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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 dexpma (double* in, double* out, int _iLeadDim){
int iIndex1 = 0;
int iMax = 0;
int iFlag = 0;
int iLoop1 = 0;
int iSquare = 0;
double dblExp = 0;
double dblS = 0;
double dblS2 = 0;
double dblCst = 0.5;
double *pdblMatrixA = NULL;/*A'*/
double *pdblMatrixX = NULL;/*X*/
double *pdblMatrixD = NULL;/*D*/
double *pdblMatrixcX = NULL;/*cX*/
double *pdblMatrixcA = NULL;/*cX*/
double *pdblMatrixEye = NULL;/*Eye*/
double *pdblMatrixTemp = NULL;/*Temp*/
double *pdblMatrixTemp2 = NULL;/*Temp2*/
iSquare = _iLeadDim * _iLeadDim;
pdblMatrixA = (double*)malloc(sizeof(double) *(unsigned int) iSquare);
pdblMatrixX = (double*)malloc(sizeof(double) *(unsigned int) iSquare);
pdblMatrixD = (double*)malloc(sizeof(double) *(unsigned int) iSquare);
pdblMatrixcX = (double*)malloc(sizeof(double) *(unsigned int) iSquare);
pdblMatrixcA = (double*)malloc(sizeof(double) *(unsigned int) iSquare);
pdblMatrixEye = (double*)malloc(sizeof(double) *(unsigned int) iSquare);
pdblMatrixTemp = (double*)malloc(sizeof(double) *(unsigned int) iSquare);
pdblMatrixTemp2 = (double*)malloc(sizeof(double) *(unsigned int) iSquare);
/* Scale A by power of 2 so that its norm is < 1/2 .*/
dfrexps( dinfnorma( in, _iLeadDim, _iLeadDim), &dblExp);
dblS = max(0, dblExp + 1);
dblS2 = dpows(2, dblS);
/*A = A./2^s*/
for ( iIndex1 = 0 ; iIndex1 < iSquare ; iIndex1++ )
pdblMatrixA[iIndex1] = in[iIndex1] / dblS2 ;
/* Pade approximation for exp(A)*/
/*X = A */
/*C2F(dcopy)(&iSquare, pdblMatrixA, &iOne, pdblMatrixX, &iOne );*/
for ( iIndex1 = 0 ; iIndex1 < iSquare ; iIndex1++ )
pdblMatrixX[iIndex1] = pdblMatrixA[iIndex1] ;
deyea(pdblMatrixEye, _iLeadDim, _iLeadDim);
/*cA = A * c*/
for ( iIndex1 = 0 ; iIndex1 < iSquare ; iIndex1++ )
pdblMatrixcA[iIndex1] = pdblMatrixA[iIndex1] * dblCst ;
/*E = Eye + cA*/
dadda (pdblMatrixEye , iSquare, pdblMatrixcA ,iSquare, out ) ;
/*D = Eye - cA*/
ddiffa (pdblMatrixEye , iSquare, pdblMatrixcA ,iSquare,pdblMatrixD ) ;
iMax = 6;
iFlag = 1;
for(iLoop1 = 2 ; iLoop1 <= iMax ; iLoop1++)
{
dblCst = dblCst * (iMax - iLoop1 + 1 ) / (iLoop1 * (2 * iMax - iLoop1 + 1));
/*Temp = X*/
/*C2F(dcopy)(&iSquare, pdblMatrixX, &iOne, pdblMatrixTemp, &iOne);*/
for ( iIndex1 = 0 ; iIndex1 < iSquare ; iIndex1++ )
pdblMatrixTemp[iIndex1] = pdblMatrixX[iIndex1] ;
/*X = A * Temp;*/
dmulma ( pdblMatrixA , _iLeadDim , _iLeadDim,
pdblMatrixTemp , _iLeadDim , _iLeadDim,
pdblMatrixX );
/*cX = c * X*/
for ( iIndex1 = 0 ; iIndex1 < iSquare ; iIndex1++ )
pdblMatrixcX[iIndex1] = pdblMatrixX[iIndex1] * dblCst ;
/*E = E + cX*/
dadda ( out, iSquare , pdblMatrixcX , iSquare , out ) ;
if(iFlag == 1) /*D = D + cX*/
{
dadda ( pdblMatrixD, iSquare , pdblMatrixcX , iSquare , pdblMatrixD ) ;
}
else /*D = D - cX*/
{
ddiffa ( pdblMatrixD, iSquare , pdblMatrixcX , iSquare , pdblMatrixD );
}
/*Toggle iFlag*/
iFlag = !iFlag;
}
/*Temp = E*/
/*C2F(dcopy)(&iSquare, out, &iOne, pdblMatrixTemp, &iOne);*/
for ( iIndex1 = 0 ; iIndex1 < iSquare ; iIndex1++ )
pdblMatrixTemp[iIndex1] = out[iIndex1] ;
/*E = D\E*/
dldivma ( pdblMatrixD , _iLeadDim , _iLeadDim , pdblMatrixTemp , _iLeadDim , _iLeadDim , out );
/* Undo scaling by repeated squaring*/
for(iLoop1 = 0 ; iLoop1 < dblS ; iLoop1++)
{
/*Temp = E*/
/*Temp2 = E*/
/*C2F(dcopy)(&iSquare, out, &iOne, pdblMatrixTemp, &iOne);
C2F(dcopy)(&iSquare, out, &iOne, pdblMatrixTemp2, &iOne);*/
for ( iIndex1 = 0 ; iIndex1 < iSquare ; iIndex1++ )
{
pdblMatrixTemp [iIndex1] = out[iIndex1] ;
pdblMatrixTemp2[iIndex1] = out[iIndex1] ;
}
/* E = E*E*/
dmulma ( pdblMatrixTemp , _iLeadDim , _iLeadDim,
pdblMatrixTemp2 , _iLeadDim , _iLeadDim,
out );
}
free(pdblMatrixA);
free(pdblMatrixX);
free(pdblMatrixD);
free(pdblMatrixcX);
free(pdblMatrixcA);
free(pdblMatrixEye);
free(pdblMatrixTemp);
free(pdblMatrixTemp2);
return ;
}
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