local void lo_randomize_coords(double *coords) {
int i;
for (i = 2*lo_dim_square-1; i >= 0; --i) {
coords[i] = wn_flat_distribution() * (lo_dim-1);
}
} /* lo_randomize_coords */
local void initialize(void)
{
int i,j;
wn_gpmake("no_free");
wn_make_vect(&solution_vect,SIZE*SIZE);
wn_make_vect(&grad_vect,SIZE*SIZE);
wn_make_mat(&solution_mat,SIZE,SIZE);
wn_make_mat(&grad_mat,SIZE,SIZE);
wn_make_mat(&cost_mat,SIZE,SIZE);
for(i=0;i<SIZE;++i)
for(j=0;j<SIZE;++j)
{
cost_mat[i][j] = wn_flat_distribution();
}
}
local void mat_test_gramm_schmidt(void)
{
double **mat, **mat_orig;
int ilen, jlen, code; /* ilen rows, jlen columns */
int a, b;
double *sum_vect, mul, mul2;
int trial;
for (trial = 0; trial < 1000; ++trial) {
wn_gpmake("no_free"); /* temp memory group */
jlen = (unsigned) wn_random_int() % 20 + 1;
ilen = (unsigned) wn_random_int() % jlen + 1;
wn_make_mat(&mat_orig, ilen, jlen);
wn_random_mat(mat_orig, ilen, jlen);
wn_make_mat(&mat, ilen, jlen);
for (a = 0; a < ilen; ++a) {
for (b = 0; b < jlen; ++b) {
mat[a][b] = mat_orig[a][b];
}
}
wn_gramm_schmidt(&code, mat, ilen, jlen);
wn_assert(WN_SUCCESS == code);
/* first ilen vects should be orthogonal */
for (a = 0; a < ilen; ++a) {
for (b = a+1; b < ilen; ++b) {
wn_assert(LO_ALMOST_EQUAL(0.0, wn_dot_vects(mat[a], mat[b], jlen)));
}
}
/* let's make the gramm_schmidt be unit vectors, to be simple */
for (a = 0; a < ilen; ++a) {
mul2 = wn_dot_vects(mat[a], mat[a], jlen);
mul = 1/sqrt(mul2);
for (b = 0; b < jlen; ++b) {
mat[a][b] *= mul;
}
wn_assert(LO_ALMOST_EQUAL(1.0, wn_dot_vects(mat[a], mat[a], jlen)));
}
/* check again orthogonality */
for (a = 0; a < ilen; ++a) {
for (b = a+1; b < ilen; ++b) {
wn_assert(LO_ALMOST_EQUAL(0.0, wn_dot_vects(mat[a], mat[b], jlen)));
}
}
/* make a vector in the space spanned by the original vectors */
wn_make_vect(&sum_vect, jlen);
wn_zero_vect(sum_vect, jlen);
for (a = 0; a < ilen; ++a) {
wn_add_scaled_vect(sum_vect, mat_orig[a], wn_flat_distribution(),
/**/ jlen);
}
/* OK, sum_vect is reached from the original matrix of vectors */
/* can we reach it from mat? */
for (a = 0; a < ilen; ++a) {
mul = wn_dot_vects(sum_vect, mat[a], jlen);
wn_add_scaled_vect(sum_vect, mat[a], -mul, jlen);
}
wn_assert(LO_ALMOST_EQUAL(0.0, wn_dot_vects(sum_vect, sum_vect, jlen)));
wn_gpfree();
} /* for trial */
} /* mat_test_gramm_schmidt */
double wn_random_double_between(double low,double high)
{
return((high-low)*wn_flat_distribution()+low);
}
