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/* SVD test */
/* Verify that the SVD solver does what it is supposed to. */
/*
* Copyright 2000 Graeme W. Gill
* All rights reserved.
*
* This material is licenced under the GNU AFFERO GENERAL PUBLIC LICENSE Version 3 :-
* see the License.txt file for licencing details.
*/
/* We assume two device dependent variables, and one objective function value */
#include <stdio.h>
#include <stdlib.h>
#include <stdarg.h>
#include <math.h>
#include <time.h>
#if defined(__IBMC__)
#include <float.h>
#endif
#include "numlib.h"
int main(void) {
int its;
int i,j,x;
double **a; /* A[0..M-1][0..N-1] input */
double **u; /* U[0..M-1][0..N-1] output */
double *w; /* W[0..N-1] output */
double **v; /* V[0..N-1][0..N-1] output */
double **a2; /* A[0..M-1][0..N-1] check on a */
double **t; /* A[0..M-1][0..N-1] temp */
int m,n;
#if defined(__IBMC__)
_control87(EM_UNDERFLOW, EM_UNDERFLOW);
_control87(EM_OVERFLOW, EM_OVERFLOW);
#endif
printf("Test SVD\n");
for (its = 400; its > 0; its--) {
int bad;
int bad0;
m = i_rand(1,30); /* Number of equations */
n = i_rand(1,30); /* Number of unknowns */
a = dmatrix(0,m-1, 0,n-1);
t = dmatrix(0,m-1, 0,n-1);
a2 = dmatrix(0,m-1, 0,n-1);
u = dmatrix(0,m-1, 0,n-1);
w = dvector(0,n-1);
v = dmatrix(0,n-1, 0,n-1);
printf("Testing %d by %d\n",m,n);
/* Create A matrix */
for (j = 0; j < m; j++)
for (i = 0; i < n; i++)
a[j][i] = d_rand(-10.0, 10.0);
/* Setup u */
for (j = 0; j < m; j++)
for (i = 0; i < n; i++)
u[j][i] = a[j][i];
/* decompose A into U, W and V */
svdecomp(u, w, v, m, n);
/* Check results by computing a2 = U.W.Vt */
for (j = 0; j < m; j++) { /* U.W */
for (i = 0; i < n; i++) {
t[j][i] = 0.0;
for (x = 0; x < n; x++) {
if (x == i)
t[j][i] += u[j][x] * w[x];
}
}
}
for (j = 0; j < m; j++) { /* .Vt */
for (i = 0; i < n; i++) {
a2[j][i] = 0.0;
for (x = 0; x < n; x++) {
a2[j][i] += t[j][x] * v[i][x];
}
}
}
/* Now check */
bad = 0;
for (j = 0; j < m; j++)
for (i = 0; i < n; i++) {
double tt;
tt = a2[j][i] - a[j][i];
tt = fabs(tt);
if (tt > 0.0000001) {
bad = 1;
}
}
if (bad)
printf("A == U.W.Vt Check failed!\n");
/* Check that U and Ut are inverses */
bad = bad0 = 0;
for (j = 0; j < n; j++) {
for (i = 0; i < n; i++) {
double t2, tt = 0.0;
for (x = 0; x < m; x++) {
tt += u[x][j] * u[x][i];
}
t2 = tt;
if (i == j)
tt -= 1.0;
tt = fabs(tt);
if (tt > 0.0000001) {
if (i == j && fabs(t2) < 0.0000001)
bad0++; /* Unexpected zero diagonal */
else {
bad = 1;
printf("Possible U error at %d %d = %f \n",j,i,tt);
}
}
}
}
/* Expect n-m diagnals to be 0 instead of 1 if m < n */
if (bad || (m >= n && bad0) || (m < n && bad0 != n-m))
printf("U,Ut == 1 Check failed!\n");
/* Check that V and Vt are inverses */
bad = 0;
for (j = 0; j < n; j++) {
for (i = 0; i < n; i++) {
double tt = 0.0;
for (x = 0; x < n; x++) {
tt += v[j][x] * v[i][x];
}
if (i == j)
tt -= 1.0;
tt = fabs(tt);
if (tt > 0.0000001) {
bad = 1;
printf("V Error at %d %d = %f \n",j,i,tt);
}
}
if (bad)
printf("V,Vt == 1 Check failed!\n");
}
#ifdef NEVER
printf("A = %f %f %f\n %f %f %f\n %f %f %f\n\n",
a[0][0], a[0][1], a[0][2], a[1][0], a[1][1], a[1][2], a[2][0], a[2][1], a[2][2]);
printf("u = %f %f %f\n %f %f %f\n %f %f %f\n\n",
u[0][0], u[0][1], u[0][2], u[1][0], u[1][1], u[1][2], u[2][0], u[2][1], u[2][2]);
printf("w = %f %f %f\n\n", w[0],w[1],w[2]);
printf("V = %f %f %f\n %f %f %f\n %f %f %f\n\n",
v[0][0], v[0][1], v[0][2], v[1][0], v[1][1], v[1][2], v[2][0], v[2][1], v[2][2]);;
printf("A2 = %f %f %f\n %f %f %f\n %f %f %f\n\n",
a2[0][0], a2[0][1], a2[0][2], a2[1][0], a2[1][1],
a2[1][2], a2[2][0], a2[2][1], a2[2][2]);
#endif
free_dmatrix(a, 0,m-1, 0,n-1);
free_dmatrix(t, 0,m-1, 0,n-1);
free_dmatrix(a2, 0,m-1, 0,n-1);
free_dmatrix(u, 0,m-1, 0,n-1);
free_dvector(w, 0,n-1);
free_dmatrix(v, 0,n-1, 0,n-1);
}
return 0;
}
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