mfuntort.c

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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();
}