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/* linalg/test_svd.c
*
* Copyright (C) 2024 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_SV_lssolve_eps(const double lambda, const gsl_matrix * A, const gsl_vector * b, const double eps, const char *desc);
static int test_SV_lssolve(gsl_rng * r);
/* solve: min ||b - A x||^2 + lambda^2 ||x||^2 */
static int
test_SV_lssolve_eps(const double lambda, const gsl_matrix * A, const gsl_vector * b, const double eps, const char *desc)
{
int s = 0;
size_t i, M = A->size1, N = A->size2;
gsl_matrix * U = gsl_matrix_alloc(M, N);
gsl_matrix * V = gsl_matrix_alloc(N, N);
gsl_vector * S = gsl_vector_alloc(N);
gsl_vector * work = gsl_vector_alloc(N);
gsl_vector * work2 = gsl_vector_alloc(M+N);
gsl_vector * x = gsl_vector_alloc(N);
gsl_vector * x_aug = gsl_vector_alloc(N);
gsl_vector * r = gsl_vector_alloc(M);
double rnorm, rnorm_expected;
{
/* form full rank augmented system B = [ A ; lambda*I_N ], f = [ rhs ; 0 ] and solve with QRPT */
gsl_vector_view v;
gsl_matrix_view m;
gsl_permutation *p = gsl_permutation_alloc(N);
gsl_matrix * B = gsl_matrix_calloc(M + N, N);
gsl_vector * f = gsl_vector_calloc(M + N);
gsl_vector * tau = gsl_vector_alloc(N);
gsl_vector * residual = gsl_vector_alloc(M + N);
int signum;
m = gsl_matrix_submatrix(B, 0, 0, M, N);
gsl_matrix_memcpy(&m.matrix, A);
m = gsl_matrix_submatrix(B, M, 0, N, N);
v = gsl_matrix_diagonal(&m.matrix);
gsl_vector_set_all(&v.vector, lambda);
v = gsl_vector_subvector(f, 0, M);
gsl_vector_memcpy(&v.vector, b);
/* solve: [ A ; lambda*I ] x_aug = [ b ; 0 ] */
gsl_linalg_QRPT_decomp(B, tau, p, &signum, work);
gsl_linalg_QRPT_lssolve(B, tau, p, f, x_aug, residual);
gsl_permutation_free(p);
gsl_matrix_free(B);
gsl_vector_free(f);
gsl_vector_free(tau);
gsl_vector_free(residual);
}
gsl_matrix_memcpy(U, A);
s += gsl_linalg_SV_decomp(U, V, S, work);
s += gsl_linalg_SV_lssolve(lambda, U, V, S, b, x, &rnorm, work2);
for (i = 0; i < N; i++)
{
double xi = gsl_vector_get(x, i);
double yi = gsl_vector_get(x_aug, i);
gsl_test_rel(xi, yi, eps,
"%s lambda=%g (%3lu,%3lu)[%lu]: %22.18g %22.18g\n",
desc, lambda, M, N, i, xi, yi);
}
/* compute residual r = b - A x */
gsl_vector_memcpy(r, b);
gsl_blas_dgemv(CblasNoTrans, -1.0, A, x, 1.0, r);
rnorm_expected = gsl_blas_dnrm2(r);
gsl_test_rel(rnorm, rnorm_expected, sqrt(eps),
"%s rnorm lambda=%g (%3lu,%3lu): %22.18g %22.18g\n",
desc, lambda, M, N, rnorm, rnorm_expected);
gsl_vector_free(r);
gsl_vector_free(x);
gsl_vector_free(x_aug);
gsl_matrix_free(U);
gsl_matrix_free(V);
gsl_vector_free(S);
gsl_vector_free(work);
gsl_vector_free(work2);
return s;
}
static int
test_SV_lssolve(gsl_rng * r)
{
int s = 0;
gsl_matrix *m;
gsl_vector *b;
size_t M, N;
const double lambda = 2.3;
M = 100;
N = 50;
m = gsl_matrix_alloc(M, N);
b = gsl_vector_alloc(M);
create_random_vector(b, r);
create_rank_matrix(26, m, r);
test_SV_lssolve_eps(lambda, m, b, 1.0e4 * M * GSL_DBL_EPSILON, "SV_lssolve rank 26");
create_rank_matrix(N, m, r);
test_SV_lssolve_eps(lambda, m, b, 1.0e4 * M * GSL_DBL_EPSILON, "SV_lssolve rank N");
test_SV_lssolve_eps(0.0, m, b, 1.0e5 * M * GSL_DBL_EPSILON, "SV_lssolve rank N unreg");
gsl_matrix_free(m);
gsl_vector_free(b);
M = 500;
N = 450;
m = gsl_matrix_alloc(M, N);
b = gsl_vector_alloc(M);
create_rank_matrix(278, m, r);
create_random_vector(b, r);
test_SV_lssolve_eps(lambda, m, b, 1.0e6 * M * GSL_DBL_EPSILON, "SV_lssolve rank 278");
gsl_matrix_free(m);
gsl_vector_free(b);
return s;
}
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