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/**************************************************************************
**
** Copyright (C) 1993 David E. Steward & Zbigniew Leyk, all rights reserved.
**
** Meschach Library
**
** This Meschach Library is provided "as is" without any express
** or implied warranty of any kind with respect to this software.
** In particular the authors shall not be liable for any direct,
** indirect, special, incidental or consequential damages arising
** in any way from use of the software.
**
** Everyone is granted permission to copy, modify and redistribute this
** Meschach Library, provided:
** 1. All copies contain this copyright notice.
** 2. All modified copies shall carry a notice stating who
** made the last modification and the date of such modification.
** 3. No charge is made for this software or works derived from it.
** This clause shall not be construed as constraining other software
** distributed on the same medium as this software, nor is a
** distribution fee considered a charge.
**
***************************************************************************/
/* mfuntort.c, 10/11/93 */
static char rcsid[] = "$Id: mfuntort.c,v 1.2 1994/01/14 01:08:06 des Exp $";
#include <stdio.h>
#include <math.h>
#include "matrix.h"
#include "matrix2.h"
#define errmesg(mesg) printf("Error: %s error: line %d\n",mesg,__LINE__)
#define notice(mesg) printf("# Testing %s...\n",mesg);
#define DIM 10
void main()
{
MAT *A, *B, *C, *OUTA, *OUTB, *TMP;
MAT *exp_A_expected, *exp_A;
VEC *x, *b;
double c, eps = 1e-10;
int i, j, q_out, j_out;
mem_info_on(TRUE);
A = m_get(DIM,DIM);
B = m_get(DIM,DIM);
C = m_get(DIM,DIM);
OUTA = m_get(DIM,DIM);
OUTB = m_get(DIM,DIM);
TMP = m_get(DIM,DIM);
x = v_get(DIM);
b = v_get(6);
notice("exponent of a matrix");
m_ident(A);
mem_stat_mark(1);
_m_exp(A,eps,OUTA,&q_out,&j_out);
printf("# q_out = %d, j_out = %d\n",q_out,j_out);
m_exp(A,eps,OUTA);
sm_mlt(exp(1.0),A,A);
m_sub(OUTA,A,TMP);
printf("# ||exp(I) - e*I|| = %g\n",m_norm_inf(TMP));
m_rand(A);
m_transp(A,TMP);
m_add(A,TMP,A);
B = m_copy(A,B);
m_exp(A,eps,OUTA);
symmeig(B,OUTB,x);
m_zero(TMP);
for (i=0; i < x->dim; i++)
TMP->me[i][i] = exp(x->ve[i]);
m_mlt(OUTB,TMP,C);
mmtr_mlt(C,OUTB,TMP);
m_sub(TMP,OUTA,TMP);
printf("# ||exp(A) - Q*exp(lambda)*Q^T|| = %g\n",m_norm_inf(TMP));
notice("polynomial of a matrix");
m_rand(A);
m_transp(A,TMP);
m_add(A,TMP,A);
B = m_copy(A,B);
v_rand(b);
m_poly(A,b,OUTA);
symmeig(B,OUTB,x);
m_zero(TMP);
for (i=0; i < x->dim; i++) {
c = b->ve[b->dim-1];
for (j=b->dim-2; j >= 0; j--)
c = c*x->ve[i] + b->ve[j];
TMP->me[i][i] = c;
}
m_mlt(OUTB,TMP,C);
mmtr_mlt(C,OUTB,TMP);
m_sub(TMP,OUTA,TMP);
printf("# ||poly(A) - Q*poly(lambda)*Q^T|| = %g\n",m_norm_inf(TMP));
mem_stat_free(1);
/* Brook Milligan's test */
M_FREE(A);
M_FREE(B);
M_FREE(C);
notice("exponent of a nonsymmetric matrix");
A = m_get (2, 2);
A -> me [0][0] = 1.0;
A -> me [0][1] = 1.0;
A -> me [1][0] = 4.0;
A -> me [1][1] = 1.0;
exp_A_expected = m_get(2, 2);
exp_A_expected -> me [0][0] = exp (3.0) / 2.0 + exp (-1.0) / 2.0;
exp_A_expected -> me [0][1] = exp (3.0) / 4.0 - exp (-1.0) / 4.0;
exp_A_expected -> me [1][0] = exp (3.0) - exp (-1.0);
exp_A_expected -> me [1][1] = exp (3.0) / 2.0 + exp (-1.0) / 2.0;
printf ("A:\n");
for (i = 0; i < 2; i++)
{
for (j = 0; j < 2; j++)
printf (" %15.8e", A -> me [i][j]);
printf ("\n");
}
printf ("\nexp(A) (expected):\n");
for (i = 0; i < 2; i++)
{
for (j = 0; j < 2; j++)
printf (" %15.8e", exp_A_expected -> me [i][j]);
printf ("\n");
}
mem_stat_mark(3);
exp_A = m_exp (A, 1e-16,NULL);
mem_stat_free(3);
printf ("\nexp(A):\n");
for (i = 0; i < 2; i++)
{
for (j = 0; j < 2; j++)
printf (" %15.8e", exp_A -> me [i][j]);
printf ("\n");
}
printf ("\nexp(A) - exp(A) (expected):\n");
for (i = 0; i < 2; i++)
{
for (j = 0; j < 2; j++)
printf (" %15.8e", exp_A -> me [i][j] - exp_A_expected -> me [i][j]);
printf ("\n");
}
M_FREE(A);
M_FREE(B);
M_FREE(C);
M_FREE(exp_A);
M_FREE(exp_A_expected);
M_FREE(OUTA);
M_FREE(OUTB);
M_FREE(TMP);
V_FREE(b);
V_FREE(x);
mem_info();
}
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