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/*
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008 - INRIA - Arnaud TORSET
*
* 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 <stdio.h>
#include <malloc.h>
#include "lapack.h"
#include "logm.h"
#include "log.h"
#include "matrixMultiplication.h"
#include "matrixTranspose.h"
#include "matrixInversion.h"
#include "max.h"
void zlogma (doubleComplex* in, int size, doubleComplex* out){
/* Algo : */
/* trouver les valeurs propres vp */
/* en déduire les vecteurs propres Vp */
/* utiliser la formule suivante
* logm = Vp * diag(log(diag(vp)) * inv(Vp) */
int i;
doubleComplex *eigenvalues, *eigenvectors, *tmp;
int symetrique = 0;
int info = 0; /* Used by LAPACK */
int iWorkSize = 0; /* Used by LAPACK */
doubleComplex *pdblWork = NULL; /* Used by LAPACK */
doubleComplex *pdblRWork = NULL; /* Used by LAPACK */
doubleComplex * pdblLeftvectors = NULL; /* Used by LAPACK */
doubleComplex * inCopy = NULL; /* Used by LAPACK */
/* Data initialization */
eigenvalues = malloc((uint)(size*size)*sizeof(doubleComplex));
eigenvectors = malloc((uint)(size*size)*sizeof(doubleComplex));
tmp = malloc((uint)(size*size)*sizeof(doubleComplex));
iWorkSize = max(1,2*size);
pdblWork = malloc((uint)(iWorkSize)*sizeof(doubleComplex));
pdblRWork = malloc((uint)(2*size)*sizeof(doubleComplex));
inCopy = malloc((uint)(size*size)*sizeof(doubleComplex));
/* Copy in in inCopy */
for (i=0;i<size*size;i++)
inCopy[i] = in[i];
/* regarde si in est symetrique */
ztransposea(in,size,size,tmp);
for (i=0;i<size*size;i++){
if ( (zreals(in[i])!=zreals(tmp[i])) || (zimags(in[i])!=zimags(tmp[i])) ) break;
}
if (i==size*size) symetrique = 1;
/* trouver les valeurs propres vp ainsi que les vecteurs propres*/
if (symetrique){
C2F(zheev)( "V", "U", &size, inCopy, &size, eigenvalues,
pdblWork, &iWorkSize, pdblRWork, &info );
eigenvectors = inCopy;
}
else {
C2F(zgeev)( "N", "V", &size, inCopy, &size, eigenvalues,
pdblLeftvectors, &size, eigenvectors, &size, pdblWork, &iWorkSize,
pdblRWork, &info );
for(i=0;i<size;i++) {
eigenvalues[i*size+i] = eigenvalues[i];
if ((i*size+i)!=i) eigenvalues[i] = DoubleComplex(0,0);
}
}
/* utiliser la formule suivante
* logm = Vp * diag(log(diag(vp)) * inv(Vp) */
/* diag(log(diag(vp)) */
for (i=0;i<size*size;i++){
if ((i%(size+1))==0) /* teste si i est sur la diagonale */
eigenvalues[i] = zlogs(eigenvalues[i]);
else eigenvalues[i] = DoubleComplex(0,0);
}
/* Vp * diag(log(diag(vp)) */
zmulma(eigenvectors, size, size, eigenvalues, size, size, tmp);
/* inv(Vp) */
zinverma(eigenvectors, eigenvectors, size);
/* Vp * diag(log(diag(vp))*inv(Vp) */
zmulma(tmp, size, size, eigenvectors, size, size, out);
free(eigenvalues);
free(eigenvectors);
free(tmp);
free(pdblWork);
free(pdblRWork);
free(inCopy);
}
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