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/* linalg/test_qr_band.c
*
* Copyright (C) 2020 Patrick Alken
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#include <config.h>
#include <stdlib.h>
#include <gsl/gsl_test.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_ieee_utils.h>
#include <gsl/gsl_permute_vector.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_permutation.h>
static int
test_QR_band_decomp_eps(const size_t p, const size_t q, const gsl_matrix * A, const double eps, const char * desc)
{
int s = 0;
const size_t M = A->size1;
const size_t N = A->size2;
size_t i, j;
gsl_matrix * AB = gsl_matrix_alloc(N, 2*p + q + 1);
gsl_vector * tau = gsl_vector_alloc(N);
gsl_matrix * Q = gsl_matrix_alloc(M, M);
gsl_matrix * R = gsl_matrix_alloc(M, N);
gsl_matrix * B = gsl_matrix_alloc(M, N);
/* convert A to packed banded format */
gen2band_matrix(p, q, A, AB);
#if 0
print_octave(A, "A");
printqrb_octave(M, p, q, AB, "AB");
#endif
s += gsl_linalg_QR_band_decomp_L2(M, p, q, AB, tau);
s += gsl_linalg_QR_band_unpack_L2(p, q, AB, tau, Q, R);
#if 0
printqrb_octave(M, p, q, AB, "QR");
printv_octave(tau, "tau");
print_octave(Q, "Q");
print_octave(R, "R");
#endif
/* compute B = Q R */
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, Q, R, 0.0, B);
for (i = 0; i < M; ++i)
{
for (j = 0; j < N; ++j)
{
double aij = gsl_matrix_get(A, i, j);
double bij = gsl_matrix_get(B, i, j);
gsl_test_rel(bij, aij, eps, "%s (M=%3lu,N=%3lu)(p=%3lu,q=%3lu)[%lu,%lu]: %22.18g %22.18g\n",
desc, M, N, p, q, i, j, aij, bij);
}
}
gsl_matrix_free(AB);
gsl_vector_free(tau);
gsl_matrix_free(Q);
gsl_matrix_free(R);
gsl_matrix_free(B);
return s;
}
static int
test_QR_band_decomp(gsl_rng * r)
{
int s = 0;
const size_t N_max = 20;
size_t M, N, p, q;
/*M = 7; N = 6; p = 2; q = 1;*/
for (M = 1; M <= N_max; ++M)
{
for (N = 1; N <= N_max; ++N)
{
gsl_matrix * A = gsl_matrix_alloc(M, N);
for (p = 0; p < GSL_MIN(M, 10); ++p)
{
for (q = 0; q < GSL_MIN(N, 10); ++q)
{
create_band_matrix(p, q, A, r);
s += test_QR_band_decomp_eps(p, q, A, 1.0e6 * GSL_MAX(M,N) * GSL_DBL_EPSILON, "QR_band_decomp random");
}
}
gsl_matrix_free(A);
}
}
return s;
}
#if 0
static int
test_QR_band_decomp(void)
{
int f;
int s = 0;
f = test_QR_decomp_dim(m35, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_decomp m(3,5)");
s += f;
f = test_QR_decomp_dim(m53, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_decomp m(5,3)");
s += f;
f = test_QR_decomp_dim(hilb2, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_decomp hilbert(2)");
s += f;
f = test_QR_decomp_dim(hilb3, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_decomp hilbert(3)");
s += f;
f = test_QR_decomp_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_decomp hilbert(4)");
s += f;
f = test_QR_decomp_dim(hilb12, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_decomp hilbert(12)");
s += f;
f = test_QR_decomp_dim(vander2, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_decomp vander(2)");
s += f;
f = test_QR_decomp_dim(vander3, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_decomp vander(3)");
s += f;
f = test_QR_decomp_dim(vander4, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_decomp vander(4)");
s += f;
f = test_QR_decomp_dim(vander12, 0.0005); /* FIXME: bad accuracy */
gsl_test(f, " QR_decomp vander(12)");
s += f;
return s;
}
#endif
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