rmserror+ae_sqr(v, _state);
rep->avgerror = rep->avgerror+ae_fabs(v, _state);
rep->maxerror = ae_maxreal(rep->maxerror, ae_fabs(v, _state), _state);
}
}
rep->rmserror = ae_sqrt(rep->rmserror/coalesce((double)(npoints*d), 1.0, _state), _state);
rep->avgerror = rep->avgerror/coalesce((double)(npoints*d), 1.0, _state);
rep->r2 = 1.0-rss/coalesce(tss, 1.0, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Recursive fitting function for FastDDM algorithm.
Works with KX*KY grid, with KX=BasecaseX*TilesCountX+1 and KY=BasecaseY*TilesCountY+1,
which is partitioned into TilesCountX*TilesCountY tiles, each having size
BasecaseX*BasecaseY.
This function processes tiles in range [TileX0,TileX1)x[TileY0,TileY1) and
recursively divides this range until we move down to single tile, which
is processed with BlockLLS solver.
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_fastddmfitlayer(/* Real */ ae_vector* xy,
ae_int_t d,
ae_int_t scalexy,
/* Integer */ ae_vector* xyindex,
ae_int_t basecasex,
ae_int_t tilex0,
ae_int_t tilex1,
ae_int_t tilescountx,
ae_int_t basecasey,
ae_int_t tiley0,
ae_int_t tiley1,
ae_int_t tilescounty,
ae_int_t maxcoresize,
ae_int_t interfacesize,
ae_int_t lsqrcnt,
double lambdareg,
spline1dinterpolant* basis1,
ae_shared_pool* pool,
spline2dinterpolant* spline,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t kx;
ae_int_t ky;
ae_int_t i;
ae_int_t j;
ae_int_t j0;
ae_int_t j1;
ae_int_t bfrad;
ae_int_t xa;
ae_int_t xb;
ae_int_t ya;
ae_int_t yb;
ae_int_t tile0;
ae_int_t tile1;
ae_int_t tilesize0;
ae_int_t tilesize1;
ae_int_t sfx;
ae_int_t sfy;
ae_int_t sfxy;
double dummytss;
double invscalexy;
ae_int_t cnt0;
ae_int_t cnt1;
ae_int_t offs;
double vs;
double vsx;
double vsy;
double vsxy;
spline2dfastddmbuf *buf;
ae_smart_ptr _buf;
ae_frame_make(_state, &_frame_block);
memset(&_buf, 0, sizeof(_buf));
ae_smart_ptr_init(&_buf, (void**)&buf, _state, ae_true);
/*
* Dataset metrics and fast integrity checks;
* no code with side effects is allowed before parallel split.
*/
bfrad = 2;
invscalexy = (double)1/(double)scalexy;
kx = basecasex*tilescountx+1;
ky = basecasey*tilescounty+1;
/*
* Parallelism; because this function is intended for
* large-scale problems, we always try to:
* * invoke parallel execution mode
* * activate spawn support
*/
if( _trypexec_spline2d_fastddmfitlayer(xy,d,scalexy,xyindex,basecasex,tilex0,tilex1,tilescountx,basecasey,tiley0,tiley1,tilescounty,maxcoresize,interfacesize,lsqrcnt,lambdareg,basis1,pool,spline, _state) )
{
ae_frame_leave(_state);
return;
}
if( imax2(tiley1-tiley0, tilex1-tilex0, _state)>=2 )
{
if( tiley1-tiley0>tilex1-tilex0 )
{
/*
* Split problem in Y dimension
*
* NOTE: recursive calls to FastDDMFitLayer() compute
* residuals in the inner cells defined by XYIndex[],
* but we still have to compute residuals for cells
* BETWEEN two recursive subdivisions of the task.
*/
tiledsplit(tiley1-tiley0, 1, &j0, &j1, _state);
spline2d_fastddmfitlayer(xy, d, scalexy, xyindex, basecasex, tilex0, tilex1, tilescountx, basecasey, tiley0, tiley0+j0, tilescounty, maxcoresize, interfacesize, lsqrcnt, lambdareg, basis1, pool, spline, _state);
spline2d_fastddmfitlayer(xy, d, scalexy, xyindex, basecasex, tilex0, tilex1, tilescountx, basecasey, tiley0+j0, tiley1, tilescounty, maxcoresize, interfacesize, lsqrcnt, lambdareg, basis1, pool, spline, _state);
}
else
{
/*
* Split problem in X dimension
*
* NOTE: recursive calls to FastDDMFitLayer() compute
* residuals in the inner cells defined by XYIndex[],
* but we still have to compute residuals for cells
* BETWEEN two recursive subdivisions of the task.
*/
tiledsplit(tilex1-tilex0, 1, &j0, &j1, _state);
spline2d_fastddmfitlayer(xy, d, scalexy, xyindex, basecasex, tilex0, tilex0+j0, tilescountx, basecasey, tiley0, tiley1, tilescounty, maxcoresize, interfacesize, lsqrcnt, lambdareg, basis1, pool, spline, _state);
spline2d_fastddmfitlayer(xy, d, scalexy, xyindex, basecasex, tilex0+j0, tilex1, tilescountx, basecasey, tiley0, tiley1, tilescounty, maxcoresize, interfacesize, lsqrcnt, lambdareg, basis1, pool, spline, _state);
}
ae_frame_leave(_state);
return;
}
ae_assert(tiley0==tiley1-1, "Spline2DFit.FastDDMFitLayer: integrity check failed", _state);
ae_assert(tilex0==tilex1-1, "Spline2DFit.FastDDMFitLayer: integrity check failed", _state);
tile1 = tiley0;
tile0 = tilex0;
/*
* Retrieve temporaries
*/
ae_shared_pool_retrieve(pool, &_buf, _state);
/*
* Analyze dataset
*/
xa = iboundval(tile0*basecasex-interfacesize, 0, kx, _state);
xb = iboundval((tile0+1)*basecasex+interfacesize, 0, kx, _state);
ya = iboundval(tile1*basecasey-interfacesize, 0, ky, _state);
yb = iboundval((tile1+1)*basecasey+interfacesize, 0, ky, _state);
tilesize0 = xb-xa;
tilesize1 = yb-ya;
/*
* Solve current chunk with BlockLLS
*/
dummytss = 1.0;
spline2d_xdesigngenerate(xy, xyindex, xa, xb, kx, ya, yb, ky, d, lambdareg, 0.0, basis1, &buf->xdesignmatrix, _state);
spline2d_blockllsfit(&buf->xdesignmatrix, lsqrcnt, &buf->tmpz, &buf->dummyrep, dummytss, &buf->blockllsbuf, _state);
buf->localmodel.d = d;
buf->localmodel.m = tilesize1;
buf->localmodel.n = tilesize0;
buf->localmodel.stype = -3;
rvectorsetlengthatleast(&buf->localmodel.x, tilesize0, _state);
rvectorsetlengthatleast(&buf->localmodel.y, tilesize1, _state);
rvectorsetlengthatleast(&buf->localmodel.f, tilesize0*tilesize1*d*4, _state);
for(i=0; i<=tilesize0-1; i++)
{
buf->localmodel.x.ptr.p_double[i] = (double)(xa+i);
}
for(i=0; i<=tilesize1-1; i++)
{
buf->localmodel.y.ptr.p_double[i] = (double)(ya+i);
}
for(i=0; i<=tilesize0*tilesize1*d*4-1; i++)
{
buf->localmodel.f.ptr.p_double[i] = 0.0;
}
spline2d_updatesplinetable(&buf->tmpz, tilesize0, tilesize1, d, basis1, bfrad, &buf->localmodel.f, tilesize1, tilesize0, 1, _state);
/*
* Transform local spline to original coordinates
*/
sfx = buf->localmodel.n*buf->localmodel.m*d;
sfy = 2*buf->localmodel.n*buf->localmodel.m*d;
sfxy = 3*buf->localmodel.n*buf->localmodel.m*d;
for(i=0; i<=tilesize0-1; i++)
{
buf->localmodel.x.ptr.p_double[i] = buf->localmodel.x.ptr.p_double[i]*scalexy;
}
for(i=0; i<=tilesize1-1; i++)
{
buf->localmodel.y.ptr.p_double[i] = buf->localmodel.y.ptr.p_double[i]*scalexy;
}
for(i=0; i<=tilesize0*tilesize1*d-1; i++)
{
buf->localmodel.f.ptr.p_double[sfx+i] = buf->localmodel.f.ptr.p_double[sfx+i]*invscalexy;
buf->localmodel.f.ptr.p_double[sfy+i] = buf->localmodel.f.ptr.p_double[sfy+i]*invscalexy;
buf->localmodel.f.ptr.p_double[sfxy+i] = buf->localmodel.f.ptr.p_double[sfxy+i]*(invscalexy*invscalexy);
}
/*
* Output results; for inner and topmost/leftmost tiles we output only BasecaseX*BasecaseY
* inner elements; for rightmost/bottom ones we also output one column/row of the interface
* part.
*
* Such complexity is explained by the fact that area size (by design) is not evenly divisible
* by the tile size; it is divisible with remainder=1, and we expect that interface size is
* at least 1, so we can fill the missing rightmost/bottom elements of Z by the interface
* values.
*/
ae_assert(interfacesize>=1, "Spline2DFit: integrity check failed", _state);
sfx = spline->n*spline->m*d;
sfy = 2*spline->n*spline->m*d;
sfxy = 3*spline->n*spline->m*d;
cnt0 = basecasex*scalexy;
cnt1 = basecasey*scalexy;
if( tile0==tilescountx-1 )
{
inc(&cnt0, _state);
}
if( tile1==tilescounty-1 )
{
inc(&cnt1, _state);
}
offs = d*(spline->n*tile1*basecasey*scalexy+tile0*basecasex*scalexy);
for(j1=0; j1<=cnt1-1; j1++)
{
for(j0=0; j0<=cnt0-1; j0++)
{
for(j=0; j<=d-1; j++)
{
spline2ddiffvi(&buf->localmodel, (double)(tile0*basecasex*scalexy+j0), (double)(tile1*basecasey*scalexy+j1), j, &vs, &vsx, &vsy, &vsxy, _state);
spline->f.ptr.p_double[offs+d*(spline->n*j1+j0)+j] = spline->f.ptr.p_double[offs+d*(spline->n*j1+j0)+j]+vs;
spline->f.ptr.p_double[sfx+offs+d*(spline->n*j1+j0)+j] = spline->f.ptr.p_double[sfx+offs+d*(spline->n*j1+j0)+j]+vsx;
spline->f.ptr.p_double[sfy+offs+d*(spline->n*j1+j0)+j] = spline->f.ptr.p_double[sfy+offs+d*(spline->n*j1+j0)+j]+vsy;
spline->f.ptr.p_double[sfxy+offs+d*(spline->n*j1+j0)+j] = spline->f.ptr.p_double[sfxy+offs+d*(spline->n*j1+j0)+j]+vsxy;
}
}
}
/*
* Recycle temporaries
*/
ae_shared_pool_recycle(pool, &_buf, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Serial stub for GPL edition.
*************************************************************************/
ae_bool _trypexec_spline2d_fastddmfitlayer(/* Real */ ae_vector* xy,
ae_int_t d,
ae_int_t scalexy,
/* Integer */ ae_vector* xyindex,
ae_int_t basecasex,
ae_int_t tilex0,
ae_int_t tilex1,
ae_int_t tilescountx,
ae_int_t basecasey,
ae_int_t tiley0,
ae_int_t tiley1,
ae_int_t tilescounty,
ae_int_t maxcoresize,
ae_int_t interfacesize,
ae_int_t lsqrcnt,
double lambdareg,
spline1dinterpolant* basis1,
ae_shared_pool* pool,
spline2dinterpolant* spline,
ae_state *_state)
{
return ae_false;
}
/*************************************************************************
This function performs fitting with BlockLLS solver. Internal function,
never use it directly.
IMPORTANT: performance and memory requirements of this function are
asymmetric w.r.t. KX and KY: it has
* O(KY*KX^2) memory requirements
* O(KY*KX^3) running time
Thus, if you have large KY and small KX, simple transposition
of your dataset may give you great speedup.
INPUT PARAMETERS:
AV - sparse matrix, [ARows,KX*KY] in size. "Vertical" version
of design matrix, rows [0,NPoints) contain values of basis
functions at dataset points. Other rows are used for
nonlinearity penalty and other stuff like that.
AH - transpose(AV), "horizontal" version of AV
ARows - rows count
XY - array[NPoints*(2+D)], dataset
KX, KY - grid size
NPoints - points count
D - number of components in vector-valued spline, D>=1
LSQRCnt - number of iterations, non-zero:
* LSQRCnt>0 means that specified amount of preconditioned
LSQR iterations will be performed to solve problem;
usually we need 2..5 its. Recommended option - best
convergence and stability/quality.
* LSQRCnt<0 means that instead of LSQR we use iterative
refinement on normal equations. Again, 2..5 its is enough.
Z - possibly preallocated buffer for solution
Rep - report structure; fields which are not set by this function
are left intact
TSS - total sum of squares; used to calculate R2
OUTPUT PARAMETERS:
XY - destroyed in process
Z - array[KX*KY*D], filled by solution; KX*KY coefficients
corresponding to each of D dimensions are stored contiguously.
Rep - following fields are set:
* Rep.RMSError
* Rep.AvgError
* Rep.MaxError
* Rep.R2
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_blockllsfit(spline2dxdesignmatrix* xdesign,
ae_int_t lsqrcnt,
/* Real */ ae_vector* z,
spline2dfitreport* rep,
double tss,
spline2dblockllsbuf* buf,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t blockbandwidth;
ae_int_t d;
ae_int_t i;
ae_int_t j;
double lambdachol;
sreal mxata;
double v;
ae_int_t celloffset;
ae_int_t i0;
ae_int_t i1;
double rss;
ae_int_t arows;
ae_int_t bw2;
ae_int_t kx;
ae_int_t ky;
ae_frame_make(_state, &_frame_block);
memset(&mxata, 0, sizeof(mxata));
_sreal_init(&mxata, _state, ae_true);
ae_assert(xdesign->blockwidth==4, "Spline2DFit: integrity check failed", _state);
blockbandwidth = 3;
d = xdesign->d;
arows = xdesign->nrows;
kx = xdesign->kx;
ky = xdesign->ky;
bw2 = xdesign->blockwidth*xdesign->blockwidth;
/*
* Initial values for Z/Residuals
*/
rvectorsetlengthatleast(z, kx*ky*d, _state);
for(i=0; i<=kx*ky*d-1; i++)
{
z->ptr.p_double[i] = (double)(0);
}
/*
* Create and factorize design matrix. Add regularizer if
* factorization failed (happens sometimes with zero
* smoothing and sparsely populated datasets).
*
* The algorithm below is refactoring of NaiveLLS algorithm,
* which uses sparsity properties and compressed block storage.
*
* Problem sparsity pattern results in block-band-diagonal
* matrix (block matrix with limited bandwidth, equal to 3
* for bicubic splines). Thus, we have KY*KY blocks, each
* of them is KX*KX in size. Design matrix is stored in
* large NROWS*KX matrix, with NROWS=(BlockBandwidth+1)*KY*KX.
*
* We use adaptation of block skyline storage format, with
* TOWERSIZE*KX skyline bands (towers) stored sequentially;
* here TOWERSIZE=(BlockBandwidth+1)*KX. So, we have KY
* "towers", stored one below other, in BlockATA matrix.
* Every "tower" is a sequence of BlockBandwidth+1 cells,
* each of them being KX*KX in size.
*/
lambdachol = spline2d_cholreg;
rmatrixsetlengthatleast(&buf->blockata, (blockbandwidth+1)*ky*kx, kx, _state);
for(;;)
{
/*
* Parallel generation of squared design matrix.
*/
spline2d_xdesignblockata(xdesign, &buf->blockata, &mxata.val, _state);
/*
* Regularization
*/
v = coalesce(mxata.val, 1.0, _state)*lambdachol;
for(i1=0; i1<=ky-1; i1++)
{
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, i1, i1, _state);
for(i0=0; i0<=kx-1; i0++)
{
buf->blockata.ptr.pp_double[celloffset+i0][i0] = buf->blockata.ptr.pp_double[celloffset+i0][i0]+v;
}
}
/*
* Try Cholesky factorization.
*/
if( !spline2d_blockllscholesky(&buf->blockata, kx, ky, &buf->trsmbuf2, &buf->cholbuf2, &buf->cholbuf1, _state) )
{
/*
* Factorization failed, increase regularizer and repeat
*/
lambdachol = coalesce(10*lambdachol, 1.0E-12, _state);
continue;
}
break;
}
/*
* Solve
*/
rss = 0.0;
rep->rmserror = (double)(0);
rep->avgerror = (double)(0);
rep->maxerror = (double)(0);
ae_assert(lsqrcnt>0, "Spline2DFit: integrity failure", _state);
rvectorsetlengthatleast(&buf->tmp0, arows, _state);
rvectorsetlengthatleast(&buf->tmp1, kx*ky, _state);
linlsqrcreatebuf(arows, kx*ky, &buf->solver, _state);
for(j=0; j<=d-1; j++)
{
/*
* Preconditioned LSQR:
*
* use Cholesky factor U of squared design matrix A'*A to
* transform min|A*x-b| to min|[A*inv(U)]*y-b| with y=U*x.
*
* Preconditioned problem is solved with LSQR solver, which
* gives superior results than normal equations.
*/
for(i=0; i<=arows-1; i++)
{
if( i<xdesign->npoints )
{
buf->tmp0.ptr.p_double[i] = xdesign->vals.ptr.pp_double[i][bw2+j];
}
else
{
buf->tmp0.ptr.p_double[i] = 0.0;
}
}
linlsqrrestart(&buf->solver, _state);
linlsqrsetb(&buf->solver, &buf->tmp0, _state);
linlsqrsetcond(&buf->solver, 1.0E-14, 1.0E-14, lsqrcnt, _state);
while(linlsqriteration(&buf->solver, _state))
{
if( buf->solver.needmv )
{
/*
* Use Cholesky factorization of the system matrix
* as preconditioner: solve TRSV(U,Solver.X)
*/
for(i=0; i<=kx*ky-1; i++)
{
buf->tmp1.ptr.p_double[i] = buf->solver.x.ptr.p_double[i];
}
spline2d_blockllstrsv(&buf->blockata, kx, ky, ae_false, &buf->tmp1, _state);
/*
* After preconditioning is done, multiply by A
*/
spline2d_xdesignmv(xdesign, &buf->tmp1, &buf->solver.mv, _state);
}
if( buf->solver.needmtv )
{
/*
* Multiply by design matrix A
*/
spline2d_xdesignmtv(xdesign, &buf->solver.x, &buf->solver.mtv, _state);
/*
* Multiply by preconditioner: solve TRSV(U',A*Solver.X)
*/
spline2d_blockllstrsv(&buf->blockata, kx, ky, ae_true, &buf->solver.mtv, _state);
}
}
/*
* Get results and post-multiply by preconditioner to get
* original variables.
*/
linlsqrresults(&buf->solver, &buf->tmp1, &buf->solverrep, _state);
spline2d_blockllstrsv(&buf->blockata, kx, ky, ae_false, &buf->tmp1, _state);
for(i=0; i<=kx*ky-1; i++)
{
z->ptr.p_double[kx*ky*j+i] = buf->tmp1.ptr.p_double[i];
}
/*
* Calculate model values
*/
spline2d_xdesignmv(xdesign, &buf->tmp1, &buf->tmp0, _state);
for(i=0; i<=xdesign->npoints-1; i++)
{
v = xdesign->vals.ptr.pp_double[i][bw2+j]-buf->tmp0.ptr.p_double[i];
rss = rss+v*v;
rep->rmserror = rep->rmserror+ae_sqr(v, _state);
rep->avgerror = rep->avgerror+ae_fabs(v, _state);
rep->maxerror = ae_maxreal(rep->maxerror, ae_fabs(v, _state), _state);
}
}
rep->rmserror = ae_sqrt(rep->rmserror/coalesce((double)(xdesign->npoints*d), 1.0, _state), _state);
rep->avgerror = rep->avgerror/coalesce((double)(xdesign->npoints*d), 1.0, _state);
rep->r2 = 1.0-rss/coalesce(tss, 1.0, _state);
ae_frame_leave(_state);
}
/*************************************************************************
This function performs fitting with NaiveLLS solver. Internal function,
never use it directly.
INPUT PARAMETERS:
AV - sparse matrix, [ARows,KX*KY] in size. "Vertical" version
of design matrix, rows [0,NPoints] contain values of basis
functions at dataset points. Other rows are used for
nonlinearity penalty and other stuff like that.
AH - transpose(AV), "horizontal" version of AV
ARows - rows count
XY - array[NPoints*(2+D)], dataset
KX, KY - grid size
NPoints - points count
D - number of components in vector-valued spline, D>=1
LSQRCnt - number of iterations, non-zero:
* LSQRCnt>0 means that specified amount of preconditioned
LSQR iterations will be performed to solve problem;
usually we need 2..5 its. Recommended option - best
convergence and stability/quality.
* LSQRCnt<0 means that instead of LSQR we use iterative
refinement on normal equations. Again, 2..5 its is enough.
Z - possibly preallocated buffer for solution
Rep - report structure; fields which are not set by this function
are left intact
TSS - total sum of squares; used to calculate R2
OUTPUT PARAMETERS:
XY - destroyed in process
Z - array[KX*KY*D], filled by solution; KX*KY coefficients
corresponding to each of D dimensions are stored contiguously.
Rep - following fields are set:
* Rep.RMSError
* Rep.AvgError
* Rep.MaxError
* Rep.R2
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_naivellsfit(sparsematrix* av,
sparsematrix* ah,
ae_int_t arows,
/* Real */ ae_vector* xy,
ae_int_t kx,
ae_int_t ky,
ae_int_t npoints,
ae_int_t d,
ae_int_t lsqrcnt,
/* Real */ ae_vector* z,
spline2dfitreport* rep,
double tss,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t ew;
ae_int_t i;
ae_int_t j;
ae_int_t i0;
ae_int_t i1;
ae_int_t j0;
ae_int_t j1;
double v;
ae_int_t blockbandwidth;
double lambdareg;
ae_int_t srci;
ae_int_t srcj;
ae_int_t idxi;
ae_int_t idxj;
ae_int_t endi;
ae_int_t endj;
ae_int_t rfsidx;
ae_matrix ata;
ae_vector tmp0;
ae_vector tmp1;
double mxata;
linlsqrstate solver;
linlsqrreport solverrep;
double rss;
ae_frame_make(_state, &_frame_block);
memset(&ata, 0, sizeof(ata));
memset(&tmp0, 0, sizeof(tmp0));
memset(&tmp1, 0, sizeof(tmp1));
memset(&solver, 0, sizeof(solver));
memset(&solverrep, 0, sizeof(solverrep));
ae_matrix_init(&ata, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp1, 0, DT_REAL, _state, ae_true);
_linlsqrstate_init(&solver, _state, ae_true);
_linlsqrreport_init(&solverrep, _state, ae_true);
blockbandwidth = 3;
ew = 2+d;
/*
* Initial values for Z/Residuals
*/
rvectorsetlengthatleast(z, kx*ky*d, _state);
for(i=0; i<=kx*ky*d-1; i++)
{
z->ptr.p_double[i] = (double)(0);
}
/*
* Create and factorize design matrix.
*
* Add regularizer if factorization failed (happens sometimes
* with zero smoothing and sparsely populated datasets).
*/
lambdareg = spline2d_cholreg;
rmatrixsetlengthatleast(&ata, kx*ky, kx*ky, _state);
for(;;)
{
mxata = 0.0;
for(i=0; i<=kx*ky-1; i++)
{
for(j=i; j<=kx*ky-1; j++)
{
/*
* Initialize by zero
*/
ata.ptr.pp_double[i][j] = (double)(0);
/*
* Determine grid nodes corresponding to I and J;
* skip if too far away
*/
i0 = i%kx;
i1 = i/kx;
j0 = j%kx;
j1 = j/kx;
if( ae_iabs(i0-j0, _state)>blockbandwidth||ae_iabs(i1-j1, _state)>blockbandwidth )
{
continue;
}
/*
* Nodes are close enough, calculate product of columns I and J of A.
*/
v = (double)(0);
srci = ah->ridx.ptr.p_int[i];
srcj = ah->ridx.ptr.p_int[j];
endi = ah->ridx.ptr.p_int[i+1];
endj = ah->ridx.ptr.p_int[j+1];
for(;;)
{
if( srci>=endi||srcj>=endj )
{
break;
}
idxi = ah->idx.ptr.p_int[srci];
idxj = ah->idx.ptr.p_int[srcj];
if( idxi==idxj )
{
v = v+ah->vals.ptr.p_double[srci]*ah->vals.ptr.p_double[srcj];
srci = srci+1;
srcj = srcj+1;
continue;
}
if( idxi<idxj )
{
srci = srci+1;
}
else
{
srcj = srcj+1;
}
}
ata.ptr.pp_double[i][j] = v;
mxata = ae_maxreal(mxata, ae_fabs(v, _state), _state);
}
}
v = coalesce(mxata, 1.0, _state)*lambdareg;
for(i=0; i<=kx*ky-1; i++)
{
ata.ptr.pp_double[i][i] = ata.ptr.pp_double[i][i]+v;
}
if( spdmatrixcholesky(&ata, kx*ky, ae_true, _state) )
{
/*
* Success!
*/
break;
}
/*
* Factorization failed, increase regularizer and repeat
*/
lambdareg = coalesce(10*lambdareg, 1.0E-12, _state);
}
/*
* Solve
*
* NOTE: we expect that Z is zero-filled, and we treat it
* like initial approximation to solution.
*/
rvectorsetlengthatleast(&tmp0, arows, _state);
rvectorsetlengthatleast(&tmp1, kx*ky, _state);
if( lsqrcnt>0 )
{
linlsqrcreate(arows, kx*ky, &solver, _state);
}
for(j=0; j<=d-1; j++)
{
ae_assert(lsqrcnt!=0, "Spline2DFit: integrity failure", _state);
if( lsqrcnt>0 )
{
/*
* Preconditioned LSQR:
*
* use Cholesky factor U of squared design matrix A'*A to
* transform min|A*x-b| to min|[A*inv(U)]*y-b| with y=U*x.
*
* Preconditioned problem is solved with LSQR solver, which
* gives superior results than normal equations.
*/
linlsqrcreate(arows, kx*ky, &solver, _state);
for(i=0; i<=arows-1; i++)
{
if( i<npoints )
{
tmp0.ptr.p_double[i] = xy->ptr.p_double[i*ew+2+j];
}
else
{
tmp0.ptr.p_double[i] = 0.0;
}
}
linlsqrsetb(&solver, &tmp0, _state);
linlsqrsetcond(&solver, 1.0E-14, 1.0E-14, lsqrcnt, _state);
while(linlsqriteration(&solver, _state))
{
if( solver.needmv )
{
/*
* Use Cholesky factorization of the system matrix
* as preconditioner: solve TRSV(U,Solver.X)
*/
for(i=0; i<=kx*ky-1; i++)
{
tmp1.ptr.p_double[i] = solver.x.ptr.p_double[i];
}
rmatrixtrsv(kx*ky, &ata, 0, 0, ae_true, ae_false, 0, &tmp1, 0, _state);
/*
* After preconditioning is done, multiply by A
*/
sparsemv(av, &tmp1, &solver.mv, _state);
}
if( solver.needmtv )
{
/*
* Multiply by design matrix A
*/
sparsemv(ah, &solver.x, &solver.mtv, _state);
/*
* Multiply by preconditioner: solve TRSV(U',A*Solver.X)
*/
rmatrixtrsv(kx*ky, &ata, 0, 0, ae_true, ae_false, 1, &solver.mtv, 0, _state);
}
}
linlsqrresults(&solver, &tmp1, &solverrep, _state);
rmatrixtrsv(kx*ky, &ata, 0, 0, ae_true, ae_false, 0, &tmp1, 0, _state);
for(i=0; i<=kx*ky-1; i++)
{
z->ptr.p_double[kx*ky*j+i] = tmp1.ptr.p_double[i];
}
/*
* Calculate model values
*/
sparsemv(av, &tmp1, &tmp0, _state);
for(i=0; i<=npoints-1; i++)
{
xy->ptr.p_double[i*ew+2+j] = xy->ptr.p_double[i*ew+2+j]-tmp0.ptr.p_double[i];
}
}
else
{
/*
* Iterative refinement, inferior to LSQR
*
* For each dimension D:
* * fetch current estimate for solution from Z to Tmp1
* * calculate residual r for current estimate, store in Tmp0
* * calculate product of residual and design matrix A'*r, store it in Tmp1
* * Cholesky solver
* * update current estimate
*/
for(rfsidx=1; rfsidx<=-lsqrcnt; rfsidx++)
{
for(i=0; i<=kx*ky-1; i++)
{
tmp1.ptr.p_double[i] = z->ptr.p_double[kx*ky*j+i];
}
sparsemv(av, &tmp1, &tmp0, _state);
for(i=0; i<=arows-1; i++)
{
if( i<npoints )
{
v = xy->ptr.p_double[i*ew+2+j];
}
else
{
v = (double)(0);
}
tmp0.ptr.p_double[i] = v-tmp0.ptr.p_double[i];
}
sparsemv(ah, &tmp0, &tmp1, _state);
rmatrixtrsv(kx*ky, &ata, 0, 0, ae_true, ae_false, 1, &tmp1, 0, _state);
rmatrixtrsv(kx*ky, &ata, 0, 0, ae_true, ae_false, 0, &tmp1, 0, _state);
for(i=0; i<=kx*ky-1; i++)
{
z->ptr.p_double[kx*ky*j+i] = z->ptr.p_double[kx*ky*j+i]+tmp1.ptr.p_double[i];
}
}
/*
* Calculate model values
*/
for(i=0; i<=kx*ky-1; i++)
{
tmp1.ptr.p_double[i] = z->ptr.p_double[kx*ky*j+i];
}
sparsemv(av, &tmp1, &tmp0, _state);
for(i=0; i<=npoints-1; i++)
{
xy->ptr.p_double[i*ew+2+j] = xy->ptr.p_double[i*ew+2+j]-tmp0.ptr.p_double[i];
}
}
}
/*
* Generate report
*/
rep->rmserror = (double)(0);
rep->avgerror = (double)(0);
rep->maxerror = (double)(0);
rss = 0.0;
for(i=0; i<=npoints-1; i++)
{
for(j=0; j<=d-1; j++)
{
v = xy->ptr.p_double[i*ew+2+j];
rss = rss+v*v;
rep->rmserror = rep->rmserror+ae_sqr(v, _state);
rep->avgerror = rep->avgerror+ae_fabs(v, _state);
rep->maxerror = ae_maxreal(rep->maxerror, ae_fabs(v, _state), _state);
}
}
rep->rmserror = ae_sqrt(rep->rmserror/coalesce((double)(npoints*d), 1.0, _state), _state);
rep->avgerror = rep->avgerror/coalesce((double)(npoints*d), 1.0, _state);
rep->r2 = 1.0-rss/coalesce(tss, 1.0, _state);
ae_frame_leave(_state);
}
/*************************************************************************
This is convenience function for band block storage format; it returns
offset of KX*KX-sized block (I,J) in a compressed 2D array.
For specific offset=OFFSET,
block (I,J) will be stored in entries BlockMatrix[OFFSET:OFFSET+KX-1,0:KX-1]
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static ae_int_t spline2d_getcelloffset(ae_int_t kx,
ae_int_t ky,
ae_int_t blockbandwidth,
ae_int_t i,
ae_int_t j,
ae_state *_state)
{
ae_int_t result;
ae_assert(i>=0&&i<ky, "Spline2DFit: GetCellOffset() integrity error", _state);
ae_assert(j>=0&&j<ky, "Spline2DFit: GetCellOffset() integrity error", _state);
ae_assert(j>=i&&j<=i+blockbandwidth, "Spline2DFit: GetCellOffset() integrity error", _state);
result = j*(blockbandwidth+1)*kx;
result = result+(blockbandwidth-(j-i))*kx;
return result;
}
/*************************************************************************
This is convenience function for band block storage format; it copies
cell (I,J) from compressed format to uncompressed general matrix, at desired
position.
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_copycellto(ae_int_t kx,
ae_int_t ky,
ae_int_t blockbandwidth,
/* Real */ ae_matrix* blockata,
ae_int_t i,
ae_int_t j,
/* Real */ ae_matrix* dst,
ae_int_t dst0,
ae_int_t dst1,
ae_state *_state)
{
ae_int_t celloffset;
ae_int_t idx0;
ae_int_t idx1;
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, i, j, _state);
for(idx0=0; idx0<=kx-1; idx0++)
{
for(idx1=0; idx1<=kx-1; idx1++)
{
dst->ptr.pp_double[dst0+idx0][dst1+idx1] = blockata->ptr.pp_double[celloffset+idx0][idx1];
}
}
}
/*************************************************************************
This is convenience function for band block storage format; it
truncates all elements of cell (I,J) which are less than Eps in magnitude.
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_flushtozerocell(ae_int_t kx,
ae_int_t ky,
ae_int_t blockbandwidth,
/* Real */ ae_matrix* blockata,
ae_int_t i,
ae_int_t j,
double eps,
ae_state *_state)
{
ae_int_t celloffset;
ae_int_t idx0;
ae_int_t idx1;
double eps2;
double v;
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, i, j, _state);
eps2 = eps*eps;
for(idx0=0; idx0<=kx-1; idx0++)
{
for(idx1=0; idx1<=kx-1; idx1++)
{
v = blockata->ptr.pp_double[celloffset+idx0][idx1];
if( v*v<eps2 )
{
blockata->ptr.pp_double[celloffset+idx0][idx1] = (double)(0);
}
}
}
}
/*************************************************************************
This function generates squared design matrix stored in block band format.
We use adaptation of block skyline storage format, with
TOWERSIZE*KX skyline bands (towers) stored sequentially;
here TOWERSIZE=(BlockBandwidth+1)*KX. So, we have KY
"towers", stored one below other, in BlockATA matrix.
Every "tower" is a sequence of BlockBandwidth+1 cells,
each of them being KX*KX in size.
INPUT PARAMETERS:
AH - sparse matrix, [KX*KY,ARows] in size. "Horizontal" version
of design matrix, cols [0,NPoints] contain values of basis
functions at dataset points. Other cols are used for
nonlinearity penalty and other stuff like that.
KY0, KY1- subset of output matrix bands to process; on entry it MUST
be set to 0 and KY respectively.
KX, KY - grid size
BlockATA- array[KY*(BlockBandwidth+1)*KX,KX], preallocated storage
for output matrix in compressed block band format
MXATA - on entry MUST be zero
OUTPUT PARAMETERS:
BlockATA- AH*AH', stored in compressed block band format
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_blockllsgenerateata(sparsematrix* ah,
ae_int_t ky0,
ae_int_t ky1,
ae_int_t kx,
ae_int_t ky,
/* Real */ ae_matrix* blockata,
sreal* mxata,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t blockbandwidth;
double avgrowlen;
double cellcost;
double totalcost;
sreal tmpmxata;
ae_int_t i;
ae_int_t j;
ae_int_t i0;
ae_int_t i1;
ae_int_t j0;
ae_int_t j1;
ae_int_t celloffset;
double v;
ae_int_t srci;
ae_int_t srcj;
ae_int_t idxi;
ae_int_t idxj;
ae_int_t endi;
ae_int_t endj;
ae_frame_make(_state, &_frame_block);
memset(&tmpmxata, 0, sizeof(tmpmxata));
_sreal_init(&tmpmxata, _state, ae_true);
ae_assert(ae_fp_greater_eq(mxata->val,(double)(0)), "BlockLLSGenerateATA: integrity check failed", _state);
blockbandwidth = 3;
/*
* Determine problem cost, perform recursive subdivision
* (with optional parallelization)
*/
avgrowlen = (double)ah->ridx.ptr.p_int[kx*ky]/(double)(kx*ky);
cellcost = rmul3((double)(kx), (double)(1+2*blockbandwidth), avgrowlen, _state);
totalcost = rmul3((double)(ky1-ky0), (double)(1+2*blockbandwidth), cellcost, _state);
if( ky1-ky0>=2&&ae_fp_greater(totalcost,smpactivationlevel(_state)) )
{
if( _trypexec_spline2d_blockllsgenerateata(ah,ky0,ky1,kx,ky,blockata,mxata, _state) )
{
ae_frame_leave(_state);
return;
}
}
if( ky1-ky0>=2 )
{
/*
* Split X: X*A = (X1 X2)^T*A
*/
j = (ky1-ky0)/2;
spline2d_blockllsgenerateata(ah, ky0, ky0+j, kx, ky, blockata, &tmpmxata, _state);
spline2d_blockllsgenerateata(ah, ky0+j, ky1, kx, ky, blockata, mxata, _state);
mxata->val = ae_maxreal(mxata->val, tmpmxata.val, _state);
ae_frame_leave(_state);
return;
}
/*
* Splitting in Y-dimension is done, fill I1-th "tower"
*/
ae_assert(ky1==ky0+1, "BlockLLSGenerateATA: integrity check failed", _state);
i1 = ky0;
for(j1=i1; j1<=ae_minint(ky-1, i1+blockbandwidth, _state); j1++)
{
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, i1, j1, _state);
/*
* Clear cell (I1,J1)
*/
for(i0=0; i0<=kx-1; i0++)
{
for(j0=0; j0<=kx-1; j0++)
{
blockata->ptr.pp_double[celloffset+i0][j0] = 0.0;
}
}
/*
* Initialize cell internals
*/
for(i0=0; i0<=kx-1; i0++)
{
for(j0=0; j0<=kx-1; j0++)
{
if( ae_iabs(i0-j0, _state)<=blockbandwidth )
{
/*
* Nodes are close enough, calculate product of columns I and J of A.
*/
v = (double)(0);
i = i1*kx+i0;
j = j1*kx+j0;
srci = ah->ridx.ptr.p_int[i];
srcj = ah->ridx.ptr.p_int[j];
endi = ah->ridx.ptr.p_int[i+1];
endj = ah->ridx.ptr.p_int[j+1];
for(;;)
{
if( srci>=endi||srcj>=endj )
{
break;
}
idxi = ah->idx.ptr.p_int[srci];
idxj = ah->idx.ptr.p_int[srcj];
if( idxi==idxj )
{
v = v+ah->vals.ptr.p_double[srci]*ah->vals.ptr.p_double[srcj];
srci = srci+1;
srcj = srcj+1;
continue;
}
if( idxi<idxj )
{
srci = srci+1;
}
else
{
srcj = srcj+1;
}
}
blockata->ptr.pp_double[celloffset+i0][j0] = v;
mxata->val = ae_maxreal(mxata->val, ae_fabs(v, _state), _state);
}
}
}
}
ae_frame_leave(_state);
}
/*************************************************************************
Serial stub for GPL edition.
*************************************************************************/
ae_bool _trypexec_spline2d_blockllsgenerateata(sparsematrix* ah,
ae_int_t ky0,
ae_int_t ky1,
ae_int_t kx,
ae_int_t ky,
/* Real */ ae_matrix* blockata,
sreal* mxata,
ae_state *_state)
{
return ae_false;
}
/*************************************************************************
This function performs Cholesky decomposition of squared design matrix
stored in block band format.
INPUT PARAMETERS:
BlockATA - array[KY*(BlockBandwidth+1)*KX,KX], matrix in compressed
block band format
KX, KY - grid size
TrsmBuf2,
CholBuf2,
CholBuf1 - buffers; reused by this function on subsequent calls,
automatically preallocated on the first call
OUTPUT PARAMETERS:
BlockATA- Cholesky factor, in compressed block band format
Result:
True on success, False on Cholesky failure
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static ae_bool spline2d_blockllscholesky(/* Real */ ae_matrix* blockata,
ae_int_t kx,
ae_int_t ky,
/* Real */ ae_matrix* trsmbuf2,
/* Real */ ae_matrix* cholbuf2,
/* Real */ ae_vector* cholbuf1,
ae_state *_state)
{
ae_int_t blockbandwidth;
ae_int_t blockidx;
ae_int_t i;
ae_int_t j;
ae_int_t celloffset;
ae_int_t celloffset1;
ae_bool result;
blockbandwidth = 3;
rmatrixsetlengthatleast(trsmbuf2, (blockbandwidth+1)*kx, (blockbandwidth+1)*kx, _state);
rmatrixsetlengthatleast(cholbuf2, kx, kx, _state);
rvectorsetlengthatleast(cholbuf1, kx, _state);
result = ae_true;
for(blockidx=0; blockidx<=ky-1; blockidx++)
{
/*
* TRSM for TRAIL*TRAIL block matrix before current cell;
* here TRAIL=MinInt(BlockIdx,BlockBandwidth).
*/
for(i=0; i<=ae_minint(blockidx, blockbandwidth, _state)-1; i++)
{
for(j=i; j<=ae_minint(blockidx, blockbandwidth, _state)-1; j++)
{
spline2d_copycellto(kx, ky, blockbandwidth, blockata, ae_maxint(blockidx-blockbandwidth, 0, _state)+i, ae_maxint(blockidx-blockbandwidth, 0, _state)+j, trsmbuf2, i*kx, j*kx, _state);
}
}
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, ae_maxint(blockidx-blockbandwidth, 0, _state), blockidx, _state);
rmatrixlefttrsm(ae_minint(blockidx, blockbandwidth, _state)*kx, kx, trsmbuf2, 0, 0, ae_true, ae_false, 1, blockata, celloffset, 0, _state);
/*
* SYRK for diagonal cell: MaxInt(BlockIdx-BlockBandwidth,0)
* cells above diagonal one are used for update.
*/
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, ae_maxint(blockidx-blockbandwidth, 0, _state), blockidx, _state);
celloffset1 = spline2d_getcelloffset(kx, ky, blockbandwidth, blockidx, blockidx, _state);
rmatrixsyrk(kx, ae_minint(blockidx, blockbandwidth, _state)*kx, -1.0, blockata, celloffset, 0, 1, 1.0, blockata, celloffset1, 0, ae_true, _state);
/*
* Factorize diagonal cell
*/
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, blockidx, blockidx, _state);
rmatrixcopy(kx, kx, blockata, celloffset, 0, cholbuf2, 0, 0, _state);
if( !spdmatrixcholeskyrec(cholbuf2, 0, kx, ae_true, cholbuf1, _state) )
{
result = ae_false;
return result;
}
rmatrixcopy(kx, kx, cholbuf2, 0, 0, blockata, celloffset, 0, _state);
/*
* PERFORMANCE TWEAK: drop nearly-denormals from last "tower".
*
* Sparse matrices like these may produce denormal numbers on
* sparse datasets, with significant (10x!) performance penalty
* on Intel chips. In order to avoid it, we manually truncate
* small enough numbers.
*
* We use 1.0E-50 as clipping level (not really denormal, but
* such small numbers are not actually important anyway).
*/
for(i=ae_maxint(blockidx-blockbandwidth, 0, _state); i<=blockidx; i++)
{
spline2d_flushtozerocell(kx, ky, blockbandwidth, blockata, i, blockidx, 1.0E-50, _state);
}
}
return result;
}
/*************************************************************************
This function performs TRSV on upper triangular Cholesky factor U, solving
either U*x=b or U'*x=b.
INPUT PARAMETERS:
BlockATA - array[KY*(BlockBandwidth+1)*KX,KX], matrix U
in compressed block band format
KX, KY - grid size
TransU - whether to transpose U or not
B - array[KX*KY], on entry - stores right part B
OUTPUT PARAMETERS:
B - replaced by X
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_blockllstrsv(/* Real */ ae_matrix* blockata,
ae_int_t kx,
ae_int_t ky,
ae_bool transu,
/* Real */ ae_vector* b,
ae_state *_state)
{
ae_int_t blockbandwidth;
ae_int_t blockidx;
ae_int_t blockidx1;
ae_int_t celloffset;
blockbandwidth = 3;
if( !transu )
{
/*
* Solve U*x=b
*/
for(blockidx=ky-1; blockidx>=0; blockidx--)
{
for(blockidx1=1; blockidx1<=ae_minint(ky-(blockidx+1), blockbandwidth, _state); blockidx1++)
{
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, blockidx, blockidx+blockidx1, _state);
rmatrixgemv(kx, kx, -1.0, blockata, celloffset, 0, 0, b, (blockidx+blockidx1)*kx, 1.0, b, blockidx*kx, _state);
}
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, blockidx, blockidx, _state);
rmatrixtrsv(kx, blockata, celloffset, 0, ae_true, ae_false, 0, b, blockidx*kx, _state);
}
}
else
{
/*
* Solve U'*x=b
*/
for(blockidx=0; blockidx<=ky-1; blockidx++)
{
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, blockidx, blockidx, _state);
rmatrixtrsv(kx, blockata, celloffset, 0, ae_true, ae_false, 1, b, blockidx*kx, _state);
for(blockidx1=1; blockidx1<=ae_minint(ky-(blockidx+1), blockbandwidth, _state); blockidx1++)
{
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, blockidx, blockidx+blockidx1, _state);
rmatrixgemv(kx, kx, -1.0, blockata, celloffset, 0, 1, b, blockidx*kx, 1.0, b, (blockidx+blockidx1)*kx, _state);
}
}
}
}
/*************************************************************************
This function computes residuals for dataset XY[], using array of original
values YRaw[], and loads residuals to XY.
Processing is performed in parallel manner.
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_computeresidualsfromscratch(/* Real */ ae_vector* xy,
/* Real */ ae_vector* yraw,
ae_int_t npoints,
ae_int_t d,
ae_int_t scalexy,
spline2dinterpolant* spline,
ae_state *_state)
{
ae_frame _frame_block;
srealarray seed;
ae_shared_pool pool;
ae_int_t chunksize;
double pointcost;
ae_frame_make(_state, &_frame_block);
memset(&seed, 0, sizeof(seed));
memset(&pool, 0, sizeof(pool));
_srealarray_init(&seed, _state, ae_true);
ae_shared_pool_init(&pool, _state, ae_true);
/*
* Setting up
*/
chunksize = 1000;
pointcost = 100.0;
if( ae_fp_greater(npoints*pointcost,smpactivationlevel(_state)) )
{
if( _trypexec_spline2d_computeresidualsfromscratch(xy,yraw,npoints,d,scalexy,spline, _state) )
{
ae_frame_leave(_state);
return;
}
}
ae_shared_pool_set_seed(&pool, &seed, sizeof(seed), _srealarray_init, _srealarray_init_copy, _srealarray_destroy, _state);
/*
* Call compute workhorse
*/
spline2d_computeresidualsfromscratchrec(xy, yraw, 0, npoints, chunksize, d, scalexy, spline, &pool, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Serial stub for GPL edition.
*************************************************************************/
ae_bool _trypexec_spline2d_computeresidualsfromscratch(/* Real */ ae_vector* xy,
/* Real */ ae_vector* yraw,
ae_int_t npoints,
ae_int_t d,
ae_int_t scalexy,
spline2dinterpolant* spline,
ae_state *_state)
{
return ae_false;
}
/*************************************************************************
Recursive workhorse for ComputeResidualsFromScratch.
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_computeresidualsfromscratchrec(/* Real */ ae_vector* xy,
/* Real */ ae_vector* yraw,
ae_int_t pt0,
ae_int_t pt1,
ae_int_t chunksize,
ae_int_t d,
ae_int_t scalexy,
spline2dinterpolant* spline,
ae_shared_pool* pool,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_int_t j;
srealarray *pbuf;
ae_smart_ptr _pbuf;
ae_int_t xew;
ae_frame_make(_state, &_frame_block);
memset(&_pbuf, 0, sizeof(_pbuf));
ae_smart_ptr_init(&_pbuf, (void**)&pbuf, _state, ae_true);
xew = 2+d;
/*
* Parallelism
*/
if( pt1-pt0>chunksize )
{
tiledsplit(pt1-pt0, chunksize, &i, &j, _state);
spline2d_computeresidualsfromscratchrec(xy, yraw, pt0, pt0+i, chunksize, d, scalexy, spline, pool, _state);
spline2d_computeresidualsfromscratchrec(xy, yraw, pt0+i, pt1, chunksize, d, scalexy, spline, pool, _state);
ae_frame_leave(_state);
return;
}
/*
* Serial execution
*/
ae_shared_pool_retrieve(pool, &_pbuf, _state);
for(i=pt0; i<=pt1-1; i++)
{
spline2dcalcvbuf(spline, xy->ptr.p_double[i*xew+0]*scalexy, xy->ptr.p_double[i*xew+1]*scalexy, &pbuf->val, _state);
for(j=0; j<=d-1; j++)
{
xy->ptr.p_double[i*xew+2+j] = yraw->ptr.p_double[i*d+j]-pbuf->val.ptr.p_double[j];
}
}
ae_shared_pool_recycle(pool, &_pbuf, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Serial stub for GPL edition.
*************************************************************************/
ae_bool _trypexec_spline2d_computeresidualsfromscratchrec(/* Real */ ae_vector* xy,
/* Real */ ae_vector* yraw,
ae_int_t pt0,
ae_int_t pt1,
ae_int_t chunksize,
ae_int_t d,
ae_int_t scalexy,
spline2dinterpolant* spline,
ae_shared_pool* pool,
ae_state *_state)
{
return ae_false;
}
/*************************************************************************
This function reorders dataset and builds index:
* it is assumed that all points have X in [0,KX-1], Y in [0,KY-1]
* area is divided into (KX-1)*(KY-1) cells
* all points are reordered in such way that points in same cell are stored
contiguously
* dataset index, array[(KX-1)*(KY-1)+1], is generated. Points of cell I
now have indexes XYIndex[I]..XYIndex[I+1]-1;
INPUT PARAMETERS:
XY - array[NPoints*(2+D)], dataset
KX, KY, D - grid size and dimensionality of the outputs
Shadow - shadow array[NPoints*NS], which is sorted together
with XY; if NS=0, it is not referenced at all.
NS - entry width of shadow array
BufI - possibly preallocated temporary buffer; resized if
needed.
OUTPUT PARAMETERS:
XY - reordered
XYIndex - array[(KX-1)*(KY-1)+1], dataset index
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_reorderdatasetandbuildindex(/* Real */ ae_vector* xy,
ae_int_t npoints,
ae_int_t d,
/* Real */ ae_vector* shadow,
ae_int_t ns,
ae_int_t kx,
ae_int_t ky,
/* Integer */ ae_vector* xyindex,
/* Integer */ ae_vector* bufi,
ae_state *_state)
{
ae_int_t i;
ae_int_t i0;
ae_int_t i1;
ae_int_t entrywidth;
/*
* Set up
*/
ae_assert(kx>=2, "Spline2DFit.ReorderDatasetAndBuildIndex: integrity check failed", _state);
ae_assert(ky>=2, "Spline2DFit.ReorderDatasetAndBuildIndex: integrity check failed", _state);
entrywidth = 2+d;
ivectorsetlengthatleast(xyindex, (kx-1)*(ky-1)+1, _state);
ivectorsetlengthatleast(bufi, npoints, _state);
for(i=0; i<=npoints-1; i++)
{
i0 = iboundval(ae_ifloor(xy->ptr.p_double[i*entrywidth+0], _state), 0, kx-2, _state);
i1 = iboundval(ae_ifloor(xy->ptr.p_double[i*entrywidth+1], _state), 0, ky-2, _state);
bufi->ptr.p_int[i] = i1*(kx-1)+i0;
}
/*
* Reorder
*/
spline2d_reorderdatasetandbuildindexrec(xy, d, shadow, ns, bufi, 0, npoints, xyindex, 0, (kx-1)*(ky-1), ae_true, _state);
xyindex->ptr.p_int[(kx-1)*(ky-1)] = npoints;
}
/*************************************************************************
This function multiplies all points in dataset by 2.0 and rebuilds index,
given previous index built for KX_prev=(KX-1)/2 and KY_prev=(KY-1)/2
INPUT PARAMETERS:
XY - array[NPoints*(2+D)], dataset BEFORE scaling
NPoints, D - dataset size and dimensionality of the outputs
Shadow - shadow array[NPoints*NS], which is sorted together
with XY; if NS=0, it is not referenced at all.
NS - entry width of shadow array
KX, KY - new grid dimensionality
XYIndex - index built for previous values of KX and KY
BufI - possibly preallocated temporary buffer; resized if
needed.
OUTPUT PARAMETERS:
XY - reordered and multiplied by 2.0
XYIndex - array[(KX-1)*(KY-1)+1], dataset index
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_rescaledatasetandrefineindex(/* Real */ ae_vector* xy,
ae_int_t npoints,
ae_int_t d,
/* Real */ ae_vector* shadow,
ae_int_t ns,
ae_int_t kx,
ae_int_t ky,
/* Integer */ ae_vector* xyindex,
/* Integer */ ae_vector* bufi,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector xyindexprev;
ae_frame_make(_state, &_frame_block);
memset(&xyindexprev, 0, sizeof(xyindexprev));
ae_vector_init(&xyindexprev, 0, DT_INT, _state, ae_true);
/*
* Set up
*/
ae_assert(kx>=2, "Spline2DFit.RescaleDataset2AndRefineIndex: integrity check failed", _state);
ae_assert(ky>=2, "Spline2DFit.RescaleDataset2AndRefineIndex: integrity check failed", _state);
ae_assert((kx-1)%2==0, "Spline2DFit.RescaleDataset2AndRefineIndex: integrity check failed", _state);
ae_assert((ky-1)%2==0, "Spline2DFit.RescaleDataset2AndRefineIndex: integrity check failed", _state);
ae_swap_vectors(xyindex, &xyindexprev);
ivectorsetlengthatleast(xyindex, (kx-1)*(ky-1)+1, _state);
ivectorsetlengthatleast(bufi, npoints, _state);
/*
* Refine
*/
spline2d_expandindexrows(xy, d, shadow, ns, bufi, 0, npoints, &xyindexprev, 0, (ky+1)/2-1, xyindex, kx, ky, ae_true, _state);
xyindex->ptr.p_int[(kx-1)*(ky-1)] = npoints;
/*
* Integrity check
*/
ae_frame_leave(_state);
}
/*************************************************************************
Recurrent divide-and-conquer indexing function
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_expandindexrows(/* Real */ ae_vector* xy,
ae_int_t d,
/* Real */ ae_vector* shadow,
ae_int_t ns,
/* Integer */ ae_vector* cidx,
ae_int_t pt0,
ae_int_t pt1,
/* Integer */ ae_vector* xyindexprev,
ae_int_t row0,
ae_int_t row1,
/* Integer */ ae_vector* xyindexnew,
ae_int_t kxnew,
ae_int_t kynew,
ae_bool rootcall,
ae_state *_state)
{
ae_int_t i;
ae_int_t entrywidth;
ae_int_t kxprev;
double v;
ae_int_t i0;
ae_int_t i1;
double efficiency;
double cost;
ae_int_t rowmid;
kxprev = (kxnew+1)/2;
entrywidth = 2+d;
efficiency = 0.1;
cost = d*(pt1-pt0+1)*(ae_log((double)(kxnew), _state)/ae_log((double)(2), _state))/efficiency;
ae_assert(xyindexprev->ptr.p_int[row0*(kxprev-1)+0]==pt0, "Spline2DFit.ExpandIndexRows: integrity check failed", _state);
ae_assert(xyindexprev->ptr.p_int[row1*(kxprev-1)+0]==pt1, "Spline2DFit.ExpandIndexRows: integrity check failed", _state);
/*
* Parallelism
*/
if( ((rootcall&&pt1-pt0>10000)&&row1-row0>=2)&&ae_fp_greater(cost,smpactivationlevel(_state)) )
{
if( _trypexec_spline2d_expandindexrows(xy,d,shadow,ns,cidx,pt0,pt1,xyindexprev,row0,row1,xyindexnew,kxnew,kynew,rootcall, _state) )
{
return;
}
}
/*
* Partition
*/
if( row1-row0>=2 )
{
tiledsplit(row1-row0, 1, &i0, &i1, _state);
rowmid = row0+i0;
spline2d_expandindexrows(xy, d, shadow, ns, cidx, pt0, xyindexprev->ptr.p_int[rowmid*(kxprev-1)+0], xyindexprev, row0, rowmid, xyindexnew, kxnew, kynew, ae_false, _state);
spline2d_expandindexrows(xy, d, shadow, ns, cidx, xyindexprev->ptr.p_int[rowmid*(kxprev-1)+0], pt1, xyindexprev, rowmid, row1, xyindexnew, kxnew, kynew, ae_false, _state);
return;
}
/*
* Serial execution
*/
for(i=pt0; i<=pt1-1; i++)
{
v = 2*xy->ptr.p_double[i*entrywidth+0];
xy->ptr.p_double[i*entrywidth+0] = v;
i0 = iboundval(ae_ifloor(v, _state), 0, kxnew-2, _state);
v = 2*xy->ptr.p_double[i*entrywidth+1];
xy->ptr.p_double[i*entrywidth+1] = v;
i1 = iboundval(ae_ifloor(v, _state), 0, kynew-2, _state);
cidx->ptr.p_int[i] = i1*(kxnew-1)+i0;
}
spline2d_reorderdatasetandbuildindexrec(xy, d, shadow, ns, cidx, pt0, pt1, xyindexnew, 2*row0*(kxnew-1)+0, 2*row1*(kxnew-1)+0, ae_false, _state);
}
/*************************************************************************
Serial stub for GPL edition.
*************************************************************************/
ae_bool _trypexec_spline2d_expandindexrows(/* Real */ ae_vector* xy,
ae_int_t d,
/* Real */ ae_vector* shadow,
ae_int_t ns,
/* Integer */ ae_vector* cidx,
ae_int_t pt0,
ae_int_t pt1,
/* Integer */ ae_vector* xyindexprev,
ae_int_t row0,
ae_int_t row1,
/* Integer */ ae_vector* xyindexnew,
ae_int_t kxnew,
ae_int_t kynew,
ae_bool rootcall,
ae_state *_state)
{
return ae_false;
}
/*************************************************************************
Recurrent divide-and-conquer indexing function
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_reorderdatasetandbuildindexrec(/* Real */ ae_vector* xy,
ae_int_t d,
/* Real */ ae_vector* shadow,
ae_int_t ns,
/* Integer */ ae_vector* cidx,
ae_int_t pt0,
ae_int_t pt1,
/* Integer */ ae_vector* xyindex,
ae_int_t idx0,
ae_int_t idx1,
ae_bool rootcall,
ae_state *_state)
{
ae_int_t entrywidth;
ae_int_t idxmid;
ae_int_t wrk0;
ae_int_t wrk1;
double efficiency;
double cost;
/*
* Efficiency - performance of the code when compared with that
* of linear algebra code.
*/
entrywidth = 2+d;
efficiency = 0.1;
cost = d*(pt1-pt0+1)*ae_log((double)(idx1-idx0+1), _state)/ae_log((double)(2), _state)/efficiency;
/*
* Parallelism
*/
if( ((rootcall&&pt1-pt0>10000)&&idx1-idx0>=2)&&ae_fp_greater(cost,smpactivationlevel(_state)) )
{
if( _trypexec_spline2d_reorderdatasetandbuildindexrec(xy,d,shadow,ns,cidx,pt0,pt1,xyindex,idx0,idx1,rootcall, _state) )
{
return;
}
}
/*
* Store left bound to XYIndex
*/
xyindex->ptr.p_int[idx0] = pt0;
/*
* Quick exit strategies
*/
if( idx1<=idx0+1 )
{
return;
}
if( pt0==pt1 )
{
for(idxmid=idx0+1; idxmid<=idx1-1; idxmid++)
{
xyindex->ptr.p_int[idxmid] = pt1;
}
return;
}
/*
* Select middle element
*/
idxmid = idx0+(idx1-idx0)/2;
ae_assert(idx0<idxmid&&idxmid<idx1, "Spline2D: integrity check failed", _state);
wrk0 = pt0;
wrk1 = pt1-1;
for(;;)
{
while(wrk0<pt1&&cidx->ptr.p_int[wrk0]<idxmid)
{
wrk0 = wrk0+1;
}
while(wrk1>=pt0&&cidx->ptr.p_int[wrk1]>=idxmid)
{
wrk1 = wrk1-1;
}
if( wrk1<=wrk0 )
{
break;
}
swapentries(xy, wrk0, wrk1, entrywidth, _state);
if( ns>0 )
{
swapentries(shadow, wrk0, wrk1, ns, _state);
}
swapelementsi(cidx, wrk0, wrk1, _state);
}
spline2d_reorderdatasetandbuildindexrec(xy, d, shadow, ns, cidx, pt0, wrk0, xyindex, idx0, idxmid, ae_false, _state);
spline2d_reorderdatasetandbuildindexrec(xy, d, shadow, ns, cidx, wrk0, pt1, xyindex, idxmid, idx1, ae_false, _state);
}
/*************************************************************************
Serial stub for GPL edition.
*************************************************************************/
ae_bool _trypexec_spline2d_reorderdatasetandbuildindexrec(/* Real */ ae_vector* xy,
ae_int_t d,
/* Real */ ae_vector* shadow,
ae_int_t ns,
/* Integer */ ae_vector* cidx,
ae_int_t pt0,
ae_int_t pt1,
/* Integer */ ae_vector* xyindex,
ae_int_t idx0,
ae_int_t idx1,
ae_bool rootcall,
ae_state *_state)
{
return ae_false;
}
/*************************************************************************
This function performs fitting with BlockLLS solver. Internal function,
never use it directly.
INPUT PARAMETERS:
XY - dataset, array[NPoints,2+D]
XYIndex - dataset index, see ReorderDatasetAndBuildIndex() for more info
KX0, KX1- X-indices of basis functions to select and fit;
range [KX0,KX1) is processed
KXTotal - total number of indexes in the entire grid
KY0, KY1- Y-indices of basis functions to select and fit;
range [KY0,KY1) is processed
KYTotal - total number of indexes in the entire grid
D - number of components in vector-valued spline, D>=1
LambdaReg- regularization coefficient
LambdaNS- nonlinearity penalty, exactly zero value is specially handled
(entire set of rows is not added to the matrix)
Basis1 - single-dimensional B-spline
OUTPUT PARAMETERS:
A - design matrix
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_xdesigngenerate(/* Real */ ae_vector* xy,
/* Integer */ ae_vector* xyindex,
ae_int_t kx0,
ae_int_t kx1,
ae_int_t kxtotal,
ae_int_t ky0,
ae_int_t ky1,
ae_int_t kytotal,
ae_int_t d,
double lambdareg,
double lambdans,
spline1dinterpolant* basis1,
spline2dxdesignmatrix* a,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t entrywidth;
ae_int_t i;
ae_int_t j;
ae_int_t j0;
ae_int_t j1;
ae_int_t k0;
ae_int_t k1;
ae_int_t kx;
ae_int_t ky;
ae_int_t rowsdone;
ae_int_t batchesdone;
ae_int_t pt0;
ae_int_t pt1;
ae_int_t base0;
ae_int_t base1;
ae_int_t baseidx;
ae_int_t nzshift;
ae_int_t nzwidth;
ae_matrix d2x;
ae_matrix d2y;
ae_matrix dxy;
double v;
double v0;
double v1;
double v2;
double w0;
double w1;
double w2;
ae_frame_make(_state, &_frame_block);
memset(&d2x, 0, sizeof(d2x));
memset(&d2y, 0, sizeof(d2y));
memset(&dxy, 0, sizeof(dxy));
ae_matrix_init(&d2x, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&d2y, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&dxy, 0, 0, DT_REAL, _state, ae_true);
nzshift = 1;
nzwidth = 4;
entrywidth = 2+d;
kx = kx1-kx0;
ky = ky1-ky0;
a->lambdareg = lambdareg;
a->blockwidth = 4;
a->kx = kx;
a->ky = ky;
a->d = d;
a->npoints = 0;
a->ndenserows = 0;
a->ndensebatches = 0;
a->maxbatch = 0;
for(j1=ky0; j1<=ky1-2; j1++)
{
for(j0=kx0; j0<=kx1-2; j0++)
{
i = xyindex->ptr.p_int[j1*(kxtotal-1)+j0+1]-xyindex->ptr.p_int[j1*(kxtotal-1)+j0];
a->npoints = a->npoints+i;
a->ndenserows = a->ndenserows+i;
a->ndensebatches = a->ndensebatches+1;
a->maxbatch = ae_maxint(a->maxbatch, i, _state);
}
}
if( ae_fp_neq(lambdans,(double)(0)) )
{
ae_assert(ae_fp_greater_eq(lambdans,(double)(0)), "Spline2DFit: integrity check failed", _state);
a->ndenserows = a->ndenserows+3*(kx-2)*(ky-2);
a->ndensebatches = a->ndensebatches+(kx-2)*(ky-2);
a->maxbatch = ae_maxint(a->maxbatch, 3, _state);
}
a->nrows = a->ndenserows+kx*ky;
rmatrixsetlengthatleast(&a->vals, a->ndenserows, a->blockwidth*a->blockwidth+d, _state);
ivectorsetlengthatleast(&a->batches, a->ndensebatches+1, _state);
ivectorsetlengthatleast(&a->batchbases, a->ndensebatches, _state);
/*
* Setup output counters
*/
batchesdone = 0;
rowsdone = 0;
/*
* Generate rows corresponding to dataset points
*/
ae_assert(kx>=nzwidth, "Spline2DFit: integrity check failed", _state);
ae_assert(ky>=nzwidth, "Spline2DFit: integrity check failed", _state);
rvectorsetlengthatleast(&a->tmp0, nzwidth, _state);
rvectorsetlengthatleast(&a->tmp1, nzwidth, _state);
a->batches.ptr.p_int[batchesdone] = 0;
for(j1=ky0; j1<=ky1-2; j1++)
{
for(j0=kx0; j0<=kx1-2; j0++)
{
pt0 = xyindex->ptr.p_int[j1*(kxtotal-1)+j0];
pt1 = xyindex->ptr.p_int[j1*(kxtotal-1)+j0+1];
base0 = iboundval(j0-kx0-nzshift, 0, kx-nzwidth, _state);
base1 = iboundval(j1-ky0-nzshift, 0, ky-nzwidth, _state);
baseidx = base1*kx+base0;
a->batchbases.ptr.p_int[batchesdone] = baseidx;
for(i=pt0; i<=pt1-1; i++)
{
for(k0=0; k0<=nzwidth-1; k0++)
{
a->tmp0.ptr.p_double[k0] = spline1dcalc(basis1, xy->ptr.p_double[i*entrywidth+0]-(base0+kx0+k0), _state);
}
for(k1=0; k1<=nzwidth-1; k1++)
{
a->tmp1.ptr.p_double[k1] = spline1dcalc(basis1, xy->ptr.p_double[i*entrywidth+1]-(base1+ky0+k1), _state);
}
for(k1=0; k1<=nzwidth-1; k1++)
{
for(k0=0; k0<=nzwidth-1; k0++)
{
a->vals.ptr.pp_double[rowsdone][k1*nzwidth+k0] = a->tmp0.ptr.p_double[k0]*a->tmp1.ptr.p_double[k1];
}
}
for(j=0; j<=d-1; j++)
{
a->vals.ptr.pp_double[rowsdone][nzwidth*nzwidth+j] = xy->ptr.p_double[i*entrywidth+2+j];
}
rowsdone = rowsdone+1;
}
batchesdone = batchesdone+1;
a->batches.ptr.p_int[batchesdone] = rowsdone;
}
}
/*
* Generate rows corresponding to nonlinearity penalty
*/
if( ae_fp_greater(lambdans,(double)(0)) )
{
/*
* Smoothing is applied. Because all grid nodes are same,
* we apply same smoothing kernel, which is calculated only
* once at the beginning of design matrix generation.
*/
ae_matrix_set_length(&d2x, 3, 3, _state);
ae_matrix_set_length(&d2y, 3, 3, _state);
ae_matrix_set_length(&dxy, 3, 3, _state);
for(j1=0; j1<=2; j1++)
{
for(j0=0; j0<=2; j0++)
{
d2x.ptr.pp_double[j0][j1] = 0.0;
d2y.ptr.pp_double[j0][j1] = 0.0;
dxy.ptr.pp_double[j0][j1] = 0.0;
}
}
for(k1=0; k1<=2; k1++)
{
for(k0=0; k0<=2; k0++)
{
spline1ddiff(basis1, (double)(-(k0-1)), &v0, &v1, &v2, _state);
spline1ddiff(basis1, (double)(-(k1-1)), &w0, &w1, &w2, _state);
d2x.ptr.pp_double[k0][k1] = d2x.ptr.pp_double[k0][k1]+v2*w0;
d2y.ptr.pp_double[k0][k1] = d2y.ptr.pp_double[k0][k1]+w2*v0;
dxy.ptr.pp_double[k0][k1] = dxy.ptr.pp_double[k0][k1]+v1*w1;
}
}
/*
* Now, kernel is ready - apply it to all inner nodes of the grid.
*/
for(j1=1; j1<=ky-2; j1++)
{
for(j0=1; j0<=kx-2; j0++)
{
base0 = imax2(j0-2, 0, _state);
base1 = imax2(j1-2, 0, _state);
baseidx = base1*kx+base0;
a->batchbases.ptr.p_int[batchesdone] = baseidx;
/*
* d2F/dx2 term
*/
v = lambdans;
for(j=0; j<=nzwidth*nzwidth+d-1; j++)
{
a->vals.ptr.pp_double[rowsdone][j] = (double)(0);
}
for(k1=j1-1; k1<=j1+1; k1++)
{
for(k0=j0-1; k0<=j0+1; k0++)
{
a->vals.ptr.pp_double[rowsdone][nzwidth*(k1-base1)+(k0-base0)] = v*d2x.ptr.pp_double[1+(k0-j0)][1+(k1-j1)];
}
}
rowsdone = rowsdone+1;
/*
* d2F/dy2 term
*/
v = lambdans;
for(j=0; j<=nzwidth*nzwidth+d-1; j++)
{
a->vals.ptr.pp_double[rowsdone][j] = (double)(0);
}
for(k1=j1-1; k1<=j1+1; k1++)
{
for(k0=j0-1; k0<=j0+1; k0++)
{
a->vals.ptr.pp_double[rowsdone][nzwidth*(k1-base1)+(k0-base0)] = v*d2y.ptr.pp_double[1+(k0-j0)][1+(k1-j1)];
}
}
rowsdone = rowsdone+1;
/*
* 2*d2F/dxdy term
*/
v = ae_sqrt((double)(2), _state)*lambdans;
for(j=0; j<=nzwidth*nzwidth+d-1; j++)
{
a->vals.ptr.pp_double[rowsdone][j] = (double)(0);
}
for(k1=j1-1; k1<=j1+1; k1++)
{
for(k0=j0-1; k0<=j0+1; k0++)
{
a->vals.ptr.pp_double[rowsdone][nzwidth*(k1-base1)+(k0-base0)] = v*dxy.ptr.pp_double[1+(k0-j0)][1+(k1-j1)];
}
}
rowsdone = rowsdone+1;
batchesdone = batchesdone+1;
a->batches.ptr.p_int[batchesdone] = rowsdone;
}
}
}
/*
* Integrity post-check
*/
ae_assert(batchesdone==a->ndensebatches, "Spline2DFit: integrity check failed", _state);
ae_assert(rowsdone==a->ndenserows, "Spline2DFit: integrity check failed", _state);
ae_frame_leave(_state);
}
/*************************************************************************
This function performs matrix-vector product of design matrix and dense
vector.
INPUT PARAMETERS:
A - design matrix, (a.nrows) X (a.kx*a.ky);
some fields of A are used for temporaries,
so it is non-constant.
X - array[A.KX*A.KY]
OUTPUT PARAMETERS:
Y - product, array[A.NRows], automatically allocated
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_xdesignmv(spline2dxdesignmatrix* a,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_int_t bidx;
ae_int_t i;
ae_int_t cnt;
double v;
ae_int_t baseidx;
ae_int_t outidx;
ae_int_t batchsize;
ae_int_t kx;
ae_int_t k0;
ae_int_t k1;
ae_int_t nzwidth;
nzwidth = 4;
ae_assert(a->blockwidth==nzwidth, "Spline2DFit: integrity check failed", _state);
ae_assert(x->cnt>=a->kx*a->ky, "Spline2DFit: integrity check failed", _state);
/*
* Prepare
*/
rvectorsetlengthatleast(y, a->nrows, _state);
rvectorsetlengthatleast(&a->tmp0, nzwidth*nzwidth, _state);
rvectorsetlengthatleast(&a->tmp1, a->maxbatch, _state);
kx = a->kx;
outidx = 0;
/*
* Process dense part
*/
for(bidx=0; bidx<=a->ndensebatches-1; bidx++)
{
if( a->batches.ptr.p_int[bidx+1]-a->batches.ptr.p_int[bidx]>0 )
{
batchsize = a->batches.ptr.p_int[bidx+1]-a->batches.ptr.p_int[bidx];
baseidx = a->batchbases.ptr.p_int[bidx];
for(k1=0; k1<=nzwidth-1; k1++)
{
for(k0=0; k0<=nzwidth-1; k0++)
{
a->tmp0.ptr.p_double[k1*nzwidth+k0] = x->ptr.p_double[baseidx+k1*kx+k0];
}
}
rmatrixgemv(batchsize, nzwidth*nzwidth, 1.0, &a->vals, a->batches.ptr.p_int[bidx], 0, 0, &a->tmp0, 0, 0.0, &a->tmp1, 0, _state);
for(i=0; i<=batchsize-1; i++)
{
y->ptr.p_double[outidx+i] = a->tmp1.ptr.p_double[i];
}
outidx = outidx+batchsize;
}
}
ae_assert(outidx==a->ndenserows, "Spline2DFit: integrity check failed", _state);
/*
* Process regularizer
*/
v = a->lambdareg;
cnt = a->kx*a->ky;
for(i=0; i<=cnt-1; i++)
{
y->ptr.p_double[outidx+i] = v*x->ptr.p_double[i];
}
outidx = outidx+cnt;
/*
* Post-check
*/
ae_assert(outidx==a->nrows, "Spline2DFit: integrity check failed", _state);
}
/*************************************************************************
This function performs matrix-vector product of transposed design matrix and dense
vector.
INPUT PARAMETERS:
A - design matrix, (a.nrows) X (a.kx*a.ky);
some fields of A are used for temporaries,
so it is non-constant.
X - array[A.NRows]
OUTPUT PARAMETERS:
Y - product, array[A.KX*A.KY], automatically allocated
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_xdesignmtv(spline2dxdesignmatrix* a,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_int_t bidx;
ae_int_t i;
ae_int_t cnt;
double v;
ae_int_t baseidx;
ae_int_t inidx;
ae_int_t batchsize;
ae_int_t kx;
ae_int_t k0;
ae_int_t k1;
ae_int_t nzwidth;
nzwidth = 4;
ae_assert(a->blockwidth==nzwidth, "Spline2DFit: integrity check failed", _state);
ae_assert(x->cnt>=a->nrows, "Spline2DFit: integrity check failed", _state);
/*
* Prepare
*/
rvectorsetlengthatleast(y, a->kx*a->ky, _state);
rvectorsetlengthatleast(&a->tmp0, nzwidth*nzwidth, _state);
rvectorsetlengthatleast(&a->tmp1, a->maxbatch, _state);
kx = a->kx;
inidx = 0;
cnt = a->kx*a->ky;
for(i=0; i<=cnt-1; i++)
{
y->ptr.p_double[i] = (double)(0);
}
/*
* Process dense part
*/
for(bidx=0; bidx<=a->ndensebatches-1; bidx++)
{
if( a->batches.ptr.p_int[bidx+1]-a->batches.ptr.p_int[bidx]>0 )
{
batchsize = a->batches.ptr.p_int[bidx+1]-a->batches.ptr.p_int[bidx];
baseidx = a->batchbases.ptr.p_int[bidx];
for(i=0; i<=batchsize-1; i++)
{
a->tmp1.ptr.p_double[i] = x->ptr.p_double[inidx+i];
}
rmatrixgemv(nzwidth*nzwidth, batchsize, 1.0, &a->vals, a->batches.ptr.p_int[bidx], 0, 1, &a->tmp1, 0, 0.0, &a->tmp0, 0, _state);
for(k1=0; k1<=nzwidth-1; k1++)
{
for(k0=0; k0<=nzwidth-1; k0++)
{
y->ptr.p_double[baseidx+k1*kx+k0] = y->ptr.p_double[baseidx+k1*kx+k0]+a->tmp0.ptr.p_double[k1*nzwidth+k0];
}
}
inidx = inidx+batchsize;
}
}
ae_assert(inidx==a->ndenserows, "Spline2DFit: integrity check failed", _state);
/*
* Process regularizer
*/
v = a->lambdareg;
cnt = a->kx*a->ky;
for(i=0; i<=cnt-1; i++)
{
y->ptr.p_double[i] = y->ptr.p_double[i]+v*x->ptr.p_double[inidx+i];
}
inidx = inidx+cnt;
/*
* Post-check
*/
ae_assert(inidx==a->nrows, "Spline2DFit: integrity check failed", _state);
}
/*************************************************************************
This function generates squared design matrix stored in block band format.
We use an adaptation of block skyline storage format, with
TOWERSIZE*KX skyline bands (towers) stored sequentially; here
TOWERSIZE=(BlockBandwidth+1)*KX. So, we have KY "towers", stored one below
other, in BlockATA matrix. Every "tower" is a sequence of BlockBandwidth+1
cells, each of them being KX*KX in size.
INPUT PARAMETERS:
A - design matrix; some of its fields are used for temporaries
BlockATA- array[KY*(BlockBandwidth+1)*KX,KX], preallocated storage
for output matrix in compressed block band format
OUTPUT PARAMETERS:
BlockATA- AH*AH', stored in compressed block band format
MXATA - max(|AH*AH'|), elementwise
-- ALGLIB --
Copyright 05.02.2018 by Bochkanov Sergey
*************************************************************************/
static void spline2d_xdesignblockata(spline2dxdesignmatrix* a,
/* Real */ ae_matrix* blockata,
double* mxata,
ae_state *_state)
{
ae_int_t blockbandwidth;
ae_int_t nzwidth;
ae_int_t kx;
ae_int_t ky;
ae_int_t i0;
ae_int_t i1;
ae_int_t j0;
ae_int_t j1;
ae_int_t celloffset;
ae_int_t bidx;
ae_int_t baseidx;
ae_int_t batchsize;
ae_int_t offs0;
ae_int_t offs1;
double v;
blockbandwidth = 3;
nzwidth = 4;
kx = a->kx;
ky = a->ky;
ae_assert(a->blockwidth==nzwidth, "Spline2DFit: integrity check failed", _state);
rmatrixsetlengthatleast(&a->tmp2, nzwidth*nzwidth, nzwidth*nzwidth, _state);
/*
* Initial zero-fill:
* * zero-fill ALL elements of BlockATA
* * zero-fill ALL elements of Tmp2
*
* Filling ALL elements, including unused ones, is essential for the
* purposes of calculating max(BlockATA).
*/
for(i1=0; i1<=ky-1; i1++)
{
for(i0=i1; i0<=ae_minint(ky-1, i1+blockbandwidth, _state); i0++)
{
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, i1, i0, _state);
for(j1=0; j1<=kx-1; j1++)
{
for(j0=0; j0<=kx-1; j0++)
{
blockata->ptr.pp_double[celloffset+j1][j0] = 0.0;
}
}
}
}
for(j1=0; j1<=nzwidth*nzwidth-1; j1++)
{
for(j0=0; j0<=nzwidth*nzwidth-1; j0++)
{
a->tmp2.ptr.pp_double[j1][j0] = 0.0;
}
}
/*
* Process dense part of A
*/
for(bidx=0; bidx<=a->ndensebatches-1; bidx++)
{
if( a->batches.ptr.p_int[bidx+1]-a->batches.ptr.p_int[bidx]>0 )
{
/*
* Generate 16x16 U = BATCH'*BATCH and add it to ATA.
*
* NOTE: it is essential that lower triangle of Tmp2 is
* filled by zeros.
*/
batchsize = a->batches.ptr.p_int[bidx+1]-a->batches.ptr.p_int[bidx];
rmatrixsyrk(nzwidth*nzwidth, batchsize, 1.0, &a->vals, a->batches.ptr.p_int[bidx], 0, 2, 0.0, &a->tmp2, 0, 0, ae_true, _state);
baseidx = a->batchbases.ptr.p_int[bidx];
for(i1=0; i1<=nzwidth-1; i1++)
{
for(j1=i1; j1<=nzwidth-1; j1++)
{
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, baseidx/kx+i1, baseidx/kx+j1, _state);
offs0 = baseidx%kx;
offs1 = baseidx%kx;
for(i0=0; i0<=nzwidth-1; i0++)
{
for(j0=0; j0<=nzwidth-1; j0++)
{
v = a->tmp2.ptr.pp_double[i1*nzwidth+i0][j1*nzwidth+j0];
blockata->ptr.pp_double[celloffset+offs1+i0][offs0+j0] = blockata->ptr.pp_double[celloffset+offs1+i0][offs0+j0]+v;
}
}
}
}
}
}
/*
* Process regularizer term
*/
for(i1=0; i1<=ky-1; i1++)
{
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, i1, i1, _state);
for(j1=0; j1<=kx-1; j1++)
{
blockata->ptr.pp_double[celloffset+j1][j1] = blockata->ptr.pp_double[celloffset+j1][j1]+ae_sqr(a->lambdareg, _state);
}
}
/*
* Calculate max(ATA)
*
* NOTE: here we rely on zero initialization of unused parts of
* BlockATA and Tmp2.
*/
*mxata = 0.0;
for(i1=0; i1<=ky-1; i1++)
{
for(i0=i1; i0<=ae_minint(ky-1, i1+blockbandwidth, _state); i0++)
{
celloffset = spline2d_getcelloffset(kx, ky, blockbandwidth, i1, i0, _state);
for(j1=0; j1<=kx-1; j1++)
{
for(j0=0; j0<=kx-1; j0++)
{
*mxata = ae_maxreal(*mxata, ae_fabs(blockata->ptr.pp_double[celloffset+j1][j0], _state), _state);
}
}
}
}
}
void _spline2dinterpolant_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
spline2dinterpolant *p = (spline2dinterpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->x, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->y, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->f, 0, DT_REAL, _state, make_automatic);
}
void _spline2dinterpolant_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
spline2dinterpolant *dst = (spline2dinterpolant*)_dst;
spline2dinterpolant *src = (spline2dinterpolant*)_src;
dst->stype = src->stype;
dst->n = src->n;
dst->m = src->m;
dst->d = src->d;
ae_vector_init_copy(&dst->x, &src->x, _state, make_automatic);
ae_vector_init_copy(&dst->y, &src->y, _state, make_automatic);
ae_vector_init_copy(&dst->f, &src->f, _state, make_automatic);
}
void _spline2dinterpolant_clear(void* _p)
{
spline2dinterpolant *p = (spline2dinterpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->x);
ae_vector_clear(&p->y);
ae_vector_clear(&p->f);
}
void _spline2dinterpolant_destroy(void* _p)
{
spline2dinterpolant *p = (spline2dinterpolant*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->x);
ae_vector_destroy(&p->y);
ae_vector_destroy(&p->f);
}
void _spline2dbuilder_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
spline2dbuilder *p = (spline2dbuilder*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->xy, 0, DT_REAL, _state, make_automatic);
}
void _spline2dbuilder_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
spline2dbuilder *dst = (spline2dbuilder*)_dst;
spline2dbuilder *src = (spline2dbuilder*)_src;
dst->priorterm = src->priorterm;
dst->priortermval = src->priortermval;
dst->areatype = src->areatype;
dst->xa = src->xa;
dst->xb = src->xb;
dst->ya = src->ya;
dst->yb = src->yb;
dst->gridtype = src->gridtype;
dst->kx = src->kx;
dst->ky = src->ky;
dst->smoothing = src->smoothing;
dst->nlayers = src->nlayers;
dst->solvertype = src->solvertype;
dst->lambdabase = src->lambdabase;
ae_vector_init_copy(&dst->xy, &src->xy, _state, make_automatic);
dst->npoints = src->npoints;
dst->d = src->d;
dst->sx = src->sx;
dst->sy = src->sy;
dst->adddegreeoffreedom = src->adddegreeoffreedom;
dst->interfacesize = src->interfacesize;
dst->lsqrcnt = src->lsqrcnt;
dst->maxcoresize = src->maxcoresize;
}
void _spline2dbuilder_clear(void* _p)
{
spline2dbuilder *p = (spline2dbuilder*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->xy);
}
void _spline2dbuilder_destroy(void* _p)
{
spline2dbuilder *p = (spline2dbuilder*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->xy);
}
void _spline2dfitreport_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
spline2dfitreport *p = (spline2dfitreport*)_p;
ae_touch_ptr((void*)p);
}
void _spline2dfitreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
spline2dfitreport *dst = (spline2dfitreport*)_dst;
spline2dfitreport *src = (spline2dfitreport*)_src;
dst->rmserror = src->rmserror;
dst->avgerror = src->avgerror;
dst->maxerror = src->maxerror;
dst->r2 = src->r2;
}
void _spline2dfitreport_clear(void* _p)
{
spline2dfitreport *p = (spline2dfitreport*)_p;
ae_touch_ptr((void*)p);
}
void _spline2dfitreport_destroy(void* _p)
{
spline2dfitreport *p = (spline2dfitreport*)_p;
ae_touch_ptr((void*)p);
}
void _spline2dxdesignmatrix_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
spline2dxdesignmatrix *p = (spline2dxdesignmatrix*)_p;
ae_touch_ptr((void*)p);
ae_matrix_init(&p->vals, 0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->batches, 0, DT_INT, _state, make_automatic);
ae_vector_init(&p->batchbases, 0, DT_INT, _state, make_automatic);
ae_vector_init(&p->tmp0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tmp1, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->tmp2, 0, 0, DT_REAL, _state, make_automatic);
}
void _spline2dxdesignmatrix_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
spline2dxdesignmatrix *dst = (spline2dxdesignmatrix*)_dst;
spline2dxdesignmatrix *src = (spline2dxdesignmatrix*)_src;
dst->blockwidth = src->blockwidth;
dst->kx = src->kx;
dst->ky = src->ky;
dst->npoints = src->npoints;
dst->nrows = src->nrows;
dst->ndenserows = src->ndenserows;
dst->ndensebatches = src->ndensebatches;
dst->d = src->d;
dst->maxbatch = src->maxbatch;
ae_matrix_init_copy(&dst->vals, &src->vals, _state, make_automatic);
ae_vector_init_copy(&dst->batches, &src->batches, _state, make_automatic);
ae_vector_init_copy(&dst->batchbases, &src->batchbases, _state, make_automatic);
dst->lambdareg = src->lambdareg;
ae_vector_init_copy(&dst->tmp0, &src->tmp0, _state, make_automatic);
ae_vector_init_copy(&dst->tmp1, &src->tmp1, _state, make_automatic);
ae_matrix_init_copy(&dst->tmp2, &src->tmp2, _state, make_automatic);
}
void _spline2dxdesignmatrix_clear(void* _p)
{
spline2dxdesignmatrix *p = (spline2dxdesignmatrix*)_p;
ae_touch_ptr((void*)p);
ae_matrix_clear(&p->vals);
ae_vector_clear(&p->batches);
ae_vector_clear(&p->batchbases);
ae_vector_clear(&p->tmp0);
ae_vector_clear(&p->tmp1);
ae_matrix_clear(&p->tmp2);
}
void _spline2dxdesignmatrix_destroy(void* _p)
{
spline2dxdesignmatrix *p = (spline2dxdesignmatrix*)_p;
ae_touch_ptr((void*)p);
ae_matrix_destroy(&p->vals);
ae_vector_destroy(&p->batches);
ae_vector_destroy(&p->batchbases);
ae_vector_destroy(&p->tmp0);
ae_vector_destroy(&p->tmp1);
ae_matrix_destroy(&p->tmp2);
}
void _spline2dblockllsbuf_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
spline2dblockllsbuf *p = (spline2dblockllsbuf*)_p;
ae_touch_ptr((void*)p);
_linlsqrstate_init(&p->solver, _state, make_automatic);
_linlsqrreport_init(&p->solverrep, _state, make_automatic);
ae_matrix_init(&p->blockata, 0, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->trsmbuf2, 0, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->cholbuf2, 0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->cholbuf1, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tmp0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tmp1, 0, DT_REAL, _state, make_automatic);
}
void _spline2dblockllsbuf_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
spline2dblockllsbuf *dst = (spline2dblockllsbuf*)_dst;
spline2dblockllsbuf *src = (spline2dblockllsbuf*)_src;
_linlsqrstate_init_copy(&dst->solver, &src->solver, _state, make_automatic);
_linlsqrreport_init_copy(&dst->solverrep, &src->solverrep, _state, make_automatic);
ae_matrix_init_copy(&dst->blockata, &src->blockata, _state, make_automatic);
ae_matrix_init_copy(&dst->trsmbuf2, &src->trsmbuf2, _state, make_automatic);
ae_matrix_init_copy(&dst->cholbuf2, &src->cholbuf2, _state, make_automatic);
ae_vector_init_copy(&dst->cholbuf1, &src->cholbuf1, _state, make_automatic);
ae_vector_init_copy(&dst->tmp0, &src->tmp0, _state, make_automatic);
ae_vector_init_copy(&dst->tmp1, &src->tmp1, _state, make_automatic);
}
void _spline2dblockllsbuf_clear(void* _p)
{
spline2dblockllsbuf *p = (spline2dblockllsbuf*)_p;
ae_touch_ptr((void*)p);
_linlsqrstate_clear(&p->solver);
_linlsqrreport_clear(&p->solverrep);
ae_matrix_clear(&p->blockata);
ae_matrix_clear(&p->trsmbuf2);
ae_matrix_clear(&p->cholbuf2);
ae_vector_clear(&p->cholbuf1);
ae_vector_clear(&p->tmp0);
ae_vector_clear(&p->tmp1);
}
void _spline2dblockllsbuf_destroy(void* _p)
{
spline2dblockllsbuf *p = (spline2dblockllsbuf*)_p;
ae_touch_ptr((void*)p);
_linlsqrstate_destroy(&p->solver);
_linlsqrreport_destroy(&p->solverrep);
ae_matrix_destroy(&p->blockata);
ae_matrix_destroy(&p->trsmbuf2);
ae_matrix_destroy(&p->cholbuf2);
ae_vector_destroy(&p->cholbuf1);
ae_vector_destroy(&p->tmp0);
ae_vector_destroy(&p->tmp1);
}
void _spline2dfastddmbuf_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
spline2dfastddmbuf *p = (spline2dfastddmbuf*)_p;
ae_touch_ptr((void*)p);
_spline2dxdesignmatrix_init(&p->xdesignmatrix, _state, make_automatic);
ae_vector_init(&p->tmp0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->tmpz, 0, DT_REAL, _state, make_automatic);
_spline2dfitreport_init(&p->dummyrep, _state, make_automatic);
_spline2dinterpolant_init(&p->localmodel, _state, make_automatic);
_spline2dblockllsbuf_init(&p->blockllsbuf, _state, make_automatic);
}
void _spline2dfastddmbuf_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
spline2dfastddmbuf *dst = (spline2dfastddmbuf*)_dst;
spline2dfastddmbuf *src = (spline2dfastddmbuf*)_src;
_spline2dxdesignmatrix_init_copy(&dst->xdesignmatrix, &src->xdesignmatrix, _state, make_automatic);
ae_vector_init_copy(&dst->tmp0, &src->tmp0, _state, make_automatic);
ae_vector_init_copy(&dst->tmpz, &src->tmpz, _state, make_automatic);
_spline2dfitreport_init_copy(&dst->dummyrep, &src->dummyrep, _state, make_automatic);
_spline2dinterpolant_init_copy(&dst->localmodel, &src->localmodel, _state, make_automatic);
_spline2dblockllsbuf_init_copy(&dst->blockllsbuf, &src->blockllsbuf, _state, make_automatic);
}
void _spline2dfastddmbuf_clear(void* _p)
{
spline2dfastddmbuf *p = (spline2dfastddmbuf*)_p;
ae_touch_ptr((void*)p);
_spline2dxdesignmatrix_clear(&p->xdesignmatrix);
ae_vector_clear(&p->tmp0);
ae_vector_clear(&p->tmpz);
_spline2dfitreport_clear(&p->dummyrep);
_spline2dinterpolant_clear(&p->localmodel);
_spline2dblockllsbuf_clear(&p->blockllsbuf);
}
void _spline2dfastddmbuf_destroy(void* _p)
{
spline2dfastddmbuf *p = (spline2dfastddmbuf*)_p;
ae_touch_ptr((void*)p);
_spline2dxdesignmatrix_destroy(&p->xdesignmatrix);
ae_vector_destroy(&p->tmp0);
ae_vector_destroy(&p->tmpz);
_spline2dfitreport_destroy(&p->dummyrep);
_spline2dinterpolant_destroy(&p->localmodel);
_spline2dblockllsbuf_destroy(&p->blockllsbuf);
}
#endif
#if defined(AE_COMPILE_RBFV1) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This function creates RBF model for a scalar (NY=1) or vector (NY>1)
function in a NX-dimensional space (NX=2 or NX=3).
INPUT PARAMETERS:
NX - dimension of the space, NX=2 or NX=3
NY - function dimension, NY>=1
OUTPUT PARAMETERS:
S - RBF model (initially equals to zero)
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfv1create(ae_int_t nx,
ae_int_t ny,
rbfv1model* s,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
_rbfv1model_clear(s);
ae_assert(nx==2||nx==3, "RBFCreate: NX<>2 and NX<>3", _state);
ae_assert(ny>=1, "RBFCreate: NY<1", _state);
s->nx = nx;
s->ny = ny;
s->nl = 0;
s->nc = 0;
ae_matrix_set_length(&s->v, ny, rbfv1_mxnx+1, _state);
for(i=0; i<=ny-1; i++)
{
for(j=0; j<=rbfv1_mxnx; j++)
{
s->v.ptr.pp_double[i][j] = (double)(0);
}
}
s->rmax = (double)(0);
}
/*************************************************************************
This function creates buffer structure which can be used to perform
parallel RBF model evaluations (with one RBF model instance being
used from multiple threads, as long as different threads use different
instances of buffer).
This buffer object can be used with rbftscalcbuf() function (here "ts"
stands for "thread-safe", "buf" is a suffix which denotes function which
reuses previously allocated output space).
How to use it:
* create RBF model structure with rbfcreate()
* load data, tune parameters
* call rbfbuildmodel()
* call rbfcreatecalcbuffer(), once per thread working with RBF model (you
should call this function only AFTER call to rbfbuildmodel(), see below
for more information)
* call rbftscalcbuf() from different threads, with each thread working
with its own copy of buffer object.
INPUT PARAMETERS
S - RBF model
OUTPUT PARAMETERS
Buf - external buffer.
IMPORTANT: buffer object should be used only with RBF model object which
was used to initialize buffer. Any attempt to use buffer with
different object is dangerous - you may get memory violation
error because sizes of internal arrays do not fit to dimensions
of RBF structure.
IMPORTANT: you should call this function only for model which was built
with rbfbuildmodel() function, after successful invocation of
rbfbuildmodel(). Sizes of some internal structures are
determined only after model is built, so buffer object created
before model construction stage will be useless (and any
attempt to use it will result in exception).
-- ALGLIB --
Copyright 02.04.2016 by Sergey Bochkanov
*************************************************************************/
void rbfv1createcalcbuffer(rbfv1model* s,
rbfv1calcbuffer* buf,
ae_state *_state)
{
_rbfv1calcbuffer_clear(buf);
kdtreecreaterequestbuffer(&s->tree, &buf->requestbuffer, _state);
}
/*************************************************************************
This function builds RBF model and returns report (contains some
information which can be used for evaluation of the algorithm properties).
Call to this function modifies RBF model by calculating its centers/radii/
weights and saving them into RBFModel structure. Initially RBFModel
contain zero coefficients, but after call to this function we will have
coefficients which were calculated in order to fit our dataset.
After you called this function you can call RBFCalc(), RBFGridCalc() and
other model calculation functions.
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
Rep - report:
* Rep.TerminationType:
* -5 - non-distinct basis function centers were detected,
interpolation aborted
* -4 - nonconvergence of the internal SVD solver
* 1 - successful termination
Fields are used for debugging purposes:
* Rep.IterationsCount - iterations count of the LSQR solver
* Rep.NMV - number of matrix-vector products
* Rep.ARows - rows count for the system matrix
* Rep.ACols - columns count for the system matrix
* Rep.ANNZ - number of significantly non-zero elements
(elements above some algorithm-determined threshold)
NOTE: failure to build model will leave current state of the structure
unchanged.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfv1buildmodel(/* Real */ ae_matrix* x,
/* Real */ ae_matrix* y,
ae_int_t n,
ae_int_t aterm,
ae_int_t algorithmtype,
ae_int_t nlayers,
double radvalue,
double radzvalue,
double lambdav,
double epsort,
double epserr,
ae_int_t maxits,
rbfv1model* s,
rbfv1report* rep,
ae_state *_state)
{
ae_frame _frame_block;
kdtree tree;
kdtree ctree;
ae_vector dist;
ae_vector xcx;
ae_matrix a;
ae_matrix v;
ae_matrix omega;
ae_matrix residualy;
ae_vector radius;
ae_matrix xc;
ae_int_t nc;
double rmax;
ae_vector tags;
ae_vector ctags;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t snnz;
ae_vector tmp0;
ae_vector tmp1;
ae_int_t layerscnt;
ae_bool modelstatus;
ae_frame_make(_state, &_frame_block);
memset(&tree, 0, sizeof(tree));
memset(&ctree, 0, sizeof(ctree));
memset(&dist, 0, sizeof(dist));
memset(&xcx, 0, sizeof(xcx));
memset(&a, 0, sizeof(a));
memset(&v, 0, sizeof(v));
memset(&omega, 0, sizeof(omega));
memset(&residualy, 0, sizeof(residualy));
memset(&radius, 0, sizeof(radius));
memset(&xc, 0, sizeof(xc));
memset(&tags, 0, sizeof(tags));
memset(&ctags, 0, sizeof(ctags));
memset(&tmp0, 0, sizeof(tmp0));
memset(&tmp1, 0, sizeof(tmp1));
_rbfv1report_clear(rep);
_kdtree_init(&tree, _state, ae_true);
_kdtree_init(&ctree, _state, ae_true);
ae_vector_init(&dist, 0, DT_REAL, _state, ae_true);
ae_vector_init(&xcx, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&a, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&v, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&omega, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&residualy, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&radius, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&xc, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tags, 0, DT_INT, _state, ae_true);
ae_vector_init(&ctags, 0, DT_INT, _state, ae_true);
ae_vector_init(&tmp0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp1, 0, DT_REAL, _state, ae_true);
ae_assert(s->nx==2||s->nx==3, "RBFBuildModel: S.NX<>2 or S.NX<>3!", _state);
/*
* Quick exit when we have no points
*/
if( n==0 )
{
rep->terminationtype = 1;
rep->iterationscount = 0;
rep->nmv = 0;
rep->arows = 0;
rep->acols = 0;
kdtreebuildtagged(&s->xc, &tags, 0, rbfv1_mxnx, 0, 2, &s->tree, _state);
ae_matrix_set_length(&s->xc, 0, 0, _state);
ae_matrix_set_length(&s->wr, 0, 0, _state);
s->nc = 0;
s->rmax = (double)(0);
ae_matrix_set_length(&s->v, s->ny, rbfv1_mxnx+1, _state);
for(i=0; i<=s->ny-1; i++)
{
for(j=0; j<=rbfv1_mxnx; j++)
{
s->v.ptr.pp_double[i][j] = (double)(0);
}
}
ae_frame_leave(_state);
return;
}
/*
* General case, N>0
*/
rep->annz = 0;
rep->iterationscount = 0;
rep->nmv = 0;
ae_vector_set_length(&xcx, rbfv1_mxnx, _state);
/*
* First model in a sequence - linear model.
* Residuals from linear regression are stored in the ResidualY variable
* (used later to build RBF models).
*/
ae_matrix_set_length(&residualy, n, s->ny, _state);
for(i=0; i<=n-1; i++)
{
for(j=0; j<=s->ny-1; j++)
{
residualy.ptr.pp_double[i][j] = y->ptr.pp_double[i][j];
}
}
if( !rbfv1_rbfv1buildlinearmodel(x, &residualy, n, s->ny, aterm, &v, _state) )
{
rep->terminationtype = -5;
ae_frame_leave(_state);
return;
}
/*
* Handle special case: multilayer model with NLayers=0.
* Quick exit.
*/
if( algorithmtype==2&&nlayers==0 )
{
rep->terminationtype = 1;
rep->iterationscount = 0;
rep->nmv = 0;
rep->arows = 0;
rep->acols = 0;
kdtreebuildtagged(&s->xc, &tags, 0, rbfv1_mxnx, 0, 2, &s->tree, _state);
ae_matrix_set_length(&s->xc, 0, 0, _state);
ae_matrix_set_length(&s->wr, 0, 0, _state);
s->nc = 0;
s->rmax = (double)(0);
ae_matrix_set_length(&s->v, s->ny, rbfv1_mxnx+1, _state);
for(i=0; i<=s->ny-1; i++)
{
for(j=0; j<=rbfv1_mxnx; j++)
{
s->v.ptr.pp_double[i][j] = v.ptr.pp_double[i][j];
}
}
ae_frame_leave(_state);
return;
}
/*
* Second model in a sequence - RBF term.
*
* NOTE: assignments below are not necessary, but without them
* MSVC complains about unitialized variables.
*/
nc = 0;
rmax = (double)(0);
layerscnt = 0;
modelstatus = ae_false;
if( algorithmtype==1 )
{
/*
* Add RBF model.
* This model uses local KD-trees to speed-up nearest neighbor searches.
*/
nc = n;
ae_matrix_set_length(&xc, nc, rbfv1_mxnx, _state);
for(i=0; i<=nc-1; i++)
{
for(j=0; j<=rbfv1_mxnx-1; j++)
{
xc.ptr.pp_double[i][j] = x->ptr.pp_double[i][j];
}
}
rmax = (double)(0);
ae_vector_set_length(&radius, nc, _state);
ae_vector_set_length(&ctags, nc, _state);
for(i=0; i<=nc-1; i++)
{
ctags.ptr.p_int[i] = i;
}
kdtreebuildtagged(&xc, &ctags, nc, rbfv1_mxnx, 0, 2, &ctree, _state);
if( nc==0 )
{
rmax = (double)(1);
}
else
{
if( nc==1 )
{
radius.ptr.p_double[0] = radvalue;
rmax = radius.ptr.p_double[0];
}
else
{
/*
* NC>1, calculate radii using distances to nearest neigbors
*/
for(i=0; i<=nc-1; i++)
{
for(j=0; j<=rbfv1_mxnx-1; j++)
{
xcx.ptr.p_double[j] = xc.ptr.pp_double[i][j];
}
if( kdtreequeryknn(&ctree, &xcx, 1, ae_false, _state)>0 )
{
kdtreequeryresultsdistances(&ctree, &dist, _state);
radius.ptr.p_double[i] = radvalue*dist.ptr.p_double[0];
}
else
{
/*
* No neighbors found (it will happen when we have only one center).
* Initialize radius with default value.
*/
radius.ptr.p_double[i] = 1.0;
}
}
/*
* Apply filtering
*/
rvectorsetlengthatleast(&tmp0, nc, _state);
for(i=0; i<=nc-1; i++)
{
tmp0.ptr.p_double[i] = radius.ptr.p_double[i];
}
tagsortfast(&tmp0, &tmp1, nc, _state);
for(i=0; i<=nc-1; i++)
{
radius.ptr.p_double[i] = ae_minreal(radius.ptr.p_double[i], radzvalue*tmp0.ptr.p_double[nc/2], _state);
}
/*
* Calculate RMax, check that all radii are non-zero
*/
for(i=0; i<=nc-1; i++)
{
rmax = ae_maxreal(rmax, radius.ptr.p_double[i], _state);
}
for(i=0; i<=nc-1; i++)
{
if( ae_fp_eq(radius.ptr.p_double[i],(double)(0)) )
{
rep->terminationtype = -5;
ae_frame_leave(_state);
return;
}
}
}
}
ivectorsetlengthatleast(&tags, n, _state);
for(i=0; i<=n-1; i++)
{
tags.ptr.p_int[i] = i;
}
kdtreebuildtagged(x, &tags, n, rbfv1_mxnx, 0, 2, &tree, _state);
rbfv1_buildrbfmodellsqr(x, &residualy, &xc, &radius, n, nc, s->ny, &tree, &ctree, epsort, epserr, maxits, &rep->annz, &snnz, &omega, &rep->terminationtype, &rep->iterationscount, &rep->nmv, _state);
layerscnt = 1;
modelstatus = ae_true;
}
if( algorithmtype==2 )
{
rmax = radvalue;
rbfv1_buildrbfmlayersmodellsqr(x, &residualy, &xc, radvalue, &radius, n, &nc, s->ny, nlayers, &ctree, 1.0E-6, 1.0E-6, 50, lambdav, &rep->annz, &omega, &rep->terminationtype, &rep->iterationscount, &rep->nmv, _state);
layerscnt = nlayers;
modelstatus = ae_true;
}
ae_assert(modelstatus, "RBFBuildModel: integrity error", _state);
if( rep->terminationtype<=0 )
{
ae_frame_leave(_state);
return;
}
/*
* Model is built
*/
s->nc = nc/layerscnt;
s->rmax = rmax;
s->nl = layerscnt;
ae_matrix_set_length(&s->xc, s->nc, rbfv1_mxnx, _state);
ae_matrix_set_length(&s->wr, s->nc, 1+s->nl*s->ny, _state);
ae_matrix_set_length(&s->v, s->ny, rbfv1_mxnx+1, _state);
for(i=0; i<=s->nc-1; i++)
{
for(j=0; j<=rbfv1_mxnx-1; j++)
{
s->xc.ptr.pp_double[i][j] = xc.ptr.pp_double[i][j];
}
}
ivectorsetlengthatleast(&tags, s->nc, _state);
for(i=0; i<=s->nc-1; i++)
{
tags.ptr.p_int[i] = i;
}
kdtreebuildtagged(&s->xc, &tags, s->nc, rbfv1_mxnx, 0, 2, &s->tree, _state);
for(i=0; i<=s->nc-1; i++)
{
s->wr.ptr.pp_double[i][0] = radius.ptr.p_double[i];
for(k=0; k<=layerscnt-1; k++)
{
for(j=0; j<=s->ny-1; j++)
{
s->wr.ptr.pp_double[i][1+k*s->ny+j] = omega.ptr.pp_double[k*s->nc+i][j];
}
}
}
for(i=0; i<=s->ny-1; i++)
{
for(j=0; j<=rbfv1_mxnx; j++)
{
s->v.ptr.pp_double[i][j] = v.ptr.pp_double[i][j];
}
}
rep->terminationtype = 1;
rep->arows = n;
rep->acols = s->nc;
ae_frame_leave(_state);
}
/*************************************************************************
Serializer: allocation
-- ALGLIB --
Copyright 02.02.2012 by Bochkanov Sergey
*************************************************************************/
void rbfv1alloc(ae_serializer* s, rbfv1model* model, ae_state *_state)
{
/*
* Data
*/
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
ae_serializer_alloc_entry(s);
kdtreealloc(s, &model->tree, _state);
allocrealmatrix(s, &model->xc, -1, -1, _state);
allocrealmatrix(s, &model->wr, -1, -1, _state);
ae_serializer_alloc_entry(s);
allocrealmatrix(s, &model->v, -1, -1, _state);
}
/*************************************************************************
Serializer: serialization
-- ALGLIB --
Copyright 02.02.2012 by Bochkanov Sergey
*************************************************************************/
void rbfv1serialize(ae_serializer* s, rbfv1model* model, ae_state *_state)
{
/*
* Data
*/
ae_serializer_serialize_int(s, model->nx, _state);
ae_serializer_serialize_int(s, model->ny, _state);
ae_serializer_serialize_int(s, model->nc, _state);
ae_serializer_serialize_int(s, model->nl, _state);
kdtreeserialize(s, &model->tree, _state);
serializerealmatrix(s, &model->xc, -1, -1, _state);
serializerealmatrix(s, &model->wr, -1, -1, _state);
ae_serializer_serialize_double(s, model->rmax, _state);
serializerealmatrix(s, &model->v, -1, -1, _state);
}
/*************************************************************************
Serializer: unserialization
-- ALGLIB --
Copyright 02.02.2012 by Bochkanov Sergey
*************************************************************************/
void rbfv1unserialize(ae_serializer* s,
rbfv1model* model,
ae_state *_state)
{
ae_int_t nx;
ae_int_t ny;
_rbfv1model_clear(model);
/*
* Unserialize primary model parameters, initialize model.
*
* It is necessary to call RBFCreate() because some internal fields
* which are NOT unserialized will need initialization.
*/
ae_serializer_unserialize_int(s, &nx, _state);
ae_serializer_unserialize_int(s, &ny, _state);
rbfv1create(nx, ny, model, _state);
ae_serializer_unserialize_int(s, &model->nc, _state);
ae_serializer_unserialize_int(s, &model->nl, _state);
kdtreeunserialize(s, &model->tree, _state);
unserializerealmatrix(s, &model->xc, _state);
unserializerealmatrix(s, &model->wr, _state);
ae_serializer_unserialize_double(s, &model->rmax, _state);
unserializerealmatrix(s, &model->v, _state);
}
/*************************************************************************
This function calculates values of the RBF model in the given point.
This function should be used when we have NY=1 (scalar function) and NX=2
(2-dimensional space). If you have 3-dimensional space, use RBFCalc3(). If
you have general situation (NX-dimensional space, NY-dimensional function)
you should use general, less efficient implementation RBFCalc().
If you want to calculate function values many times, consider using
RBFGridCalc2(), which is far more efficient than many subsequent calls to
RBFCalc2().
This function returns 0.0 when:
* model is not initialized
* NX<>2
*NY<>1
INPUT PARAMETERS:
S - RBF model
X0 - first coordinate, finite number
X1 - second coordinate, finite number
RESULT:
value of the model or 0.0 (as defined above)
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
double rbfv1calc2(rbfv1model* s, double x0, double x1, ae_state *_state)
{
ae_int_t i;
ae_int_t j;
ae_int_t lx;
ae_int_t tg;
double d2;
double t;
double bfcur;
double rcur;
double result;
ae_assert(ae_isfinite(x0, _state), "RBFCalc2: invalid value for X0 (X0 is Inf)!", _state);
ae_assert(ae_isfinite(x1, _state), "RBFCalc2: invalid value for X1 (X1 is Inf)!", _state);
if( s->ny!=1||s->nx!=2 )
{
result = (double)(0);
return result;
}
result = s->v.ptr.pp_double[0][0]*x0+s->v.ptr.pp_double[0][1]*x1+s->v.ptr.pp_double[0][rbfv1_mxnx];
if( s->nc==0 )
{
return result;
}
rvectorsetlengthatleast(&s->calcbufxcx, rbfv1_mxnx, _state);
for(i=0; i<=rbfv1_mxnx-1; i++)
{
s->calcbufxcx.ptr.p_double[i] = 0.0;
}
s->calcbufxcx.ptr.p_double[0] = x0;
s->calcbufxcx.ptr.p_double[1] = x1;
lx = kdtreequeryrnn(&s->tree, &s->calcbufxcx, s->rmax*rbfv1_rbffarradius, ae_true, _state);
kdtreequeryresultsx(&s->tree, &s->calcbufx, _state);
kdtreequeryresultstags(&s->tree, &s->calcbuftags, _state);
for(i=0; i<=lx-1; i++)
{
tg = s->calcbuftags.ptr.p_int[i];
d2 = ae_sqr(x0-s->calcbufx.ptr.pp_double[i][0], _state)+ae_sqr(x1-s->calcbufx.ptr.pp_double[i][1], _state);
rcur = s->wr.ptr.pp_double[tg][0];
bfcur = ae_exp(-d2/(rcur*rcur), _state);
for(j=0; j<=s->nl-1; j++)
{
result = result+bfcur*s->wr.ptr.pp_double[tg][1+j];
rcur = 0.5*rcur;
t = bfcur*bfcur;
bfcur = t*t;
}
}
return result;
}
/*************************************************************************
This function calculates values of the RBF model in the given point.
This function should be used when we have NY=1 (scalar function) and NX=3
(3-dimensional space). If you have 2-dimensional space, use RBFCalc2(). If
you have general situation (NX-dimensional space, NY-dimensional function)
you should use general, less efficient implementation RBFCalc().
This function returns 0.0 when:
* model is not initialized
* NX<>3
*NY<>1
INPUT PARAMETERS:
S - RBF model
X0 - first coordinate, finite number
X1 - second coordinate, finite number
X2 - third coordinate, finite number
RESULT:
value of the model or 0.0 (as defined above)
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
double rbfv1calc3(rbfv1model* s,
double x0,
double x1,
double x2,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
ae_int_t lx;
ae_int_t tg;
double t;
double rcur;
double bf;
double result;
ae_assert(ae_isfinite(x0, _state), "RBFCalc3: invalid value for X0 (X0 is Inf or NaN)!", _state);
ae_assert(ae_isfinite(x1, _state), "RBFCalc3: invalid value for X1 (X1 is Inf or NaN)!", _state);
ae_assert(ae_isfinite(x2, _state), "RBFCalc3: invalid value for X2 (X2 is Inf or NaN)!", _state);
if( s->ny!=1||s->nx!=3 )
{
result = (double)(0);
return result;
}
result = s->v.ptr.pp_double[0][0]*x0+s->v.ptr.pp_double[0][1]*x1+s->v.ptr.pp_double[0][2]*x2+s->v.ptr.pp_double[0][rbfv1_mxnx];
if( s->nc==0 )
{
return result;
}
/*
* calculating value for F(X)
*/
rvectorsetlengthatleast(&s->calcbufxcx, rbfv1_mxnx, _state);
for(i=0; i<=rbfv1_mxnx-1; i++)
{
s->calcbufxcx.ptr.p_double[i] = 0.0;
}
s->calcbufxcx.ptr.p_double[0] = x0;
s->calcbufxcx.ptr.p_double[1] = x1;
s->calcbufxcx.ptr.p_double[2] = x2;
lx = kdtreequeryrnn(&s->tree, &s->calcbufxcx, s->rmax*rbfv1_rbffarradius, ae_true, _state);
kdtreequeryresultsx(&s->tree, &s->calcbufx, _state);
kdtreequeryresultstags(&s->tree, &s->calcbuftags, _state);
for(i=0; i<=lx-1; i++)
{
tg = s->calcbuftags.ptr.p_int[i];
rcur = s->wr.ptr.pp_double[tg][0];
bf = ae_exp(-(ae_sqr(x0-s->calcbufx.ptr.pp_double[i][0], _state)+ae_sqr(x1-s->calcbufx.ptr.pp_double[i][1], _state)+ae_sqr(x2-s->calcbufx.ptr.pp_double[i][2], _state))/ae_sqr(rcur, _state), _state);
for(j=0; j<=s->nl-1; j++)
{
result = result+bf*s->wr.ptr.pp_double[tg][1+j];
t = bf*bf;
bf = t*t;
}
}
return result;
}
/*************************************************************************
This function calculates values of the RBF model at the given point.
Same as RBFCalc(), but does not reallocate Y when in is large enough to
store function values.
INPUT PARAMETERS:
S - RBF model
X - coordinates, array[NX].
X may have more than NX elements, in this case only
leading NX will be used.
Y - possibly preallocated array
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is not reallocated when it
is larger than NY.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfv1calcbuf(rbfv1model* s,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t lx;
ae_int_t tg;
double t;
double rcur;
double bf;
ae_assert(x->cnt>=s->nx, "RBFCalcBuf: Length(X)<NX", _state);
ae_assert(isfinitevector(x, s->nx, _state), "RBFCalcBuf: X contains infinite or NaN values", _state);
if( y->cnt<s->ny )
{
ae_vector_set_length(y, s->ny, _state);
}
for(i=0; i<=s->ny-1; i++)
{
y->ptr.p_double[i] = s->v.ptr.pp_double[i][rbfv1_mxnx];
for(j=0; j<=s->nx-1; j++)
{
y->ptr.p_double[i] = y->ptr.p_double[i]+s->v.ptr.pp_double[i][j]*x->ptr.p_double[j];
}
}
if( s->nc==0 )
{
return;
}
rvectorsetlengthatleast(&s->calcbufxcx, rbfv1_mxnx, _state);
for(i=0; i<=rbfv1_mxnx-1; i++)
{
s->calcbufxcx.ptr.p_double[i] = 0.0;
}
for(i=0; i<=s->nx-1; i++)
{
s->calcbufxcx.ptr.p_double[i] = x->ptr.p_double[i];
}
lx = kdtreequeryrnn(&s->tree, &s->calcbufxcx, s->rmax*rbfv1_rbffarradius, ae_true, _state);
kdtreequeryresultsx(&s->tree, &s->calcbufx, _state);
kdtreequeryresultstags(&s->tree, &s->calcbuftags, _state);
for(i=0; i<=s->ny-1; i++)
{
for(j=0; j<=lx-1; j++)
{
tg = s->calcbuftags.ptr.p_int[j];
rcur = s->wr.ptr.pp_double[tg][0];
bf = ae_exp(-(ae_sqr(s->calcbufxcx.ptr.p_double[0]-s->calcbufx.ptr.pp_double[j][0], _state)+ae_sqr(s->calcbufxcx.ptr.p_double[1]-s->calcbufx.ptr.pp_double[j][1], _state)+ae_sqr(s->calcbufxcx.ptr.p_double[2]-s->calcbufx.ptr.pp_double[j][2], _state))/ae_sqr(rcur, _state), _state);
for(k=0; k<=s->nl-1; k++)
{
y->ptr.p_double[i] = y->ptr.p_double[i]+bf*s->wr.ptr.pp_double[tg][1+k*s->ny+i];
t = bf*bf;
bf = t*t;
}
}
}
}
/*************************************************************************
This function calculates values of the RBF model at the given point, using
external buffer object (internal temporaries of RBF model are not
modified).
This function allows to use same RBF model object in different threads,
assuming that different threads use different instances of buffer
structure.
INPUT PARAMETERS:
S - RBF model, may be shared between different threads
Buf - buffer object created for this particular instance of RBF
model with rbfcreatecalcbuffer().
X - coordinates, array[NX].
X may have more than NX elements, in this case only
leading NX will be used.
Y - possibly preallocated array
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is not reallocated when it
is larger than NY.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfv1tscalcbuf(rbfv1model* s,
rbfv1calcbuffer* buf,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t lx;
ae_int_t tg;
double t;
double rcur;
double bf;
ae_assert(x->cnt>=s->nx, "RBFCalcBuf: Length(X)<NX", _state);
ae_assert(isfinitevector(x, s->nx, _state), "RBFCalcBuf: X contains infinite or NaN values", _state);
if( y->cnt<s->ny )
{
ae_vector_set_length(y, s->ny, _state);
}
for(i=0; i<=s->ny-1; i++)
{
y->ptr.p_double[i] = s->v.ptr.pp_double[i][rbfv1_mxnx];
for(j=0; j<=s->nx-1; j++)
{
y->ptr.p_double[i] = y->ptr.p_double[i]+s->v.ptr.pp_double[i][j]*x->ptr.p_double[j];
}
}
if( s->nc==0 )
{
return;
}
rvectorsetlengthatleast(&buf->calcbufxcx, rbfv1_mxnx, _state);
for(i=0; i<=rbfv1_mxnx-1; i++)
{
buf->calcbufxcx.ptr.p_double[i] = 0.0;
}
for(i=0; i<=s->nx-1; i++)
{
buf->calcbufxcx.ptr.p_double[i] = x->ptr.p_double[i];
}
lx = kdtreetsqueryrnn(&s->tree, &buf->requestbuffer, &buf->calcbufxcx, s->rmax*rbfv1_rbffarradius, ae_true, _state);
kdtreetsqueryresultsx(&s->tree, &buf->requestbuffer, &buf->calcbufx, _state);
kdtreetsqueryresultstags(&s->tree, &buf->requestbuffer, &buf->calcbuftags, _state);
for(i=0; i<=s->ny-1; i++)
{
for(j=0; j<=lx-1; j++)
{
tg = buf->calcbuftags.ptr.p_int[j];
rcur = s->wr.ptr.pp_double[tg][0];
bf = ae_exp(-(ae_sqr(buf->calcbufxcx.ptr.p_double[0]-buf->calcbufx.ptr.pp_double[j][0], _state)+ae_sqr(buf->calcbufxcx.ptr.p_double[1]-buf->calcbufx.ptr.pp_double[j][1], _state)+ae_sqr(buf->calcbufxcx.ptr.p_double[2]-buf->calcbufx.ptr.pp_double[j][2], _state))/ae_sqr(rcur, _state), _state);
for(k=0; k<=s->nl-1; k++)
{
y->ptr.p_double[i] = y->ptr.p_double[i]+bf*s->wr.ptr.pp_double[tg][1+k*s->ny+i];
t = bf*bf;
bf = t*t;
}
}
}
}
/*************************************************************************
This function calculates values of the RBF model at the regular grid.
Grid have N0*N1 points, with Point[I,J] = (X0[I], X1[J])
This function returns 0.0 when:
* model is not initialized
* NX<>2
*NY<>1
INPUT PARAMETERS:
S - RBF model
X0 - array of grid nodes, first coordinates, array[N0]
N0 - grid size (number of nodes) in the first dimension
X1 - array of grid nodes, second coordinates, array[N1]
N1 - grid size (number of nodes) in the second dimension
OUTPUT PARAMETERS:
Y - function values, array[N0,N1]. Y is out-variable and
is reallocated by this function.
NOTE: as a special exception, this function supports unordered arrays X0
and X1. However, future versions may be more efficient for X0/X1
ordered by ascending.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfv1gridcalc2(rbfv1model* s,
/* Real */ ae_vector* x0,
ae_int_t n0,
/* Real */ ae_vector* x1,
ae_int_t n1,
/* Real */ ae_matrix* y,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector cpx0;
ae_vector cpx1;
ae_vector p01;
ae_vector p11;
ae_vector p2;
double rlimit;
double xcnorm2;
ae_int_t hp01;
double hcpx0;
double xc0;
double xc1;
double omega;
double radius;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t d;
ae_int_t i00;
ae_int_t i01;
ae_int_t i10;
ae_int_t i11;
ae_frame_make(_state, &_frame_block);
memset(&cpx0, 0, sizeof(cpx0));
memset(&cpx1, 0, sizeof(cpx1));
memset(&p01, 0, sizeof(p01));
memset(&p11, 0, sizeof(p11));
memset(&p2, 0, sizeof(p2));
ae_matrix_clear(y);
ae_vector_init(&cpx0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&cpx1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&p01, 0, DT_INT, _state, ae_true);
ae_vector_init(&p11, 0, DT_INT, _state, ae_true);
ae_vector_init(&p2, 0, DT_INT, _state, ae_true);
ae_assert(n0>0, "RBFGridCalc2: invalid value for N0 (N0<=0)!", _state);
ae_assert(n1>0, "RBFGridCalc2: invalid value for N1 (N1<=0)!", _state);
ae_assert(x0->cnt>=n0, "RBFGridCalc2: Length(X0)<N0", _state);
ae_assert(x1->cnt>=n1, "RBFGridCalc2: Length(X1)<N1", _state);
ae_assert(isfinitevector(x0, n0, _state), "RBFGridCalc2: X0 contains infinite or NaN values!", _state);
ae_assert(isfinitevector(x1, n1, _state), "RBFGridCalc2: X1 contains infinite or NaN values!", _state);
ae_matrix_set_length(y, n0, n1, _state);
for(i=0; i<=n0-1; i++)
{
for(j=0; j<=n1-1; j++)
{
y->ptr.pp_double[i][j] = (double)(0);
}
}
if( (s->ny!=1||s->nx!=2)||s->nc==0 )
{
ae_frame_leave(_state);
return;
}
/*
*create and sort arrays
*/
ae_vector_set_length(&cpx0, n0, _state);
for(i=0; i<=n0-1; i++)
{
cpx0.ptr.p_double[i] = x0->ptr.p_double[i];
}
tagsort(&cpx0, n0, &p01, &p2, _state);
ae_vector_set_length(&cpx1, n1, _state);
for(i=0; i<=n1-1; i++)
{
cpx1.ptr.p_double[i] = x1->ptr.p_double[i];
}
tagsort(&cpx1, n1, &p11, &p2, _state);
/*
*calculate function's value
*/
for(i=0; i<=s->nc-1; i++)
{
radius = s->wr.ptr.pp_double[i][0];
for(d=0; d<=s->nl-1; d++)
{
omega = s->wr.ptr.pp_double[i][1+d];
rlimit = radius*rbfv1_rbffarradius;
/*
*search lower and upper indexes
*/
i00 = lowerbound(&cpx0, n0, s->xc.ptr.pp_double[i][0]-rlimit, _state);
i01 = upperbound(&cpx0, n0, s->xc.ptr.pp_double[i][0]+rlimit, _state);
i10 = lowerbound(&cpx1, n1, s->xc.ptr.pp_double[i][1]-rlimit, _state);
i11 = upperbound(&cpx1, n1, s->xc.ptr.pp_double[i][1]+rlimit, _state);
xc0 = s->xc.ptr.pp_double[i][0];
xc1 = s->xc.ptr.pp_double[i][1];
for(j=i00; j<=i01-1; j++)
{
hcpx0 = cpx0.ptr.p_double[j];
hp01 = p01.ptr.p_int[j];
for(k=i10; k<=i11-1; k++)
{
xcnorm2 = ae_sqr(hcpx0-xc0, _state)+ae_sqr(cpx1.ptr.p_double[k]-xc1, _state);
if( ae_fp_less_eq(xcnorm2,rlimit*rlimit) )
{
y->ptr.pp_double[hp01][p11.ptr.p_int[k]] = y->ptr.pp_double[hp01][p11.ptr.p_int[k]]+ae_exp(-xcnorm2/ae_sqr(radius, _state), _state)*omega;
}
}
}
radius = 0.5*radius;
}
}
/*
*add linear term
*/
for(i=0; i<=n0-1; i++)
{
for(j=0; j<=n1-1; j++)
{
y->ptr.pp_double[i][j] = y->ptr.pp_double[i][j]+s->v.ptr.pp_double[0][0]*x0->ptr.p_double[i]+s->v.ptr.pp_double[0][1]*x1->ptr.p_double[j]+s->v.ptr.pp_double[0][rbfv1_mxnx];
}
}
ae_frame_leave(_state);
}
void rbfv1gridcalc3vrec(rbfv1model* s,
/* Real */ ae_vector* x0,
ae_int_t n0,
/* Real */ ae_vector* x1,
ae_int_t n1,
/* Real */ ae_vector* x2,
ae_int_t n2,
/* Integer */ ae_vector* blocks0,
ae_int_t block0a,
ae_int_t block0b,
/* Integer */ ae_vector* blocks1,
ae_int_t block1a,
ae_int_t block1b,
/* Integer */ ae_vector* blocks2,
ae_int_t block2a,
ae_int_t block2b,
/* Boolean */ ae_vector* flagy,
ae_bool sparsey,
double searchradius,
double avgfuncpernode,
ae_shared_pool* bufpool,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t t;
ae_int_t l;
ae_int_t i0;
ae_int_t i1;
ae_int_t i2;
ae_int_t ic;
gridcalc3v1buf *pbuf;
ae_smart_ptr _pbuf;
ae_int_t flag12dim1;
ae_int_t flag12dim2;
double problemcost;
ae_int_t maxbs;
ae_int_t nx;
ae_int_t ny;
double v;
ae_int_t kc;
ae_int_t tg;
double rcur;
double rcur2;
double basisfuncval;
ae_int_t dstoffs;
ae_int_t srcoffs;
ae_int_t ubnd;
double w0;
double w1;
double w2;
ae_bool allnodes;
ae_bool somenodes;
ae_frame_make(_state, &_frame_block);
memset(&_pbuf, 0, sizeof(_pbuf));
ae_smart_ptr_init(&_pbuf, (void**)&pbuf, _state, ae_true);
nx = s->nx;
ny = s->ny;
/*
* Try to split large problem
*/
problemcost = (s->nl+1)*s->ny*2*(avgfuncpernode+1);
problemcost = problemcost*(blocks0->ptr.p_int[block0b]-blocks0->ptr.p_int[block0a]);
problemcost = problemcost*(blocks1->ptr.p_int[block1b]-blocks1->ptr.p_int[block1a]);
problemcost = problemcost*(blocks2->ptr.p_int[block2b]-blocks2->ptr.p_int[block2a]);
maxbs = 0;
maxbs = ae_maxint(maxbs, block0b-block0a, _state);
maxbs = ae_maxint(maxbs, block1b-block1a, _state);
maxbs = ae_maxint(maxbs, block2b-block2a, _state);
if( ae_fp_greater_eq(problemcost,rbfv1_minbasecasecost)&&maxbs>=2 )
{
if( block0b-block0a==maxbs )
{
rbfv1gridcalc3vrec(s, x0, n0, x1, n1, x2, n2, blocks0, block0a, block0a+maxbs/2, blocks1, block1a, block1b, blocks2, block2a, block2b, flagy, sparsey, searchradius, avgfuncpernode, bufpool, y, _state);
rbfv1gridcalc3vrec(s, x0, n0, x1, n1, x2, n2, blocks0, block0a+maxbs/2, block0b, blocks1, block1a, block1b, blocks2, block2a, block2b, flagy, sparsey, searchradius, avgfuncpernode, bufpool, y, _state);
ae_frame_leave(_state);
return;
}
if( block1b-block1a==maxbs )
{
rbfv1gridcalc3vrec(s, x0, n0, x1, n1, x2, n2, blocks0, block0a, block0b, blocks1, block1a, block1a+maxbs/2, blocks2, block2a, block2b, flagy, sparsey, searchradius, avgfuncpernode, bufpool, y, _state);
rbfv1gridcalc3vrec(s, x0, n0, x1, n1, x2, n2, blocks0, block0a, block0b, blocks1, block1a+maxbs/2, block1b, blocks2, block2a, block2b, flagy, sparsey, searchradius, avgfuncpernode, bufpool, y, _state);
ae_frame_leave(_state);
return;
}
if( block2b-block2a==maxbs )
{
rbfv1gridcalc3vrec(s, x0, n0, x1, n1, x2, n2, blocks0, block0a, block0b, blocks1, block1a, block1b, blocks2, block2a, block2a+maxbs/2, flagy, sparsey, searchradius, avgfuncpernode, bufpool, y, _state);
rbfv1gridcalc3vrec(s, x0, n0, x1, n1, x2, n2, blocks0, block0a, block0b, blocks1, block1a, block1b, blocks2, block2a+maxbs/2, block2b, flagy, sparsey, searchradius, avgfuncpernode, bufpool, y, _state);
ae_frame_leave(_state);
return;
}
}
/*
* Retrieve buffer object from pool (it will be returned later)
*/
ae_shared_pool_retrieve(bufpool, &_pbuf, _state);
/*
* Calculate RBF model
*/
for(i2=block2a; i2<=block2b-1; i2++)
{
for(i1=block1a; i1<=block1b-1; i1++)
{
for(i0=block0a; i0<=block0b-1; i0++)
{
/*
* Analyze block - determine what elements are needed and what are not.
*
* After this block is done, two flag variables can be used:
* * SomeNodes, which is True when there are at least one node which have
* to be calculated
* * AllNodes, which is True when all nodes are required
*/
somenodes = ae_true;
allnodes = ae_true;
flag12dim1 = blocks1->ptr.p_int[i1+1]-blocks1->ptr.p_int[i1];
flag12dim2 = blocks2->ptr.p_int[i2+1]-blocks2->ptr.p_int[i2];
if( sparsey )
{
/*
* Use FlagY to determine what is required.
*/
bvectorsetlengthatleast(&pbuf->flag0, n0, _state);
bvectorsetlengthatleast(&pbuf->flag1, n1, _state);
bvectorsetlengthatleast(&pbuf->flag2, n2, _state);
bvectorsetlengthatleast(&pbuf->flag12, flag12dim1*flag12dim2, _state);
for(i=blocks0->ptr.p_int[i0]; i<=blocks0->ptr.p_int[i0+1]-1; i++)
{
pbuf->flag0.ptr.p_bool[i] = ae_false;
}
for(j=blocks1->ptr.p_int[i1]; j<=blocks1->ptr.p_int[i1+1]-1; j++)
{
pbuf->flag1.ptr.p_bool[j] = ae_false;
}
for(k=blocks2->ptr.p_int[i2]; k<=blocks2->ptr.p_int[i2+1]-1; k++)
{
pbuf->flag2.ptr.p_bool[k] = ae_false;
}
for(i=0; i<=flag12dim1*flag12dim2-1; i++)
{
pbuf->flag12.ptr.p_bool[i] = ae_false;
}
somenodes = ae_false;
allnodes = ae_true;
for(k=blocks2->ptr.p_int[i2]; k<=blocks2->ptr.p_int[i2+1]-1; k++)
{
for(j=blocks1->ptr.p_int[i1]; j<=blocks1->ptr.p_int[i1+1]-1; j++)
{
dstoffs = j-blocks1->ptr.p_int[i1]+flag12dim1*(k-blocks2->ptr.p_int[i2]);
srcoffs = j*n0+k*n0*n1;
for(i=blocks0->ptr.p_int[i0]; i<=blocks0->ptr.p_int[i0+1]-1; i++)
{
if( flagy->ptr.p_bool[srcoffs+i] )
{
pbuf->flag0.ptr.p_bool[i] = ae_true;
pbuf->flag1.ptr.p_bool[j] = ae_true;
pbuf->flag2.ptr.p_bool[k] = ae_true;
pbuf->flag12.ptr.p_bool[dstoffs] = ae_true;
somenodes = ae_true;
}
else
{
allnodes = ae_false;
}
}
}
}
}
/*
* Skip block if it is completely empty.
*/
if( !somenodes )
{
continue;
}
/*
* compute linear term for block (I0,I1,I2)
*/
for(k=blocks2->ptr.p_int[i2]; k<=blocks2->ptr.p_int[i2+1]-1; k++)
{
for(j=blocks1->ptr.p_int[i1]; j<=blocks1->ptr.p_int[i1+1]-1; j++)
{
/*
* do we need this micro-row?
*/
if( !allnodes&&!pbuf->flag12.ptr.p_bool[j-blocks1->ptr.p_int[i1]+flag12dim1*(k-blocks2->ptr.p_int[i2])] )
{
continue;
}
/*
* Compute linear term
*/
for(i=blocks0->ptr.p_int[i0]; i<=blocks0->ptr.p_int[i0+1]-1; i++)
{
pbuf->tx.ptr.p_double[0] = x0->ptr.p_double[i];
pbuf->tx.ptr.p_double[1] = x1->ptr.p_double[j];
pbuf->tx.ptr.p_double[2] = x2->ptr.p_double[k];
for(l=0; l<=s->ny-1; l++)
{
v = s->v.ptr.pp_double[l][rbfv1_mxnx];
for(t=0; t<=nx-1; t++)
{
v = v+s->v.ptr.pp_double[l][t]*pbuf->tx.ptr.p_double[t];
}
y->ptr.p_double[l+ny*(i+j*n0+k*n0*n1)] = v;
}
}
}
}
/*
* compute RBF term for block (I0,I1,I2)
*/
pbuf->tx.ptr.p_double[0] = 0.5*(x0->ptr.p_double[blocks0->ptr.p_int[i0]]+x0->ptr.p_double[blocks0->ptr.p_int[i0+1]-1]);
pbuf->tx.ptr.p_double[1] = 0.5*(x1->ptr.p_double[blocks1->ptr.p_int[i1]]+x1->ptr.p_double[blocks1->ptr.p_int[i1+1]-1]);
pbuf->tx.ptr.p_double[2] = 0.5*(x2->ptr.p_double[blocks2->ptr.p_int[i2]]+x2->ptr.p_double[blocks2->ptr.p_int[i2+1]-1]);
kc = kdtreetsqueryrnn(&s->tree, &pbuf->requestbuf, &pbuf->tx, searchradius, ae_true, _state);
kdtreetsqueryresultsx(&s->tree, &pbuf->requestbuf, &pbuf->calcbufx, _state);
kdtreetsqueryresultstags(&s->tree, &pbuf->requestbuf, &pbuf->calcbuftags, _state);
for(ic=0; ic<=kc-1; ic++)
{
pbuf->cx.ptr.p_double[0] = pbuf->calcbufx.ptr.pp_double[ic][0];
pbuf->cx.ptr.p_double[1] = pbuf->calcbufx.ptr.pp_double[ic][1];
pbuf->cx.ptr.p_double[2] = pbuf->calcbufx.ptr.pp_double[ic][2];
tg = pbuf->calcbuftags.ptr.p_int[ic];
rcur = s->wr.ptr.pp_double[tg][0];
rcur2 = rcur*rcur;
for(i=blocks0->ptr.p_int[i0]; i<=blocks0->ptr.p_int[i0+1]-1; i++)
{
if( allnodes||pbuf->flag0.ptr.p_bool[i] )
{
pbuf->expbuf0.ptr.p_double[i] = ae_exp(-ae_sqr(x0->ptr.p_double[i]-pbuf->cx.ptr.p_double[0], _state)/rcur2, _state);
}
else
{
pbuf->expbuf0.ptr.p_double[i] = 0.0;
}
}
for(j=blocks1->ptr.p_int[i1]; j<=blocks1->ptr.p_int[i1+1]-1; j++)
{
if( allnodes||pbuf->flag1.ptr.p_bool[j] )
{
pbuf->expbuf1.ptr.p_double[j] = ae_exp(-ae_sqr(x1->ptr.p_double[j]-pbuf->cx.ptr.p_double[1], _state)/rcur2, _state);
}
else
{
pbuf->expbuf1.ptr.p_double[j] = 0.0;
}
}
for(k=blocks2->ptr.p_int[i2]; k<=blocks2->ptr.p_int[i2+1]-1; k++)
{
if( allnodes||pbuf->flag2.ptr.p_bool[k] )
{
pbuf->expbuf2.ptr.p_double[k] = ae_exp(-ae_sqr(x2->ptr.p_double[k]-pbuf->cx.ptr.p_double[2], _state)/rcur2, _state);
}
else
{
pbuf->expbuf2.ptr.p_double[k] = 0.0;
}
}
for(t=0; t<=s->nl-1; t++)
{
/*
* Calculate
*/
for(k=blocks2->ptr.p_int[i2]; k<=blocks2->ptr.p_int[i2+1]-1; k++)
{
for(j=blocks1->ptr.p_int[i1]; j<=blocks1->ptr.p_int[i1+1]-1; j++)
{
/*
* do we need this micro-row?
*/
if( !allnodes&&!pbuf->flag12.ptr.p_bool[j-blocks1->ptr.p_int[i1]+flag12dim1*(k-blocks2->ptr.p_int[i2])] )
{
continue;
}
/*
* Prepare local variables
*/
dstoffs = ny*(blocks0->ptr.p_int[i0]+j*n0+k*n0*n1);
v = pbuf->expbuf1.ptr.p_double[j]*pbuf->expbuf2.ptr.p_double[k];
/*
* Optimized for NY=1
*/
if( s->ny==1 )
{
w0 = s->wr.ptr.pp_double[tg][1+t*s->ny+0];
ubnd = blocks0->ptr.p_int[i0+1]-1;
for(i=blocks0->ptr.p_int[i0]; i<=ubnd; i++)
{
basisfuncval = pbuf->expbuf0.ptr.p_double[i]*v;
y->ptr.p_double[dstoffs] = y->ptr.p_double[dstoffs]+basisfuncval*w0;
dstoffs = dstoffs+1;
}
continue;
}
/*
* Optimized for NY=2
*/
if( s->ny==2 )
{
w0 = s->wr.ptr.pp_double[tg][1+t*s->ny+0];
w1 = s->wr.ptr.pp_double[tg][1+t*s->ny+1];
ubnd = blocks0->ptr.p_int[i0+1]-1;
for(i=blocks0->ptr.p_int[i0]; i<=ubnd; i++)
{
basisfuncval = pbuf->expbuf0.ptr.p_double[i]*v;
y->ptr.p_double[dstoffs+0] = y->ptr.p_double[dstoffs+0]+basisfuncval*w0;
y->ptr.p_double[dstoffs+1] = y->ptr.p_double[dstoffs+1]+basisfuncval*w1;
dstoffs = dstoffs+2;
}
continue;
}
/*
* Optimized for NY=3
*/
if( s->ny==3 )
{
w0 = s->wr.ptr.pp_double[tg][1+t*s->ny+0];
w1 = s->wr.ptr.pp_double[tg][1+t*s->ny+1];
w2 = s->wr.ptr.pp_double[tg][1+t*s->ny+2];
ubnd = blocks0->ptr.p_int[i0+1]-1;
for(i=blocks0->ptr.p_int[i0]; i<=ubnd; i++)
{
basisfuncval = pbuf->expbuf0.ptr.p_double[i]*v;
y->ptr.p_double[dstoffs+0] = y->ptr.p_double[dstoffs+0]+basisfuncval*w0;
y->ptr.p_double[dstoffs+1] = y->ptr.p_double[dstoffs+1]+basisfuncval*w1;
y->ptr.p_double[dstoffs+2] = y->ptr.p_double[dstoffs+2]+basisfuncval*w2;
dstoffs = dstoffs+3;
}
continue;
}
/*
* General case
*/
for(i=blocks0->ptr.p_int[i0]; i<=blocks0->ptr.p_int[i0+1]-1; i++)
{
basisfuncval = pbuf->expbuf0.ptr.p_double[i]*v;
for(l=0; l<=s->ny-1; l++)
{
y->ptr.p_double[l+dstoffs] = y->ptr.p_double[l+dstoffs]+basisfuncval*s->wr.ptr.pp_double[tg][1+t*s->ny+l];
}
dstoffs = dstoffs+ny;
}
}
}
/*
* Update basis functions
*/
if( t!=s->nl-1 )
{
ubnd = blocks0->ptr.p_int[i0+1]-1;
for(i=blocks0->ptr.p_int[i0]; i<=ubnd; i++)
{
if( allnodes||pbuf->flag0.ptr.p_bool[i] )
{
v = pbuf->expbuf0.ptr.p_double[i]*pbuf->expbuf0.ptr.p_double[i];
pbuf->expbuf0.ptr.p_double[i] = v*v;
}
}
ubnd = blocks1->ptr.p_int[i1+1]-1;
for(j=blocks1->ptr.p_int[i1]; j<=ubnd; j++)
{
if( allnodes||pbuf->flag1.ptr.p_bool[j] )
{
v = pbuf->expbuf1.ptr.p_double[j]*pbuf->expbuf1.ptr.p_double[j];
pbuf->expbuf1.ptr.p_double[j] = v*v;
}
}
ubnd = blocks2->ptr.p_int[i2+1]-1;
for(k=blocks2->ptr.p_int[i2]; k<=ubnd; k++)
{
if( allnodes||pbuf->flag2.ptr.p_bool[k] )
{
v = pbuf->expbuf2.ptr.p_double[k]*pbuf->expbuf2.ptr.p_double[k];
pbuf->expbuf2.ptr.p_double[k] = v*v;
}
}
}
}
}
}
}
}
/*
* Recycle buffer object back to pool
*/
ae_shared_pool_recycle(bufpool, &_pbuf, _state);
ae_frame_leave(_state);
}
/*************************************************************************
Serial stub for GPL edition.
*************************************************************************/
ae_bool _trypexec_rbfv1gridcalc3vrec(rbfv1model* s,
/* Real */ ae_vector* x0,
ae_int_t n0,
/* Real */ ae_vector* x1,
ae_int_t n1,
/* Real */ ae_vector* x2,
ae_int_t n2,
/* Integer */ ae_vector* blocks0,
ae_int_t block0a,
ae_int_t block0b,
/* Integer */ ae_vector* blocks1,
ae_int_t block1a,
ae_int_t block1b,
/* Integer */ ae_vector* blocks2,
ae_int_t block2a,
ae_int_t block2b,
/* Boolean */ ae_vector* flagy,
ae_bool sparsey,
double searchradius,
double avgfuncpernode,
ae_shared_pool* bufpool,
/* Real */ ae_vector* y,
ae_state *_state)
{
return ae_false;
}
/*************************************************************************
This function "unpacks" RBF model by extracting its coefficients.
INPUT PARAMETERS:
S - RBF model
OUTPUT PARAMETERS:
NX - dimensionality of argument
NY - dimensionality of the target function
XWR - model information, array[NC,NX+NY+1].
One row of the array corresponds to one basis function:
* first NX columns - coordinates of the center
* next NY columns - weights, one per dimension of the
function being modelled
* last column - radius, same for all dimensions of
the function being modelled
NC - number of the centers
V - polynomial term , array[NY,NX+1]. One row per one
dimension of the function being modelled. First NX
elements are linear coefficients, V[NX] is equal to the
constant part.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfv1unpack(rbfv1model* s,
ae_int_t* nx,
ae_int_t* ny,
/* Real */ ae_matrix* xwr,
ae_int_t* nc,
/* Real */ ae_matrix* v,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
double rcur;
*nx = 0;
*ny = 0;
ae_matrix_clear(xwr);
*nc = 0;
ae_matrix_clear(v);
*nx = s->nx;
*ny = s->ny;
*nc = s->nc;
/*
* Fill V
*/
ae_matrix_set_length(v, s->ny, s->nx+1, _state);
for(i=0; i<=s->ny-1; i++)
{
ae_v_move(&v->ptr.pp_double[i][0], 1, &s->v.ptr.pp_double[i][0], 1, ae_v_len(0,s->nx-1));
v->ptr.pp_double[i][s->nx] = s->v.ptr.pp_double[i][rbfv1_mxnx];
}
/*
* Fill XWR and V
*/
if( *nc*s->nl>0 )
{
ae_matrix_set_length(xwr, s->nc*s->nl, s->nx+s->ny+1, _state);
for(i=0; i<=s->nc-1; i++)
{
rcur = s->wr.ptr.pp_double[i][0];
for(j=0; j<=s->nl-1; j++)
{
ae_v_move(&xwr->ptr.pp_double[i*s->nl+j][0], 1, &s->xc.ptr.pp_double[i][0], 1, ae_v_len(0,s->nx-1));
ae_v_move(&xwr->ptr.pp_double[i*s->nl+j][s->nx], 1, &s->wr.ptr.pp_double[i][1+j*s->ny], 1, ae_v_len(s->nx,s->nx+s->ny-1));
xwr->ptr.pp_double[i*s->nl+j][s->nx+s->ny] = rcur;
rcur = 0.5*rcur;
}
}
}
}
static ae_bool rbfv1_rbfv1buildlinearmodel(/* Real */ ae_matrix* x,
/* Real */ ae_matrix* y,
ae_int_t n,
ae_int_t ny,
ae_int_t modeltype,
/* Real */ ae_matrix* v,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector tmpy;
ae_matrix a;
double scaling;
ae_vector shifting;
double mn;
double mx;
ae_vector c;
lsfitreport rep;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t info;
ae_bool result;
ae_frame_make(_state, &_frame_block);
memset(&tmpy, 0, sizeof(tmpy));
memset(&a, 0, sizeof(a));
memset(&shifting, 0, sizeof(shifting));
memset(&c, 0, sizeof(c));
memset(&rep, 0, sizeof(rep));
ae_matrix_clear(v);
ae_vector_init(&tmpy, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&a, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&shifting, 0, DT_REAL, _state, ae_true);
ae_vector_init(&c, 0, DT_REAL, _state, ae_true);
_lsfitreport_init(&rep, _state, ae_true);
ae_assert(n>=0, "BuildLinearModel: N<0", _state);
ae_assert(ny>0, "BuildLinearModel: NY<=0", _state);
/*
* Handle degenerate case (N=0)
*/
result = ae_true;
ae_matrix_set_length(v, ny, rbfv1_mxnx+1, _state);
if( n==0 )
{
for(j=0; j<=rbfv1_mxnx; j++)
{
for(i=0; i<=ny-1; i++)
{
v->ptr.pp_double[i][j] = (double)(0);
}
}
ae_frame_leave(_state);
return result;
}
/*
* Allocate temporaries
*/
ae_vector_set_length(&tmpy, n, _state);
/*
* General linear model.
*/
if( modeltype==1 )
{
/*
* Calculate scaling/shifting, transform variables, prepare LLS problem
*/
ae_matrix_set_length(&a, n, rbfv1_mxnx+1, _state);
ae_vector_set_length(&shifting, rbfv1_mxnx, _state);
scaling = (double)(0);
for(i=0; i<=rbfv1_mxnx-1; i++)
{
mn = x->ptr.pp_double[0][i];
mx = mn;
for(j=1; j<=n-1; j++)
{
if( ae_fp_greater(mn,x->ptr.pp_double[j][i]) )
{
mn = x->ptr.pp_double[j][i];
}
if( ae_fp_less(mx,x->ptr.pp_double[j][i]) )
{
mx = x->ptr.pp_double[j][i];
}
}
scaling = ae_maxreal(scaling, mx-mn, _state);
shifting.ptr.p_double[i] = 0.5*(mx+mn);
}
if( ae_fp_eq(scaling,(double)(0)) )
{
scaling = (double)(1);
}
else
{
scaling = 0.5*scaling;
}
for(i=0; i<=n-1; i++)
{
for(j=0; j<=rbfv1_mxnx-1; j++)
{
a.ptr.pp_double[i][j] = (x->ptr.pp_double[i][j]-shifting.ptr.p_double[j])/scaling;
}
}
for(i=0; i<=n-1; i++)
{
a.ptr.pp_double[i][rbfv1_mxnx] = (double)(1);
}
/*
* Solve linear system in transformed variables, make backward
*/
for(i=0; i<=ny-1; i++)
{
for(j=0; j<=n-1; j++)
{
tmpy.ptr.p_double[j] = y->ptr.pp_double[j][i];
}
lsfitlinear(&tmpy, &a, n, rbfv1_mxnx+1, &info, &c, &rep, _state);
if( info<=0 )
{
result = ae_false;
ae_frame_leave(_state);
return result;
}
for(j=0; j<=rbfv1_mxnx-1; j++)
{
v->ptr.pp_double[i][j] = c.ptr.p_double[j]/scaling;
}
v->ptr.pp_double[i][rbfv1_mxnx] = c.ptr.p_double[rbfv1_mxnx];
for(j=0; j<=rbfv1_mxnx-1; j++)
{
v->ptr.pp_double[i][rbfv1_mxnx] = v->ptr.pp_double[i][rbfv1_mxnx]-shifting.ptr.p_double[j]*v->ptr.pp_double[i][j];
}
for(j=0; j<=n-1; j++)
{
for(k=0; k<=rbfv1_mxnx-1; k++)
{
y->ptr.pp_double[j][i] = y->ptr.pp_double[j][i]-x->ptr.pp_double[j][k]*v->ptr.pp_double[i][k];
}
y->ptr.pp_double[j][i] = y->ptr.pp_double[j][i]-v->ptr.pp_double[i][rbfv1_mxnx];
}
}
ae_frame_leave(_state);
return result;
}
/*
* Constant model, very simple
*/
if( modeltype==2 )
{
for(i=0; i<=ny-1; i++)
{
for(j=0; j<=rbfv1_mxnx; j++)
{
v->ptr.pp_double[i][j] = (double)(0);
}
for(j=0; j<=n-1; j++)
{
v->ptr.pp_double[i][rbfv1_mxnx] = v->ptr.pp_double[i][rbfv1_mxnx]+y->ptr.pp_double[j][i];
}
if( n>0 )
{
v->ptr.pp_double[i][rbfv1_mxnx] = v->ptr.pp_double[i][rbfv1_mxnx]/n;
}
for(j=0; j<=n-1; j++)
{
y->ptr.pp_double[j][i] = y->ptr.pp_double[j][i]-v->ptr.pp_double[i][rbfv1_mxnx];
}
}
ae_frame_leave(_state);
return result;
}
/*
* Zero model
*/
ae_assert(modeltype==3, "BuildLinearModel: unknown model type", _state);
for(i=0; i<=ny-1; i++)
{
for(j=0; j<=rbfv1_mxnx; j++)
{
v->ptr.pp_double[i][j] = (double)(0);
}
}
ae_frame_leave(_state);
return result;
}
static void rbfv1_buildrbfmodellsqr(/* Real */ ae_matrix* x,
/* Real */ ae_matrix* y,
/* Real */ ae_matrix* xc,
/* Real */ ae_vector* r,
ae_int_t n,
ae_int_t nc,
ae_int_t ny,
kdtree* pointstree,
kdtree* centerstree,
double epsort,
double epserr,
ae_int_t maxits,
ae_int_t* gnnz,
ae_int_t* snnz,
/* Real */ ae_matrix* w,
ae_int_t* info,
ae_int_t* iterationscount,
ae_int_t* nmv,
ae_state *_state)
{
ae_frame _frame_block;
linlsqrstate state;
linlsqrreport lsqrrep;
sparsematrix spg;
sparsematrix sps;
ae_vector nearcenterscnt;
ae_vector nearpointscnt;
ae_vector skipnearpointscnt;
ae_vector farpointscnt;
ae_int_t maxnearcenterscnt;
ae_int_t maxnearpointscnt;
ae_int_t maxfarpointscnt;
ae_int_t sumnearcenterscnt;
ae_int_t sumnearpointscnt;
ae_int_t sumfarpointscnt;
double maxrad;
ae_vector pointstags;
ae_vector centerstags;
ae_matrix nearpoints;
ae_matrix nearcenters;
ae_matrix farpoints;
ae_int_t tmpi;
ae_int_t pointscnt;
ae_int_t centerscnt;
ae_vector xcx;
ae_vector tmpy;
ae_vector tc;
ae_vector g;
ae_vector c;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t sind;
ae_matrix a;
double vv;
double vx;
double vy;
double vz;
double vr;
double gnorm2;
ae_vector tmp0;
ae_vector tmp1;
ae_vector tmp2;
double fx;
ae_matrix xx;
ae_matrix cx;
double mrad;
ae_frame_make(_state, &_frame_block);
memset(&state, 0, sizeof(state));
memset(&lsqrrep, 0, sizeof(lsqrrep));
memset(&spg, 0, sizeof(spg));
memset(&sps, 0, sizeof(sps));
memset(&nearcenterscnt, 0, sizeof(nearcenterscnt));
memset(&nearpointscnt, 0, sizeof(nearpointscnt));
memset(&skipnearpointscnt, 0, sizeof(skipnearpointscnt));
memset(&farpointscnt, 0, sizeof(farpointscnt));
memset(&pointstags, 0, sizeof(pointstags));
memset(&centerstags, 0, sizeof(centerstags));
memset(&nearpoints, 0, sizeof(nearpoints));
memset(&nearcenters, 0, sizeof(nearcenters));
memset(&farpoints, 0, sizeof(farpoints));
memset(&xcx, 0, sizeof(xcx));
memset(&tmpy, 0, sizeof(tmpy));
memset(&tc, 0, sizeof(tc));
memset(&g, 0, sizeof(g));
memset(&c, 0, sizeof(c));
memset(&a, 0, sizeof(a));
memset(&tmp0, 0, sizeof(tmp0));
memset(&tmp1, 0, sizeof(tmp1));
memset(&tmp2, 0, sizeof(tmp2));
memset(&xx, 0, sizeof(xx));
memset(&cx, 0, sizeof(cx));
*gnnz = 0;
*snnz = 0;
ae_matrix_clear(w);
*info = 0;
*iterationscount = 0;
*nmv = 0;
_linlsqrstate_init(&state, _state, ae_true);
_linlsqrreport_init(&lsqrrep, _state, ae_true);
_sparsematrix_init(&spg, _state, ae_true);
_sparsematrix_init(&sps, _state, ae_true);
ae_vector_init(&nearcenterscnt, 0, DT_INT, _state, ae_true);
ae_vector_init(&nearpointscnt, 0, DT_INT, _state, ae_true);
ae_vector_init(&skipnearpointscnt, 0, DT_INT, _state, ae_true);
ae_vector_init(&farpointscnt, 0, DT_INT, _state, ae_true);
ae_vector_init(&pointstags, 0, DT_INT, _state, ae_true);
ae_vector_init(&centerstags, 0, DT_INT, _state, ae_true);
ae_matrix_init(&nearpoints, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&nearcenters, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&farpoints, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&xcx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmpy, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tc, 0, DT_REAL, _state, ae_true);
ae_vector_init(&g, 0, DT_REAL, _state, ae_true);
ae_vector_init(&c, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&a, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp2, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&xx, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&cx, 0, 0, DT_REAL, _state, ae_true);
/*
* Handle special cases: NC=0
*/
if( nc==0 )
{
*info = 1;
*iterationscount = 0;
*nmv = 0;
ae_frame_leave(_state);
return;
}
/*
* Prepare for general case, NC>0
*/
ae_vector_set_length(&xcx, rbfv1_mxnx, _state);
ae_vector_set_length(&pointstags, n, _state);
ae_vector_set_length(&centerstags, nc, _state);
*info = -1;
*iterationscount = 0;
*nmv = 0;
/*
* This block prepares quantities used to compute approximate cardinal basis functions (ACBFs):
* * NearCentersCnt[] - array[NC], whose elements store number of near centers used to build ACBF
* * NearPointsCnt[] - array[NC], number of near points used to build ACBF
* * FarPointsCnt[] - array[NC], number of far points (ones where ACBF is nonzero)
* * MaxNearCentersCnt - max(NearCentersCnt)
* * MaxNearPointsCnt - max(NearPointsCnt)
* * SumNearCentersCnt - sum(NearCentersCnt)
* * SumNearPointsCnt - sum(NearPointsCnt)
* * SumFarPointsCnt - sum(FarPointsCnt)
*/
ae_vector_set_length(&nearcenterscnt, nc, _state);
ae_vector_set_length(&nearpointscnt, nc, _state);
ae_vector_set_length(&skipnearpointscnt, nc, _state);
ae_vector_set_length(&farpointscnt, nc, _state);
maxnearcenterscnt = 0;
maxnearpointscnt = 0;
maxfarpointscnt = 0;
sumnearcenterscnt = 0;
sumnearpointscnt = 0;
sumfarpointscnt = 0;
for(i=0; i<=nc-1; i++)
{
for(j=0; j<=rbfv1_mxnx-1; j++)
{
xcx.ptr.p_double[j] = xc->ptr.pp_double[i][j];
}
/*
* Determine number of near centers and maximum radius of near centers
*/
nearcenterscnt.ptr.p_int[i] = kdtreequeryrnn(centerstree, &xcx, r->ptr.p_double[i]*rbfv1_rbfnearradius, ae_true, _state);
kdtreequeryresultstags(centerstree, &centerstags, _state);
maxrad = (double)(0);
for(j=0; j<=nearcenterscnt.ptr.p_int[i]-1; j++)
{
maxrad = ae_maxreal(maxrad, ae_fabs(r->ptr.p_double[centerstags.ptr.p_int[j]], _state), _state);
}
/*
* Determine number of near points (ones which used to build ACBF)
* and skipped points (the most near points which are NOT used to build ACBF
* and are NOT included in the near points count
*/
skipnearpointscnt.ptr.p_int[i] = kdtreequeryrnn(pointstree, &xcx, 0.1*r->ptr.p_double[i], ae_true, _state);
nearpointscnt.ptr.p_int[i] = kdtreequeryrnn(pointstree, &xcx, (r->ptr.p_double[i]+maxrad)*rbfv1_rbfnearradius, ae_true, _state)-skipnearpointscnt.ptr.p_int[i];
ae_assert(nearpointscnt.ptr.p_int[i]>=0, "BuildRBFModelLSQR: internal error", _state);
/*
* Determine number of far points
*/
farpointscnt.ptr.p_int[i] = kdtreequeryrnn(pointstree, &xcx, ae_maxreal(r->ptr.p_double[i]*rbfv1_rbfnearradius+maxrad*rbfv1_rbffarradius, r->ptr.p_double[i]*rbfv1_rbffarradius, _state), ae_true, _state);
/*
* calculate sum and max, make some basic checks
*/
ae_assert(nearcenterscnt.ptr.p_int[i]>0, "BuildRBFModelLSQR: internal error", _state);
maxnearcenterscnt = ae_maxint(maxnearcenterscnt, nearcenterscnt.ptr.p_int[i], _state);
maxnearpointscnt = ae_maxint(maxnearpointscnt, nearpointscnt.ptr.p_int[i], _state);
maxfarpointscnt = ae_maxint(maxfarpointscnt, farpointscnt.ptr.p_int[i], _state);
sumnearcenterscnt = sumnearcenterscnt+nearcenterscnt.ptr.p_int[i];
sumnearpointscnt = sumnearpointscnt+nearpointscnt.ptr.p_int[i];
sumfarpointscnt = sumfarpointscnt+farpointscnt.ptr.p_int[i];
}
*snnz = sumnearcenterscnt;
*gnnz = sumfarpointscnt;
ae_assert(maxnearcenterscnt>0, "BuildRBFModelLSQR: internal error", _state);
/*
* Allocate temporaries.
*
* NOTE: we want to avoid allocation of zero-size arrays, so we
* use max(desired_size,1) instead of desired_size when performing
* memory allocation.
*/
ae_matrix_set_length(&a, maxnearpointscnt+maxnearcenterscnt, maxnearcenterscnt, _state);
ae_vector_set_length(&tmpy, maxnearpointscnt+maxnearcenterscnt, _state);
ae_vector_set_length(&g, maxnearcenterscnt, _state);
ae_vector_set_length(&c, maxnearcenterscnt, _state);
ae_matrix_set_length(&nearcenters, maxnearcenterscnt, rbfv1_mxnx, _state);
ae_matrix_set_length(&nearpoints, ae_maxint(maxnearpointscnt, 1, _state), rbfv1_mxnx, _state);
ae_matrix_set_length(&farpoints, ae_maxint(maxfarpointscnt, 1, _state), rbfv1_mxnx, _state);
/*
* fill matrix SpG
*/
sparsecreate(n, nc, *gnnz, &spg, _state);
sparsecreate(nc, nc, *snnz, &sps, _state);
for(i=0; i<=nc-1; i++)
{
centerscnt = nearcenterscnt.ptr.p_int[i];
/*
* main center
*/
for(j=0; j<=rbfv1_mxnx-1; j++)
{
xcx.ptr.p_double[j] = xc->ptr.pp_double[i][j];
}
/*
* center's tree
*/
tmpi = kdtreequeryknn(centerstree, &xcx, centerscnt, ae_true, _state);
ae_assert(tmpi==centerscnt, "BuildRBFModelLSQR: internal error", _state);
kdtreequeryresultsx(centerstree, &cx, _state);
kdtreequeryresultstags(centerstree, &centerstags, _state);
/*
* point's tree
*/
mrad = (double)(0);
for(j=0; j<=centerscnt-1; j++)
{
mrad = ae_maxreal(mrad, r->ptr.p_double[centerstags.ptr.p_int[j]], _state);
}
/*
* we need to be sure that 'CTree' contains
* at least one side center
*/
sparseset(&sps, i, i, (double)(1), _state);
c.ptr.p_double[0] = 1.0;
for(j=1; j<=centerscnt-1; j++)
{
c.ptr.p_double[j] = 0.0;
}
if( centerscnt>1&&nearpointscnt.ptr.p_int[i]>0 )
{
/*
* first KDTree request for points
*/
pointscnt = nearpointscnt.ptr.p_int[i];
tmpi = kdtreequeryknn(pointstree, &xcx, skipnearpointscnt.ptr.p_int[i]+nearpointscnt.ptr.p_int[i], ae_true, _state);
ae_assert(tmpi==skipnearpointscnt.ptr.p_int[i]+nearpointscnt.ptr.p_int[i], "BuildRBFModelLSQR: internal error", _state);
kdtreequeryresultsx(pointstree, &xx, _state);
sind = skipnearpointscnt.ptr.p_int[i];
for(j=0; j<=pointscnt-1; j++)
{
vx = xx.ptr.pp_double[sind+j][0];
vy = xx.ptr.pp_double[sind+j][1];
vz = xx.ptr.pp_double[sind+j][2];
for(k=0; k<=centerscnt-1; k++)
{
vr = 0.0;
vv = vx-cx.ptr.pp_double[k][0];
vr = vr+vv*vv;
vv = vy-cx.ptr.pp_double[k][1];
vr = vr+vv*vv;
vv = vz-cx.ptr.pp_double[k][2];
vr = vr+vv*vv;
vv = r->ptr.p_double[centerstags.ptr.p_int[k]];
a.ptr.pp_double[j][k] = ae_exp(-vr/(vv*vv), _state);
}
}
for(j=0; j<=centerscnt-1; j++)
{
g.ptr.p_double[j] = ae_exp(-(ae_sqr(xcx.ptr.p_double[0]-cx.ptr.pp_double[j][0], _state)+ae_sqr(xcx.ptr.p_double[1]-cx.ptr.pp_double[j][1], _state)+ae_sqr(xcx.ptr.p_double[2]-cx.ptr.pp_double[j][2], _state))/ae_sqr(r->ptr.p_double[centerstags.ptr.p_int[j]], _state), _state);
}
/*
* calculate the problem
*/
gnorm2 = ae_v_dotproduct(&g.ptr.p_double[0], 1, &g.ptr.p_double[0], 1, ae_v_len(0,centerscnt-1));
for(j=0; j<=pointscnt-1; j++)
{
vv = ae_v_dotproduct(&a.ptr.pp_double[j][0], 1, &g.ptr.p_double[0], 1, ae_v_len(0,centerscnt-1));
vv = vv/gnorm2;
tmpy.ptr.p_double[j] = -vv;
ae_v_subd(&a.ptr.pp_double[j][0], 1, &g.ptr.p_double[0], 1, ae_v_len(0,centerscnt-1), vv);
}
for(j=pointscnt; j<=pointscnt+centerscnt-1; j++)
{
for(k=0; k<=centerscnt-1; k++)
{
a.ptr.pp_double[j][k] = 0.0;
}
a.ptr.pp_double[j][j-pointscnt] = 1.0E-6;
tmpy.ptr.p_double[j] = 0.0;
}
fblssolvels(&a, &tmpy, pointscnt+centerscnt, centerscnt, &tmp0, &tmp1, &tmp2, _state);
ae_v_move(&c.ptr.p_double[0], 1, &tmpy.ptr.p_double[0], 1, ae_v_len(0,centerscnt-1));
vv = ae_v_dotproduct(&g.ptr.p_double[0], 1, &c.ptr.p_double[0], 1, ae_v_len(0,centerscnt-1));
vv = vv/gnorm2;
ae_v_subd(&c.ptr.p_double[0], 1, &g.ptr.p_double[0], 1, ae_v_len(0,centerscnt-1), vv);
vv = 1/gnorm2;
ae_v_addd(&c.ptr.p_double[0], 1, &g.ptr.p_double[0], 1, ae_v_len(0,centerscnt-1), vv);
for(j=0; j<=centerscnt-1; j++)
{
sparseset(&sps, i, centerstags.ptr.p_int[j], c.ptr.p_double[j], _state);
}
}
/*
* second KDTree request for points
*/
pointscnt = farpointscnt.ptr.p_int[i];
tmpi = kdtreequeryknn(pointstree, &xcx, pointscnt, ae_true, _state);
ae_assert(tmpi==pointscnt, "BuildRBFModelLSQR: internal error", _state);
kdtreequeryresultsx(pointstree, &xx, _state);
kdtreequeryresultstags(pointstree, &pointstags, _state);
/*
*fill SpG matrix
*/
for(j=0; j<=pointscnt-1; j++)
{
fx = (double)(0);
vx = xx.ptr.pp_double[j][0];
vy = xx.ptr.pp_double[j][1];
vz = xx.ptr.pp_double[j][2];
for(k=0; k<=centerscnt-1; k++)
{
vr = 0.0;
vv = vx-cx.ptr.pp_double[k][0];
vr = vr+vv*vv;
vv = vy-cx.ptr.pp_double[k][1];
vr = vr+vv*vv;
vv = vz-cx.ptr.pp_double[k][2];
vr = vr+vv*vv;
vv = r->ptr.p_double[centerstags.ptr.p_int[k]];
vv = vv*vv;
fx = fx+c.ptr.p_double[k]*ae_exp(-vr/vv, _state);
}
sparseset(&spg, pointstags.ptr.p_int[j], i, fx, _state);
}
}
sparseconverttocrs(&spg, _state);
sparseconverttocrs(&sps, _state);
/*
* solve by LSQR method
*/
ae_vector_set_length(&tmpy, n, _state);
ae_vector_set_length(&tc, nc, _state);
ae_matrix_set_length(w, nc, ny, _state);
linlsqrcreate(n, nc, &state, _state);
linlsqrsetcond(&state, epsort, epserr, maxits, _state);
for(i=0; i<=ny-1; i++)
{
for(j=0; j<=n-1; j++)
{
tmpy.ptr.p_double[j] = y->ptr.pp_double[j][i];
}
linlsqrsolvesparse(&state, &spg, &tmpy, _state);
linlsqrresults(&state, &c, &lsqrrep, _state);
if( lsqrrep.terminationtype<=0 )
{
*info = -4;
ae_frame_leave(_state);
return;
}
sparsemtv(&sps, &c, &tc, _state);
for(j=0; j<=nc-1; j++)
{
w->ptr.pp_double[j][i] = tc.ptr.p_double[j];
}
*iterationscount = *iterationscount+lsqrrep.iterationscount;
*nmv = *nmv+lsqrrep.nmv;
}
*info = 1;
ae_frame_leave(_state);
}
static void rbfv1_buildrbfmlayersmodellsqr(/* Real */ ae_matrix* x,
/* Real */ ae_matrix* y,
/* Real */ ae_matrix* xc,
double rval,
/* Real */ ae_vector* r,
ae_int_t n,
ae_int_t* nc,
ae_int_t ny,
ae_int_t nlayers,
kdtree* centerstree,
double epsort,
double epserr,
ae_int_t maxits,
double lambdav,
ae_int_t* annz,
/* Real */ ae_matrix* w,
ae_int_t* info,
ae_int_t* iterationscount,
ae_int_t* nmv,
ae_state *_state)
{
ae_frame _frame_block;
linlsqrstate state;
linlsqrreport lsqrrep;
sparsematrix spa;
double anorm;
ae_vector omega;
ae_vector xx;
ae_vector tmpy;
ae_matrix cx;
double yval;
ae_int_t nec;
ae_vector centerstags;
ae_int_t layer;
ae_int_t i;
ae_int_t j;
ae_int_t k;
double v;
double rmaxbefore;
double rmaxafter;
ae_frame_make(_state, &_frame_block);
memset(&state, 0, sizeof(state));
memset(&lsqrrep, 0, sizeof(lsqrrep));
memset(&spa, 0, sizeof(spa));
memset(&omega, 0, sizeof(omega));
memset(&xx, 0, sizeof(xx));
memset(&tmpy, 0, sizeof(tmpy));
memset(&cx, 0, sizeof(cx));
memset(&centerstags, 0, sizeof(centerstags));
ae_matrix_clear(xc);
ae_vector_clear(r);
*nc = 0;
*annz = 0;
ae_matrix_clear(w);
*info = 0;
*iterationscount = 0;
*nmv = 0;
_linlsqrstate_init(&state, _state, ae_true);
_linlsqrreport_init(&lsqrrep, _state, ae_true);
_sparsematrix_init(&spa, _state, ae_true);
ae_vector_init(&omega, 0, DT_REAL, _state, ae_true);
ae_vector_init(&xx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmpy, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&cx, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&centerstags, 0, DT_INT, _state, ae_true);
ae_assert(nlayers>=0, "BuildRBFMLayersModelLSQR: invalid argument(NLayers<0)", _state);
ae_assert(n>=0, "BuildRBFMLayersModelLSQR: invalid argument(N<0)", _state);
ae_assert(rbfv1_mxnx>0&&rbfv1_mxnx<=3, "BuildRBFMLayersModelLSQR: internal error(invalid global const MxNX: either MxNX<=0 or MxNX>3)", _state);
*annz = 0;
if( n==0||nlayers==0 )
{
*info = 1;
*iterationscount = 0;
*nmv = 0;
ae_frame_leave(_state);
return;
}
*nc = n*nlayers;
ae_vector_set_length(&xx, rbfv1_mxnx, _state);
ae_vector_set_length(&centerstags, n, _state);
ae_matrix_set_length(xc, *nc, rbfv1_mxnx, _state);
ae_vector_set_length(r, *nc, _state);
for(i=0; i<=*nc-1; i++)
{
for(j=0; j<=rbfv1_mxnx-1; j++)
{
xc->ptr.pp_double[i][j] = x->ptr.pp_double[i%n][j];
}
}
for(i=0; i<=*nc-1; i++)
{
r->ptr.p_double[i] = rval/ae_pow((double)(2), (double)(i/n), _state);
}
for(i=0; i<=n-1; i++)
{
centerstags.ptr.p_int[i] = i;
}
kdtreebuildtagged(xc, &centerstags, n, rbfv1_mxnx, 0, 2, centerstree, _state);
ae_vector_set_length(&omega, n, _state);
ae_vector_set_length(&tmpy, n, _state);
ae_matrix_set_length(w, *nc, ny, _state);
*info = -1;
*iterationscount = 0;
*nmv = 0;
linlsqrcreate(n, n, &state, _state);
linlsqrsetcond(&state, epsort, epserr, maxits, _state);
linlsqrsetlambdai(&state, 1.0E-6, _state);
/*
* calculate number of non-zero elements for sparse matrix
*/
for(i=0; i<=n-1; i++)
{
for(j=0; j<=rbfv1_mxnx-1; j++)
{
xx.ptr.p_double[j] = x->ptr.pp_double[i][j];
}
*annz = *annz+kdtreequeryrnn(centerstree, &xx, r->ptr.p_double[0]*rbfv1_rbfmlradius, ae_true, _state);
}
for(layer=0; layer<=nlayers-1; layer++)
{
/*
* Fill sparse matrix, calculate norm(A)
*/
anorm = 0.0;
sparsecreate(n, n, *annz, &spa, _state);
for(i=0; i<=n-1; i++)
{
for(j=0; j<=rbfv1_mxnx-1; j++)
{
xx.ptr.p_double[j] = x->ptr.pp_double[i][j];
}
nec = kdtreequeryrnn(centerstree, &xx, r->ptr.p_double[layer*n]*rbfv1_rbfmlradius, ae_true, _state);
kdtreequeryresultsx(centerstree, &cx, _state);
kdtreequeryresultstags(centerstree, &centerstags, _state);
for(j=0; j<=nec-1; j++)
{
v = ae_exp(-(ae_sqr(xx.ptr.p_double[0]-cx.ptr.pp_double[j][0], _state)+ae_sqr(xx.ptr.p_double[1]-cx.ptr.pp_double[j][1], _state)+ae_sqr(xx.ptr.p_double[2]-cx.ptr.pp_double[j][2], _state))/ae_sqr(r->ptr.p_double[layer*n+centerstags.ptr.p_int[j]], _state), _state);
sparseset(&spa, i, centerstags.ptr.p_int[j], v, _state);
anorm = anorm+ae_sqr(v, _state);
}
}
anorm = ae_sqrt(anorm, _state);
sparseconverttocrs(&spa, _state);
/*
* Calculate maximum residual before adding new layer.
* This value is not used by algorithm, the only purpose is to make debugging easier.
*/
rmaxbefore = 0.0;
for(j=0; j<=n-1; j++)
{
for(i=0; i<=ny-1; i++)
{
rmaxbefore = ae_maxreal(rmaxbefore, ae_fabs(y->ptr.pp_double[j][i], _state), _state);
}
}
/*
* Process NY dimensions of the target function
*/
for(i=0; i<=ny-1; i++)
{
for(j=0; j<=n-1; j++)
{
tmpy.ptr.p_double[j] = y->ptr.pp_double[j][i];
}
/*
* calculate Omega for current layer
*/
linlsqrsetlambdai(&state, lambdav*anorm/n, _state);
linlsqrsolvesparse(&state, &spa, &tmpy, _state);
linlsqrresults(&state, &omega, &lsqrrep, _state);
if( lsqrrep.terminationtype<=0 )
{
*info = -4;
ae_frame_leave(_state);
return;
}
/*
* calculate error for current layer
*/
for(j=0; j<=n-1; j++)
{
yval = (double)(0);
for(k=0; k<=rbfv1_mxnx-1; k++)
{
xx.ptr.p_double[k] = x->ptr.pp_double[j][k];
}
nec = kdtreequeryrnn(centerstree, &xx, r->ptr.p_double[layer*n]*rbfv1_rbffarradius, ae_true, _state);
kdtreequeryresultsx(centerstree, &cx, _state);
kdtreequeryresultstags(centerstree, &centerstags, _state);
for(k=0; k<=nec-1; k++)
{
yval = yval+omega.ptr.p_double[centerstags.ptr.p_int[k]]*ae_exp(-(ae_sqr(xx.ptr.p_double[0]-cx.ptr.pp_double[k][0], _state)+ae_sqr(xx.ptr.p_double[1]-cx.ptr.pp_double[k][1], _state)+ae_sqr(xx.ptr.p_double[2]-cx.ptr.pp_double[k][2], _state))/ae_sqr(r->ptr.p_double[layer*n+centerstags.ptr.p_int[k]], _state), _state);
}
y->ptr.pp_double[j][i] = y->ptr.pp_double[j][i]-yval;
}
/*
* write Omega in out parameter W
*/
for(j=0; j<=n-1; j++)
{
w->ptr.pp_double[layer*n+j][i] = omega.ptr.p_double[j];
}
*iterationscount = *iterationscount+lsqrrep.iterationscount;
*nmv = *nmv+lsqrrep.nmv;
}
/*
* Calculate maximum residual before adding new layer.
* This value is not used by algorithm, the only purpose is to make debugging easier.
*/
rmaxafter = 0.0;
for(j=0; j<=n-1; j++)
{
for(i=0; i<=ny-1; i++)
{
rmaxafter = ae_maxreal(rmaxafter, ae_fabs(y->ptr.pp_double[j][i], _state), _state);
}
}
}
*info = 1;
ae_frame_leave(_state);
}
void _rbfv1calcbuffer_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
rbfv1calcbuffer *p = (rbfv1calcbuffer*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->calcbufxcx, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->calcbufx, 0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->calcbuftags, 0, DT_INT, _state, make_automatic);
_kdtreerequestbuffer_init(&p->requestbuffer, _state, make_automatic);
}
void _rbfv1calcbuffer_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
rbfv1calcbuffer *dst = (rbfv1calcbuffer*)_dst;
rbfv1calcbuffer *src = (rbfv1calcbuffer*)_src;
ae_vector_init_copy(&dst->calcbufxcx, &src->calcbufxcx, _state, make_automatic);
ae_matrix_init_copy(&dst->calcbufx, &src->calcbufx, _state, make_automatic);
ae_vector_init_copy(&dst->calcbuftags, &src->calcbuftags, _state, make_automatic);
_kdtreerequestbuffer_init_copy(&dst->requestbuffer, &src->requestbuffer, _state, make_automatic);
}
void _rbfv1calcbuffer_clear(void* _p)
{
rbfv1calcbuffer *p = (rbfv1calcbuffer*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->calcbufxcx);
ae_matrix_clear(&p->calcbufx);
ae_vector_clear(&p->calcbuftags);
_kdtreerequestbuffer_clear(&p->requestbuffer);
}
void _rbfv1calcbuffer_destroy(void* _p)
{
rbfv1calcbuffer *p = (rbfv1calcbuffer*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->calcbufxcx);
ae_matrix_destroy(&p->calcbufx);
ae_vector_destroy(&p->calcbuftags);
_kdtreerequestbuffer_destroy(&p->requestbuffer);
}
void _rbfv1model_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
rbfv1model *p = (rbfv1model*)_p;
ae_touch_ptr((void*)p);
_kdtree_init(&p->tree, _state, make_automatic);
ae_matrix_init(&p->xc, 0, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->wr, 0, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->v, 0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->calcbufxcx, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->calcbufx, 0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->calcbuftags, 0, DT_INT, _state, make_automatic);
}
void _rbfv1model_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
rbfv1model *dst = (rbfv1model*)_dst;
rbfv1model *src = (rbfv1model*)_src;
dst->ny = src->ny;
dst->nx = src->nx;
dst->nc = src->nc;
dst->nl = src->nl;
_kdtree_init_copy(&dst->tree, &src->tree, _state, make_automatic);
ae_matrix_init_copy(&dst->xc, &src->xc, _state, make_automatic);
ae_matrix_init_copy(&dst->wr, &src->wr, _state, make_automatic);
dst->rmax = src->rmax;
ae_matrix_init_copy(&dst->v, &src->v, _state, make_automatic);
ae_vector_init_copy(&dst->calcbufxcx, &src->calcbufxcx, _state, make_automatic);
ae_matrix_init_copy(&dst->calcbufx, &src->calcbufx, _state, make_automatic);
ae_vector_init_copy(&dst->calcbuftags, &src->calcbuftags, _state, make_automatic);
}
void _rbfv1model_clear(void* _p)
{
rbfv1model *p = (rbfv1model*)_p;
ae_touch_ptr((void*)p);
_kdtree_clear(&p->tree);
ae_matrix_clear(&p->xc);
ae_matrix_clear(&p->wr);
ae_matrix_clear(&p->v);
ae_vector_clear(&p->calcbufxcx);
ae_matrix_clear(&p->calcbufx);
ae_vector_clear(&p->calcbuftags);
}
void _rbfv1model_destroy(void* _p)
{
rbfv1model *p = (rbfv1model*)_p;
ae_touch_ptr((void*)p);
_kdtree_destroy(&p->tree);
ae_matrix_destroy(&p->xc);
ae_matrix_destroy(&p->wr);
ae_matrix_destroy(&p->v);
ae_vector_destroy(&p->calcbufxcx);
ae_matrix_destroy(&p->calcbufx);
ae_vector_destroy(&p->calcbuftags);
}
void _gridcalc3v1buf_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
gridcalc3v1buf *p = (gridcalc3v1buf*)_p;
ae_touch_ptr((void*)p);
ae_vector_init(&p->tx, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->cx, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->ty, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->flag0, 0, DT_BOOL, _state, make_automatic);
ae_vector_init(&p->flag1, 0, DT_BOOL, _state, make_automatic);
ae_vector_init(&p->flag2, 0, DT_BOOL, _state, make_automatic);
ae_vector_init(&p->flag12, 0, DT_BOOL, _state, make_automatic);
ae_vector_init(&p->expbuf0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->expbuf1, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->expbuf2, 0, DT_REAL, _state, make_automatic);
_kdtreerequestbuffer_init(&p->requestbuf, _state, make_automatic);
ae_matrix_init(&p->calcbufx, 0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->calcbuftags, 0, DT_INT, _state, make_automatic);
}
void _gridcalc3v1buf_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
gridcalc3v1buf *dst = (gridcalc3v1buf*)_dst;
gridcalc3v1buf *src = (gridcalc3v1buf*)_src;
ae_vector_init_copy(&dst->tx, &src->tx, _state, make_automatic);
ae_vector_init_copy(&dst->cx, &src->cx, _state, make_automatic);
ae_vector_init_copy(&dst->ty, &src->ty, _state, make_automatic);
ae_vector_init_copy(&dst->flag0, &src->flag0, _state, make_automatic);
ae_vector_init_copy(&dst->flag1, &src->flag1, _state, make_automatic);
ae_vector_init_copy(&dst->flag2, &src->flag2, _state, make_automatic);
ae_vector_init_copy(&dst->flag12, &src->flag12, _state, make_automatic);
ae_vector_init_copy(&dst->expbuf0, &src->expbuf0, _state, make_automatic);
ae_vector_init_copy(&dst->expbuf1, &src->expbuf1, _state, make_automatic);
ae_vector_init_copy(&dst->expbuf2, &src->expbuf2, _state, make_automatic);
_kdtreerequestbuffer_init_copy(&dst->requestbuf, &src->requestbuf, _state, make_automatic);
ae_matrix_init_copy(&dst->calcbufx, &src->calcbufx, _state, make_automatic);
ae_vector_init_copy(&dst->calcbuftags, &src->calcbuftags, _state, make_automatic);
}
void _gridcalc3v1buf_clear(void* _p)
{
gridcalc3v1buf *p = (gridcalc3v1buf*)_p;
ae_touch_ptr((void*)p);
ae_vector_clear(&p->tx);
ae_vector_clear(&p->cx);
ae_vector_clear(&p->ty);
ae_vector_clear(&p->flag0);
ae_vector_clear(&p->flag1);
ae_vector_clear(&p->flag2);
ae_vector_clear(&p->flag12);
ae_vector_clear(&p->expbuf0);
ae_vector_clear(&p->expbuf1);
ae_vector_clear(&p->expbuf2);
_kdtreerequestbuffer_clear(&p->requestbuf);
ae_matrix_clear(&p->calcbufx);
ae_vector_clear(&p->calcbuftags);
}
void _gridcalc3v1buf_destroy(void* _p)
{
gridcalc3v1buf *p = (gridcalc3v1buf*)_p;
ae_touch_ptr((void*)p);
ae_vector_destroy(&p->tx);
ae_vector_destroy(&p->cx);
ae_vector_destroy(&p->ty);
ae_vector_destroy(&p->flag0);
ae_vector_destroy(&p->flag1);
ae_vector_destroy(&p->flag2);
ae_vector_destroy(&p->flag12);
ae_vector_destroy(&p->expbuf0);
ae_vector_destroy(&p->expbuf1);
ae_vector_destroy(&p->expbuf2);
_kdtreerequestbuffer_destroy(&p->requestbuf);
ae_matrix_destroy(&p->calcbufx);
ae_vector_destroy(&p->calcbuftags);
}
void _rbfv1report_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
rbfv1report *p = (rbfv1report*)_p;
ae_touch_ptr((void*)p);
}
void _rbfv1report_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
rbfv1report *dst = (rbfv1report*)_dst;
rbfv1report *src = (rbfv1report*)_src;
dst->arows = src->arows;
dst->acols = src->acols;
dst->annz = src->annz;
dst->iterationscount = src->iterationscount;
dst->nmv = src->nmv;
dst->terminationtype = src->terminationtype;
}
void _rbfv1report_clear(void* _p)
{
rbfv1report *p = (rbfv1report*)_p;
ae_touch_ptr((void*)p);
}
void _rbfv1report_destroy(void* _p)
{
rbfv1report *p = (rbfv1report*)_p;
ae_touch_ptr((void*)p);
}
#endif
#if defined(AE_COMPILE_RBF) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This function creates RBF model for a scalar (NY=1) or vector (NY>1)
function in a NX-dimensional space (NX>=1).
Newly created model is empty. It can be used for interpolation right after
creation, but it just returns zeros. You have to add points to the model,
tune interpolation settings, and then call model construction function
rbfbuildmodel() which will update model according to your specification.
USAGE:
1. User creates model with rbfcreate()
2. User adds dataset with rbfsetpoints() (points do NOT have to be on a
regular grid) or rbfsetpointsandscales().
3. (OPTIONAL) User chooses polynomial term by calling:
* rbflinterm() to set linear term
* rbfconstterm() to set constant term
* rbfzeroterm() to set zero term
By default, linear term is used.
4. User tweaks algorithm properties with rbfsetalgohierarchical() method
(or chooses one of the legacy algorithms - QNN (rbfsetalgoqnn) or ML
(rbfsetalgomultilayer)).
5. User calls rbfbuildmodel() function which rebuilds model according to
the specification
6. User may call rbfcalc() to calculate model value at the specified point,
rbfgridcalc() to calculate model values at the points of the regular
grid. User may extract model coefficients with rbfunpack() call.
IMPORTANT: we recommend you to use latest model construction algorithm -
hierarchical RBFs, which is activated by rbfsetalgohierarchical()
function. This algorithm is the fastest one, and most memory-
efficient.
However, it is incompatible with older versions of ALGLIB
(pre-3.11). So, if you serialize hierarchical model, you will
be unable to load it in pre-3.11 ALGLIB. Other model types (QNN
and RBF-ML) are still backward-compatible.
INPUT PARAMETERS:
NX - dimension of the space, NX>=1
NY - function dimension, NY>=1
OUTPUT PARAMETERS:
S - RBF model (initially equals to zero)
NOTE 1: memory requirements. RBF models require amount of memory which is
proportional to the number of data points. Some additional memory
is allocated during model construction, but most of this memory is
freed after model coefficients are calculated. Amount of this
additional memory depends on model construction algorithm being
used.
NOTE 2: prior to ALGLIB version 3.11, RBF models supported only NX=2 or
NX=3. Any attempt to create single-dimensional or more than
3-dimensional RBF model resulted in exception.
ALGLIB 3.11 supports any NX>0, but models created with NX!=2 and
NX!=3 are incompatible with (a) older versions of ALGLIB, (b) old
model construction algorithms (QNN or RBF-ML).
So, if you create a model with NX=2 or NX=3, then, depending on
specific model construction algorithm being chosen, you will (QNN
and RBF-ML) or will not (HierarchicalRBF) get backward compatibility
with older versions of ALGLIB. You have a choice here.
However, if you create a model with NX neither 2 nor 3, you have
no backward compatibility from the start, and you are forced to
use hierarchical RBFs and ALGLIB 3.11 or later.
-- ALGLIB --
Copyright 13.12.2011, 20.06.2016 by Bochkanov Sergey
*************************************************************************/
void rbfcreate(ae_int_t nx, ae_int_t ny, rbfmodel* s, ae_state *_state)
{
_rbfmodel_clear(s);
ae_assert(nx>=1, "RBFCreate: NX<1", _state);
ae_assert(ny>=1, "RBFCreate: NY<1", _state);
s->nx = nx;
s->ny = ny;
rbf_rbfpreparenonserializablefields(s, _state);
/*
* Select default model version according to NX.
*
* The idea is that when we call this function with NX=2 or NX=3, backward
* compatible dummy (zero) V1 model is created, so serialization produces
* model which are compatible with pre-3.11 ALGLIB.
*/
rbf_initializev1(nx, ny, &s->model1, _state);
rbf_initializev2(nx, ny, &s->model2, _state);
if( nx==2||nx==3 )
{
s->modelversion = 1;
}
else
{
s->modelversion = 2;
}
/*
* Report fields
*/
s->progress10000 = 0;
s->terminationrequest = ae_false;
}
/*************************************************************************
This function creates buffer structure which can be used to perform
parallel RBF model evaluations (with one RBF model instance being
used from multiple threads, as long as different threads use different
instances of buffer).
This buffer object can be used with rbftscalcbuf() function (here "ts"
stands for "thread-safe", "buf" is a suffix which denotes function which
reuses previously allocated output space).
How to use it:
* create RBF model structure with rbfcreate()
* load data, tune parameters
* call rbfbuildmodel()
* call rbfcreatecalcbuffer(), once per thread working with RBF model (you
should call this function only AFTER call to rbfbuildmodel(), see below
for more information)
* call rbftscalcbuf() from different threads, with each thread working
with its own copy of buffer object.
INPUT PARAMETERS
S - RBF model
OUTPUT PARAMETERS
Buf - external buffer.
IMPORTANT: buffer object should be used only with RBF model object which
was used to initialize buffer. Any attempt to use buffer with
different object is dangerous - you may get memory violation
error because sizes of internal arrays do not fit to dimensions
of RBF structure.
IMPORTANT: you should call this function only for model which was built
with rbfbuildmodel() function, after successful invocation of
rbfbuildmodel(). Sizes of some internal structures are
determined only after model is built, so buffer object created
before model construction stage will be useless (and any
attempt to use it will result in exception).
-- ALGLIB --
Copyright 02.04.2016 by Sergey Bochkanov
*************************************************************************/
void rbfcreatecalcbuffer(rbfmodel* s,
rbfcalcbuffer* buf,
ae_state *_state)
{
_rbfcalcbuffer_clear(buf);
if( s->modelversion==1 )
{
buf->modelversion = 1;
rbfv1createcalcbuffer(&s->model1, &buf->bufv1, _state);
return;
}
if( s->modelversion==2 )
{
buf->modelversion = 2;
rbfv2createcalcbuffer(&s->model2, &buf->bufv2, _state);
return;
}
ae_assert(ae_false, "RBFCreateCalcBuffer: integrity check failed", _state);
}
/*************************************************************************
This function adds dataset.
This function overrides results of the previous calls, i.e. multiple calls
of this function will result in only the last set being added.
IMPORTANT: ALGLIB version 3.11 and later allows you to specify a set of
per-dimension scales. Interpolation radii are multiplied by the
scale vector. It may be useful if you have mixed spatio-temporal
data (say, a set of 3D slices recorded at different times).
You should call rbfsetpointsandscales() function to use this
feature.
INPUT PARAMETERS:
S - RBF model, initialized by rbfcreate() call.
XY - points, array[N,NX+NY]. One row corresponds to one point
in the dataset. First NX elements are coordinates, next
NY elements are function values. Array may be larger than
specified, in this case only leading [N,NX+NY] elements
will be used.
N - number of points in the dataset
After you've added dataset and (optionally) tuned algorithm settings you
should call rbfbuildmodel() in order to build a model for you.
NOTE: dataset added by this function is not saved during model serialization.
MODEL ITSELF is serialized, but data used to build it are not.
So, if you 1) add dataset to empty RBF model, 2) serialize and
unserialize it, then you will get an empty RBF model with no dataset
being attached.
From the other side, if you call rbfbuildmodel() between (1) and (2),
then after (2) you will get your fully constructed RBF model - but
again with no dataset attached, so subsequent calls to rbfbuildmodel()
will produce empty model.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfsetpoints(rbfmodel* s,
/* Real */ ae_matrix* xy,
ae_int_t n,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
ae_assert(n>0, "RBFSetPoints: N<0", _state);
ae_assert(xy->rows>=n, "RBFSetPoints: Rows(XY)<N", _state);
ae_assert(xy->cols>=s->nx+s->ny, "RBFSetPoints: Cols(XY)<NX+NY", _state);
ae_assert(apservisfinitematrix(xy, n, s->nx+s->ny, _state), "RBFSetPoints: XY contains infinite or NaN values!", _state);
s->n = n;
s->hasscale = ae_false;
ae_matrix_set_length(&s->x, s->n, s->nx, _state);
ae_matrix_set_length(&s->y, s->n, s->ny, _state);
for(i=0; i<=s->n-1; i++)
{
for(j=0; j<=s->nx-1; j++)
{
s->x.ptr.pp_double[i][j] = xy->ptr.pp_double[i][j];
}
for(j=0; j<=s->ny-1; j++)
{
s->y.ptr.pp_double[i][j] = xy->ptr.pp_double[i][j+s->nx];
}
}
}
/*************************************************************************
This function adds dataset and a vector of per-dimension scales.
It may be useful if you have mixed spatio-temporal data - say, a set of 3D
slices recorded at different times. Such data typically require different
RBF radii for spatial and temporal dimensions. ALGLIB solves this problem
by specifying single RBF radius, which is (optionally) multiplied by the
scale vector.
This function overrides results of the previous calls, i.e. multiple calls
of this function will result in only the last set being added.
IMPORTANT: only HierarchicalRBF algorithm can work with scaled points. So,
using this function results in RBF models which can be used in
ALGLIB 3.11 or later. Previous versions of the library will be
unable to unserialize models produced by HierarchicalRBF algo.
Any attempt to use this function with RBF-ML or QNN algorithms
will result in -3 error code being returned (incorrect
algorithm).
INPUT PARAMETERS:
R - RBF model, initialized by rbfcreate() call.
XY - points, array[N,NX+NY]. One row corresponds to one point
in the dataset. First NX elements are coordinates, next
NY elements are function values. Array may be larger than
specified, in this case only leading [N,NX+NY] elements
will be used.
N - number of points in the dataset
S - array[NX], scale vector, S[i]>0.
After you've added dataset and (optionally) tuned algorithm settings you
should call rbfbuildmodel() in order to build a model for you.
NOTE: dataset added by this function is not saved during model serialization.
MODEL ITSELF is serialized, but data used to build it are not.
So, if you 1) add dataset to empty RBF model, 2) serialize and
unserialize it, then you will get an empty RBF model with no dataset
being attached.
From the other side, if you call rbfbuildmodel() between (1) and (2),
then after (2) you will get your fully constructed RBF model - but
again with no dataset attached, so subsequent calls to rbfbuildmodel()
will produce empty model.
-- ALGLIB --
Copyright 20.06.2016 by Bochkanov Sergey
*************************************************************************/
void rbfsetpointsandscales(rbfmodel* r,
/* Real */ ae_matrix* xy,
ae_int_t n,
/* Real */ ae_vector* s,
ae_state *_state)
{
ae_int_t i;
ae_int_t j;
ae_assert(n>0, "RBFSetPointsAndScales: N<0", _state);
ae_assert(xy->rows>=n, "RBFSetPointsAndScales: Rows(XY)<N", _state);
ae_assert(xy->cols>=r->nx+r->ny, "RBFSetPointsAndScales: Cols(XY)<NX+NY", _state);
ae_assert(s->cnt>=r->nx, "RBFSetPointsAndScales: Length(S)<NX", _state);
r->n = n;
r->hasscale = ae_true;
ae_matrix_set_length(&r->x, r->n, r->nx, _state);
ae_matrix_set_length(&r->y, r->n, r->ny, _state);
for(i=0; i<=r->n-1; i++)
{
for(j=0; j<=r->nx-1; j++)
{
r->x.ptr.pp_double[i][j] = xy->ptr.pp_double[i][j];
}
for(j=0; j<=r->ny-1; j++)
{
r->y.ptr.pp_double[i][j] = xy->ptr.pp_double[i][j+r->nx];
}
}
ae_vector_set_length(&r->s, r->nx, _state);
for(i=0; i<=r->nx-1; i++)
{
ae_assert(ae_isfinite(s->ptr.p_double[i], _state), "RBFSetPointsAndScales: S[i] is not finite number", _state);
ae_assert(ae_fp_greater(s->ptr.p_double[i],(double)(0)), "RBFSetPointsAndScales: S[i]<=0", _state);
r->s.ptr.p_double[i] = s->ptr.p_double[i];
}
}
/*************************************************************************
DEPRECATED:since version 3.11 ALGLIB includes new RBF model construction
algorithm, Hierarchical RBF. This algorithm is faster and
requires less memory than QNN and RBF-ML. It is especially good
for large-scale interpolation problems. So, we recommend you to
consider Hierarchical RBF as default option.
==========================================================================
This function sets RBF interpolation algorithm. ALGLIB supports several
RBF algorithms with different properties.
This algorithm is called RBF-QNN and it is good for point sets with
following properties:
a) all points are distinct
b) all points are well separated.
c) points distribution is approximately uniform. There is no "contour
lines", clusters of points, or other small-scale structures.
Algorithm description:
1) interpolation centers are allocated to data points
2) interpolation radii are calculated as distances to the nearest centers
times Q coefficient (where Q is a value from [0.75,1.50]).
3) after performing (2) radii are transformed in order to avoid situation
when single outlier has very large radius and influences many points
across all dataset. Transformation has following form:
new_r[i] = min(r[i],Z*median(r[]))
where r[i] is I-th radius, median() is a median radius across entire
dataset, Z is user-specified value which controls amount of deviation
from median radius.
When (a) is violated, we will be unable to build RBF model. When (b) or
(c) are violated, model will be built, but interpolation quality will be
low. See http://www.alglib.net/interpolation/ for more information on this
subject.
This algorithm is used by default.
Additional Q parameter controls smoothness properties of the RBF basis:
* Q<0.75 will give perfectly conditioned basis, but terrible smoothness
properties (RBF interpolant will have sharp peaks around function values)
* Q around 1.0 gives good balance between smoothness and condition number
* Q>1.5 will lead to badly conditioned systems and slow convergence of the
underlying linear solver (although smoothness will be very good)
* Q>2.0 will effectively make optimizer useless because it won't converge
within reasonable amount of iterations. It is possible to set such large
Q, but it is advised not to do so.
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
Q - Q parameter, Q>0, recommended value - 1.0
Z - Z parameter, Z>0, recommended value - 5.0
NOTE: this function has some serialization-related subtleties. We
recommend you to study serialization examples from ALGLIB Reference
Manual if you want to perform serialization of your models.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfsetalgoqnn(rbfmodel* s, double q, double z, ae_state *_state)
{
ae_assert(ae_isfinite(q, _state), "RBFSetAlgoQNN: Q is infinite or NAN", _state);
ae_assert(ae_fp_greater(q,(double)(0)), "RBFSetAlgoQNN: Q<=0", _state);
ae_assert(ae_isfinite(z, _state), "RBFSetAlgoQNN: Z is infinite or NAN", _state);
ae_assert(ae_fp_greater(z,(double)(0)), "RBFSetAlgoQNN: Z<=0", _state);
s->radvalue = q;
s->radzvalue = z;
s->algorithmtype = 1;
}
/*************************************************************************
DEPRECATED:since version 3.11 ALGLIB includes new RBF model construction
algorithm, Hierarchical RBF. This algorithm is faster and
requires less memory than QNN and RBF-ML. It is especially good
for large-scale interpolation problems. So, we recommend you to
consider Hierarchical RBF as default option.
==========================================================================
This function sets RBF interpolation algorithm. ALGLIB supports several
RBF algorithms with different properties.
This algorithm is called RBF-ML. It builds multilayer RBF model, i.e.
model with subsequently decreasing radii, which allows us to combine
smoothness (due to large radii of the first layers) with exactness (due
to small radii of the last layers) and fast convergence.
Internally RBF-ML uses many different means of acceleration, from sparse
matrices to KD-trees, which results in algorithm whose working time is
roughly proportional to N*log(N)*Density*RBase^2*NLayers, where N is a
number of points, Density is an average density if points per unit of the
interpolation space, RBase is an initial radius, NLayers is a number of
layers.
RBF-ML is good for following kinds of interpolation problems:
1. "exact" problems (perfect fit) with well separated points
2. least squares problems with arbitrary distribution of points (algorithm
gives perfect fit where it is possible, and resorts to least squares
fit in the hard areas).
3. noisy problems where we want to apply some controlled amount of
smoothing.
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
RBase - RBase parameter, RBase>0
NLayers - NLayers parameter, NLayers>0, recommended value to start
with - about 5.
LambdaV - regularization value, can be useful when solving problem
in the least squares sense. Optimal lambda is problem-
dependent and require trial and error. In our experience,
good lambda can be as large as 0.1, and you can use 0.001
as initial guess.
Default value - 0.01, which is used when LambdaV is not
given. You can specify zero value, but it is not
recommended to do so.
TUNING ALGORITHM
In order to use this algorithm you have to choose three parameters:
* initial radius RBase
* number of layers in the model NLayers
* regularization coefficient LambdaV
Initial radius is easy to choose - you can pick any number several times
larger than the average distance between points. Algorithm won't break
down if you choose radius which is too large (model construction time will
increase, but model will be built correctly).
Choose such number of layers that RLast=RBase/2^(NLayers-1) (radius used
by the last layer) will be smaller than the typical distance between
points. In case model error is too large, you can increase number of
layers. Having more layers will make model construction and evaluation
proportionally slower, but it will allow you to have model which precisely
fits your data. From the other side, if you want to suppress noise, you
can DECREASE number of layers to make your model less flexible.
Regularization coefficient LambdaV controls smoothness of the individual
models built for each layer. We recommend you to use default value in case
you don't want to tune this parameter, because having non-zero LambdaV
accelerates and stabilizes internal iterative algorithm. In case you want
to suppress noise you can use LambdaV as additional parameter (larger
value = more smoothness) to tune.
TYPICAL ERRORS
1. Using initial radius which is too large. Memory requirements of the
RBF-ML are roughly proportional to N*Density*RBase^2 (where Density is
an average density of points per unit of the interpolation space). In
the extreme case of the very large RBase we will need O(N^2) units of
memory - and many layers in order to decrease radius to some reasonably
small value.
2. Using too small number of layers - RBF models with large radius are not
flexible enough to reproduce small variations in the target function.
You need many layers with different radii, from large to small, in
order to have good model.
3. Using initial radius which is too small. You will get model with
"holes" in the areas which are too far away from interpolation centers.
However, algorithm will work correctly (and quickly) in this case.
4. Using too many layers - you will get too large and too slow model. This
model will perfectly reproduce your function, but maybe you will be
able to achieve similar results with less layers (and less memory).
-- ALGLIB --
Copyright 02.03.2012 by Bochkanov Sergey
*************************************************************************/
void rbfsetalgomultilayer(rbfmodel* s,
double rbase,
ae_int_t nlayers,
double lambdav,
ae_state *_state)
{
ae_assert(ae_isfinite(rbase, _state), "RBFSetAlgoMultiLayer: RBase is infinite or NaN", _state);
ae_assert(ae_fp_greater(rbase,(double)(0)), "RBFSetAlgoMultiLayer: RBase<=0", _state);
ae_assert(nlayers>=0, "RBFSetAlgoMultiLayer: NLayers<0", _state);
ae_assert(ae_isfinite(lambdav, _state), "RBFSetAlgoMultiLayer: LambdaV is infinite or NAN", _state);
ae_assert(ae_fp_greater_eq(lambdav,(double)(0)), "RBFSetAlgoMultiLayer: LambdaV<0", _state);
s->radvalue = rbase;
s->nlayers = nlayers;
s->algorithmtype = 2;
s->lambdav = lambdav;
}
/*************************************************************************
This function sets RBF interpolation algorithm. ALGLIB supports several
RBF algorithms with different properties.
This algorithm is called Hierarchical RBF. It similar to its previous
incarnation, RBF-ML, i.e. it also builds a sequence of models with
decreasing radii. However, it uses more economical way of building upper
layers (ones with large radii), which results in faster model construction
and evaluation, as well as smaller memory footprint during construction.
This algorithm has following important features:
* ability to handle millions of points
* controllable smoothing via nonlinearity penalization
* support for NX-dimensional models with NX=1 or NX>3 (unlike QNN or RBF-ML)
* support for specification of per-dimensional radii via scale vector,
which is set by means of rbfsetpointsandscales() function. This feature
is useful if you solve spatio-temporal interpolation problems, where
different radii are required for spatial and temporal dimensions.
Running times are roughly proportional to:
* N*log(N)*NLayers - for model construction
* N*NLayers - for model evaluation
You may see that running time does not depend on search radius or points
density, just on number of layers in the hierarchy.
IMPORTANT: this model construction algorithm was introduced in ALGLIB 3.11
and produces models which are INCOMPATIBLE with previous
versions of ALGLIB. You can not unserialize models produced
with this function in ALGLIB 3.10 or earlier.
INPUT PARAMETERS:
S - RBF model, initialized by rbfcreate() call
RBase - RBase parameter, RBase>0
NLayers - NLayers parameter, NLayers>0, recommended value to start
with - about 5.
LambdaNS- >=0, nonlinearity penalty coefficient, negative values are
not allowed. This parameter adds controllable smoothing to
the problem, which may reduce noise. Specification of non-
zero lambda means that in addition to fitting error solver
will also minimize LambdaNS*|S''(x)|^2 (appropriately
generalized to multiple dimensions.
Specification of exactly zero value means that no penalty
is added (we do not even evaluate matrix of second
derivatives which is necessary for smoothing).
Calculation of nonlinearity penalty is costly - it results
in several-fold increase of model construction time.
Evaluation time remains the same.
Optimal lambda is problem-dependent and requires trial
and error. Good value to start from is 1e-5...1e-6,
which corresponds to slightly noticeable smoothing of the
function. Value 1e-2 usually means that quite heavy
smoothing is applied.
TUNING ALGORITHM
In order to use this algorithm you have to choose three parameters:
* initial radius RBase
* number of layers in the model NLayers
* penalty coefficient LambdaNS
Initial radius is easy to choose - you can pick any number several times
larger than the average distance between points. Algorithm won't break
down if you choose radius which is too large (model construction time will
increase, but model will be built correctly).
Choose such number of layers that RLast=RBase/2^(NLayers-1) (radius used
by the last layer) will be smaller than the typical distance between
points. In case model error is too large, you can increase number of
layers. Having more layers will make model construction and evaluation
proportionally slower, but it will allow you to have model which precisely
fits your data. From the other side, if you want to suppress noise, you
can DECREASE number of layers to make your model less flexible (or specify
non-zero LambdaNS).
TYPICAL ERRORS
1. Using too small number of layers - RBF models with large radius are not
flexible enough to reproduce small variations in the target function.
You need many layers with different radii, from large to small, in
order to have good model.
2. Using initial radius which is too small. You will get model with
"holes" in the areas which are too far away from interpolation centers.
However, algorithm will work correctly (and quickly) in this case.
-- ALGLIB --
Copyright 20.06.2016 by Bochkanov Sergey
*************************************************************************/
void rbfsetalgohierarchical(rbfmodel* s,
double rbase,
ae_int_t nlayers,
double lambdans,
ae_state *_state)
{
ae_assert(ae_isfinite(rbase, _state), "RBFSetAlgoHierarchical: RBase is infinite or NaN", _state);
ae_assert(ae_fp_greater(rbase,(double)(0)), "RBFSetAlgoHierarchical: RBase<=0", _state);
ae_assert(nlayers>=0, "RBFSetAlgoHierarchical: NLayers<0", _state);
ae_assert(ae_isfinite(lambdans, _state)&&ae_fp_greater_eq(lambdans,(double)(0)), "RBFSetAlgoHierarchical: LambdaNS<0 or infinite", _state);
s->radvalue = rbase;
s->nlayers = nlayers;
s->algorithmtype = 3;
s->lambdav = lambdans;
}
/*************************************************************************
This function sets linear term (model is a sum of radial basis functions
plus linear polynomial). This function won't have effect until next call
to RBFBuildModel().
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
NOTE: this function has some serialization-related subtleties. We
recommend you to study serialization examples from ALGLIB Reference
Manual if you want to perform serialization of your models.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfsetlinterm(rbfmodel* s, ae_state *_state)
{
s->aterm = 1;
}
/*************************************************************************
This function sets constant term (model is a sum of radial basis functions
plus constant). This function won't have effect until next call to
RBFBuildModel().
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
NOTE: this function has some serialization-related subtleties. We
recommend you to study serialization examples from ALGLIB Reference
Manual if you want to perform serialization of your models.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfsetconstterm(rbfmodel* s, ae_state *_state)
{
s->aterm = 2;
}
/*************************************************************************
This function sets zero term (model is a sum of radial basis functions
without polynomial term). This function won't have effect until next call
to RBFBuildModel().
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
NOTE: this function has some serialization-related subtleties. We
recommend you to study serialization examples from ALGLIB Reference
Manual if you want to perform serialization of your models.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfsetzeroterm(rbfmodel* s, ae_state *_state)
{
s->aterm = 3;
}
/*************************************************************************
This function sets basis function type, which can be:
* 0 for classic Gaussian
* 1 for fast and compact bell-like basis function, which becomes exactly
zero at distance equal to 3*R (default option).
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
BF - basis function type:
* 0 - classic Gaussian
* 1 - fast and compact one
-- ALGLIB --
Copyright 01.02.2017 by Bochkanov Sergey
*************************************************************************/
void rbfsetv2bf(rbfmodel* s, ae_int_t bf, ae_state *_state)
{
ae_assert(bf==0||bf==1, "RBFSetV2Its: BF<>0 and BF<>1", _state);
s->model2.basisfunction = bf;
}
/*************************************************************************
This function sets stopping criteria of the underlying linear solver for
hierarchical (version 2) RBF constructor.
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
MaxIts - this criterion will stop algorithm after MaxIts iterations.
Typically a few hundreds iterations is required, with 400
being a good default value to start experimentation.
Zero value means that default value will be selected.
-- ALGLIB --
Copyright 01.02.2017 by Bochkanov Sergey
*************************************************************************/
void rbfsetv2its(rbfmodel* s, ae_int_t maxits, ae_state *_state)
{
ae_assert(maxits>=0, "RBFSetV2Its: MaxIts is negative", _state);
s->model2.maxits = maxits;
}
/*************************************************************************
This function sets support radius parameter of hierarchical (version 2)
RBF constructor.
Hierarchical RBF model achieves great speed-up by removing from the model
excessive (too dense) nodes. Say, if you have RBF radius equal to 1 meter,
and two nodes are just 1 millimeter apart, you may remove one of them
without reducing model quality.
Support radius parameter is used to justify which points need removal, and
which do not. If two points are less than SUPPORT_R*CUR_RADIUS units of
distance apart, one of them is removed from the model. The larger support
radius is, the faster model construction AND evaluation are. However,
too large values result in "bumpy" models.
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
R - support radius coefficient, >=0.
Recommended values are [0.1,0.4] range, with 0.1 being
default value.
-- ALGLIB --
Copyright 01.02.2017 by Bochkanov Sergey
*************************************************************************/
void rbfsetv2supportr(rbfmodel* s, double r, ae_state *_state)
{
ae_assert(ae_isfinite(r, _state), "RBFSetV2SupportR: R is not finite", _state);
ae_assert(ae_fp_greater_eq(r,(double)(0)), "RBFSetV2SupportR: R<0", _state);
s->model2.supportr = r;
}
/*************************************************************************
This function sets stopping criteria of the underlying linear solver.
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
EpsOrt - orthogonality stopping criterion, EpsOrt>=0. Algorithm will
stop when ||A'*r||<=EpsOrt where A' is a transpose of the
system matrix, r is a residual vector.
Recommended value of EpsOrt is equal to 1E-6.
This criterion will stop algorithm when we have "bad fit"
situation, i.e. when we should stop in a point with large,
nonzero residual.
EpsErr - residual stopping criterion. Algorithm will stop when
||r||<=EpsErr*||b||, where r is a residual vector, b is a
right part of the system (function values).
Recommended value of EpsErr is equal to 1E-3 or 1E-6.
This criterion will stop algorithm in a "good fit"
situation when we have near-zero residual near the desired
solution.
MaxIts - this criterion will stop algorithm after MaxIts iterations.
It should be used for debugging purposes only!
Zero MaxIts means that no limit is placed on the number of
iterations.
We recommend to set moderate non-zero values EpsOrt and EpsErr
simultaneously. Values equal to 10E-6 are good to start with. In case you
need high performance and do not need high precision , you may decrease
EpsErr down to 0.001. However, we do not recommend decreasing EpsOrt.
As for MaxIts, we recommend to leave it zero unless you know what you do.
NOTE: this function has some serialization-related subtleties. We
recommend you to study serialization examples from ALGLIB Reference
Manual if you want to perform serialization of your models.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfsetcond(rbfmodel* s,
double epsort,
double epserr,
ae_int_t maxits,
ae_state *_state)
{
ae_assert(ae_isfinite(epsort, _state)&&ae_fp_greater_eq(epsort,(double)(0)), "RBFSetCond: EpsOrt is negative, INF or NAN", _state);
ae_assert(ae_isfinite(epserr, _state)&&ae_fp_greater_eq(epserr,(double)(0)), "RBFSetCond: EpsB is negative, INF or NAN", _state);
ae_assert(maxits>=0, "RBFSetCond: MaxIts is negative", _state);
if( (ae_fp_eq(epsort,(double)(0))&&ae_fp_eq(epserr,(double)(0)))&&maxits==0 )
{
s->epsort = rbf_eps;
s->epserr = rbf_eps;
s->maxits = 0;
}
else
{
s->epsort = epsort;
s->epserr = epserr;
s->maxits = maxits;
}
}
/*************************************************************************
This function builds RBF model and returns report (contains some
information which can be used for evaluation of the algorithm properties).
Call to this function modifies RBF model by calculating its centers/radii/
weights and saving them into RBFModel structure. Initially RBFModel
contain zero coefficients, but after call to this function we will have
coefficients which were calculated in order to fit our dataset.
After you called this function you can call RBFCalc(), RBFGridCalc() and
other model calculation functions.
INPUT PARAMETERS:
S - RBF model, initialized by RBFCreate() call
Rep - report:
* Rep.TerminationType:
* -5 - non-distinct basis function centers were detected,
interpolation aborted; only QNN returns this
error code, other algorithms can handle non-
distinct nodes.
* -4 - nonconvergence of the internal SVD solver
* -3 incorrect model construction algorithm was chosen:
QNN or RBF-ML, combined with one of the incompatible
features - NX=1 or NX>3; points with per-dimension
scales.
* 1 - successful termination
* 8 - a termination request was submitted via
rbfrequesttermination() function.
Fields which are set only by modern RBF solvers (hierarchical
or nonnegative; older solvers like QNN and ML initialize these
fields by NANs):
* rep.rmserror - root-mean-square error at nodes
* rep.maxerror - maximum error at nodes
Fields are used for debugging purposes:
* Rep.IterationsCount - iterations count of the LSQR solver
* Rep.NMV - number of matrix-vector products
* Rep.ARows - rows count for the system matrix
* Rep.ACols - columns count for the system matrix
* Rep.ANNZ - number of significantly non-zero elements
(elements above some algorithm-determined threshold)
NOTE: failure to build model will leave current state of the structure
unchanged.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfbuildmodel(rbfmodel* s, rbfreport* rep, ae_state *_state)
{
ae_frame _frame_block;
rbfv1report rep1;
rbfv2report rep2;
ae_matrix x3;
ae_vector scalevec;
ae_int_t i;
ae_int_t curalgorithmtype;
ae_frame_make(_state, &_frame_block);
memset(&rep1, 0, sizeof(rep1));
memset(&rep2, 0, sizeof(rep2));
memset(&x3, 0, sizeof(x3));
memset(&scalevec, 0, sizeof(scalevec));
_rbfreport_clear(rep);
_rbfv1report_init(&rep1, _state, ae_true);
_rbfv2report_init(&rep2, _state, ae_true);
ae_matrix_init(&x3, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&scalevec, 0, DT_REAL, _state, ae_true);
/*
* Clean fields prior to processing
*/
rbf_clearreportfields(rep, _state);
s->progress10000 = 0;
s->terminationrequest = ae_false;
/*
* Autoselect algorithm
*/
if( s->algorithmtype==0 )
{
if( (s->nx<2||s->nx>3)||s->hasscale )
{
curalgorithmtype = 3;
}
else
{
curalgorithmtype = 1;
}
}
else
{
curalgorithmtype = s->algorithmtype;
}
/*
* Algorithms which generate V1 models
*/
if( curalgorithmtype==1||curalgorithmtype==2 )
{
/*
* Perform compatibility checks
*/
if( (s->nx<2||s->nx>3)||s->hasscale )
{
rep->terminationtype = -3;
ae_frame_leave(_state);
return;
}
/*
* Try to build model.
*
* NOTE: due to historical reasons RBFV1BuildModel() accepts points
* cast to 3-dimensional space, even if they are really 2-dimensional.
* So, for 2D data we have to explicitly convert them to 3D.
*/
if( s->nx==2 )
{
/*
* Convert data to 3D
*/
rmatrixsetlengthatleast(&x3, s->n, 3, _state);
for(i=0; i<=s->n-1; i++)
{
x3.ptr.pp_double[i][0] = s->x.ptr.pp_double[i][0];
x3.ptr.pp_double[i][1] = s->x.ptr.pp_double[i][1];
x3.ptr.pp_double[i][2] = (double)(0);
}
rbfv1buildmodel(&x3, &s->y, s->n, s->aterm, curalgorithmtype, s->nlayers, s->radvalue, s->radzvalue, s->lambdav, s->epsort, s->epserr, s->maxits, &s->model1, &rep1, _state);
}
else
{
/*
* Work with raw data
*/
rbfv1buildmodel(&s->x, &s->y, s->n, s->aterm, curalgorithmtype, s->nlayers, s->radvalue, s->radzvalue, s->lambdav, s->epsort, s->epserr, s->maxits, &s->model1, &rep1, _state);
}
s->modelversion = 1;
/*
* Convert report fields
*/
rep->arows = rep1.arows;
rep->acols = rep1.acols;
rep->annz = rep1.annz;
rep->iterationscount = rep1.iterationscount;
rep->nmv = rep1.nmv;
rep->terminationtype = rep1.terminationtype;
/*
* Done
*/
ae_frame_leave(_state);
return;
}
/*
* Algorithms which generate V2 models
*/
if( curalgorithmtype==3 )
{
/*
* Prepare scale vector - use unit values or user supplied ones
*/
ae_vector_set_length(&scalevec, s->nx, _state);
for(i=0; i<=s->nx-1; i++)
{
if( s->hasscale )
{
scalevec.ptr.p_double[i] = s->s.ptr.p_double[i];
}
else
{
scalevec.ptr.p_double[i] = (double)(1);
}
}
/*
* Build model
*/
rbfv2buildhierarchical(&s->x, &s->y, s->n, &scalevec, s->aterm, s->nlayers, s->radvalue, s->lambdav, &s->model2, &s->progress10000, &s->terminationrequest, &rep2, _state);
s->modelversion = 2;
/*
* Convert report fields
*/
rep->terminationtype = rep2.terminationtype;
rep->rmserror = rep2.rmserror;
rep->maxerror = rep2.maxerror;
/*
* Done
*/
ae_frame_leave(_state);
return;
}
/*
* Critical error
*/
ae_assert(ae_false, "RBFBuildModel: integrity check failure", _state);
ae_frame_leave(_state);
}
/*************************************************************************
This function calculates values of the RBF model in the given point.
IMPORTANT: this function works only with modern (hierarchical) RBFs. It
can not be used with legacy (version 1) RBFs because older RBF
code does not support 1-dimensional models.
This function should be used when we have NY=1 (scalar function) and NX=1
(1-dimensional space). If you have 3-dimensional space, use rbfcalc3(). If
you have 2-dimensional space, use rbfcalc3(). If you have general
situation (NX-dimensional space, NY-dimensional function) you should use
generic rbfcalc().
If you want to perform parallel model evaluation from multiple threads,
use rbftscalcbuf() with per-thread buffer object.
This function returns 0.0 when:
* model is not initialized
* NX<>1
* NY<>1
INPUT PARAMETERS:
S - RBF model
X0 - X-coordinate, finite number
RESULT:
value of the model or 0.0 (as defined above)
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
double rbfcalc1(rbfmodel* s, double x0, ae_state *_state)
{
double result;
ae_assert(ae_isfinite(x0, _state), "RBFCalc1: invalid value for X0 (X0 is Inf)!", _state);
result = (double)(0);
if( s->ny!=1||s->nx!=1 )
{
return result;
}
if( s->modelversion==1 )
{
result = (double)(0);
return result;
}
if( s->modelversion==2 )
{
result = rbfv2calc1(&s->model2, x0, _state);
return result;
}
ae_assert(ae_false, "RBFCalc1: integrity check failed", _state);
return result;
}
/*************************************************************************
This function calculates values of the RBF model in the given point.
This function should be used when we have NY=1 (scalar function) and NX=2
(2-dimensional space). If you have 3-dimensional space, use rbfcalc3(). If
you have general situation (NX-dimensional space, NY-dimensional function)
you should use generic rbfcalc().
If you want to calculate function values many times, consider using
rbfgridcalc2v(), which is far more efficient than many subsequent calls to
rbfcalc2().
If you want to perform parallel model evaluation from multiple threads,
use rbftscalcbuf() with per-thread buffer object.
This function returns 0.0 when:
* model is not initialized
* NX<>2
*NY<>1
INPUT PARAMETERS:
S - RBF model
X0 - first coordinate, finite number
X1 - second coordinate, finite number
RESULT:
value of the model or 0.0 (as defined above)
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
double rbfcalc2(rbfmodel* s, double x0, double x1, ae_state *_state)
{
double result;
ae_assert(ae_isfinite(x0, _state), "RBFCalc2: invalid value for X0 (X0 is Inf)!", _state);
ae_assert(ae_isfinite(x1, _state), "RBFCalc2: invalid value for X1 (X1 is Inf)!", _state);
result = (double)(0);
if( s->ny!=1||s->nx!=2 )
{
return result;
}
if( s->modelversion==1 )
{
result = rbfv1calc2(&s->model1, x0, x1, _state);
return result;
}
if( s->modelversion==2 )
{
result = rbfv2calc2(&s->model2, x0, x1, _state);
return result;
}
ae_assert(ae_false, "RBFCalc2: integrity check failed", _state);
return result;
}
/*************************************************************************
This function calculates value of the RBF model in the given point.
This function should be used when we have NY=1 (scalar function) and NX=3
(3-dimensional space). If you have 2-dimensional space, use rbfcalc2(). If
you have general situation (NX-dimensional space, NY-dimensional function)
you should use generic rbfcalc().
If you want to calculate function values many times, consider using
rbfgridcalc3v(), which is far more efficient than many subsequent calls to
rbfcalc3().
If you want to perform parallel model evaluation from multiple threads,
use rbftscalcbuf() with per-thread buffer object.
This function returns 0.0 when:
* model is not initialized
* NX<>3
*NY<>1
INPUT PARAMETERS:
S - RBF model
X0 - first coordinate, finite number
X1 - second coordinate, finite number
X2 - third coordinate, finite number
RESULT:
value of the model or 0.0 (as defined above)
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
double rbfcalc3(rbfmodel* s,
double x0,
double x1,
double x2,
ae_state *_state)
{
double result;
ae_assert(ae_isfinite(x0, _state), "RBFCalc3: invalid value for X0 (X0 is Inf or NaN)!", _state);
ae_assert(ae_isfinite(x1, _state), "RBFCalc3: invalid value for X1 (X1 is Inf or NaN)!", _state);
ae_assert(ae_isfinite(x2, _state), "RBFCalc3: invalid value for X2 (X2 is Inf or NaN)!", _state);
result = (double)(0);
if( s->ny!=1||s->nx!=3 )
{
return result;
}
if( s->modelversion==1 )
{
result = rbfv1calc3(&s->model1, x0, x1, x2, _state);
return result;
}
if( s->modelversion==2 )
{
result = rbfv2calc3(&s->model2, x0, x1, x2, _state);
return result;
}
ae_assert(ae_false, "RBFCalc3: integrity check failed", _state);
return result;
}
/*************************************************************************
This function calculates values of the RBF model at the given point.
This is general function which can be used for arbitrary NX (dimension of
the space of arguments) and NY (dimension of the function itself). However
when you have NY=1 you may find more convenient to use rbfcalc2() or
rbfcalc3().
If you want to perform parallel model evaluation from multiple threads,
use rbftscalcbuf() with per-thread buffer object.
This function returns 0.0 when model is not initialized.
INPUT PARAMETERS:
S - RBF model
X - coordinates, array[NX].
X may have more than NX elements, in this case only
leading NX will be used.
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is out-parameter and
reallocated after call to this function. In case you want
to reuse previously allocated Y, you may use RBFCalcBuf(),
which reallocates Y only when it is too small.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfcalc(rbfmodel* s,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_vector_clear(y);
ae_assert(x->cnt>=s->nx, "RBFCalc: Length(X)<NX", _state);
ae_assert(isfinitevector(x, s->nx, _state), "RBFCalc: X contains infinite or NaN values", _state);
rbfcalcbuf(s, x, y, _state);
}
/*************************************************************************
This function calculates values of the RBF model at the given point.
Same as rbfcalc(), but does not reallocate Y when in is large enough to
store function values.
If you want to perform parallel model evaluation from multiple threads,
use rbftscalcbuf() with per-thread buffer object.
INPUT PARAMETERS:
S - RBF model
X - coordinates, array[NX].
X may have more than NX elements, in this case only
leading NX will be used.
Y - possibly preallocated array
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is not reallocated when it
is larger than NY.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfcalcbuf(rbfmodel* s,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_int_t i;
ae_assert(x->cnt>=s->nx, "RBFCalcBuf: Length(X)<NX", _state);
ae_assert(isfinitevector(x, s->nx, _state), "RBFCalcBuf: X contains infinite or NaN values", _state);
if( y->cnt<s->ny )
{
ae_vector_set_length(y, s->ny, _state);
}
for(i=0; i<=s->ny-1; i++)
{
y->ptr.p_double[i] = (double)(0);
}
if( s->modelversion==1 )
{
rbfv1calcbuf(&s->model1, x, y, _state);
return;
}
if( s->modelversion==2 )
{
rbfv2calcbuf(&s->model2, x, y, _state);
return;
}
ae_assert(ae_false, "RBFCalcBuf: integrity check failed", _state);
}
/*************************************************************************
This function calculates values of the RBF model at the given point, using
external buffer object (internal temporaries of RBF model are not
modified).
This function allows to use same RBF model object in different threads,
assuming that different threads use different instances of buffer
structure.
INPUT PARAMETERS:
S - RBF model, may be shared between different threads
Buf - buffer object created for this particular instance of RBF
model with rbfcreatecalcbuffer().
X - coordinates, array[NX].
X may have more than NX elements, in this case only
leading NX will be used.
Y - possibly preallocated array
OUTPUT PARAMETERS:
Y - function value, array[NY]. Y is not reallocated when it
is larger than NY.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbftscalcbuf(rbfmodel* s,
rbfcalcbuffer* buf,
/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_int_t i;
ae_assert(x->cnt>=s->nx, "RBFCalcBuf: Length(X)<NX", _state);
ae_assert(isfinitevector(x, s->nx, _state), "RBFCalcBuf: X contains infinite or NaN values", _state);
ae_assert(s->modelversion==buf->modelversion, "RBFCalcBuf: buffer object is not compatible with RBF model", _state);
if( y->cnt<s->ny )
{
ae_vector_set_length(y, s->ny, _state);
}
for(i=0; i<=s->ny-1; i++)
{
y->ptr.p_double[i] = (double)(0);
}
if( s->modelversion==1 )
{
rbfv1tscalcbuf(&s->model1, &buf->bufv1, x, y, _state);
return;
}
if( s->modelversion==2 )
{
rbfv2tscalcbuf(&s->model2, &buf->bufv2, x, y, _state);
return;
}
ae_assert(ae_false, "RBFTsCalcBuf: integrity check failed", _state);
}
/*************************************************************************
This is legacy function for gridded calculation of RBF model.
It is superseded by rbfgridcalc2v() and rbfgridcalc2vsubset() functions.
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfgridcalc2(rbfmodel* s,
/* Real */ ae_vector* x0,
ae_int_t n0,
/* Real */ ae_vector* x1,
ae_int_t n1,
/* Real */ ae_matrix* y,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector cpx0;
ae_vector cpx1;
ae_vector p01;
ae_vector p11;
ae_vector p2;
ae_frame_make(_state, &_frame_block);
memset(&cpx0, 0, sizeof(cpx0));
memset(&cpx1, 0, sizeof(cpx1));
memset(&p01, 0, sizeof(p01));
memset(&p11, 0, sizeof(p11));
memset(&p2, 0, sizeof(p2));
ae_matrix_clear(y);
ae_vector_init(&cpx0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&cpx1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&p01, 0, DT_INT, _state, ae_true);
ae_vector_init(&p11, 0, DT_INT, _state, ae_true);
ae_vector_init(&p2, 0, DT_INT, _state, ae_true);
ae_assert(n0>0, "RBFGridCalc2: invalid value for N0 (N0<=0)!", _state);
ae_assert(n1>0, "RBFGridCalc2: invalid value for N1 (N1<=0)!", _state);
ae_assert(x0->cnt>=n0, "RBFGridCalc2: Length(X0)<N0", _state);
ae_assert(x1->cnt>=n1, "RBFGridCalc2: Length(X1)<N1", _state);
ae_assert(isfinitevector(x0, n0, _state), "RBFGridCalc2: X0 contains infinite or NaN values!", _state);
ae_assert(isfinitevector(x1, n1, _state), "RBFGridCalc2: X1 contains infinite or NaN values!", _state);
if( s->modelversion==1 )
{
rbfv1gridcalc2(&s->model1, x0, n0, x1, n1, y, _state);
ae_frame_leave(_state);
return;
}
if( s->modelversion==2 )
{
rbfv2gridcalc2(&s->model2, x0, n0, x1, n1, y, _state);
ae_frame_leave(_state);
return;
}
ae_assert(ae_false, "RBFGridCalc2: integrity check failed", _state);
ae_frame_leave(_state);
}
/*************************************************************************
This function calculates values of the RBF model at the regular grid,
which has N0*N1 points, with Point[I,J] = (X0[I], X1[J]). Vector-valued
RBF models are supported.
This function returns 0.0 when:
* model is not initialized
* NX<>2
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
NOTE: Parallel processing is implemented only for modern (hierarchical)
RBFs. Legacy version 1 RBFs (created by QNN or RBF-ML) are still
processed serially.
INPUT PARAMETERS:
S - RBF model, used in read-only mode, can be shared between
multiple invocations of this function from multiple
threads.
X0 - array of grid nodes, first coordinates, array[N0].
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N0 - grid size (number of nodes) in the first dimension
X1 - array of grid nodes, second coordinates, array[N1]
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N1 - grid size (number of nodes) in the second dimension
OUTPUT PARAMETERS:
Y - function values, array[NY*N0*N1], where NY is a number of
"output" vector values (this function supports vector-
valued RBF models). Y is out-variable and is reallocated
by this function.
Y[K+NY*(I0+I1*N0)]=F_k(X0[I0],X1[I1]), for:
* K=0...NY-1
* I0=0...N0-1
* I1=0...N1-1
NOTE: this function supports weakly ordered grid nodes, i.e. you may have
X[i]=X[i+1] for some i. It does not provide you any performance
benefits due to duplication of points, just convenience and
flexibility.
NOTE: this function is re-entrant, i.e. you may use same rbfmodel
structure in multiple threads calling this function for different
grids.
NOTE: if you need function values on some subset of regular grid, which
may be described as "several compact and dense islands", you may
use rbfgridcalc2vsubset().
-- ALGLIB --
Copyright 27.01.2017 by Bochkanov Sergey
*************************************************************************/
void rbfgridcalc2v(rbfmodel* s,
/* Real */ ae_vector* x0,
ae_int_t n0,
/* Real */ ae_vector* x1,
ae_int_t n1,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_vector dummy;
ae_frame_make(_state, &_frame_block);
memset(&dummy, 0, sizeof(dummy));
ae_vector_clear(y);
ae_vector_init(&dummy, 0, DT_BOOL, _state, ae_true);
ae_assert(n0>0, "RBFGridCalc2V: invalid value for N0 (N0<=0)!", _state);
ae_assert(n1>0, "RBFGridCalc2V: invalid value for N1 (N1<=0)!", _state);
ae_assert(x0->cnt>=n0, "RBFGridCalc2V: Length(X0)<N0", _state);
ae_assert(x1->cnt>=n1, "RBFGridCalc2V: Length(X1)<N1", _state);
ae_assert(isfinitevector(x0, n0, _state), "RBFGridCalc2V: X0 contains infinite or NaN values!", _state);
ae_assert(isfinitevector(x1, n1, _state), "RBFGridCalc2V: X1 contains infinite or NaN values!", _state);
for(i=0; i<=n0-2; i++)
{
ae_assert(ae_fp_less_eq(x0->ptr.p_double[i],x0->ptr.p_double[i+1]), "RBFGridCalc2V: X0 is not ordered by ascending", _state);
}
for(i=0; i<=n1-2; i++)
{
ae_assert(ae_fp_less_eq(x1->ptr.p_double[i],x1->ptr.p_double[i+1]), "RBFGridCalc2V: X1 is not ordered by ascending", _state);
}
rbfgridcalc2vx(s, x0, n0, x1, n1, &dummy, ae_false, y, _state);
ae_frame_leave(_state);
}
/*************************************************************************
This function calculates values of the RBF model at some subset of regular
grid:
* grid has N0*N1 points, with Point[I,J] = (X0[I], X1[J])
* only values at some subset of this grid are required
Vector-valued RBF models are supported.
This function returns 0.0 when:
* model is not initialized
* NX<>2
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
NOTE: Parallel processing is implemented only for modern (hierarchical)
RBFs. Legacy version 1 RBFs (created by QNN or RBF-ML) are still
processed serially.
INPUT PARAMETERS:
S - RBF model, used in read-only mode, can be shared between
multiple invocations of this function from multiple
threads.
X0 - array of grid nodes, first coordinates, array[N0].
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N0 - grid size (number of nodes) in the first dimension
X1 - array of grid nodes, second coordinates, array[N1]
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N1 - grid size (number of nodes) in the second dimension
FlagY - array[N0*N1]:
* Y[I0+I1*N0] corresponds to node (X0[I0],X1[I1])
* it is a "bitmap" array which contains False for nodes
which are NOT calculated, and True for nodes which are
required.
OUTPUT PARAMETERS:
Y - function values, array[NY*N0*N1*N2], where NY is a number
of "output" vector values (this function supports vector-
valued RBF models):
* Y[K+NY*(I0+I1*N0)]=F_k(X0[I0],X1[I1]),
for K=0...NY-1, I0=0...N0-1, I1=0...N1-1.
* elements of Y[] which correspond to FlagY[]=True are
loaded by model values (which may be exactly zero for
some nodes).
* elements of Y[] which correspond to FlagY[]=False MAY be
initialized by zeros OR may be calculated. This function
processes grid as a hierarchy of nested blocks and
micro-rows. If just one element of micro-row is required,
entire micro-row (up to 8 nodes in the current version,
but no promises) is calculated.
NOTE: this function supports weakly ordered grid nodes, i.e. you may have
X[i]=X[i+1] for some i. It does not provide you any performance
benefits due to duplication of points, just convenience and
flexibility.
NOTE: this function is re-entrant, i.e. you may use same rbfmodel
structure in multiple threads calling this function for different
grids.
-- ALGLIB --
Copyright 04.03.2016 by Bochkanov Sergey
*************************************************************************/
void rbfgridcalc2vsubset(rbfmodel* s,
/* Real */ ae_vector* x0,
ae_int_t n0,
/* Real */ ae_vector* x1,
ae_int_t n1,
/* Boolean */ ae_vector* flagy,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_int_t i;
ae_vector_clear(y);
ae_assert(n0>0, "RBFGridCalc2VSubset: invalid value for N0 (N0<=0)!", _state);
ae_assert(n1>0, "RBFGridCalc2VSubset: invalid value for N1 (N1<=0)!", _state);
ae_assert(x0->cnt>=n0, "RBFGridCalc2VSubset: Length(X0)<N0", _state);
ae_assert(x1->cnt>=n1, "RBFGridCalc2VSubset: Length(X1)<N1", _state);
ae_assert(flagy->cnt>=n0*n1, "RBFGridCalc2VSubset: Length(FlagY)<N0*N1*N2", _state);
ae_assert(isfinitevector(x0, n0, _state), "RBFGridCalc2VSubset: X0 contains infinite or NaN values!", _state);
ae_assert(isfinitevector(x1, n1, _state), "RBFGridCalc2VSubset: X1 contains infinite or NaN values!", _state);
for(i=0; i<=n0-2; i++)
{
ae_assert(ae_fp_less_eq(x0->ptr.p_double[i],x0->ptr.p_double[i+1]), "RBFGridCalc2VSubset: X0 is not ordered by ascending", _state);
}
for(i=0; i<=n1-2; i++)
{
ae_assert(ae_fp_less_eq(x1->ptr.p_double[i],x1->ptr.p_double[i+1]), "RBFGridCalc2VSubset: X1 is not ordered by ascending", _state);
}
rbfgridcalc2vx(s, x0, n0, x1, n1, flagy, ae_true, y, _state);
}
/*************************************************************************
This function calculates values of the RBF model at the regular grid,
which has N0*N1*N2 points, with Point[I,J,K] = (X0[I], X1[J], X2[K]).
Vector-valued RBF models are supported.
This function returns 0.0 when:
* model is not initialized
* NX<>3
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
NOTE: Parallel processing is implemented only for modern (hierarchical)
RBFs. Legacy version 1 RBFs (created by QNN or RBF-ML) are still
processed serially.
INPUT PARAMETERS:
S - RBF model, used in read-only mode, can be shared between
multiple invocations of this function from multiple
threads.
X0 - array of grid nodes, first coordinates, array[N0].
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N0 - grid size (number of nodes) in the first dimension
X1 - array of grid nodes, second coordinates, array[N1]
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N1 - grid size (number of nodes) in the second dimension
X2 - array of grid nodes, third coordinates, array[N2]
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N2 - grid size (number of nodes) in the third dimension
OUTPUT PARAMETERS:
Y - function values, array[NY*N0*N1*N2], where NY is a number
of "output" vector values (this function supports vector-
valued RBF models). Y is out-variable and is reallocated
by this function.
Y[K+NY*(I0+I1*N0+I2*N0*N1)]=F_k(X0[I0],X1[I1],X2[I2]), for:
* K=0...NY-1
* I0=0...N0-1
* I1=0...N1-1
* I2=0...N2-1
NOTE: this function supports weakly ordered grid nodes, i.e. you may have
X[i]=X[i+1] for some i. It does not provide you any performance
benefits due to duplication of points, just convenience and
flexibility.
NOTE: this function is re-entrant, i.e. you may use same rbfmodel
structure in multiple threads calling this function for different
grids.
NOTE: if you need function values on some subset of regular grid, which
may be described as "several compact and dense islands", you may
use rbfgridcalc3vsubset().
-- ALGLIB --
Copyright 04.03.2016 by Bochkanov Sergey
*************************************************************************/
void rbfgridcalc3v(rbfmodel* s,
/* Real */ ae_vector* x0,
ae_int_t n0,
/* Real */ ae_vector* x1,
ae_int_t n1,
/* Real */ ae_vector* x2,
ae_int_t n2,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_vector dummy;
ae_frame_make(_state, &_frame_block);
memset(&dummy, 0, sizeof(dummy));
ae_vector_clear(y);
ae_vector_init(&dummy, 0, DT_BOOL, _state, ae_true);
ae_assert(n0>0, "RBFGridCalc3V: invalid value for N0 (N0<=0)!", _state);
ae_assert(n1>0, "RBFGridCalc3V: invalid value for N1 (N1<=0)!", _state);
ae_assert(n2>0, "RBFGridCalc3V: invalid value for N2 (N2<=0)!", _state);
ae_assert(x0->cnt>=n0, "RBFGridCalc3V: Length(X0)<N0", _state);
ae_assert(x1->cnt>=n1, "RBFGridCalc3V: Length(X1)<N1", _state);
ae_assert(x2->cnt>=n2, "RBFGridCalc3V: Length(X2)<N2", _state);
ae_assert(isfinitevector(x0, n0, _state), "RBFGridCalc3V: X0 contains infinite or NaN values!", _state);
ae_assert(isfinitevector(x1, n1, _state), "RBFGridCalc3V: X1 contains infinite or NaN values!", _state);
ae_assert(isfinitevector(x2, n2, _state), "RBFGridCalc3V: X2 contains infinite or NaN values!", _state);
for(i=0; i<=n0-2; i++)
{
ae_assert(ae_fp_less_eq(x0->ptr.p_double[i],x0->ptr.p_double[i+1]), "RBFGridCalc3V: X0 is not ordered by ascending", _state);
}
for(i=0; i<=n1-2; i++)
{
ae_assert(ae_fp_less_eq(x1->ptr.p_double[i],x1->ptr.p_double[i+1]), "RBFGridCalc3V: X1 is not ordered by ascending", _state);
}
for(i=0; i<=n2-2; i++)
{
ae_assert(ae_fp_less_eq(x2->ptr.p_double[i],x2->ptr.p_double[i+1]), "RBFGridCalc3V: X2 is not ordered by ascending", _state);
}
rbfgridcalc3vx(s, x0, n0, x1, n1, x2, n2, &dummy, ae_false, y, _state);
ae_frame_leave(_state);
}
/*************************************************************************
This function calculates values of the RBF model at some subset of regular
grid:
* grid has N0*N1*N2 points, with Point[I,J,K] = (X0[I], X1[J], X2[K])
* only values at some subset of this grid are required
Vector-valued RBF models are supported.
This function returns 0.0 when:
* model is not initialized
* NX<>3
! COMMERCIAL EDITION OF ALGLIB:
!
! Commercial Edition of ALGLIB includes following important improvements
! of this function:
! * high-performance native backend with same C# interface (C# version)
! * multithreading support (C++ and C# versions)
!
! We recommend you to read 'Working with commercial version' section of
! ALGLIB Reference Manual in order to find out how to use performance-
! related features provided by commercial edition of ALGLIB.
NOTE: Parallel processing is implemented only for modern (hierarchical)
RBFs. Legacy version 1 RBFs (created by QNN or RBF-ML) are still
processed serially.
INPUT PARAMETERS:
S - RBF model, used in read-only mode, can be shared between
multiple invocations of this function from multiple
threads.
X0 - array of grid nodes, first coordinates, array[N0].
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N0 - grid size (number of nodes) in the first dimension
X1 - array of grid nodes, second coordinates, array[N1]
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N1 - grid size (number of nodes) in the second dimension
X2 - array of grid nodes, third coordinates, array[N2]
Must be ordered by ascending. Exception is generated
if the array is not correctly ordered.
N2 - grid size (number of nodes) in the third dimension
FlagY - array[N0*N1*N2]:
* Y[I0+I1*N0+I2*N0*N1] corresponds to node (X0[I0],X1[I1],X2[I2])
* it is a "bitmap" array which contains False for nodes
which are NOT calculated, and True for nodes which are
required.
OUTPUT PARAMETERS:
Y - function values, array[NY*N0*N1*N2], where NY is a number
of "output" vector values (this function supports vector-
valued RBF models):
* Y[K+NY*(I0+I1*N0+I2*N0*N1)]=F_k(X0[I0],X1[I1],X2[I2]),
for K=0...NY-1, I0=0...N0-1, I1=0...N1-1, I2=0...N2-1.
* elements of Y[] which correspond to FlagY[]=True are
loaded by model values (which may be exactly zero for
some nodes).
* elements of Y[] which correspond to FlagY[]=False MAY be
initialized by zeros OR may be calculated. This function
processes grid as a hierarchy of nested blocks and
micro-rows. If just one element of micro-row is required,
entire micro-row (up to 8 nodes in the current version,
but no promises) is calculated.
NOTE: this function supports weakly ordered grid nodes, i.e. you may have
X[i]=X[i+1] for some i. It does not provide you any performance
benefits due to duplication of points, just convenience and
flexibility.
NOTE: this function is re-entrant, i.e. you may use same rbfmodel
structure in multiple threads calling this function for different
grids.
-- ALGLIB --
Copyright 04.03.2016 by Bochkanov Sergey
*************************************************************************/
void rbfgridcalc3vsubset(rbfmodel* s,
/* Real */ ae_vector* x0,
ae_int_t n0,
/* Real */ ae_vector* x1,
ae_int_t n1,
/* Real */ ae_vector* x2,
ae_int_t n2,
/* Boolean */ ae_vector* flagy,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_int_t i;
ae_vector_clear(y);
ae_assert(n0>0, "RBFGridCalc3VSubset: invalid value for N0 (N0<=0)!", _state);
ae_assert(n1>0, "RBFGridCalc3VSubset: invalid value for N1 (N1<=0)!", _state);
ae_assert(n2>0, "RBFGridCalc3VSubset: invalid value for N2 (N2<=0)!", _state);
ae_assert(x0->cnt>=n0, "RBFGridCalc3VSubset: Length(X0)<N0", _state);
ae_assert(x1->cnt>=n1, "RBFGridCalc3VSubset: Length(X1)<N1", _state);
ae_assert(x2->cnt>=n2, "RBFGridCalc3VSubset: Length(X2)<N2", _state);
ae_assert(flagy->cnt>=n0*n1*n2, "RBFGridCalc3VSubset: Length(FlagY)<N0*N1*N2", _state);
ae_assert(isfinitevector(x0, n0, _state), "RBFGridCalc3VSubset: X0 contains infinite or NaN values!", _state);
ae_assert(isfinitevector(x1, n1, _state), "RBFGridCalc3VSubset: X1 contains infinite or NaN values!", _state);
ae_assert(isfinitevector(x2, n2, _state), "RBFGridCalc3VSubset: X2 contains infinite or NaN values!", _state);
for(i=0; i<=n0-2; i++)
{
ae_assert(ae_fp_less_eq(x0->ptr.p_double[i],x0->ptr.p_double[i+1]), "RBFGridCalc3VSubset: X0 is not ordered by ascending", _state);
}
for(i=0; i<=n1-2; i++)
{
ae_assert(ae_fp_less_eq(x1->ptr.p_double[i],x1->ptr.p_double[i+1]), "RBFGridCalc3VSubset: X1 is not ordered by ascending", _state);
}
for(i=0; i<=n2-2; i++)
{
ae_assert(ae_fp_less_eq(x2->ptr.p_double[i],x2->ptr.p_double[i+1]), "RBFGridCalc3VSubset: X2 is not ordered by ascending", _state);
}
rbfgridcalc3vx(s, x0, n0, x1, n1, x2, n2, flagy, ae_true, y, _state);
}
/*************************************************************************
This function, depending on SparseY, acts as RBFGridCalc2V (SparseY=False)
or RBFGridCalc2VSubset (SparseY=True) function. See comments for these
functions for more information
-- ALGLIB --
Copyright 04.03.2016 by Bochkanov Sergey
*************************************************************************/
void rbfgridcalc2vx(rbfmodel* s,
/* Real */ ae_vector* x0,
ae_int_t n0,
/* Real */ ae_vector* x1,
ae_int_t n1,
/* Boolean */ ae_vector* flagy,
ae_bool sparsey,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t nx;
ae_int_t ny;
ae_int_t ylen;
hqrndstate rs;
ae_vector dummyx2;
ae_vector dummyx3;
ae_int_t i;
ae_int_t j;
ae_int_t k;
ae_int_t l;
ae_vector tx;
ae_vector ty;
ae_int_t dstoffs;
rbfcalcbuffer calcbuf;
ae_frame_make(_state, &_frame_block);
memset(&rs, 0, sizeof(rs));
memset(&dummyx2, 0, sizeof(dummyx2));
memset(&dummyx3, 0, sizeof(dummyx3));
memset(&tx, 0, sizeof(tx));
memset(&ty, 0, sizeof(ty));
memset(&calcbuf, 0, sizeof(calcbuf));
_hqrndstate_init(&rs, _state, ae_true);
ae_vector_init(&dummyx2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dummyx3, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&ty, 0, DT_REAL, _state, ae_true);
_rbfcalcbuffer_init(&calcbuf, _state, ae_true);
ae_assert(n0>0, "RBFGridCalc2VX: invalid value for N0 (N0<=0)!", _state);
ae_assert(n1>0, "RBFGridCalc2VX: invalid value for N1 (N1<=0)!", _state);
ae_assert(x0->cnt>=n0, "RBFGridCalc2VX: Length(X0)<N0", _state);
ae_assert(x1->cnt>=n1, "RBFGridCalc2VX: Length(X1)<N1", _state);
ae_assert(isfinitevector(x0, n0, _state), "RBFGridCalc2VX: X0 contains infinite or NaN values!", _state);
ae_assert(isfinitevector(x1, n1, _state), "RBFGridCalc2VX: X1 contains infinite or NaN values!", _state);
for(i=0; i<=n0-2; i++)
{
ae_assert(ae_fp_less_eq(x0->ptr.p_double[i],x0->ptr.p_double[i+1]), "RBFGridCalc2VX: X0 is not ordered by ascending", _state);
}
for(i=0; i<=n1-2; i++)
{
ae_assert(ae_fp_less_eq(x1->ptr.p_double[i],x1->ptr.p_double[i+1]), "RBFGridCalc2VX: X1 is not ordered by ascending", _state);
}
/*
* Prepare local variables
*/
nx = s->nx;
ny = s->ny;
hqrndseed(325, 46345, &rs, _state);
/*
* Prepare output array
*/
ylen = ny*n0*n1;
ae_vector_set_length(y, ylen, _state);
for(i=0; i<=ylen-1; i++)
{
y->ptr.p_double[i] = (double)(0);
}
if( s->nx!=2 )
{
ae_frame_leave(_state);
return;
}
/*
* Process V2 model
*/
if( s->modelversion==2 )
{
ae_vector_set_length(&dummyx2, 1, _state);
dummyx2.ptr.p_double[0] = (double)(0);
ae_vector_set_length(&dummyx3, 1, _state);
dummyx3.ptr.p_double[0] = (double)(0);
rbfv2gridcalcvx(&s->model2, x0, n0, x1, n1, &dummyx2, 1, &dummyx3, 1, flagy, sparsey, y, _state);
ae_frame_leave(_state);
return;
}
/*
* Reference code for V1 models
*/
if( s->modelversion==1 )
{
ae_vector_set_length(&tx, nx, _state);
rbfcreatecalcbuffer(s, &calcbuf, _state);
for(i=0; i<=n0-1; i++)
{
for(j=0; j<=n1-1; j++)
{
k = i+j*n0;
dstoffs = ny*k;
if( sparsey&&!flagy->ptr.p_bool[k] )
{
for(l=0; l<=ny-1; l++)
{
y->ptr.p_double[l+dstoffs] = (double)(0);
}
continue;
}
tx.ptr.p_double[0] = x0->ptr.p_double[i];
tx.ptr.p_double[1] = x1->ptr.p_double[j];
rbftscalcbuf(s, &calcbuf, &tx, &ty, _state);
for(l=0; l<=ny-1; l++)
{
y->ptr.p_double[l+dstoffs] = ty.ptr.p_double[l];
}
}
}
ae_frame_leave(_state);
return;
}
/*
* Unknown model
*/
ae_assert(ae_false, "RBFGradCalc3VX: integrity check failed", _state);
ae_frame_leave(_state);
}
/*************************************************************************
This function, depending on SparseY, acts as RBFGridCalc3V (SparseY=False)
or RBFGridCalc3VSubset (SparseY=True) function. See comments for these
functions for more information
-- ALGLIB --
Copyright 04.03.2016 by Bochkanov Sergey
*************************************************************************/
void rbfgridcalc3vx(rbfmodel* s,
/* Real */ ae_vector* x0,
ae_int_t n0,
/* Real */ ae_vector* x1,
ae_int_t n1,
/* Real */ ae_vector* x2,
ae_int_t n2,
/* Boolean */ ae_vector* flagy,
ae_bool sparsey,
/* Real */ ae_vector* y,
ae_state *_state)
{
ae_frame _frame_block;
ae_int_t i;
ae_int_t ylen;
ae_int_t nx;
ae_int_t ny;
double rmax;
ae_vector blocks0;
ae_vector blocks1;
ae_vector blocks2;
ae_int_t blockscnt0;
ae_int_t blockscnt1;
ae_int_t blockscnt2;
double blockwidth;
double searchradius;
double avgfuncpernode;
ae_int_t ntrials;
ae_int_t maxblocksize;
gridcalc3v1buf bufseedv1;
ae_shared_pool bufpool;
hqrndstate rs;
ae_vector dummyx3;
ae_frame_make(_state, &_frame_block);
memset(&blocks0, 0, sizeof(blocks0));
memset(&blocks1, 0, sizeof(blocks1));
memset(&blocks2, 0, sizeof(blocks2));
memset(&bufseedv1, 0, sizeof(bufseedv1));
memset(&bufpool, 0, sizeof(bufpool));
memset(&rs, 0, sizeof(rs));
memset(&dummyx3, 0, sizeof(dummyx3));
ae_vector_init(&blocks0, 0, DT_INT, _state, ae_true);
ae_vector_init(&blocks1, 0, DT_INT, _state, ae_true);
ae_vector_init(&blocks2, 0, DT_INT, _state, ae_true);
_gridcalc3v1buf_init(&bufseedv1, _state, ae_true);
ae_shared_pool_init(&bufpool, _state, ae_true);
_hqrndstate_init(&rs, _state, ae_true);
ae_vector_init(&dummyx3, 0, DT_REAL, _state, ae_true);
ae_assert(n0>0, "RBFGridCalc3V: invalid value for N0 (N0<=0)!", _state);
ae_assert(n1>0, "RBFGridCalc3V: invalid value for N1 (N1<=0)!", _state);
ae_assert(n2>0, "RBFGridCalc3V: invalid value for N2 (N2<=0)!", _state);
ae_assert(x0->cnt>=n0, "RBFGridCalc3V: Length(X0)<N0", _state);
ae_assert(x1->cnt>=n1, "RBFGridCalc3V: Length(X1)<N1", _state);
ae_assert(x2->cnt>=n2, "RBFGridCalc3V: Length(X2)<N2", _state);
ae_assert(isfinitevector(x0, n0, _state), "RBFGridCalc3V: X0 contains infinite or NaN values!", _state);
ae_assert(isfinitevector(x1, n1, _state), "RBFGridCalc3V: X1 contains infinite or NaN values!", _state);
ae_assert(isfinitevector(x2, n2, _state), "RBFGridCalc3V: X2 contains infinite or NaN values!", _state);
for(i=0; i<=n0-2; i++)
{
ae_assert(ae_fp_less_eq(x0->ptr.p_double[i],x0->ptr.p_double[i+1]), "RBFGridCalc3V: X0 is not ordered by ascending", _state);
}
for(i=0; i<=n1-2; i++)
{
ae_assert(ae_fp_less_eq(x1->ptr.p_double[i],x1->ptr.p_double[i+1]), "RBFGridCalc3V: X1 is not ordered by ascending", _state);
}
for(i=0; i<=n2-2; i++)
{
ae_assert(ae_fp_less_eq(x2->ptr.p_double[i],x2->ptr.p_double[i+1]), "RBFGridCalc3V: X2 is not ordered by ascending", _state);
}
/*
* Prepare local variables
*/
nx = s->nx;
ny = s->ny;
hqrndseed(325, 46345, &rs, _state);
/*
* Prepare output array
*/
ylen = ny*n0*n1*n2;
ae_vector_set_length(y, ylen, _state);
for(i=0; i<=ylen-1; i++)
{
y->ptr.p_double[i] = (double)(0);
}
if( s->nx!=3 )
{
ae_frame_leave(_state);
return;
}
/*
* Process V1 model
*/
if( s->modelversion==1 )
{
/*
* Fast exit for models without centers
*/
if( s->model1.nc==0 )
{
ae_frame_leave(_state);
return;
}
/*
* Prepare seed, create shared pool of temporary buffers
*/
ae_vector_set_length(&bufseedv1.cx, nx, _state);
ae_vector_set_length(&bufseedv1.tx, nx, _state);
ae_vector_set_length(&bufseedv1.ty, ny, _state);
ae_vector_set_length(&bufseedv1.expbuf0, n0, _state);
ae_vector_set_length(&bufseedv1.expbuf1, n1, _state);
ae_vector_set_length(&bufseedv1.expbuf2, n2, _state);
kdtreecreaterequestbuffer(&s->model1.tree, &bufseedv1.requestbuf, _state);
ae_shared_pool_set_seed(&bufpool, &bufseedv1, sizeof(bufseedv1), _gridcalc3v1buf_init, _gridcalc3v1buf_init_copy, _gridcalc3v1buf_destroy, _state);
/*
* Analyze input grid:
* * analyze average number of basis functions per grid node
* * partition grid in into blocks
*/
rmax = s->model1.rmax;
blockwidth = 2*rmax;
maxblocksize = 8;
searchradius = rmax*rbf_rbffarradius+0.5*ae_sqrt((double)(s->nx), _state)*blockwidth;
ntrials = 100;
avgfuncpernode = 0.0;
for(i=0; i<=ntrials-1; i++)
{
bufseedv1.tx.ptr.p_double[0] = x0->ptr.p_double[hqrnduniformi(&rs, n0, _state)];
bufseedv1.tx.ptr.p_double[1] = x1->ptr.p_double[hqrnduniformi(&rs, n1, _state)];
bufseedv1.tx.ptr.p_double[2] = x2->ptr.p_double[hqrnduniformi(&rs, n2, _state)];
avgfuncpernode = avgfuncpernode+(double)kdtreetsqueryrnn(&s->model1.tree, &bufseedv1.requestbuf, &bufseedv1.tx, searchradius, ae_true, _state)/(double)ntrials;
}
ae_vector_set_length(&blocks0, n0+1, _state);
blockscnt0 = 0;
blocks0.ptr.p_int[0] = 0;
for(i=1; i<=n0-1; i++)
{
if( ae_fp_greater(x0->ptr.p_double[i]-x0->ptr.p_double[blocks0.ptr.p_int[blockscnt0]],blockwidth)||i-blocks0.ptr.p_int[blockscnt0]>=maxblocksize )
{
inc(&blockscnt0, _state);
blocks0.ptr.p_int[blockscnt0] = i;
}
}
inc(&blockscnt0, _state);
blocks0.ptr.p_int[blockscnt0] = n0;
ae_vector_set_length(&blocks1, n1+1, _state);
blockscnt1 = 0;
blocks1.ptr.p_int[0] = 0;
for(i=1; i<=n1-1; i++)
{
if( ae_fp_greater(x1->ptr.p_double[i]-x1->ptr.p_double[blocks1.ptr.p_int[blockscnt1]],blockwidth)||i-blocks1.ptr.p_int[blockscnt1]>=maxblocksize )
{
inc(&blockscnt1, _state);
blocks1.ptr.p_int[blockscnt1] = i;
}
}
inc(&blockscnt1, _state);
blocks1.ptr.p_int[blockscnt1] = n1;
ae_vector_set_length(&blocks2, n2+1, _state);
blockscnt2 = 0;
blocks2.ptr.p_int[0] = 0;
for(i=1; i<=n2-1; i++)
{
if( ae_fp_greater(x2->ptr.p_double[i]-x2->ptr.p_double[blocks2.ptr.p_int[blockscnt2]],blockwidth)||i-blocks2.ptr.p_int[blockscnt2]>=maxblocksize )
{
inc(&blockscnt2, _state);
blocks2.ptr.p_int[blockscnt2] = i;
}
}
inc(&blockscnt2, _state);
blocks2.ptr.p_int[blockscnt2] = n2;
/*
* Perform calculation in multithreaded mode
*/
rbfv1gridcalc3vrec(&s->model1, x0, n0, x1, n1, x2, n2, &blocks0, 0, blockscnt0, &blocks1, 0, blockscnt1, &blocks2, 0, blockscnt2, flagy, sparsey, searchradius, avgfuncpernode, &bufpool, y, _state);
/*
* Done
*/
ae_frame_leave(_state);
return;
}
/*
* Process V2 model
*/
if( s->modelversion==2 )
{
ae_vector_set_length(&dummyx3, 1, _state);
dummyx3.ptr.p_double[0] = (double)(0);
rbfv2gridcalcvx(&s->model2, x0, n0, x1, n1, x2, n2, &dummyx3, 1, flagy, sparsey, y, _state);
ae_frame_leave(_state);
return;
}
/*
* Unknown model
*/
ae_assert(ae_false, "RBFGradCalc3VX: integrity check failed", _state);
ae_frame_leave(_state);
}
/*************************************************************************
This function "unpacks" RBF model by extracting its coefficients.
INPUT PARAMETERS:
S - RBF model
OUTPUT PARAMETERS:
NX - dimensionality of argument
NY - dimensionality of the target function
XWR - model information, array[NC,NX+NY+1].
One row of the array corresponds to one basis function:
* first NX columns - coordinates of the center
* next NY columns - weights, one per dimension of the
function being modelled
For ModelVersion=1:
* last column - radius, same for all dimensions of
the function being modelled
For ModelVersion=2:
* last NX columns - radii, one per dimension
NC - number of the centers
V - polynomial term , array[NY,NX+1]. One row per one
dimension of the function being modelled. First NX
elements are linear coefficients, V[NX] is equal to the
constant part.
ModelVersion-version of the RBF model:
* 1 - for models created by QNN and RBF-ML algorithms,
compatible with ALGLIB 3.10 or earlier.
* 2 - for models created by HierarchicalRBF, requires
ALGLIB 3.11 or later
-- ALGLIB --
Copyright 13.12.2011 by Bochkanov Sergey
*************************************************************************/
void rbfunpack(rbfmodel* s,
ae_int_t* nx,
ae_int_t* ny,
/* Real */ ae_matrix* xwr,
ae_int_t* nc,
/* Real */ ae_matrix* v,
ae_int_t* modelversion,
ae_state *_state)
{
*nx = 0;
*ny = 0;
ae_matrix_clear(xwr);
*nc = 0;
ae_matrix_clear(v);
*modelversion = 0;
if( s->modelversion==1 )
{
*modelversion = 1;
rbfv1unpack(&s->model1, nx, ny, xwr, nc, v, _state);
return;
}
if( s->modelversion==2 )
{
*modelversion = 2;
rbfv2unpack(&s->model2, nx, ny, xwr, nc, v, _state);
return;
}
ae_assert(ae_false, "RBFUnpack: integrity check failure", _state);
}
/*************************************************************************
This function returns model version.
INPUT PARAMETERS:
S - RBF model
RESULT:
* 1 - for models created by QNN and RBF-ML algorithms,
compatible with ALGLIB 3.10 or earlier.
* 2 - for models created by HierarchicalRBF, requires
ALGLIB 3.11 or later
-- ALGLIB --
Copyright 06.07.2016 by Bochkanov Sergey
*************************************************************************/
ae_int_t rbfgetmodelversion(rbfmodel* s, ae_state *_state)
{
ae_int_t result;
result = s->modelversion;
return result;
}
/*************************************************************************
This function is used to peek into hierarchical RBF construction process
from some other thread and get current progress indicator. It returns
value in [0,1].
IMPORTANT: only HRBFs (hierarchical RBFs) support peeking into progress
indicator. Legacy RBF-ML and RBF-QNN do not support it. You
will always get 0 value.
INPUT PARAMETERS:
S - RBF model object
RESULT:
progress value, in [0,1]
-- ALGLIB --
Copyright 17.11.2018 by Bochkanov Sergey
*************************************************************************/
double rbfpeekprogress(rbfmodel* s, ae_state *_state)
{
double result;
result = (double)s->progress10000/(double)10000;
return result;
}
/*************************************************************************
This function is used to submit a request for termination of the
hierarchical RBF construction process from some other thread. As result,
RBF construction is terminated smoothly (with proper deallocation of all
necessary resources) and resultant model is filled by zeros.
A rep.terminationtype=8 will be returned upon receiving such request.
IMPORTANT: only HRBFs (hierarchical RBFs) support termination requests.
Legacy RBF-ML and RBF-QNN do not support it. An attempt to
terminate their construction will be ignored.
IMPORTANT: termination request flag is cleared when the model construction
starts. Thus, any pre-construction termination requests will be
silently ignored - only ones submitted AFTER construction has
actually began will be handled.
INPUT PARAMETERS:
S - RBF model object
-- ALGLIB --
Copyright 17.11.2018 by Bochkanov Sergey
*************************************************************************/
void rbfrequesttermination(rbfmodel* s, ae_state *_state)
{
s->terminationrequest = ae_true;
}
/*************************************************************************
Serializer: allocation
-- ALGLIB --
Copyright 02.02.2012 by Bochkanov Sergey
*************************************************************************/
void rbfalloc(ae_serializer* s, rbfmodel* model, ae_state *_state)
{
/*
* Header
*/
ae_serializer_alloc_entry(s);
/*
* V1 model
*/
if( model->modelversion==1 )
{
/*
* Header
*/
ae_serializer_alloc_entry(s);
rbfv1alloc(s, &model->model1, _state);
return;
}
/*
* V2 model
*/
if( model->modelversion==2 )
{
/*
* Header
*/
ae_serializer_alloc_entry(s);
rbfv2alloc(s, &model->model2, _state);
return;
}
ae_assert(ae_false, "Assertion failed", _state);
}
/*************************************************************************
Serializer: serialization
-- ALGLIB --
Copyright 02.02.2012 by Bochkanov Sergey
*************************************************************************/
void rbfserialize(ae_serializer* s, rbfmodel* model, ae_state *_state)
{
/*
* Header
*/
ae_serializer_serialize_int(s, getrbfserializationcode(_state), _state);
/*
* V1 model
*/
if( model->modelversion==1 )
{
ae_serializer_serialize_int(s, rbf_rbffirstversion, _state);
rbfv1serialize(s, &model->model1, _state);
return;
}
/*
* V2 model
*/
if( model->modelversion==2 )
{
/*
* Header
*/
ae_serializer_serialize_int(s, rbf_rbfversion2, _state);
rbfv2serialize(s, &model->model2, _state);
return;
}
ae_assert(ae_false, "Assertion failed", _state);
}
/*************************************************************************
Serializer: unserialization
-- ALGLIB --
Copyright 02.02.2012 by Bochkanov Sergey
*************************************************************************/
void rbfunserialize(ae_serializer* s, rbfmodel* model, ae_state *_state)
{
ae_int_t i0;
ae_int_t i1;
_rbfmodel_clear(model);
rbf_rbfpreparenonserializablefields(model, _state);
/*
* Header
*/
ae_serializer_unserialize_int(s, &i0, _state);
ae_assert(i0==getrbfserializationcode(_state), "RBFUnserialize: stream header corrupted", _state);
ae_serializer_unserialize_int(s, &i1, _state);
ae_assert(i1==rbf_rbffirstversion||i1==rbf_rbfversion2, "RBFUnserialize: stream header corrupted", _state);
/*
* V1 model
*/
if( i1==rbf_rbffirstversion )
{
rbfv1unserialize(s, &model->model1, _state);
model->modelversion = 1;
model->ny = model->model1.ny;
model->nx = model->model1.nx;
rbf_initializev2(model->nx, model->ny, &model->model2, _state);
return;
}
/*
* V2 model
*/
if( i1==rbf_rbfversion2 )
{
rbfv2unserialize(s, &model->model2, _state);
model->modelversion = 2;
model->ny = model->model2.ny;
model->nx = model->model2.nx;
rbf_initializev1(model->nx, model->ny, &model->model1, _state);
return;
}
ae_assert(ae_false, "Assertion failed", _state);
}
/*************************************************************************
Initialize empty model
-- ALGLIB --
Copyright 12.05.2016 by Bochkanov Sergey
*************************************************************************/
static void rbf_rbfpreparenonserializablefields(rbfmodel* s,
ae_state *_state)
{
s->n = 0;
s->hasscale = ae_false;
s->radvalue = (double)(1);
s->radzvalue = (double)(5);
s->nlayers = 0;
s->lambdav = (double)(0);
s->aterm = 1;
s->algorithmtype = 0;
s->epsort = rbf_eps;
s->epserr = rbf_eps;
s->maxits = 0;
s->nnmaxits = 100;
}
/*************************************************************************
Initialize V1 model (skip initialization for NX=1 or NX>3)
-- ALGLIB --
Copyright 12.05.2016 by Bochkanov Sergey
*************************************************************************/
static void rbf_initializev1(ae_int_t nx,
ae_int_t ny,
rbfv1model* s,
ae_state *_state)
{
_rbfv1model_clear(s);
if( nx==2||nx==3 )
{
rbfv1create(nx, ny, s, _state);
}
}
/*************************************************************************
Initialize V2 model
-- ALGLIB --
Copyright 12.05.2016 by Bochkanov Sergey
*************************************************************************/
static void rbf_initializev2(ae_int_t nx,
ae_int_t ny,
rbfv2model* s,
ae_state *_state)
{
_rbfv2model_clear(s);
rbfv2create(nx, ny, s, _state);
}
/*************************************************************************
Cleans report fields
-- ALGLIB --
Copyright 16.06.2016 by Bochkanov Sergey
*************************************************************************/
static void rbf_clearreportfields(rbfreport* rep, ae_state *_state)
{
rep->rmserror = _state->v_nan;
rep->maxerror = _state->v_nan;
rep->arows = 0;
rep->acols = 0;
rep->annz = 0;
rep->iterationscount = 0;
rep->nmv = 0;
rep->terminationtype = 0;
}
void _rbfcalcbuffer_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
rbfcalcbuffer *p = (rbfcalcbuffer*)_p;
ae_touch_ptr((void*)p);
_rbfv1calcbuffer_init(&p->bufv1, _state, make_automatic);
_rbfv2calcbuffer_init(&p->bufv2, _state, make_automatic);
}
void _rbfcalcbuffer_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
rbfcalcbuffer *dst = (rbfcalcbuffer*)_dst;
rbfcalcbuffer *src = (rbfcalcbuffer*)_src;
dst->modelversion = src->modelversion;
_rbfv1calcbuffer_init_copy(&dst->bufv1, &src->bufv1, _state, make_automatic);
_rbfv2calcbuffer_init_copy(&dst->bufv2, &src->bufv2, _state, make_automatic);
}
void _rbfcalcbuffer_clear(void* _p)
{
rbfcalcbuffer *p = (rbfcalcbuffer*)_p;
ae_touch_ptr((void*)p);
_rbfv1calcbuffer_clear(&p->bufv1);
_rbfv2calcbuffer_clear(&p->bufv2);
}
void _rbfcalcbuffer_destroy(void* _p)
{
rbfcalcbuffer *p = (rbfcalcbuffer*)_p;
ae_touch_ptr((void*)p);
_rbfv1calcbuffer_destroy(&p->bufv1);
_rbfv2calcbuffer_destroy(&p->bufv2);
}
void _rbfmodel_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
rbfmodel *p = (rbfmodel*)_p;
ae_touch_ptr((void*)p);
_rbfv1model_init(&p->model1, _state, make_automatic);
_rbfv2model_init(&p->model2, _state, make_automatic);
ae_matrix_init(&p->x, 0, 0, DT_REAL, _state, make_automatic);
ae_matrix_init(&p->y, 0, 0, DT_REAL, _state, make_automatic);
ae_vector_init(&p->s, 0, DT_REAL, _state, make_automatic);
}
void _rbfmodel_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
rbfmodel *dst = (rbfmodel*)_dst;
rbfmodel *src = (rbfmodel*)_src;
dst->nx = src->nx;
dst->ny = src->ny;
dst->modelversion = src->modelversion;
_rbfv1model_init_copy(&dst->model1, &src->model1, _state, make_automatic);
_rbfv2model_init_copy(&dst->model2, &src->model2, _state, make_automatic);
dst->lambdav = src->lambdav;
dst->radvalue = src->radvalue;
dst->radzvalue = src->radzvalue;
dst->nlayers = src->nlayers;
dst->aterm = src->aterm;
dst->algorithmtype = src->algorithmtype;
dst->epsort = src->epsort;
dst->epserr = src->epserr;
dst->maxits = src->maxits;
dst->nnmaxits = src->nnmaxits;
dst->n = src->n;
ae_matrix_init_copy(&dst->x, &src->x, _state, make_automatic);
ae_matrix_init_copy(&dst->y, &src->y, _state, make_automatic);
dst->hasscale = src->hasscale;
ae_vector_init_copy(&dst->s, &src->s, _state, make_automatic);
dst->progress10000 = src->progress10000;
dst->terminationrequest = src->terminationrequest;
}
void _rbfmodel_clear(void* _p)
{
rbfmodel *p = (rbfmodel*)_p;
ae_touch_ptr((void*)p);
_rbfv1model_clear(&p->model1);
_rbfv2model_clear(&p->model2);
ae_matrix_clear(&p->x);
ae_matrix_clear(&p->y);
ae_vector_clear(&p->s);
}
void _rbfmodel_destroy(void* _p)
{
rbfmodel *p = (rbfmodel*)_p;
ae_touch_ptr((void*)p);
_rbfv1model_destroy(&p->model1);
_rbfv2model_destroy(&p->model2);
ae_matrix_destroy(&p->x);
ae_matrix_destroy(&p->y);
ae_vector_destroy(&p->s);
}
void _rbfreport_init(void* _p, ae_state *_state, ae_bool make_automatic)
{
rbfreport *p = (rbfreport*)_p;
ae_touch_ptr((void*)p);
}
void _rbfreport_init_copy(void* _dst, void* _src, ae_state *_state, ae_bool make_automatic)
{
rbfreport *dst = (rbfreport*)_dst;
rbfreport *src = (rbfreport*)_src;
dst->rmserror = src->rmserror;
dst->maxerror = src->maxerror;
dst->arows = src->arows;
dst->acols = src->acols;
dst->annz = src->annz;
dst->iterationscount = src->iterationscount;
dst->nmv = src->nmv;
dst->terminationtype = src->terminationtype;
}
void _rbfreport_clear(void* _p)
{
rbfreport *p = (rbfreport*)_p;
ae_touch_ptr((void*)p);
}
void _rbfreport_destroy(void* _p)
{
rbfreport *p = (rbfreport*)_p;
ae_touch_ptr((void*)p);
}
#endif
#if defined(AE_COMPILE_INTCOMP) || !defined(AE_PARTIAL_BUILD)
/*************************************************************************
This function is left for backward compatibility.
Use fitspheremc() instead.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void nsfitspheremcc(/* Real */ ae_matrix* xy,
ae_int_t npoints,
ae_int_t nx,
/* Real */ ae_vector* cx,
double* rhi,
ae_state *_state)
{
double dummy;
ae_vector_clear(cx);
*rhi = 0;
nsfitspherex(xy, npoints, nx, 1, 0.0, 0, 0.0, cx, &dummy, rhi, _state);
}
/*************************************************************************
This function is left for backward compatibility.
Use fitspheremi() instead.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void nsfitspheremic(/* Real */ ae_matrix* xy,
ae_int_t npoints,
ae_int_t nx,
/* Real */ ae_vector* cx,
double* rlo,
ae_state *_state)
{
double dummy;
ae_vector_clear(cx);
*rlo = 0;
nsfitspherex(xy, npoints, nx, 2, 0.0, 0, 0.0, cx, rlo, &dummy, _state);
}
/*************************************************************************
This function is left for backward compatibility.
Use fitspheremz() instead.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void nsfitspheremzc(/* Real */ ae_matrix* xy,
ae_int_t npoints,
ae_int_t nx,
/* Real */ ae_vector* cx,
double* rlo,
double* rhi,
ae_state *_state)
{
ae_vector_clear(cx);
*rlo = 0;
*rhi = 0;
nsfitspherex(xy, npoints, nx, 3, 0.0, 0, 0.0, cx, rlo, rhi, _state);
}
/*************************************************************************
This function is left for backward compatibility.
Use fitspherex() instead.
-- ALGLIB --
Copyright 14.04.2017 by Bochkanov Sergey
*************************************************************************/
void nsfitspherex(/* Real */ ae_matrix* xy,
ae_int_t npoints,
ae_int_t nx,
ae_int_t problemtype,
double epsx,
ae_int_t aulits,
double penalty,
/* Real */ ae_vector* cx,
double* rlo,
double* rhi,
ae_state *_state)
{
ae_vector_clear(cx);
*rlo = 0;
*rhi = 0;
fitspherex(xy, npoints, nx, problemtype, epsx, aulits, penalty, cx, rlo, rhi, _state);
}
/*************************************************************************
This function is an obsolete and deprecated version of fitting by
penalized cubic spline.
It was superseded by spline1dfit(), which is an orders of magnitude faster
and more memory-efficient implementation.
Do NOT use this function in the new code!
-- ALGLIB PROJECT --
Copyright 18.08.2009 by Bochkanov Sergey
*************************************************************************/
void spline1dfitpenalized(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
ae_int_t n,
ae_int_t m,
double rho,
ae_int_t* info,
spline1dinterpolant* s,
spline1dfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_vector w;
ae_int_t i;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&w, 0, sizeof(w));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
*info = 0;
_spline1dinterpolant_clear(s);
_spline1dfitreport_clear(rep);
ae_vector_init(&w, 0, DT_REAL, _state, ae_true);
ae_assert(n>=1, "Spline1DFitPenalized: N<1!", _state);
ae_assert(m>=4, "Spline1DFitPenalized: M<4!", _state);
ae_assert(x->cnt>=n, "Spline1DFitPenalized: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DFitPenalized: Length(Y)<N!", _state);
ae_assert(isfinitevector(x, n, _state), "Spline1DFitPenalized: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, n, _state), "Spline1DFitPenalized: Y contains infinite or NAN values!", _state);
ae_assert(ae_isfinite(rho, _state), "Spline1DFitPenalized: Rho is infinite!", _state);
ae_vector_set_length(&w, n, _state);
for(i=0; i<=n-1; i++)
{
w.ptr.p_double[i] = (double)(1);
}
spline1dfitpenalizedw(x, y, &w, n, m, rho, info, s, rep, _state);
ae_frame_leave(_state);
}
/*************************************************************************
This function is an obsolete and deprecated version of fitting by
penalized cubic spline.
It was superseded by spline1dfit(), which is an orders of magnitude faster
and more memory-efficient implementation.
Do NOT use this function in the new code!
-- ALGLIB PROJECT --
Copyright 19.10.2010 by Bochkanov Sergey
*************************************************************************/
void spline1dfitpenalizedw(/* Real */ ae_vector* x,
/* Real */ ae_vector* y,
/* Real */ ae_vector* w,
ae_int_t n,
ae_int_t m,
double rho,
ae_int_t* info,
spline1dinterpolant* s,
spline1dfitreport* rep,
ae_state *_state)
{
ae_frame _frame_block;
ae_vector _x;
ae_vector _y;
ae_vector _w;
ae_int_t i;
ae_int_t j;
ae_int_t b;
double v;
double relcnt;
double xa;
double xb;
double sa;
double sb;
ae_vector xoriginal;
ae_vector yoriginal;
double pdecay;
double tdecay;
ae_matrix fmatrix;
ae_vector fcolumn;
ae_vector y2;
ae_vector w2;
ae_vector xc;
ae_vector yc;
ae_vector dc;
double fdmax;
double admax;
ae_matrix amatrix;
ae_matrix d2matrix;
double fa;
double ga;
double fb;
double gb;
double lambdav;
ae_vector bx;
ae_vector by;
ae_vector bd1;
ae_vector bd2;
ae_vector tx;
ae_vector ty;
ae_vector td;
spline1dinterpolant bs;
ae_matrix nmatrix;
ae_vector rightpart;
fblslincgstate cgstate;
ae_vector c;
ae_vector tmp0;
ae_frame_make(_state, &_frame_block);
memset(&_x, 0, sizeof(_x));
memset(&_y, 0, sizeof(_y));
memset(&_w, 0, sizeof(_w));
memset(&xoriginal, 0, sizeof(xoriginal));
memset(&yoriginal, 0, sizeof(yoriginal));
memset(&fmatrix, 0, sizeof(fmatrix));
memset(&fcolumn, 0, sizeof(fcolumn));
memset(&y2, 0, sizeof(y2));
memset(&w2, 0, sizeof(w2));
memset(&xc, 0, sizeof(xc));
memset(&yc, 0, sizeof(yc));
memset(&dc, 0, sizeof(dc));
memset(&amatrix, 0, sizeof(amatrix));
memset(&d2matrix, 0, sizeof(d2matrix));
memset(&bx, 0, sizeof(bx));
memset(&by, 0, sizeof(by));
memset(&bd1, 0, sizeof(bd1));
memset(&bd2, 0, sizeof(bd2));
memset(&tx, 0, sizeof(tx));
memset(&ty, 0, sizeof(ty));
memset(&td, 0, sizeof(td));
memset(&bs, 0, sizeof(bs));
memset(&nmatrix, 0, sizeof(nmatrix));
memset(&rightpart, 0, sizeof(rightpart));
memset(&cgstate, 0, sizeof(cgstate));
memset(&c, 0, sizeof(c));
memset(&tmp0, 0, sizeof(tmp0));
ae_vector_init_copy(&_x, x, _state, ae_true);
x = &_x;
ae_vector_init_copy(&_y, y, _state, ae_true);
y = &_y;
ae_vector_init_copy(&_w, w, _state, ae_true);
w = &_w;
*info = 0;
_spline1dinterpolant_clear(s);
_spline1dfitreport_clear(rep);
ae_vector_init(&xoriginal, 0, DT_REAL, _state, ae_true);
ae_vector_init(&yoriginal, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&fmatrix, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&fcolumn, 0, DT_REAL, _state, ae_true);
ae_vector_init(&y2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&w2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&xc, 0, DT_REAL, _state, ae_true);
ae_vector_init(&yc, 0, DT_REAL, _state, ae_true);
ae_vector_init(&dc, 0, DT_INT, _state, ae_true);
ae_matrix_init(&amatrix, 0, 0, DT_REAL, _state, ae_true);
ae_matrix_init(&d2matrix, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&by, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bd1, 0, DT_REAL, _state, ae_true);
ae_vector_init(&bd2, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tx, 0, DT_REAL, _state, ae_true);
ae_vector_init(&ty, 0, DT_REAL, _state, ae_true);
ae_vector_init(&td, 0, DT_REAL, _state, ae_true);
_spline1dinterpolant_init(&bs, _state, ae_true);
ae_matrix_init(&nmatrix, 0, 0, DT_REAL, _state, ae_true);
ae_vector_init(&rightpart, 0, DT_REAL, _state, ae_true);
_fblslincgstate_init(&cgstate, _state, ae_true);
ae_vector_init(&c, 0, DT_REAL, _state, ae_true);
ae_vector_init(&tmp0, 0, DT_REAL, _state, ae_true);
ae_assert(n>=1, "Spline1DFitPenalizedW: N<1!", _state);
ae_assert(m>=4, "Spline1DFitPenalizedW: M<4!", _state);
ae_assert(x->cnt>=n, "Spline1DFitPenalizedW: Length(X)<N!", _state);
ae_assert(y->cnt>=n, "Spline1DFitPenalizedW: Length(Y)<N!", _state);
ae_assert(w->cnt>=n, "Spline1DFitPenalizedW: Length(W)<N!", _state);
ae_assert(isfinitevector(x, n, _state), "Spline1DFitPenalizedW: X contains infinite or NAN values!", _state);
ae_assert(isfinitevector(y, n, _state), "Spline1DFitPenalizedW: Y contains infinite or NAN values!", _state);
ae_assert(isfinitevector(w, n, _state), "Spline1DFitPenalizedW: Y contains infinite or NAN values!", _state);
ae_assert(ae_isfinite(rho, _state), "Spline1DFitPenalizedW: Rho is infinite!", _state);
/*
* Prepare LambdaV
*/
v = -ae_log(ae_machineepsilon, _state)/ae_log((double)(10), _state);
if( ae_fp_less(rho,-v) )
{
rho = -v;
}
if( ae_fp_greater(rho,v) )
{
rho = v;
}
lambdav = ae_pow((double)(10), rho, _state);
/*
* Sort X, Y, W
*/
heapsortdpoints(x, y, w, n, _state);
/*
* Scale X, Y, XC, YC
*/
lsfitscalexy(x, y, w, n, &xc, &yc, &dc, 0, &xa, &xb, &sa, &sb, &xoriginal, &yoriginal, _state);
/*
* Allocate space
*/
ae_matrix_set_length(&fmatrix, n, m, _state);
ae_matrix_set_length(&amatrix, m, m, _state);
ae_matrix_set_length(&d2matrix, m, m, _state);
ae_vector_set_length(&bx, m, _state);
ae_vector_set_length(&by, m, _state);
ae_vector_set_length(&fcolumn, n, _state);
ae_matrix_set_length(&nmatrix, m, m, _state);
ae_vector_set_length(&rightpart, m, _state);
ae_vector_set_length(&tmp0, ae_maxint(m, n, _state), _state);
ae_vector_set_length(&c, m, _state);
/*
* Fill:
* * FMatrix by values of basis functions
* * TmpAMatrix by second derivatives of I-th function at J-th point
* * CMatrix by constraints
*/
fdmax = (double)(0);
for(b=0; b<=m-1; b++)
{
/*
* Prepare I-th basis function
*/
for(j=0; j<=m-1; j++)
{
bx.ptr.p_double[j] = (double)(2*j)/(double)(m-1)-1;
by.ptr.p_double[j] = (double)(0);
}
by.ptr.p_double[b] = (double)(1);
spline1dgriddiff2cubic(&bx, &by, m, 2, 0.0, 2, 0.0, &bd1, &bd2, _state);
spline1dbuildcubic(&bx, &by, m, 2, 0.0, 2, 0.0, &bs, _state);
/*
* Calculate B-th column of FMatrix
* Update FDMax (maximum column norm)
*/
spline1dconvcubic(&bx, &by, m, 2, 0.0, 2, 0.0, x, n, &fcolumn, _state);
ae_v_move(&fmatrix.ptr.pp_double[0][b], fmatrix.stride, &fcolumn.ptr.p_double[0], 1, ae_v_len(0,n-1));
v = (double)(0);
for(i=0; i<=n-1; i++)
{
v = v+ae_sqr(w->ptr.p_double[i]*fcolumn.ptr.p_double[i], _state);
}
fdmax = ae_maxreal(fdmax, v, _state);
/*
* Fill temporary with second derivatives of basis function
*/
ae_v_move(&d2matrix.ptr.pp_double[b][0], 1, &bd2.ptr.p_double[0], 1, ae_v_len(0,m-1));
}
/*
* * calculate penalty matrix A
* * calculate max of diagonal elements of A
* * calculate PDecay - coefficient before penalty matrix
*/
for(i=0; i<=m-1; i++)
{
for(j=i; j<=m-1; j++)
{
/*
* calculate integral(B_i''*B_j'') where B_i and B_j are
* i-th and j-th basis splines.
* B_i and B_j are piecewise linear functions.
*/
v = (double)(0);
for(b=0; b<=m-2; b++)
{
fa = d2matrix.ptr.pp_double[i][b];
fb = d2matrix.ptr.pp_double[i][b+1];
ga = d2matrix.ptr.pp_double[j][b];
gb = d2matrix.ptr.pp_double[j][b+1];
v = v+(bx.ptr.p_double[b+1]-bx.ptr.p_double[b])*(fa*ga+(fa*(gb-ga)+ga*(fb-fa))/2+(fb-fa)*(gb-ga)/3);
}
amatrix.ptr.pp_double[i][j] = v;
amatrix.ptr.pp_double[j][i] = v;
}
}
admax = (double)(0);
for(i=0; i<=m-1; i++)
{
admax = ae_maxreal(admax, ae_fabs(amatrix.ptr.pp_double[i][i], _state), _state);
}
pdecay = lambdav*fdmax/admax;
/*
* Calculate TDecay for Tikhonov regularization
*/
tdecay = fdmax*(1+pdecay)*10*ae_machineepsilon;
/*
* Prepare system
*
* NOTE: FMatrix is spoiled during this process
*/
for(i=0; i<=n-1; i++)
{
v = w->ptr.p_double[i];
ae_v_muld(&fmatrix.ptr.pp_double[i][0], 1, ae_v_len(0,m-1), v);
}
rmatrixgemm(m, m, n, 1.0, &fmatrix, 0, 0, 1, &fmatrix, 0, 0, 0, 0.0, &nmatrix, 0, 0, _state);
for(i=0; i<=m-1; i++)
{
for(j=0; j<=m-1; j++)
{
nmatrix.ptr.pp_double[i][j] = nmatrix.ptr.pp_double[i][j]+pdecay*amatrix.ptr.pp_double[i][j];
}
}
for(i=0; i<=m-1; i++)
{
nmatrix.ptr.pp_double[i][i] = nmatrix.ptr.pp_double[i][i]+tdecay;
}
for(i=0; i<=m-1; i++)
{
rightpart.ptr.p_double[i] = (double)(0);
}
for(i=0; i<=n-1; i++)
{
v = y->ptr.p_double[i]*w->ptr.p_double[i];
ae_v_addd(&rightpart.ptr.p_double[0], 1, &fmatrix.ptr.pp_double[i][0], 1, ae_v_len(0,m-1), v);
}
/*
* Solve system
*/
if( !spdmatrixcholesky(&nmatrix, m, ae_true, _state) )
{
*info = -4;
ae_frame_leave(_state);
return;
}
fblscholeskysolve(&nmatrix, 1.0, m, ae_true, &rightpart, &tmp0, _state);
ae_v_move(&c.ptr.p_double[0], 1, &rightpart.ptr.p_double[0], 1, ae_v_len(0,m-1));
/*
* add nodes to force linearity outside of the fitting interval
*/
spline1dgriddiffcubic(&bx, &c, m, 2, 0.0, 2, 0.0, &bd1, _state);
ae_vector_set_length(&tx, m+2, _state);
ae_vector_set_length(&ty, m+2, _state);
ae_vector_set_length(&td, m+2, _state);
ae_v_move(&tx.ptr.p_double[1], 1, &bx.ptr.p_double[0], 1, ae_v_len(1,m));
ae_v_move(&ty.ptr.p_double[1], 1, &rightpart.ptr.p_double[0], 1, ae_v_len(1,m));
ae_v_move(&td.ptr.p_double[1], 1, &bd1.ptr.p_double[0], 1, ae_v_len(1,m));
tx.ptr.p_double[0] = tx.ptr.p_double[1]-(tx.ptr.p_double[2]-tx.ptr.p_double[1]);
ty.ptr.p_double[0] = ty.ptr.p_double[1]-td.ptr.p_double[1]*(tx.ptr.p_double[2]-tx.ptr.p_double[1]);
td.ptr.p_double[0] = td.ptr.p_double[1];
tx.ptr.p_double[m+1] = tx.ptr.p_double[m]+(tx.ptr.p_double[m]-tx.ptr.p_double[m-1]);
ty.ptr.p_double[m+1] = ty.ptr.p_double[m]+td.ptr.p_double[m]*(tx.ptr.p_double[m]-tx.ptr.p_double[m-1]);
td.ptr.p_double[m+1] = td.ptr.p_double[m];
spline1dbuildhermite(&tx, &ty, &td, m+2, s, _state);
spline1dlintransx(s, 2/(xb-xa), -(xa+xb)/(xb-xa), _state);
spline1dlintransy(s, sb-sa, sa, _state);
*info = 1;
/*
* Fill report
*/
rep->rmserror = (double)(0);
rep->avgerror = (double)(0);
rep->avgrelerror = (double)(0);
rep->maxerror = (double)(0);
relcnt = (double)(0);
spline1dconvcubic(&bx, &rightpart, m, 2, 0.0, 2, 0.0, x, n, &fcolumn, _state);
for(i=0; i<=n-1; i++)
{
v = (sb-sa)*fcolumn.ptr.p_double[i]+sa;
rep->rmserror = rep->rmserror+ae_sqr(v-yoriginal.ptr.p_double[i], _state);
rep->avgerror = rep->avgerror+ae_fabs(v-yoriginal.ptr.p_double[i], _state);
if( ae_fp_neq(yoriginal.ptr.p_double[i],(double)(0)) )
{
rep->avgrelerror = rep->avgrelerror+ae_fabs(v-yoriginal.ptr.p_double[i], _state)/ae_fabs(yoriginal.ptr.p_double[i], _state);
relcnt = relcnt+1;
}
rep->maxerror = ae_maxreal(rep->maxerror, ae_fabs(v-yoriginal.ptr.p_double[i], _state), _state);
}
rep->rmserror = ae_sqrt(rep->rmserror/n, _state);
rep->avgerror = rep->avgerror/n;
if( ae_fp_neq(relcnt,(double)(0)) )
{
rep->avgrelerror = rep->avgrelerror/relcnt;
}
ae_frame_leave(_state);
}
#endif
}
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