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/* linalg/test_common.c
*
* Copyright (C) 2017, 2018, 2019, 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_math.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_rng.h>
static int create_random_vector(gsl_vector * v, gsl_rng * r);
static int create_random_matrix(gsl_matrix * m, gsl_rng * r);
static int create_posdef_matrix(gsl_matrix * m, gsl_rng * r);
static int create_hilbert_matrix2(gsl_matrix * m);
static int
create_random_vector(gsl_vector * v, gsl_rng * r)
{
const size_t N = v->size;
size_t i;
for (i = 0; i < N; ++i)
{
double vi = gsl_rng_uniform(r);
gsl_vector_set(v, i, vi);
}
return GSL_SUCCESS;
}
static int
create_random_complex_vector(gsl_vector_complex * v, gsl_rng * r)
{
const size_t N = v->size;
size_t i;
for (i = 0; i < N; ++i)
{
gsl_complex vi;
GSL_REAL(vi) = gsl_rng_uniform(r);
GSL_IMAG(vi) = gsl_rng_uniform(r);
gsl_vector_complex_set(v, i, vi);
}
return GSL_SUCCESS;
}
static int
create_random_matrix(gsl_matrix * m, gsl_rng * r)
{
const size_t M = m->size1;
const size_t N = m->size2;
size_t i, j;
for (i = 0; i < M; ++i)
{
for (j = 0; j < N; ++j)
{
double mij = gsl_rng_uniform(r);
gsl_matrix_set(m, i, j, mij);
}
}
return GSL_SUCCESS;
}
static int
create_random_complex_matrix(gsl_matrix_complex * m, gsl_rng * r)
{
const size_t M = m->size1;
const size_t N = m->size2;
size_t i, j;
for (i = 0; i < M; ++i)
{
for (j = 0; j < N; ++j)
{
gsl_complex mij;
GSL_REAL(mij) = gsl_rng_uniform(r);
GSL_IMAG(mij) = gsl_rng_uniform(r);
gsl_matrix_complex_set(m, i, j, mij);
}
}
return GSL_SUCCESS;
}
static int
create_symm_matrix(gsl_matrix * m, gsl_rng * r)
{
const size_t N = m->size1;
size_t i, j;
for (i = 0; i < N; ++i)
{
for (j = 0; j <= i; ++j)
{
double mij = gsl_rng_uniform(r);
gsl_matrix_set(m, i, j, mij);
}
}
/* copy lower triangle to upper */
gsl_matrix_transpose_tricpy(CblasLower, CblasUnit, m, m);
return GSL_SUCCESS;
}
static int
create_herm_matrix(gsl_matrix_complex * m, gsl_rng * r)
{
const size_t N = m->size1;
size_t i, j;
for (i = 0; i < N; ++i)
{
for (j = 0; j <= i; ++j)
{
double re = gsl_rng_uniform(r);
double im = (i != j) ? gsl_rng_uniform(r) : 0.0;
gsl_complex z = gsl_complex_rect(re, im);
gsl_matrix_complex_set(m, i, j, z);
if (i != j)
gsl_matrix_complex_set(m, j, i, gsl_complex_conjugate(z));
}
}
return GSL_SUCCESS;
}
/* create symmetric banded matrix with p sub/super-diagonals */
static int
create_symm_band_matrix(const size_t p, gsl_matrix * m, gsl_rng * r)
{
size_t i;
gsl_matrix_set_zero(m);
for (i = 0; i < p + 1; ++i)
{
gsl_vector_view subdiag = gsl_matrix_subdiagonal(m, i);
create_random_vector(&subdiag.vector, r);
if (i > 0)
{
gsl_vector_view superdiag = gsl_matrix_superdiagonal(m, i);
gsl_vector_memcpy(&superdiag.vector, &subdiag.vector);
}
}
return GSL_SUCCESS;
}
/* create (p,q) banded matrix */
static int
create_band_matrix(const size_t p, const size_t q, gsl_matrix * m, gsl_rng * r)
{
size_t i;
gsl_matrix_set_zero(m);
for (i = 0; i <= p; ++i)
{
gsl_vector_view v = gsl_matrix_subdiagonal(m, i);
create_random_vector(&v.vector, r);
}
for (i = 1; i <= q; ++i)
{
gsl_vector_view v = gsl_matrix_superdiagonal(m, i);
create_random_vector(&v.vector, r);
}
return GSL_SUCCESS;
}
static int
create_posdef_matrix(gsl_matrix * m, gsl_rng * r)
{
const size_t N = m->size1;
const double alpha = 10.0 * N;
size_t i;
/* The idea is to make a symmetric diagonally dominant
* matrix. Make a symmetric matrix and add alpha*I to
* its diagonal */
create_symm_matrix(m, r);
for (i = 0; i < N; ++i)
{
double mii = gsl_matrix_get(m, i, i);
gsl_matrix_set(m, i, i, mii + alpha);
}
return GSL_SUCCESS;
}
static int
create_posdef_complex_matrix(gsl_matrix_complex *m, gsl_rng *r)
{
const size_t N = m->size1;
const double alpha = 10.0 * N;
size_t i;
create_herm_matrix(m, r);
for (i = 0; i < N; ++i)
{
gsl_complex * mii = gsl_matrix_complex_ptr(m, i, i);
GSL_REAL(*mii) += alpha;
}
return GSL_SUCCESS;
}
static int
create_hilbert_matrix2(gsl_matrix * m)
{
const size_t N = m->size1;
size_t i, j;
for (i = 0; i < N; i++)
{
for (j = 0; j < N; j++)
{
gsl_matrix_set(m, i, j, 1.0/(i+j+1.0));
}
}
return GSL_SUCCESS;
}
/* create a matrix of a given rank */
static int
create_rank_matrix(const size_t rank, gsl_matrix * m, gsl_rng * r)
{
const size_t M = m->size1;
const size_t N = m->size2;
size_t i;
gsl_vector *u = gsl_vector_alloc(M);
gsl_vector *v = gsl_vector_alloc(N);
gsl_matrix_set_zero(m);
/* add several rank-1 matrices together */
for (i = 0; i < rank; ++i)
{
create_random_vector(u, r);
create_random_vector(v, r);
gsl_blas_dger(1.0, u, v, m);
}
gsl_vector_free(u);
gsl_vector_free(v);
return GSL_SUCCESS;
}
static int
create_posdef_band_matrix(const size_t p, gsl_matrix * m, gsl_rng * r)
{
const size_t N = m->size1;
const double alpha = 10.0 * N;
size_t i;
/* The idea is to make a symmetric diagonally dominant
* matrix. Make a symmetric matrix and add alpha*I to
* its diagonal */
create_symm_band_matrix(p, m, r);
for (i = 0; i < N; ++i)
{
double *mii = gsl_matrix_ptr(m, i, i);
*mii += alpha;
}
return GSL_SUCCESS;
}
/* transform dense symmetric banded matrix to compact form, with bandwidth p */
static int
symm2band_matrix(const size_t p, const gsl_matrix * m, gsl_matrix * bm)
{
const size_t N = m->size1;
if (bm->size1 != N)
{
GSL_ERROR("banded matrix requires N rows", GSL_EBADLEN);
}
else if (bm->size2 != p + 1)
{
GSL_ERROR("banded matrix requires p + 1 columns", GSL_EBADLEN);
}
else
{
size_t i;
gsl_matrix_set_zero(bm);
for (i = 0; i < p + 1; ++i)
{
gsl_vector_const_view diag = gsl_matrix_const_subdiagonal(m, i);
gsl_vector_view v = gsl_matrix_subcolumn(bm, i, 0, N - i);
gsl_vector_memcpy(&v.vector, &diag.vector);
}
return GSL_SUCCESS;
}
}
/* transform general dense (p,q) banded matrix to compact banded form */
static int
gen2band_matrix(const size_t p, const size_t q, const gsl_matrix * A, gsl_matrix * AB)
{
const size_t N = A->size2;
if (AB->size1 != N)
{
GSL_ERROR("banded matrix requires N rows", GSL_EBADLEN);
}
else if (AB->size2 != 2*p + q + 1)
{
GSL_ERROR("banded matrix requires 2*p + q + 1 columns", GSL_EBADLEN);
}
else
{
size_t i;
gsl_matrix_set_zero(AB);
/* copy diagonal and subdiagonals */
for (i = 0; i <= p; ++i)
{
gsl_vector_const_view v = gsl_matrix_const_subdiagonal(A, i);
gsl_vector_view w = gsl_matrix_subcolumn(AB, p + q + i, 0, v.vector.size);
gsl_vector_memcpy(&w.vector, &v.vector);
}
/* copy superdiagonals */
for (i = 1; i <= q; ++i)
{
gsl_vector_const_view v = gsl_matrix_const_superdiagonal(A, i);
gsl_vector_view w = gsl_matrix_subcolumn(AB, p + q - i, i, v.vector.size);
gsl_vector_memcpy(&w.vector, &v.vector);
}
return GSL_SUCCESS;
}
}
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