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/* linalg/test_tri.c
*
* Copyright (C) 2019 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_blas.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_rng.h>
static int
test_symmtd_decomp_eps(const gsl_matrix * m, const double eps, const char * desc)
{
int s = 0;
const size_t N = m->size1;
size_t i, j;
gsl_matrix * Q = gsl_matrix_alloc(N, N);
gsl_matrix * T = gsl_matrix_calloc(N, N);
gsl_matrix * A = gsl_matrix_alloc(N, N);
gsl_matrix * B = gsl_matrix_alloc(N, N);
gsl_vector * tau = gsl_vector_alloc(N - 1);
gsl_vector_view diag = gsl_matrix_diagonal(T);
gsl_vector_view subdiag = gsl_matrix_subdiagonal(T, 1);
gsl_vector_view superdiag = gsl_matrix_superdiagonal(T, 1);
gsl_matrix_memcpy(A, m);
s += gsl_linalg_symmtd_decomp(A, tau);
s += gsl_linalg_symmtd_unpack(A, tau, Q, &diag.vector, &subdiag.vector);
gsl_vector_memcpy(&superdiag.vector, &subdiag.vector);
gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, Q, T, 0.0, A); /* A := Q T */
gsl_blas_dgemm(CblasNoTrans, CblasTrans, 1.0, A, Q, 0.0, B); /* B := Q T Q^T */
for (i = 0; i < N; i++)
{
for (j = 0; j <= i; j++)
{
double bij = gsl_matrix_get(B, i, j);
double mij = gsl_matrix_get(m, i, j);
gsl_test_rel(bij, mij, eps, "%s (%3lu)[%lu,%lu]: %22.18g %22.18g\n",
desc, N, i, j, bij, mij);
}
}
gsl_matrix_free(T);
gsl_matrix_free(A);
gsl_matrix_free(Q);
gsl_matrix_free(B);
gsl_vector_free(tau);
return s;
}
static int
test_symmtd_decomp(gsl_rng * r)
{
int s = 0;
size_t N;
for (N = 2; N <= 50; ++N)
{
gsl_matrix * A = gsl_matrix_alloc(N, N);
create_symm_matrix(A, r);
s += test_symmtd_decomp_eps(A, 1.0e5 * N * GSL_DBL_EPSILON, "symmtd_decomp random");
gsl_matrix_free(A);
}
return s;
}
static int
test_hermtd_decomp_eps(const gsl_matrix_complex * m, const double eps, const char * desc)
{
int s = 0;
const size_t N = m->size1;
size_t i, j;
gsl_matrix_complex * Q = gsl_matrix_complex_alloc(N, N);
gsl_matrix_complex * T = gsl_matrix_complex_calloc(N, N);
gsl_matrix_complex * A = gsl_matrix_complex_alloc(N, N);
gsl_matrix_complex * B = gsl_matrix_complex_alloc(N, N);
gsl_vector_complex * tau = gsl_vector_complex_alloc(N - 1);
gsl_vector_view diag, subdiag, superdiag;
gsl_vector_complex_view v;
v = gsl_matrix_complex_diagonal(T);
diag = gsl_vector_complex_real(&v.vector);
v = gsl_matrix_complex_subdiagonal(T, 1);
subdiag = gsl_vector_complex_real(&v.vector);
v = gsl_matrix_complex_superdiagonal(T, 1);
superdiag = gsl_vector_complex_real(&v.vector);
gsl_matrix_complex_memcpy(A, m);
s += gsl_linalg_hermtd_decomp(A, tau);
s += gsl_linalg_hermtd_unpack(A, tau, Q, &diag.vector, &subdiag.vector);
gsl_vector_memcpy(&superdiag.vector, &subdiag.vector);
gsl_blas_zgemm(CblasNoTrans, CblasNoTrans, GSL_COMPLEX_ONE, Q, T, GSL_COMPLEX_ZERO, A); /* A := Q T */
gsl_blas_zgemm(CblasNoTrans, CblasConjTrans, GSL_COMPLEX_ONE, A, Q, GSL_COMPLEX_ZERO, B); /* B := Q T Q^T */
for (i = 0; i < N; i++)
{
for (j = 0; j <= i; j++)
{
gsl_complex bij = gsl_matrix_complex_get(B, i, j);
gsl_complex mij = gsl_matrix_complex_get(m, i, j);
gsl_test_rel(GSL_REAL(bij), GSL_REAL(mij), eps, "%s real (%3lu)[%lu,%lu]: %22.18g %22.18g\n",
desc, N, i, j, GSL_REAL(bij), GSL_REAL(mij));
gsl_test_rel(GSL_IMAG(bij), GSL_IMAG(mij), eps, "%s imag (%3lu)[%lu,%lu]: %22.18g %22.18g\n",
desc, N, i, j, GSL_IMAG(bij), GSL_IMAG(mij));
}
}
gsl_matrix_complex_free(T);
gsl_matrix_complex_free(A);
gsl_matrix_complex_free(Q);
gsl_matrix_complex_free(B);
gsl_vector_complex_free(tau);
return s;
}
static int
test_hermtd_decomp(gsl_rng * r)
{
int s = 0;
size_t N;
for (N = 2; N <= 50; ++N)
{
gsl_matrix_complex * A = gsl_matrix_complex_alloc(N, N);
create_herm_matrix(A, r);
s += test_hermtd_decomp_eps(A, 1.0e5 * N * GSL_DBL_EPSILON, "hermtd_decomp random");
gsl_matrix_complex_free(A);
}
return s;
}
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