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/*
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008-2008 - INRIA - Allan SIMON
*
* This file must be used under the terms of the CeCILL.
* This source file is licensed as described in the file COPYING, which
* you should have received as part of this distribution. The terms
* are also available at
* http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
*
*/
#include "matrixExponential.h"
void sexpma (float* in, float* out, int _iLeadDim){
int iIndex1 = 0;
int iMax = 0;
int iFlag = 0;
int iLoop1 = 0;
int iSquare = 0;
float fltExp = 0;
float fltS = 0;
float fltS2 = 0;
float fltCst = 0.5f;
double dblCst = 0.5;
float *pfltMatrixA = NULL;/*A'*/
float *pfltMatrixX = NULL;/*X*/
float *pfltMatrixD = NULL;/*D*/
float *pfltMatrixcX = NULL;/*cX*/
float *pfltMatrixcA = NULL;/*cX*/
float *pfltMatrixEye = NULL;/*Eye*/
float *pfltMatrixTemp = NULL;/*Temp*/
float *pfltMatrixTemp2 = NULL;/*Temp2*/
iSquare = _iLeadDim * _iLeadDim;
pfltMatrixA = (float*)malloc(sizeof(float) *(unsigned int) iSquare);
pfltMatrixX = (float*)malloc(sizeof(float) *(unsigned int) iSquare);
pfltMatrixD = (float*)malloc(sizeof(float) *(unsigned int) iSquare);
pfltMatrixcX = (float*)malloc(sizeof(float) *(unsigned int) iSquare);
pfltMatrixcA = (float*)malloc(sizeof(float) *(unsigned int) iSquare);
pfltMatrixEye = (float*)malloc(sizeof(float) *(unsigned int) iSquare);
pfltMatrixTemp = (float*)malloc(sizeof(float) *(unsigned int) iSquare);
pfltMatrixTemp2 = (float*)malloc(sizeof(float) *(unsigned int) iSquare);
/* Scale A by power of 2 so that its norm is < 1/2 .*/
sfrexps( sinfnorma( in, _iLeadDim, _iLeadDim), &fltExp);
fltS = max(0, fltExp + 1);
fltS2 = spows(2, fltS);
/*A = A./2^s*/
for ( iIndex1 = 0 ; iIndex1 < iSquare ; iIndex1++ )
pfltMatrixA[iIndex1] = in[iIndex1] / fltS2;
/* Pade approximation for exp(A)*/
/*X = A */
/*C2F(dcopy)(&iSquare, pfltMatrixA, &iOne, pfltMatrixX, &iOne );*/
for ( iIndex1 = 0 ; iIndex1 < iSquare ; iIndex1++ )
pfltMatrixX[iIndex1] = pfltMatrixA[iIndex1] ;
seyea(pfltMatrixEye, _iLeadDim, _iLeadDim);
/*cA = A * c*/
for ( iIndex1 = 0 ; iIndex1 < iSquare ; iIndex1++ )
pfltMatrixcA[iIndex1] = pfltMatrixA[iIndex1] * fltCst ;
/*E = Eye + cA*/
sadda (pfltMatrixEye , iSquare, pfltMatrixcA ,iSquare, out ) ;
/*D = Eye - cA*/
sdiffa (pfltMatrixEye , iSquare, pfltMatrixcA ,iSquare,pfltMatrixD ) ;
iMax = 6;
iFlag = 1;
for(iLoop1 = 2 ; iLoop1 <= iMax ; iLoop1++)
{
dblCst = dblCst * (iMax - iLoop1 + 1 ) / (iLoop1 * (2 * iMax - iLoop1 + 1));
dblCst += 0 ;
/*Temp = X*/
/*C2F(dcopy)(&iSquare, pfltMatrixX, &iOne, pfltMatrixTemp, &iOne);*/
for ( iIndex1 = 0 ; iIndex1 < iSquare ; iIndex1++ )
pfltMatrixTemp[iIndex1] = pfltMatrixX[iIndex1] ;
/*X = A * Temp;*/
smulma ( pfltMatrixA , _iLeadDim , _iLeadDim,
pfltMatrixTemp , _iLeadDim , _iLeadDim,
pfltMatrixX );
/*cX = c * X*/
for ( iIndex1 = 0 ; iIndex1 < iSquare ; iIndex1++ )
pfltMatrixcX[iIndex1] = pfltMatrixX[iIndex1] * (float) dblCst ;
/*E = E + cX*/
sadda ( out, iSquare , pfltMatrixcX , iSquare , out ) ;
if(iFlag == 1) /*D = D + cX*/
{
sadda ( pfltMatrixD, iSquare , pfltMatrixcX , iSquare , pfltMatrixD ) ;
}
else /*D = D - cX*/
{
sdiffa ( pfltMatrixD, iSquare , pfltMatrixcX , iSquare , pfltMatrixD );
}
/*Toggle iFlag*/
iFlag = !iFlag;
}
/*Temp = E*/
/*C2F(dcopy)(&iSquare, out, &iOne, pfltMatrixTemp, &iOne);*/
for ( iIndex1 = 0 ; iIndex1 < iSquare ; iIndex1++ )
pfltMatrixTemp[iIndex1] = out[iIndex1] ;
/*E = D\E*/
sldivma ( pfltMatrixD , _iLeadDim , _iLeadDim , pfltMatrixTemp , _iLeadDim , _iLeadDim , out );
/* Undo scaling by repeated squaring*/
for(iLoop1 = 0 ; iLoop1 < fltS ; iLoop1++)
{
/*Temp = E*/
/*Temp2 = E*/
/*C2F(dcopy)(&iSquare, out, &iOne, pfltMatrixTemp, &iOne);
C2F(dcopy)(&iSquare, out, &iOne, pfltMatrixTemp2, &iOne);*/
for ( iIndex1 = 0 ; iIndex1 < iSquare ; iIndex1++ )
{
pfltMatrixTemp [iIndex1] = out[iIndex1] ;
pfltMatrixTemp2[iIndex1] = out[iIndex1] ;
}
/* E = E*E*/
smulma ( pfltMatrixTemp , _iLeadDim , _iLeadDim,
pfltMatrixTemp2 , _iLeadDim , _iLeadDim,
out );
}
free(pfltMatrixA);
free(pfltMatrixX);
free(pfltMatrixD);
free(pfltMatrixcX);
free(pfltMatrixcA);
free(pfltMatrixEye);
free(pfltMatrixTemp);
free(pfltMatrixTemp2);
return ;
}
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