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gem5 / public / gem5-resources / 8ccd059d5dcaaeffe15cd93c17f1e76e92907662 / . / src / parsec / disk-image / parsec / parsec-benchmark / pkgs / libs / gsl / src / linalg / test.c
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/* linalg/test.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004, 2005
* Gerard Jungman, Brian Gough
*
* 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 2 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.
*/
/* Author: G. Jungman
*/
#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_complex_math.h>
#include <gsl/gsl_linalg.h>
#define TEST_SVD_4X4 1
int check (double x, double actual, double eps);
gsl_matrix * create_hilbert_matrix(unsigned long size);
gsl_matrix * create_general_matrix(unsigned long size1, unsigned long size2);
gsl_matrix * create_vandermonde_matrix(unsigned long size);
gsl_matrix * create_moler_matrix(unsigned long size);
gsl_matrix * create_row_matrix(unsigned long size1, unsigned long size2);
gsl_matrix * create_2x2_matrix(double a11, double a12, double a21, double a22);
gsl_matrix * create_diagonal_matrix(double a[], unsigned long size);
int test_matmult(void);
int test_matmult_mod(void);
int test_LU_solve_dim(const gsl_matrix * m, const double * actual, double eps);
int test_LU_solve(void);
int test_LUc_solve_dim(const gsl_matrix_complex * m, const double * actual, double eps);
int test_LUc_solve(void);
int test_QR_solve_dim(const gsl_matrix * m, const double * actual, double eps);
int test_QR_solve(void);
int test_QR_QRsolve_dim(const gsl_matrix * m, const double * actual, double eps);
int test_QR_QRsolve(void);
int test_QR_lssolve_dim(const gsl_matrix * m, const double * actual, double eps);
int test_QR_lssolve(void);
int test_QR_decomp_dim(const gsl_matrix * m, double eps);
int test_QR_decomp(void);
int test_QRPT_solve_dim(const gsl_matrix * m, const double * actual, double eps);
int test_QRPT_solve(void);
int test_QRPT_QRsolve_dim(const gsl_matrix * m, const double * actual, double eps);
int test_QRPT_QRsolve(void);
int test_QRPT_decomp_dim(const gsl_matrix * m, double eps);
int test_QRPT_decomp(void);
int test_QR_update_dim(const gsl_matrix * m, double eps);
int test_QR_update(void);
int test_LQ_solve_dim(const gsl_matrix * m, const double * actual, double eps);
int test_LQ_solve(void);
int test_LQ_LQsolve_dim(const gsl_matrix * m, const double * actual, double eps);
int test_LQ_LQsolve(void);
int test_LQ_lssolve_dim(const gsl_matrix * m, const double * actual, double eps);
int test_LQ_lssolve(void);
int test_LQ_decomp_dim(const gsl_matrix * m, double eps);
int test_LQ_decomp(void);
int test_PTLQ_solve_dim(const gsl_matrix * m, const double * actual, double eps);
int test_PTLQ_solve(void);
int test_PTLQ_LQsolve_dim(const gsl_matrix * m, const double * actual, double eps);
int test_PTLQ_LQsolve(void);
int test_PTLQ_decomp_dim(const gsl_matrix * m, double eps);
int test_PTLQ_decomp(void);
int test_LQ_update_dim(const gsl_matrix * m, double eps);
int test_LQ_update(void);
int test_SV_solve_dim(const gsl_matrix * m, const double * actual, double eps);
int test_SV_solve(void);
int test_SV_decomp_dim(const gsl_matrix * m, double eps);
int test_SV_decomp(void);
int test_SV_decomp_mod_dim(const gsl_matrix * m, double eps);
int test_SV_decomp_mod(void);
int test_SV_decomp_jacobi_dim(const gsl_matrix * m, double eps);
int test_SV_decomp_jacobi(void);
int test_cholesky_solve_dim(const gsl_matrix * m, const double * actual, double eps);
int test_cholesky_solve(void);
int test_cholesky_decomp_dim(const gsl_matrix * m, double eps);
int test_cholesky_decomp(void);
int test_HH_solve_dim(const gsl_matrix * m, const double * actual, double eps);
int test_HH_solve(void);
int test_TDS_solve_dim(unsigned long dim, double d, double od, const double * actual, double eps);
int test_TDS_solve(void);
int test_TDN_solve_dim(unsigned long dim, double d, double a, double b, const double * actual, double eps);
int test_TDN_solve(void);
int test_TDS_cyc_solve_one(const unsigned long dim, const double * d, const double * od, const double * r,
const double * actual, double eps);
int test_TDS_cyc_solve(void);
int test_TDN_cyc_solve_dim(unsigned long dim, double d, double a, double b, const double * actual, double eps);
int test_TDN_cyc_solve(void);
int test_bidiag_decomp_dim(const gsl_matrix * m, double eps);
int test_bidiag_decomp(void);
int
check (double x, double actual, double eps)
{
if (x == actual)
{
return 0;
}
else if (actual == 0)
{
return fabs(x) > eps;
}
else
{
return (fabs(x - actual)/fabs(actual)) > eps;
}
}
gsl_matrix *
create_hilbert_matrix(unsigned long size)
{
unsigned long i, j;
gsl_matrix * m = gsl_matrix_alloc(size, size);
for(i=0; i<size; i++) {
for(j=0; j<size; j++) {
gsl_matrix_set(m, i, j, 1.0/(i+j+1.0));
}
}
return m;
}
gsl_matrix *
create_general_matrix(unsigned long size1, unsigned long size2)
{
unsigned long i, j;
gsl_matrix * m = gsl_matrix_alloc(size1, size2);
for(i=0; i<size1; i++) {
for(j=0; j<size2; j++) {
gsl_matrix_set(m, i, j, 1.0/(i+j+1.0));
}
}
return m;
}
gsl_matrix *
create_singular_matrix(unsigned long size1, unsigned long size2)
{
unsigned long i, j;
gsl_matrix * m = gsl_matrix_alloc(size1, size2);
for(i=0; i<size1; i++) {
for(j=0; j<size2; j++) {
gsl_matrix_set(m, i, j, 1.0/(i+j+1.0));
}
}
/* zero the first column */
for(j = 0; j <size2; j++)
gsl_matrix_set(m,0,j,0.0);
return m;
}
gsl_matrix *
create_vandermonde_matrix(unsigned long size)
{
unsigned long i, j;
gsl_matrix * m = gsl_matrix_alloc(size, size);
for(i=0; i<size; i++) {
for(j=0; j<size; j++) {
gsl_matrix_set(m, i, j, pow(i + 1.0, size - j - 1.0));
}
}
return m;
}
gsl_matrix *
create_moler_matrix(unsigned long size)
{
unsigned long i, j;
gsl_matrix * m = gsl_matrix_alloc(size, size);
for(i=0; i<size; i++) {
for(j=0; j<size; j++) {
gsl_matrix_set(m, i, j, GSL_MIN(i+1,j+1)-2.0);
}
}
return m;
}
gsl_matrix_complex *
create_complex_matrix(unsigned long size)
{
unsigned long i, j;
gsl_matrix_complex * m = gsl_matrix_complex_alloc(size, size);
for(i=0; i<size; i++) {
for(j=0; j<size; j++) {
gsl_complex z = gsl_complex_rect(1.0/(i+j+1.0), 1/(i*i+j*j+0.5));
gsl_matrix_complex_set(m, i, j, z);
}
}
return m;
}
gsl_matrix *
create_row_matrix(unsigned long size1, unsigned long size2)
{
unsigned long i;
gsl_matrix * m = gsl_matrix_calloc(size1, size2);
for(i=0; i<size1; i++) {
gsl_matrix_set(m, i, 0, 1.0/(i+1.0));
}
return m;
}
gsl_matrix *
create_2x2_matrix(double a11, double a12, double a21, double a22)
{
gsl_matrix * m = gsl_matrix_alloc(2, 2);
gsl_matrix_set(m, 0, 0, a11);
gsl_matrix_set(m, 0, 1, a12);
gsl_matrix_set(m, 1, 0, a21);
gsl_matrix_set(m, 1, 1, a22);
return m;
}
gsl_matrix *
create_diagonal_matrix(double a[], unsigned long size)
{
unsigned long i;
gsl_matrix * m = gsl_matrix_calloc(size, size);
for(i=0; i<size; i++) {
gsl_matrix_set(m, i, i, a[i]);
}
return m;
}
gsl_matrix * m11;
gsl_matrix * m51;
gsl_matrix * m35;
gsl_matrix * m53;
gsl_matrix * m97;
gsl_matrix * s35;
gsl_matrix * s53;
gsl_matrix * hilb2;
gsl_matrix * hilb3;
gsl_matrix * hilb4;
gsl_matrix * hilb12;
gsl_matrix * row3;
gsl_matrix * row5;
gsl_matrix * row12;
gsl_matrix * A22;
gsl_matrix * A33;
gsl_matrix * A44;
gsl_matrix * A55;
gsl_matrix_complex * c7;
gsl_matrix * inf5; double inf5_data[] = {1.0, 0.0, -3.0, 0.0, -5.0};
gsl_matrix * nan5;
double m53_lssolution[] = {52.5992295702070, -337.7263113752073,
351.8823436427604};
double hilb2_solution[] = {-8.0, 18.0} ;
double hilb3_solution[] = {27.0, -192.0, 210.0};
double hilb4_solution[] = {-64.0, 900.0, -2520.0, 1820.0};
double hilb12_solution[] = {-1728.0, 245388.0, -8528520.0,
127026900.0, -1009008000.0, 4768571808.0,
-14202796608.0, 27336497760.0, -33921201600.0,
26189163000.0, -11437874448.0, 2157916488.0 };
double c7_solution[] = { 2.40717272023734e+01, -9.84612797621247e+00,
-2.69338853034031e+02, 8.75455232472528e+01,
2.96661356736296e+03, -1.02624473923993e+03,
-1.82073812124749e+04, 5.67384473042410e+03,
5.57693879019068e+04, -1.61540963210502e+04,
-7.88941207561151e+04, 1.95053812987858e+04,
3.95548551241728e+04, -7.76593696255317e+03 };
gsl_matrix * vander2;
gsl_matrix * vander3;
gsl_matrix * vander4;
gsl_matrix * vander12;
double vander2_solution[] = {1.0, 0.0};
double vander3_solution[] = {0.0, 1.0, 0.0};
double vander4_solution[] = {0.0, 0.0, 1.0, 0.0};
double vander12_solution[] = {0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0};
gsl_matrix * moler10;
/* matmult now obsolete */
#ifdef MATMULT
int
test_matmult(void)
{
int s = 0;
gsl_matrix * A = gsl_matrix_calloc(2, 2);
gsl_matrix * B = gsl_matrix_calloc(2, 3);
gsl_matrix * C = gsl_matrix_calloc(2, 3);
gsl_matrix_set(A, 0, 0, 10.0);
gsl_matrix_set(A, 0, 1, 5.0);
gsl_matrix_set(A, 1, 0, 1.0);
gsl_matrix_set(A, 1, 1, 20.0);
gsl_matrix_set(B, 0, 0, 10.0);
gsl_matrix_set(B, 0, 1, 5.0);
gsl_matrix_set(B, 0, 2, 2.0);
gsl_matrix_set(B, 1, 0, 1.0);
gsl_matrix_set(B, 1, 1, 3.0);
gsl_matrix_set(B, 1, 2, 2.0);
gsl_linalg_matmult(A, B, C);
s += ( fabs(gsl_matrix_get(C, 0, 0) - 105.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 0, 1) - 65.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 0, 2) - 30.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 0) - 30.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 1) - 65.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 2) - 42.0) > GSL_DBL_EPSILON );
gsl_matrix_free(A);
gsl_matrix_free(B);
gsl_matrix_free(C);
return s;
}
int
test_matmult_mod(void)
{
int s = 0;
gsl_matrix * A = gsl_matrix_calloc(3, 3);
gsl_matrix * B = gsl_matrix_calloc(3, 3);
gsl_matrix * C = gsl_matrix_calloc(3, 3);
gsl_matrix * D = gsl_matrix_calloc(2, 3);
gsl_matrix * E = gsl_matrix_calloc(2, 3);
gsl_matrix * F = gsl_matrix_calloc(2, 2);
gsl_matrix_set(A, 0, 0, 10.0);
gsl_matrix_set(A, 0, 1, 5.0);
gsl_matrix_set(A, 0, 2, 1.0);
gsl_matrix_set(A, 1, 0, 1.0);
gsl_matrix_set(A, 1, 1, 20.0);
gsl_matrix_set(A, 1, 2, 5.0);
gsl_matrix_set(A, 2, 0, 1.0);
gsl_matrix_set(A, 2, 1, 3.0);
gsl_matrix_set(A, 2, 2, 7.0);
gsl_matrix_set(B, 0, 0, 10.0);
gsl_matrix_set(B, 0, 1, 5.0);
gsl_matrix_set(B, 0, 2, 2.0);
gsl_matrix_set(B, 1, 0, 1.0);
gsl_matrix_set(B, 1, 1, 3.0);
gsl_matrix_set(B, 1, 2, 2.0);
gsl_matrix_set(B, 2, 0, 1.0);
gsl_matrix_set(B, 2, 1, 3.0);
gsl_matrix_set(B, 2, 2, 2.0);
gsl_matrix_set(D, 0, 0, 10.0);
gsl_matrix_set(D, 0, 1, 5.0);
gsl_matrix_set(D, 0, 2, 1.0);
gsl_matrix_set(D, 1, 0, 1.0);
gsl_matrix_set(D, 1, 1, 20.0);
gsl_matrix_set(D, 1, 2, 5.0);
gsl_matrix_set(E, 0, 0, 10.0);
gsl_matrix_set(E, 0, 1, 5.0);
gsl_matrix_set(E, 0, 2, 2.0);
gsl_matrix_set(E, 1, 0, 1.0);
gsl_matrix_set(E, 1, 1, 3.0);
gsl_matrix_set(E, 1, 2, 2.0);
gsl_linalg_matmult_mod(A, GSL_LINALG_MOD_NONE, B, GSL_LINALG_MOD_NONE, C);
s += ( fabs(gsl_matrix_get(C, 0, 0) - 106.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 0, 1) - 68.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 0, 2) - 32.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 0) - 35.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 1) - 80.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 2) - 52.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 0) - 20.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 1) - 35.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 2) - 22.0) > GSL_DBL_EPSILON );
gsl_linalg_matmult_mod(A, GSL_LINALG_MOD_TRANSPOSE, B, GSL_LINALG_MOD_NONE, C);
s += ( fabs(gsl_matrix_get(C, 0, 0) - 102.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 0, 1) - 56.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 0, 2) - 24.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 0) - 73.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 1) - 94.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 2) - 56.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 0) - 22.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 1) - 41.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 2) - 26.0) > GSL_DBL_EPSILON );
gsl_linalg_matmult_mod(A, GSL_LINALG_MOD_NONE, B, GSL_LINALG_MOD_TRANSPOSE, C);
s += ( fabs(gsl_matrix_get(C, 0, 0) - 127.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 0, 1) - 27.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 0, 2) - 27.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 0) - 120.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 1) - 71.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 2) - 71.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 0) - 39.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 1) - 24.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 2) - 24.0) > GSL_DBL_EPSILON );
gsl_linalg_matmult_mod(A, GSL_LINALG_MOD_TRANSPOSE, B, GSL_LINALG_MOD_TRANSPOSE, C);
s += ( fabs(gsl_matrix_get(C, 0, 0) - 107.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 0, 1) - 15.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 0, 2) - 15.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 0) - 156.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 1) - 71.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 2) - 71.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 0) - 49.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 1) - 30.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 2) - 30.0) > GSL_DBL_EPSILON );
/* now try for non-symmetric matrices */
gsl_linalg_matmult_mod(D, GSL_LINALG_MOD_TRANSPOSE, E, GSL_LINALG_MOD_NONE, C);
s += ( fabs(gsl_matrix_get(C, 0, 0) - 101.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 0, 1) - 53.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 0, 2) - 22.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 0) - 70.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 1) - 85.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 1, 2) - 50.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 0) - 15.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 1) - 20.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(C, 2, 2) - 12.0) > GSL_DBL_EPSILON );
gsl_linalg_matmult_mod(D, GSL_LINALG_MOD_NONE, E, GSL_LINALG_MOD_TRANSPOSE, F);
s += ( fabs(gsl_matrix_get(F, 0, 0) - 127.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(F, 0, 1) - 27.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(F, 1, 0) - 120.0) > GSL_DBL_EPSILON );
s += ( fabs(gsl_matrix_get(F, 1, 1) - 71.0) > GSL_DBL_EPSILON );
gsl_matrix_free(A);
gsl_matrix_free(B);
gsl_matrix_free(C);
gsl_matrix_free(D);
gsl_matrix_free(E);
gsl_matrix_free(F);
return s;
}
#endif
int
test_LU_solve_dim(const gsl_matrix * m, const double * actual, double eps)
{
int s = 0;
int signum;
unsigned long i, dim = m->size1;
gsl_permutation * perm = gsl_permutation_alloc(dim);
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_matrix * lu = gsl_matrix_alloc(dim,dim);
gsl_vector * x = gsl_vector_alloc(dim);
gsl_vector * residual = gsl_vector_alloc(dim);
gsl_matrix_memcpy(lu,m);
for(i=0; i<dim; i++) gsl_vector_set(rhs, i, i+1.0);
s += gsl_linalg_LU_decomp(lu, perm, &signum);
s += gsl_linalg_LU_solve(lu, perm, rhs, x);
for(i=0; i<dim; i++) {
int foo = check(gsl_vector_get(x, i),actual[i],eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
s += gsl_linalg_LU_refine(m, lu, perm, rhs, x, residual);
for(i=0; i<dim; i++) {
int foo = check(gsl_vector_get(x, i),actual[i],eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g (improved)\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(residual);
gsl_vector_free(x);
gsl_matrix_free(lu);
gsl_vector_free(rhs);
gsl_permutation_free(perm);
return s;
}
int test_LU_solve(void)
{
int f;
int s = 0;
f = test_LU_solve_dim(hilb2, hilb2_solution, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " LU_solve hilbert(2)");
s += f;
f = test_LU_solve_dim(hilb3, hilb3_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " LU_solve hilbert(3)");
s += f;
f = test_LU_solve_dim(hilb4, hilb4_solution, 2048.0 * GSL_DBL_EPSILON);
gsl_test(f, " LU_solve hilbert(4)");
s += f;
f = test_LU_solve_dim(hilb12, hilb12_solution, 0.5);
gsl_test(f, " LU_solve hilbert(12)");
s += f;
f = test_LU_solve_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " LU_solve vander(2)");
s += f;
f = test_LU_solve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " LU_solve vander(3)");
s += f;
f = test_LU_solve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " LU_solve vander(4)");
s += f;
f = test_LU_solve_dim(vander12, vander12_solution, 0.05);
gsl_test(f, " LU_solve vander(12)");
s += f;
return s;
}
int
test_LUc_solve_dim(const gsl_matrix_complex * m, const double * actual, double eps)
{
int s = 0;
int signum;
unsigned long i, dim = m->size1;
gsl_permutation * perm = gsl_permutation_alloc(dim);
gsl_vector_complex * rhs = gsl_vector_complex_alloc(dim);
gsl_matrix_complex * lu = gsl_matrix_complex_alloc(dim,dim);
gsl_vector_complex * x = gsl_vector_complex_alloc(dim);
gsl_vector_complex * residual = gsl_vector_complex_alloc(dim);
gsl_matrix_complex_memcpy(lu,m);
for(i=0; i<dim; i++)
{
gsl_complex z = gsl_complex_rect (2.0*i+1.0, 2.0*i+2.0);
gsl_vector_complex_set(rhs, i, z);
}
s += gsl_linalg_complex_LU_decomp(lu, perm, &signum);
s += gsl_linalg_complex_LU_solve(lu, perm, rhs, x);
for(i=0; i<dim; i++) {
gsl_complex z = gsl_vector_complex_get(x, i);
int foo_r = check(GSL_REAL(z),actual[2*i],eps);
int foo_i = check(GSL_IMAG(z),actual[2*i+1],eps);
if(foo_r || foo_i) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, GSL_REAL(z), actual[2*i]);
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, GSL_IMAG(z), actual[2*i+1]);
}
s += foo_r + foo_i;
}
s += gsl_linalg_complex_LU_refine(m, lu, perm, rhs, x, residual);
for(i=0; i<dim; i++) {
gsl_complex z = gsl_vector_complex_get(x, i);
int foo_r = check(GSL_REAL(z),actual[2*i],eps);
int foo_i = check(GSL_IMAG(z),actual[2*i+1],eps);
if(foo_r || foo_i) {
printf("%3lu[%lu]: %22.18g %22.18g (improved)\n", dim, i, GSL_REAL(z), actual[2*i]);
printf("%3lu[%lu]: %22.18g %22.18g (improved)\n", dim, i, GSL_IMAG(z), actual[2*i+1]);
}
s += foo_r + foo_i;
}
gsl_vector_complex_free(residual);
gsl_vector_complex_free(x);
gsl_matrix_complex_free(lu);
gsl_vector_complex_free(rhs);
gsl_permutation_free(perm);
return s;
}
int test_LUc_solve(void)
{
int f;
int s = 0;
f = test_LUc_solve_dim(c7, c7_solution, 1024.0 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " complex_LU_solve complex(7)");
s += f;
return s;
}
int
test_QR_solve_dim(const gsl_matrix * m, const double * actual, double eps)
{
int s = 0;
unsigned long i, dim = m->size1;
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_matrix * qr = gsl_matrix_alloc(dim,dim);
gsl_vector * d = gsl_vector_alloc(dim);
gsl_vector * x = gsl_vector_alloc(dim);
gsl_matrix_memcpy(qr,m);
for(i=0; i<dim; i++) gsl_vector_set(rhs, i, i+1.0);
s += gsl_linalg_QR_decomp(qr, d);
s += gsl_linalg_QR_solve(qr, d, rhs, x);
for(i=0; i<dim; i++) {
int foo = check(gsl_vector_get(x, i), actual[i], eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(x);
gsl_vector_free(d);
gsl_matrix_free(qr);
gsl_vector_free(rhs);
return s;
}
int test_QR_solve(void)
{
int f;
int s = 0;
f = test_QR_solve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_solve hilbert(2)");
s += f;
f = test_QR_solve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_solve hilbert(3)");
s += f;
f = test_QR_solve_dim(hilb4, hilb4_solution, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_solve hilbert(4)");
s += f;
f = test_QR_solve_dim(hilb12, hilb12_solution, 0.5);
gsl_test(f, " QR_solve hilbert(12)");
s += f;
f = test_QR_solve_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_solve vander(2)");
s += f;
f = test_QR_solve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_solve vander(3)");
s += f;
f = test_QR_solve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_solve vander(4)");
s += f;
f = test_QR_solve_dim(vander12, vander12_solution, 0.05);
gsl_test(f, " QR_solve vander(12)");
s += f;
return s;
}
int
test_QR_QRsolve_dim(const gsl_matrix * m, const double * actual, double eps)
{
int s = 0;
unsigned long i, dim = m->size1;
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_matrix * qr = gsl_matrix_alloc(dim,dim);
gsl_matrix * q = gsl_matrix_alloc(dim,dim);
gsl_matrix * r = gsl_matrix_alloc(dim,dim);
gsl_vector * d = gsl_vector_alloc(dim);
gsl_vector * x = gsl_vector_alloc(dim);
gsl_matrix_memcpy(qr,m);
for(i=0; i<dim; i++) gsl_vector_set(rhs, i, i+1.0);
s += gsl_linalg_QR_decomp(qr, d);
s += gsl_linalg_QR_unpack(qr, d, q, r);
s += gsl_linalg_QR_QRsolve(q, r, rhs, x);
for(i=0; i<dim; i++) {
int foo = check(gsl_vector_get(x, i), actual[i], eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(x);
gsl_vector_free(d);
gsl_matrix_free(qr);
gsl_matrix_free(q);
gsl_matrix_free(r);
gsl_vector_free(rhs);
return s;
}
int test_QR_QRsolve(void)
{
int f;
int s = 0;
f = test_QR_QRsolve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_QRsolve hilbert(2)");
s += f;
f = test_QR_QRsolve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_QRsolve hilbert(3)");
s += f;
f = test_QR_QRsolve_dim(hilb4, hilb4_solution, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_QRsolve hilbert(4)");
s += f;
f = test_QR_QRsolve_dim(hilb12, hilb12_solution, 0.5);
gsl_test(f, " QR_QRsolve hilbert(12)");
s += f;
f = test_QR_QRsolve_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_QRsolve vander(2)");
s += f;
f = test_QR_QRsolve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_QRsolve vander(3)");
s += f;
f = test_QR_QRsolve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_QRsolve vander(4)");
s += f;
f = test_QR_QRsolve_dim(vander12, vander12_solution, 0.05);
gsl_test(f, " QR_QRsolve vander(12)");
s += f;
return s;
}
int
test_QR_lssolve_dim(const gsl_matrix * m, const double * actual, double eps)
{
int s = 0;
unsigned long i, M = m->size1, N = m->size2;
gsl_vector * rhs = gsl_vector_alloc(M);
gsl_matrix * qr = gsl_matrix_alloc(M,N);
gsl_vector * d = gsl_vector_alloc(N);
gsl_vector * x = gsl_vector_alloc(N);
gsl_vector * r = gsl_vector_alloc(M);
gsl_vector * res = gsl_vector_alloc(M);
gsl_matrix_memcpy(qr,m);
for(i=0; i<M; i++) gsl_vector_set(rhs, i, i+1.0);
s += gsl_linalg_QR_decomp(qr, d);
s += gsl_linalg_QR_lssolve(qr, d, rhs, x, res);
for(i=0; i<N; i++) {
int foo = check(gsl_vector_get(x, i), actual[i], eps);
if(foo) {
printf("(%3lu,%3lu)[%lu]: %22.18g %22.18g\n", M, N, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
/* compute residual r = b - m x */
if (M == N) {
gsl_vector_set_zero(r);
} else {
gsl_vector_memcpy(r, rhs);
gsl_blas_dgemv(CblasNoTrans, -1.0, m, x, 1.0, r);
};
for(i=0; i<N; i++) {
int foo = check(gsl_vector_get(res, i), gsl_vector_get(r,i), sqrt(eps));
if(foo) {
printf("(%3lu,%3lu)[%lu]: %22.18g %22.18g\n", M, N, i, gsl_vector_get(res, i), gsl_vector_get(r,i));
}
s += foo;
}
gsl_vector_free(r);
gsl_vector_free(res);
gsl_vector_free(x);
gsl_vector_free(d);
gsl_matrix_free(qr);
gsl_vector_free(rhs);
return s;
}
int test_QR_lssolve(void)
{
int f;
int s = 0;
f = test_QR_lssolve_dim(m53, m53_lssolution, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_lssolve m(5,3)");
s += f;
f = test_QR_lssolve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_lssolve hilbert(2)");
s += f;
f = test_QR_lssolve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_lssolve hilbert(3)");
s += f;
f = test_QR_lssolve_dim(hilb4, hilb4_solution, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_lssolve hilbert(4)");
s += f;
f = test_QR_lssolve_dim(hilb12, hilb12_solution, 0.5);
gsl_test(f, " QR_lssolve hilbert(12)");
s += f;
f = test_QR_lssolve_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_lssolve vander(2)");
s += f;
f = test_QR_lssolve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_lssolve vander(3)");
s += f;
f = test_QR_lssolve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_lssolve vander(4)");
s += f;
f = test_QR_lssolve_dim(vander12, vander12_solution, 0.05);
gsl_test(f, " QR_lssolve vander(12)");
s += f;
return s;
}
int
test_QR_decomp_dim(const gsl_matrix * m, double eps)
{
int s = 0;
unsigned long i,j, M = m->size1, N = m->size2;
gsl_matrix * qr = gsl_matrix_alloc(M,N);
gsl_matrix * a = gsl_matrix_alloc(M,N);
gsl_matrix * q = gsl_matrix_alloc(M,M);
gsl_matrix * r = gsl_matrix_alloc(M,N);
gsl_vector * d = gsl_vector_alloc(GSL_MIN(M,N));
gsl_matrix_memcpy(qr,m);
s += gsl_linalg_QR_decomp(qr, d);
s += gsl_linalg_QR_unpack(qr, d, q, r);
/* compute a = q r */
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, q, r, 0.0, a);
for(i=0; i<M; i++) {
for(j=0; j<N; j++) {
double aij = gsl_matrix_get(a, i, j);
double mij = gsl_matrix_get(m, i, j);
int foo = check(aij, mij, eps);
if(foo) {
printf("(%3lu,%3lu)[%lu,%lu]: %22.18g %22.18g\n", M, N, i,j, aij, mij);
}
s += foo;
}
}
gsl_vector_free(d);
gsl_matrix_free(qr);
gsl_matrix_free(a);
gsl_matrix_free(q);
gsl_matrix_free(r);
return s;
}
int test_QR_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;
}
int
test_QRPT_solve_dim(const gsl_matrix * m, const double * actual, double eps)
{
int s = 0;
int signum;
unsigned long i, dim = m->size1;
gsl_permutation * perm = gsl_permutation_alloc(dim);
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_matrix * qr = gsl_matrix_alloc(dim,dim);
gsl_vector * d = gsl_vector_alloc(dim);
gsl_vector * x = gsl_vector_alloc(dim);
gsl_vector * norm = gsl_vector_alloc(dim);
gsl_matrix_memcpy(qr,m);
for(i=0; i<dim; i++) gsl_vector_set(rhs, i, i+1.0);
s += gsl_linalg_QRPT_decomp(qr, d, perm, &signum, norm);
s += gsl_linalg_QRPT_solve(qr, d, perm, rhs, x);
for(i=0; i<dim; i++) {
int foo = check(gsl_vector_get(x, i), actual[i], eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(norm);
gsl_vector_free(x);
gsl_vector_free(d);
gsl_matrix_free(qr);
gsl_vector_free(rhs);
gsl_permutation_free(perm);
return s;
}
int test_QRPT_solve(void)
{
int f;
int s = 0;
f = test_QRPT_solve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_solve hilbert(2)");
s += f;
f = test_QRPT_solve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_solve hilbert(3)");
s += f;
f = test_QRPT_solve_dim(hilb4, hilb4_solution, 2 * 2048.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_solve hilbert(4)");
s += f;
f = test_QRPT_solve_dim(hilb12, hilb12_solution, 0.5);
gsl_test(f, " QRPT_solve hilbert(12)");
s += f;
f = test_QRPT_solve_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_solve vander(2)");
s += f;
f = test_QRPT_solve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_solve vander(3)");
s += f;
f = test_QRPT_solve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_solve vander(4)");
s += f;
f = test_QRPT_solve_dim(vander12, vander12_solution, 0.05);
gsl_test(f, " QRPT_solve vander(12)");
s += f;
return s;
}
int
test_QRPT_QRsolve_dim(const gsl_matrix * m, const double * actual, double eps)
{
int s = 0;
int signum;
unsigned long i, dim = m->size1;
gsl_permutation * perm = gsl_permutation_alloc(dim);
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_matrix * qr = gsl_matrix_alloc(dim,dim);
gsl_matrix * q = gsl_matrix_alloc(dim,dim);
gsl_matrix * r = gsl_matrix_alloc(dim,dim);
gsl_vector * d = gsl_vector_alloc(dim);
gsl_vector * x = gsl_vector_alloc(dim);
gsl_vector * norm = gsl_vector_alloc(dim);
gsl_matrix_memcpy(qr,m);
for(i=0; i<dim; i++) gsl_vector_set(rhs, i, i+1.0);
s += gsl_linalg_QRPT_decomp2(qr, q, r, d, perm, &signum, norm);
s += gsl_linalg_QRPT_QRsolve(q, r, perm, rhs, x);
for(i=0; i<dim; i++) {
int foo = check(gsl_vector_get(x, i), actual[i], eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(norm);
gsl_vector_free(x);
gsl_vector_free(d);
gsl_matrix_free(qr);
gsl_matrix_free(q);
gsl_matrix_free(r);
gsl_vector_free(rhs);
gsl_permutation_free(perm);
return s;
}
int test_QRPT_QRsolve(void)
{
int f;
int s = 0;
f = test_QRPT_QRsolve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_QRsolve hilbert(2)");
s += f;
f = test_QRPT_QRsolve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_QRsolve hilbert(3)");
s += f;
f = test_QRPT_QRsolve_dim(hilb4, hilb4_solution, 2 * 2048.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_QRsolve hilbert(4)");
s += f;
f = test_QRPT_QRsolve_dim(hilb12, hilb12_solution, 0.5);
gsl_test(f, " QRPT_QRsolve hilbert(12)");
s += f;
f = test_QRPT_QRsolve_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_QRsolve vander(2)");
s += f;
f = test_QRPT_QRsolve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_QRsolve vander(3)");
s += f;
f = test_QRPT_QRsolve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_QRsolve vander(4)");
s += f;
f = test_QRPT_QRsolve_dim(vander12, vander12_solution, 0.05);
gsl_test(f, " QRPT_QRsolve vander(12)");
s += f;
return s;
}
int
test_QRPT_decomp_dim(const gsl_matrix * m, double eps)
{
int s = 0, signum;
unsigned long i,j, M = m->size1, N = m->size2;
gsl_matrix * qr = gsl_matrix_alloc(M,N);
gsl_matrix * a = gsl_matrix_alloc(M,N);
gsl_matrix * q = gsl_matrix_alloc(M,M);
gsl_matrix * r = gsl_matrix_alloc(M,N);
gsl_vector * d = gsl_vector_alloc(GSL_MIN(M,N));
gsl_vector * norm = gsl_vector_alloc(N);
gsl_permutation * perm = gsl_permutation_alloc(N);
gsl_matrix_memcpy(qr,m);
s += gsl_linalg_QRPT_decomp(qr, d, perm, &signum, norm);
s += gsl_linalg_QR_unpack(qr, d, q, r);
/* compute a = q r */
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, q, r, 0.0, a);
/* Compute QR P^T by permuting the elements of the rows of QR */
for (i = 0; i < M; i++) {
gsl_vector_view row = gsl_matrix_row (a, i);
gsl_permute_vector_inverse (perm, &row.vector);
}
for(i=0; i<M; i++) {
for(j=0; j<N; j++) {
double aij = gsl_matrix_get(a, i, j);
double mij = gsl_matrix_get(m, i, j);
int foo = check(aij, mij, eps);
if(foo) {
printf("(%3lu,%3lu)[%lu,%lu]: %22.18g %22.18g\n", M, N, i,j, aij, mij);
}
s += foo;
}
}
gsl_permutation_free (perm);
gsl_vector_free(norm);
gsl_vector_free(d);
gsl_matrix_free(qr);
gsl_matrix_free(a);
gsl_matrix_free(q);
gsl_matrix_free(r);
return s;
}
int test_QRPT_decomp(void)
{
int f;
int s = 0;
f = test_QRPT_decomp_dim(m35, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_decomp m(3,5)");
s += f;
f = test_QRPT_decomp_dim(m53, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_decomp m(5,3)");
s += f;
f = test_QRPT_decomp_dim(s35, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_decomp s(3,5)");
s += f;
f = test_QRPT_decomp_dim(s53, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_decomp s(5,3)");
s += f;
f = test_QRPT_decomp_dim(hilb2, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_decomp hilbert(2)");
s += f;
f = test_QRPT_decomp_dim(hilb3, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_decomp hilbert(3)");
s += f;
f = test_QRPT_decomp_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_decomp hilbert(4)");
s += f;
f = test_QRPT_decomp_dim(hilb12, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_decomp hilbert(12)");
s += f;
f = test_QRPT_decomp_dim(vander2, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_decomp vander(2)");
s += f;
f = test_QRPT_decomp_dim(vander3, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_decomp vander(3)");
s += f;
f = test_QRPT_decomp_dim(vander4, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QRPT_decomp vander(4)");
s += f;
f = test_QRPT_decomp_dim(vander12, 0.0005); /* FIXME: bad accuracy */
gsl_test(f, " QRPT_decomp vander(12)");
s += f;
return s;
}
int
test_QR_update_dim(const gsl_matrix * m, double eps)
{
int s = 0;
unsigned long i,j,k, M = m->size1, N = m->size2;
gsl_vector * rhs = gsl_vector_alloc(N);
gsl_matrix * qr1 = gsl_matrix_alloc(M,N);
gsl_matrix * qr2 = gsl_matrix_alloc(M,N);
gsl_matrix * q1 = gsl_matrix_alloc(M,M);
gsl_matrix * r1 = gsl_matrix_alloc(M,N);
gsl_matrix * q2 = gsl_matrix_alloc(M,M);
gsl_matrix * r2 = gsl_matrix_alloc(M,N);
gsl_vector * d = gsl_vector_alloc(GSL_MIN(M,N));
gsl_vector * solution1 = gsl_vector_alloc(N);
gsl_vector * solution2 = gsl_vector_alloc(N);
gsl_vector * u = gsl_vector_alloc(M);
gsl_vector * v = gsl_vector_alloc(N);
gsl_vector * w = gsl_vector_alloc(M);
gsl_matrix_memcpy(qr1,m);
gsl_matrix_memcpy(qr2,m);
for(i=0; i<N; i++) gsl_vector_set(rhs, i, i+1.0);
for(i=0; i<M; i++) gsl_vector_set(u, i, sin(i+1.0));
for(i=0; i<N; i++) gsl_vector_set(v, i, cos(i+2.0) + sin(i*i+3.0));
for(i=0; i<M; i++)
{
double ui = gsl_vector_get(u, i);
for(j=0; j<N; j++)
{
double vj = gsl_vector_get(v, j);
double qij = gsl_matrix_get(qr1, i, j);
gsl_matrix_set(qr1, i, j, qij + ui * vj);
}
}
s += gsl_linalg_QR_decomp(qr2, d);
s += gsl_linalg_QR_unpack(qr2, d, q2, r2);
/* compute w = Q^T u */
for (j = 0; j < M; j++)
{
double sum = 0;
for (i = 0; i < M; i++)
sum += gsl_matrix_get (q2, i, j) * gsl_vector_get (u, i);
gsl_vector_set (w, j, sum);
}
s += gsl_linalg_QR_update(q2, r2, w, v);
/* compute qr2 = q2 * r2 */
for (i = 0; i < M; i++)
{
for (j = 0; j< N; j++)
{
double sum = 0;
for (k = 0; k <= GSL_MIN(j,M-1); k++)
{
double qik = gsl_matrix_get(q2, i, k);
double rkj = gsl_matrix_get(r2, k, j);
sum += qik * rkj ;
}
gsl_matrix_set (qr2, i, j, sum);
}
}
for(i=0; i<M; i++) {
for(j=0; j<N; j++) {
double s1 = gsl_matrix_get(qr1, i, j);
double s2 = gsl_matrix_get(qr2, i, j);
int foo = check(s1, s2, eps);
if(foo) {
printf("(%3lu,%3lu)[%lu,%lu]: %22.18g %22.18g\n", M, N, i,j, s1, s2);
}
s += foo;
}
}
gsl_vector_free(solution1);
gsl_vector_free(solution2);
gsl_vector_free(d);
gsl_vector_free(u);
gsl_vector_free(v);
gsl_vector_free(w);
gsl_matrix_free(qr1);
gsl_matrix_free(qr2);
gsl_matrix_free(q1);
gsl_matrix_free(r1);
gsl_matrix_free(q2);
gsl_matrix_free(r2);
gsl_vector_free(rhs);
return s;
}
int test_QR_update(void)
{
int f;
int s = 0;
f = test_QR_update_dim(m35, 2 * 512.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_update m(3,5)");
s += f;
f = test_QR_update_dim(m53, 2 * 512.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_update m(5,3)");
s += f;
f = test_QR_update_dim(hilb2, 2 * 512.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_update hilbert(2)");
s += f;
f = test_QR_update_dim(hilb3, 2 * 512.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_update hilbert(3)");
s += f;
f = test_QR_update_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_update hilbert(4)");
s += f;
f = test_QR_update_dim(hilb12, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_update hilbert(12)");
s += f;
f = test_QR_update_dim(vander2, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_update vander(2)");
s += f;
f = test_QR_update_dim(vander3, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_update vander(3)");
s += f;
f = test_QR_update_dim(vander4, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " QR_update vander(4)");
s += f;
f = test_QR_update_dim(vander12, 0.0005); /* FIXME: bad accuracy */
gsl_test(f, " QR_update vander(12)");
s += f;
return s;
}
int
test_LQ_solve_dim(const gsl_matrix * m, const double * actual, double eps)
{
int s = 0;
unsigned long i, dim = m->size1;
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_matrix * lq = gsl_matrix_alloc(dim,dim);
gsl_vector * d = gsl_vector_alloc(dim);
gsl_vector * x = gsl_vector_alloc(dim);
gsl_matrix_transpose_memcpy(lq,m);
for(i=0; i<dim; i++) gsl_vector_set(rhs, i, i+1.0);
s += gsl_linalg_LQ_decomp(lq, d);
s += gsl_linalg_LQ_solve_T(lq, d, rhs, x);
for(i=0; i<dim; i++) {
int foo = check(gsl_vector_get(x, i), actual[i], eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(x);
gsl_vector_free(d);
gsl_matrix_free(lq);
gsl_vector_free(rhs);
return s;
}
int test_LQ_solve(void)
{
int f;
int s = 0;
f = test_LQ_solve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_solve hilbert(2)");
s += f;
f = test_LQ_solve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_solve hilbert(3)");
s += f;
f = test_LQ_solve_dim(hilb4, hilb4_solution, 4 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_solve hilbert(4)");
s += f;
f = test_LQ_solve_dim(hilb12, hilb12_solution, 0.5);
gsl_test(f, " LQ_solve hilbert(12)");
s += f;
f = test_LQ_solve_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_solve vander(2)");
s += f;
f = test_LQ_solve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_solve vander(3)");
s += f;
f = test_LQ_solve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_solve vander(4)");
s += f;
f = test_LQ_solve_dim(vander12, vander12_solution, 0.05);
gsl_test(f, " LQ_solve vander(12)");
s += f;
return s;
}
int
test_LQ_LQsolve_dim(const gsl_matrix * m, const double * actual, double eps)
{
int s = 0;
unsigned long i, dim = m->size1;
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_matrix * lq = gsl_matrix_alloc(dim,dim);
gsl_matrix * q = gsl_matrix_alloc(dim,dim);
gsl_matrix * l = gsl_matrix_alloc(dim,dim);
gsl_vector * d = gsl_vector_alloc(dim);
gsl_vector * x = gsl_vector_alloc(dim);
gsl_matrix_transpose_memcpy(lq,m);
for(i=0; i<dim; i++) gsl_vector_set(rhs, i, i+1.0);
s += gsl_linalg_LQ_decomp(lq, d);
s += gsl_linalg_LQ_unpack(lq, d, q, l);
s += gsl_linalg_LQ_LQsolve(q, l, rhs, x);
for(i=0; i<dim; i++) {
int foo = check(gsl_vector_get(x, i), actual[i], eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(x);
gsl_vector_free(d);
gsl_matrix_free(lq);
gsl_matrix_free(q);
gsl_matrix_free(l);
gsl_vector_free(rhs);
return s;
}
int test_LQ_LQsolve(void)
{
int f;
int s = 0;
f = test_LQ_LQsolve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_LQsolve hilbert(2)");
s += f;
f = test_LQ_LQsolve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_LQsolve hilbert(3)");
s += f;
f = test_LQ_LQsolve_dim(hilb4, hilb4_solution, 4 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_LQsolve hilbert(4)");
s += f;
f = test_LQ_LQsolve_dim(hilb12, hilb12_solution, 0.5);
gsl_test(f, " LQ_LQsolve hilbert(12)");
s += f;
f = test_LQ_LQsolve_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_LQsolve vander(2)");
s += f;
f = test_LQ_LQsolve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_LQsolve vander(3)");
s += f;
f = test_LQ_LQsolve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_LQsolve vander(4)");
s += f;
f = test_LQ_LQsolve_dim(vander12, vander12_solution, 0.05);
gsl_test(f, " LQ_LQsolve vander(12)");
s += f;
return s;
}
int
test_LQ_lssolve_dim(const gsl_matrix * m, const double * actual, double eps)
{
int s = 0;
unsigned long i, M = m->size1, N = m->size2;
gsl_vector * rhs = gsl_vector_alloc(M);
gsl_matrix * lq = gsl_matrix_alloc(N,M);
gsl_vector * d = gsl_vector_alloc(N);
gsl_vector * x = gsl_vector_alloc(N);
gsl_vector * r = gsl_vector_alloc(M);
gsl_vector * res = gsl_vector_alloc(M);
gsl_matrix_transpose_memcpy(lq,m);
for(i=0; i<M; i++) gsl_vector_set(rhs, i, i+1.0);
s += gsl_linalg_LQ_decomp(lq, d);
s += gsl_linalg_LQ_lssolve_T(lq, d, rhs, x, res);
for(i=0; i<N; i++) {
int foo = check(gsl_vector_get(x, i), actual[i], eps);
if(foo) {
printf("(%3lu,%3lu)[%lu]: %22.18g %22.18g\n", M, N, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
/* compute residual r = b - m x */
if (M == N) {
gsl_vector_set_zero(r);
} else {
gsl_vector_memcpy(r, rhs);
gsl_blas_dgemv(CblasNoTrans, -1.0, m, x, 1.0, r);
};
for(i=0; i<N; i++) {
int foo = check(gsl_vector_get(res, i), gsl_vector_get(r,i), sqrt(eps));
if(foo) {
printf("(%3lu,%3lu)[%lu]: %22.18g %22.18g\n", M, N, i, gsl_vector_get(res, i), gsl_vector_get(r,i));
}
s += foo;
}
gsl_vector_free(r);
gsl_vector_free(res);
gsl_vector_free(x);
gsl_vector_free(d);
gsl_matrix_free(lq);
gsl_vector_free(rhs);
return s;
}
int test_LQ_lssolve(void)
{
int f;
int s = 0;
f = test_LQ_lssolve_dim(m53, m53_lssolution, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_lssolve m(5,3)");
s += f;
f = test_LQ_lssolve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_lssolve hilbert(2)");
s += f;
f = test_LQ_lssolve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_lssolve hilbert(3)");
s += f;
f = test_LQ_lssolve_dim(hilb4, hilb4_solution, 4 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_lssolve hilbert(4)");
s += f;
f = test_LQ_lssolve_dim(hilb12, hilb12_solution, 0.5);
gsl_test(f, " LQ_lssolve hilbert(12)");
s += f;
f = test_LQ_lssolve_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_lssolve vander(2)");
s += f;
f = test_LQ_lssolve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_lssolve vander(3)");
s += f;
f = test_LQ_lssolve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_lssolve vander(4)");
s += f;
f = test_LQ_lssolve_dim(vander12, vander12_solution, 0.05);
gsl_test(f, " LQ_lssolve vander(12)");
s += f;
return s;
}
int
test_LQ_decomp_dim(const gsl_matrix * m, double eps)
{
int s = 0;
unsigned long i,j, M = m->size1, N = m->size2;
gsl_matrix * lq = gsl_matrix_alloc(M,N);
gsl_matrix * a = gsl_matrix_alloc(M,N);
gsl_matrix * q = gsl_matrix_alloc(N,N);
gsl_matrix * l = gsl_matrix_alloc(M,N);
gsl_vector * d = gsl_vector_alloc(GSL_MIN(M,N));
gsl_matrix_memcpy(lq,m);
s += gsl_linalg_LQ_decomp(lq, d);
s += gsl_linalg_LQ_unpack(lq, d, q, l);
/* compute a = q r */
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, l, q, 0.0, a);
for(i=0; i<M; i++) {
for(j=0; j<N; j++) {
double aij = gsl_matrix_get(a, i, j);
double mij = gsl_matrix_get(m, i, j);
int foo = check(aij, mij, eps);
if(foo) {
printf("(%3lu,%3lu)[%lu,%lu]: %22.18g %22.18g\n", M, N, i,j, aij, mij);
}
s += foo;
}
}
gsl_vector_free(d);
gsl_matrix_free(lq);
gsl_matrix_free(a);
gsl_matrix_free(q);
gsl_matrix_free(l);
return s;
}
int test_LQ_decomp(void)
{
int f;
int s = 0;
f = test_LQ_decomp_dim(m35, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_decomp m(3,5)");
s += f;
f = test_LQ_decomp_dim(m53, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_decomp m(5,3)");
s += f;
f = test_LQ_decomp_dim(hilb2, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_decomp hilbert(2)");
s += f;
f = test_LQ_decomp_dim(hilb3, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_decomp hilbert(3)");
s += f;
f = test_LQ_decomp_dim(hilb4, 4 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_decomp hilbert(4)");
s += f;
f = test_LQ_decomp_dim(hilb12, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_decomp hilbert(12)");
s += f;
f = test_LQ_decomp_dim(vander2, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_decomp vander(2)");
s += f;
f = test_LQ_decomp_dim(vander3, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_decomp vander(3)");
s += f;
f = test_LQ_decomp_dim(vander4, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_decomp vander(4)");
s += f;
f = test_LQ_decomp_dim(vander12, 0.0005); /* FIXME: bad accuracy */
gsl_test(f, " LQ_decomp vander(12)");
s += f;
return s;
}
int
test_PTLQ_solve_dim(const gsl_matrix * m, const double * actual, double eps)
{
int s = 0;
int signum;
unsigned long i, dim = m->size1;
gsl_permutation * perm = gsl_permutation_alloc(dim);
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_matrix * lq = gsl_matrix_alloc(dim,dim);
gsl_vector * d = gsl_vector_alloc(dim);
gsl_vector * x = gsl_vector_alloc(dim);
gsl_vector * norm = gsl_vector_alloc(dim);
gsl_matrix_transpose_memcpy(lq,m);
for(i=0; i<dim; i++) gsl_vector_set(rhs, i, i+1.0);
s += gsl_linalg_PTLQ_decomp(lq, d, perm, &signum, norm);
s += gsl_linalg_PTLQ_solve_T(lq, d, perm, rhs, x);
for(i=0; i<dim; i++) {
int foo = check(gsl_vector_get(x, i), actual[i], eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(norm);
gsl_vector_free(x);
gsl_vector_free(d);
gsl_matrix_free(lq);
gsl_vector_free(rhs);
gsl_permutation_free(perm);
return s;
}
int test_PTLQ_solve(void)
{
int f;
int s = 0;
f = test_PTLQ_solve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_solve hilbert(2)");
s += f;
f = test_PTLQ_solve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_solve hilbert(3)");
s += f;
f = test_PTLQ_solve_dim(hilb4, hilb4_solution, 2 * 2048.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_solve hilbert(4)");
s += f;
f = test_PTLQ_solve_dim(hilb12, hilb12_solution, 0.5);
gsl_test(f, " PTLQ_solve hilbert(12)");
s += f;
f = test_PTLQ_solve_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_solve vander(2)");
s += f;
f = test_PTLQ_solve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_solve vander(3)");
s += f;
f = test_PTLQ_solve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_solve vander(4)");
s += f;
f = test_PTLQ_solve_dim(vander12, vander12_solution, 0.05);
gsl_test(f, " PTLQ_solve vander(12)");
s += f;
return s;
}
int
test_PTLQ_LQsolve_dim(const gsl_matrix * m, const double * actual, double eps)
{
int s = 0;
int signum;
unsigned long i, dim = m->size1;
gsl_permutation * perm = gsl_permutation_alloc(dim);
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_matrix * lq = gsl_matrix_alloc(dim,dim);
gsl_matrix * q = gsl_matrix_alloc(dim,dim);
gsl_matrix * l = gsl_matrix_alloc(dim,dim);
gsl_vector * d = gsl_vector_alloc(dim);
gsl_vector * x = gsl_vector_alloc(dim);
gsl_vector * norm = gsl_vector_alloc(dim);
gsl_matrix_transpose_memcpy(lq,m);
for(i=0; i<dim; i++) gsl_vector_set(rhs, i, i+1.0);
s += gsl_linalg_PTLQ_decomp2(lq, q, l, d, perm, &signum, norm);
s += gsl_linalg_PTLQ_LQsolve_T(q, l, perm, rhs, x);
for(i=0; i<dim; i++) {
int foo = check(gsl_vector_get(x, i), actual[i], eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(norm);
gsl_vector_free(x);
gsl_vector_free(d);
gsl_matrix_free(lq);
gsl_vector_free(rhs);
gsl_permutation_free(perm);
return s;
}
int test_PTLQ_LQsolve(void)
{
int f;
int s = 0;
f = test_PTLQ_LQsolve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_LQsolve hilbert(2)");
s += f;
f = test_PTLQ_LQsolve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_LQsolve hilbert(3)");
s += f;
f = test_PTLQ_LQsolve_dim(hilb4, hilb4_solution, 2 * 2048.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_LQsolve hilbert(4)");
s += f;
f = test_PTLQ_LQsolve_dim(hilb12, hilb12_solution, 0.5);
gsl_test(f, " PTLQ_LQsolve hilbert(12)");
s += f;
f = test_PTLQ_LQsolve_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_LQsolve vander(2)");
s += f;
f = test_PTLQ_LQsolve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_LQsolve vander(3)");
s += f;
f = test_PTLQ_LQsolve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_LQsolve vander(4)");
s += f;
f = test_PTLQ_LQsolve_dim(vander12, vander12_solution, 0.05);
gsl_test(f, " PTLQ_LQsolve vander(12)");
s += f;
return s;
}
int
test_PTLQ_decomp_dim(const gsl_matrix * m, double eps)
{
int s = 0, signum;
unsigned long i,j, M = m->size1, N = m->size2;
gsl_matrix * lq = gsl_matrix_alloc(N,M);
gsl_matrix * a = gsl_matrix_alloc(N,M);
gsl_matrix * q = gsl_matrix_alloc(M,M);
gsl_matrix * l = gsl_matrix_alloc(N,M);
gsl_vector * d = gsl_vector_alloc(GSL_MIN(M,N));
gsl_vector * norm = gsl_vector_alloc(N);
gsl_permutation * perm = gsl_permutation_alloc(N);
gsl_matrix_transpose_memcpy(lq,m);
s += gsl_linalg_PTLQ_decomp(lq, d, perm, &signum, norm);
s += gsl_linalg_LQ_unpack(lq, d, q, l);
/* compute a = l q */
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, l, q, 0.0, a);
/* Compute P LQ by permuting the rows of LQ */
for (i = 0; i < M; i++) {
gsl_vector_view col = gsl_matrix_column (a, i);
gsl_permute_vector_inverse (perm, &col.vector);
}
for(i=0; i<M; i++) {
for(j=0; j<N; j++) {
double aij = gsl_matrix_get(a, j, i);
double mij = gsl_matrix_get(m, i, j);
int foo = check(aij, mij, eps);
if(foo) {
printf("(%3lu,%3lu)[%lu,%lu]: %22.18g %22.18g\n", M, N, i,j, aij, mij);
}
s += foo;
}
}
gsl_permutation_free (perm);
gsl_vector_free(norm);
gsl_vector_free(d);
gsl_matrix_free(lq);
gsl_matrix_free(a);
gsl_matrix_free(q);
gsl_matrix_free(l);
return s;
}
int test_PTLQ_decomp(void)
{
int f;
int s = 0;
f = test_PTLQ_decomp_dim(m35, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_decomp m(3,5)");
s += f;
f = test_PTLQ_decomp_dim(m53, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_decomp m(5,3)");
s += f;
f = test_PTLQ_decomp_dim(s35, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_decomp s(3,5)");
s += f;
f = test_PTLQ_decomp_dim(s53, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_decomp s(5,3)");
s += f;
f = test_PTLQ_decomp_dim(hilb2, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_decomp hilbert(2)");
s += f;
f = test_PTLQ_decomp_dim(hilb3, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_decomp hilbert(3)");
s += f;
f = test_PTLQ_decomp_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_decomp hilbert(4)");
s += f;
f = test_PTLQ_decomp_dim(hilb12, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_decomp hilbert(12)");
s += f;
f = test_PTLQ_decomp_dim(vander2, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_decomp vander(2)");
s += f;
f = test_PTLQ_decomp_dim(vander3, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_decomp vander(3)");
s += f;
f = test_PTLQ_decomp_dim(vander4, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " PTLQ_decomp vander(4)");
s += f;
f = test_PTLQ_decomp_dim(vander12, 0.0005); /* FIXME: bad accuracy */
gsl_test(f, " PTLQ_decomp vander(12)");
s += f;
return s;
}
int
test_LQ_update_dim(const gsl_matrix * m, double eps)
{
int s = 0;
unsigned long i,j, M = m->size1, N = m->size2;
gsl_matrix * lq1 = gsl_matrix_alloc(N,M);
gsl_matrix * lq2 = gsl_matrix_alloc(N,M);
gsl_matrix * q1 = gsl_matrix_alloc(M,M);
gsl_matrix * l1 = gsl_matrix_alloc(N,M);
gsl_matrix * q2 = gsl_matrix_alloc(M,M);
gsl_matrix * l2 = gsl_matrix_alloc(N,M);
gsl_vector * d2 = gsl_vector_alloc(GSL_MIN(M,N));
gsl_vector * u = gsl_vector_alloc(M);
gsl_vector * v = gsl_vector_alloc(N);
gsl_vector * w = gsl_vector_alloc(M);
gsl_matrix_transpose_memcpy(lq1,m);
gsl_matrix_transpose_memcpy(lq2,m);
for(i=0; i<M; i++) gsl_vector_set(u, i, sin(i+1.0));
for(i=0; i<N; i++) gsl_vector_set(v, i, cos(i+2.0) + sin(i*i+3.0));
/* lq1 is updated */
gsl_blas_dger(1.0, v, u, lq1);
/* lq2 is first decomposed, updated later */
s += gsl_linalg_LQ_decomp(lq2, d2);
s += gsl_linalg_LQ_unpack(lq2, d2, q2, l2);
/* compute w = Q^T u */
gsl_blas_dgemv(CblasNoTrans, 1.0, q2, u, 0.0, w);
/* now lq2 is updated */
s += gsl_linalg_LQ_update(q2, l2, v, w);
/* multiply q2*l2 */
gsl_blas_dgemm(CblasNoTrans,CblasNoTrans,1.0,l2,q2,0.0,lq2);
/* check lq1==lq2 */
for(i=0; i<N; i++) {
for(j=0; j<M; j++) {
double s1 = gsl_matrix_get(lq1, i, j);
double s2 = gsl_matrix_get(lq2, i, j);
int foo = check(s1, s2, eps);
#if 0
if(foo) {
printf("LQ:(%3lu,%3lu)[%lu,%lu]: %22.18g %22.18g\n", M, N, i,j, s1, s2);
}
#endif
s += foo;
}
}
gsl_vector_free(d2);
gsl_vector_free(u);
gsl_vector_free(v);
gsl_vector_free(w);
gsl_matrix_free(lq1);
gsl_matrix_free(lq2);
gsl_matrix_free(q1);
gsl_matrix_free(l1);
gsl_matrix_free(q2);
gsl_matrix_free(l2);
return s;
}
int test_LQ_update(void)
{
int f;
int s = 0;
f = test_LQ_update_dim(m35, 2 * 512.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_update m(3,5)");
s += f;
f = test_LQ_update_dim(m53, 2 * 512.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_update m(5,3)");
s += f;
f = test_LQ_update_dim(hilb2, 2 * 512.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_update hilbert(2)");
s += f;
f = test_LQ_update_dim(hilb3, 2 * 512.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_update hilbert(3)");
s += f;
f = test_LQ_update_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_update hilbert(4)");
s += f;
f = test_LQ_update_dim(hilb12, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_update hilbert(12)");
s += f;
f = test_LQ_update_dim(vander2, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_update vander(2)");
s += f;
f = test_LQ_update_dim(vander3, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_update vander(3)");
s += f;
f = test_LQ_update_dim(vander4, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " LQ_update vander(4)");
s += f;
f = test_LQ_update_dim(vander12, 0.0005); /* FIXME: bad accuracy */
gsl_test(f, " LQ_update vander(12)");
s += f;
return s;
}
int
test_SV_solve_dim(const gsl_matrix * m, const double * actual, double eps)
{
int s = 0;
unsigned long i, dim = m->size1;
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_matrix * u = gsl_matrix_alloc(dim,dim);
gsl_matrix * q = gsl_matrix_alloc(dim,dim);
gsl_vector * d = gsl_vector_alloc(dim);
gsl_vector * x = gsl_vector_calloc(dim);
gsl_matrix_memcpy(u,m);
for(i=0; i<dim; i++) gsl_vector_set(rhs, i, i+1.0);
s += gsl_linalg_SV_decomp(u, q, d, x);
s += gsl_linalg_SV_solve(u, q, d, rhs, x);
for(i=0; i<dim; i++) {
int foo = check(gsl_vector_get(x, i), actual[i], eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(x);
gsl_vector_free(d);
gsl_matrix_free(u);
gsl_matrix_free(q);
gsl_vector_free(rhs);
return s;
}
int test_SV_solve(void)
{
int f;
int s = 0;
f = test_SV_solve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_solve hilbert(2)");
s += f;
f = test_SV_solve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_solve hilbert(3)");
s += f;
f = test_SV_solve_dim(hilb4, hilb4_solution, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_solve hilbert(4)");
s += f;
f = test_SV_solve_dim(hilb12, hilb12_solution, 0.5);
gsl_test(f, " SV_solve hilbert(12)");
s += f;
f = test_SV_solve_dim(vander2, vander2_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_solve vander(2)");
s += f;
f = test_SV_solve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_solve vander(3)");
s += f;
f = test_SV_solve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_solve vander(4)");
s += f;
f = test_SV_solve_dim(vander12, vander12_solution, 0.05);
gsl_test(f, " SV_solve vander(12)");
s += f;
return s;
}
int
test_SV_decomp_dim(const gsl_matrix * m, double eps)
{
int s = 0;
double di1;
unsigned long i,j, M = m->size1, N = m->size2;
gsl_matrix * v = gsl_matrix_alloc(M,N);
gsl_matrix * a = gsl_matrix_alloc(M,N);
gsl_matrix * q = gsl_matrix_alloc(N,N);
gsl_matrix * dqt = gsl_matrix_alloc(N,N);
gsl_vector * d = gsl_vector_alloc(N);
gsl_vector * w = gsl_vector_alloc(N);
gsl_matrix_memcpy(v,m);
s += gsl_linalg_SV_decomp(v, q, d, w);
/* Check that singular values are non-negative and in non-decreasing
order */
di1 = 0.0;
for (i = 0; i < N; i++)
{
double di = gsl_vector_get (d, i);
if (gsl_isnan (di))
{
continue; /* skip NaNs */
}
if (di < 0) {
s++;
printf("singular value %lu = %22.18g < 0\n", i, di);
}
if(i > 0 && di > di1) {
s++;
printf("singular value %lu = %22.18g vs previous %22.18g\n", i, di, di1);
}
di1 = di;
}
/* Scale dqt = D Q^T */
for (i = 0; i < N ; i++)
{
double di = gsl_vector_get (d, i);
for (j = 0; j < N; j++)
{
double qji = gsl_matrix_get(q, j, i);
gsl_matrix_set (dqt, i, j, qji * di);
}
}
/* compute a = v dqt */
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, v, dqt, 0.0, a);
for(i=0; i<M; i++) {
for(j=0; j<N; j++) {
double aij = gsl_matrix_get(a, i, j);
double mij = gsl_matrix_get(m, i, j);
int foo = check(aij, mij, eps);
if(foo) {
printf("(%3lu,%3lu)[%lu,%lu]: %22.18g %22.18g\n", M, N, i,j, aij, mij);
}
s += foo;
}
}
gsl_vector_free(w);
gsl_vector_free(d);
gsl_matrix_free(v);
gsl_matrix_free(a);
gsl_matrix_free(q);
gsl_matrix_free(dqt);
return s;
}
int test_SV_decomp(void)
{
int f;
int s = 0;
f = test_SV_decomp_dim(m11, 2 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp m(1,1)");
s += f;
f = test_SV_decomp_dim(m51, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp m(5,1)");
s += f;
/* M<N not implemented yet */
#if 0
f = test_SV_decomp_dim(m35, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp m(3,5)");
s += f;
#endif
f = test_SV_decomp_dim(m53, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp m(5,3)");
s += f;
f = test_SV_decomp_dim(moler10, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp moler(10)");
s += f;
f = test_SV_decomp_dim(hilb2, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp hilbert(2)");
s += f;
f = test_SV_decomp_dim(hilb3, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp hilbert(3)");
s += f;
f = test_SV_decomp_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp hilbert(4)");
s += f;
f = test_SV_decomp_dim(hilb12, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp hilbert(12)");
s += f;
f = test_SV_decomp_dim(vander2, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp vander(2)");
s += f;
f = test_SV_decomp_dim(vander3, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp vander(3)");
s += f;
f = test_SV_decomp_dim(vander4, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp vander(4)");
s += f;
f = test_SV_decomp_dim(vander12, 1e-4);
gsl_test(f, " SV_decomp vander(12)");
s += f;
f = test_SV_decomp_dim(row3, 10 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp row3");
s += f;
f = test_SV_decomp_dim(row5, 128 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp row5");
s += f;
f = test_SV_decomp_dim(row12, 1024 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp row12");
s += f;
f = test_SV_decomp_dim(inf5, 1024 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp inf5");
s += f;
f = test_SV_decomp_dim(nan5, 1024 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp nan5");
s += f;
{
double i1, i2, i3, i4;
double lower = -2, upper = 2;
for (i1 = lower; i1 <= upper; i1++)
{
for (i2 = lower; i2 <= upper; i2++)
{
for (i3 = lower; i3 <= upper; i3++)
{
for (i4 = lower; i4 <= upper; i4++)
{
gsl_matrix_set (A22, 0,0, i1);
gsl_matrix_set (A22, 0,1, i2);
gsl_matrix_set (A22, 1,0, i3);
gsl_matrix_set (A22, 1,1, i4);
f = test_SV_decomp_dim(A22, 16 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp (2x2) A=[%g, %g; %g, %g]", i1,i2,i3,i4);
s += f;
}
}
}
}
}
{
int i;
double carry = 0, lower = 0, upper = 1;
double *a = A33->data;
for (i=0; i<9; i++) {
a[i] = lower;
}
while (carry == 0.0) {
f = test_SV_decomp_dim(A33, 64 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp (3x3) A=[ %g, %g, %g; %g, %g, %g; %g, %g, %g]",
a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8]);
/* increment */
carry=1.0;
for (i=9; carry > 0.0 && i>0 && i--;)
{
double v=a[i]+carry;
carry = (v>upper) ? 1.0 : 0.0;
a[i] = (v>upper) ? lower : v;
}
}
}
#ifdef TEST_SVD_4X4
{
int i;
double carry = 0, lower = 0, upper = 1;
double *a = A44->data;
for (i=0; i<16; i++) {
a[i] = lower;
}
while (carry == 0.0) {
f = test_SV_decomp_dim(A44, 64 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp (4x4) A=[ %g, %g, %g, %g; %g, %g, %g, %g; %g, %g, %g, %g; %g, %g, %g, %g]",
a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9],
a[10], a[11], a[12], a[13], a[14], a[15]);
/* increment */
carry=1.0;
for (i=16; carry > 0.0 && i>0 && i--;)
{
double v=a[i]+carry;
carry = (v>upper) ? 1.0 : 0.0;
a[i] = (v>upper) ? lower : v;
}
}
}
#endif
return s;
}
int
test_SV_decomp_mod_dim(const gsl_matrix * m, double eps)
{
int s = 0;
double di1;
unsigned long i,j, M = m->size1, N = m->size2;
gsl_matrix * v = gsl_matrix_alloc(M,N);
gsl_matrix * a = gsl_matrix_alloc(M,N);
gsl_matrix * q = gsl_matrix_alloc(N,N);
gsl_matrix * x = gsl_matrix_alloc(N,N);
gsl_matrix * dqt = gsl_matrix_alloc(N,N);
gsl_vector * d = gsl_vector_alloc(N);
gsl_vector * w = gsl_vector_alloc(N);
gsl_matrix_memcpy(v,m);
s += gsl_linalg_SV_decomp_mod(v, x, q, d, w);
/* Check that singular values are non-negative and in non-decreasing
order */
di1 = 0.0;
for (i = 0; i < N; i++)
{
double di = gsl_vector_get (d, i);
if (gsl_isnan (di))
{
continue; /* skip NaNs */
}
if (di < 0) {
s++;
printf("singular value %lu = %22.18g < 0\n", i, di);
}
if(i > 0 && di > di1) {
s++;
printf("singular value %lu = %22.18g vs previous %22.18g\n", i, di, di1);
}
di1 = di;
}
/* Scale dqt = D Q^T */
for (i = 0; i < N ; i++)
{
double di = gsl_vector_get (d, i);
for (j = 0; j < N; j++)
{
double qji = gsl_matrix_get(q, j, i);
gsl_matrix_set (dqt, i, j, qji * di);
}
}
/* compute a = v dqt */
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, v, dqt, 0.0, a);
for(i=0; i<M; i++) {
for(j=0; j<N; j++) {
double aij = gsl_matrix_get(a, i, j);
double mij = gsl_matrix_get(m, i, j);
int foo = check(aij, mij, eps);
if(foo) {
printf("(%3lu,%3lu)[%lu,%lu]: %22.18g %22.18g\n", M, N, i,j, aij, mij);
}
s += foo;
}
}
gsl_vector_free(w);
gsl_vector_free(d);
gsl_matrix_free(v);
gsl_matrix_free(a);
gsl_matrix_free(q);
gsl_matrix_free(dqt);
gsl_matrix_free (x);
return s;
}
int test_SV_decomp_mod(void)
{
int f;
int s = 0;
f = test_SV_decomp_mod_dim(m11, 2 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod m(1,1)");
s += f;
f = test_SV_decomp_mod_dim(m51, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod m(5,1)");
s += f;
/* M<N not implemented yet */
#if 0
f = test_SV_decomp_mod_dim(m35, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod m(3,5)");
s += f;
#endif
f = test_SV_decomp_mod_dim(m53, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod m(5,3)");
s += f;
f = test_SV_decomp_mod_dim(moler10, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod moler(10)");
s += f;
f = test_SV_decomp_mod_dim(hilb2, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod hilbert(2)");
s += f;
f = test_SV_decomp_mod_dim(hilb3, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod hilbert(3)");
s += f;
f = test_SV_decomp_mod_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod hilbert(4)");
s += f;
f = test_SV_decomp_mod_dim(hilb12, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod hilbert(12)");
s += f;
f = test_SV_decomp_mod_dim(vander2, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod vander(2)");
s += f;
f = test_SV_decomp_mod_dim(vander3, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod vander(3)");
s += f;
f = test_SV_decomp_mod_dim(vander4, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod vander(4)");
s += f;
f = test_SV_decomp_mod_dim(vander12, 1e-4);
gsl_test(f, " SV_decomp_mod vander(12)");
s += f;
f = test_SV_decomp_mod_dim(row3, 10 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod row3");
s += f;
f = test_SV_decomp_mod_dim(row5, 128 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod row5");
s += f;
f = test_SV_decomp_mod_dim(row12, 1024 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod row12");
s += f;
f = test_SV_decomp_mod_dim(inf5, 1024 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod inf5");
s += f;
f = test_SV_decomp_mod_dim(nan5, 1024 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod nan5");
s += f;
{
double i1, i2, i3, i4;
double lower = -2, upper = 2;
for (i1 = lower; i1 <= upper; i1++)
{
for (i2 = lower; i2 <= upper; i2++)
{
for (i3 = lower; i3 <= upper; i3++)
{
for (i4 = lower; i4 <= upper; i4++)
{
gsl_matrix_set (A22, 0,0, i1);
gsl_matrix_set (A22, 0,1, i2);
gsl_matrix_set (A22, 1,0, i3);
gsl_matrix_set (A22, 1,1, i4);
f = test_SV_decomp_mod_dim(A22, 16 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod (2x2) A=[%g, %g; %g, %g]", i1,i2,i3,i4);
s += f;
}
}
}
}
}
{
int i;
double carry = 0, lower = 0, upper = 1;
double *a = A33->data;
for (i=0; i<9; i++) {
a[i] = lower;
}
while (carry == 0.0) {
f = test_SV_decomp_mod_dim(A33, 64 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod (3x3) A=[ %g, %g, %g; %g, %g, %g; %g, %g, %g]",
a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8]);
/* increment */
carry=1.0;
for (i=9; carry > 0.0 && i>0 && i--;)
{
double v=a[i]+carry;
carry = (v>upper) ? 1.0 : 0.0;
a[i] = (v>upper) ? lower : v;
}
}
}
#ifdef TEST_SVD_4X4
{
int i;
double carry = 0, lower = 0, upper = 1;
double *a = A44->data;
for (i=0; i<16; i++) {
a[i] = lower;
}
while (carry == 0.0) {
f = test_SV_decomp_mod_dim(A44, 64 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_mod (4x4) A=[ %g, %g, %g, %g; %g, %g, %g, %g; %g, %g, %g, %g; %g, %g, %g, %g]",
a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9],
a[10], a[11], a[12], a[13], a[14], a[15]);
/* increment */
carry=1.0;
for (i=16; carry>0.0 && i>0 && i--;)
{
double v=a[i]+carry;
carry = (v>upper) ? 1.0 : 0.0;
a[i] = (v>upper) ? lower : v;
}
}
}
#endif
return s;
}
int
test_SV_decomp_jacobi_dim(const gsl_matrix * m, double eps)
{
int s = 0;
double di1;
unsigned long i,j, M = m->size1, N = m->size2;
gsl_matrix * v = gsl_matrix_alloc(M,N);
gsl_matrix * a = gsl_matrix_alloc(M,N);
gsl_matrix * q = gsl_matrix_alloc(N,N);
gsl_matrix * dqt = gsl_matrix_alloc(N,N);
gsl_vector * d = gsl_vector_alloc(N);
gsl_matrix_memcpy(v,m);
s += gsl_linalg_SV_decomp_jacobi(v, q, d);
if (s)
printf("call returned status = %d\n", s);
/* Check that singular values are non-negative and in non-decreasing
order */
di1 = 0.0;
for (i = 0; i < N; i++)
{
double di = gsl_vector_get (d, i);
if (gsl_isnan (di))
{
continue; /* skip NaNs */
}
if (di < 0) {
s++;
printf("singular value %lu = %22.18g < 0\n", i, di);
}
if(i > 0 && di > di1) {
s++;
printf("singular value %lu = %22.18g vs previous %22.18g\n", i, di, di1);
}
di1 = di;
}
/* Scale dqt = D Q^T */
for (i = 0; i < N ; i++)
{
double di = gsl_vector_get (d, i);
for (j = 0; j < N; j++)
{
double qji = gsl_matrix_get(q, j, i);
gsl_matrix_set (dqt, i, j, qji * di);
}
}
/* compute a = v dqt */
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, v, dqt, 0.0, a);
for(i=0; i<M; i++) {
for(j=0; j<N; j++) {
double aij = gsl_matrix_get(a, i, j);
double mij = gsl_matrix_get(m, i, j);
int foo = check(aij, mij, eps);
if(foo) {
printf("(%3lu,%3lu)[%lu,%lu]: %22.18g %22.18g\n", M, N, i,j, aij, mij);
}
s += foo;
}
}
gsl_vector_free(d);
gsl_matrix_free(v);
gsl_matrix_free(a);
gsl_matrix_free(q);
gsl_matrix_free(dqt);
return s;
}
int test_SV_decomp_jacobi(void)
{
int f;
int s = 0;
f = test_SV_decomp_jacobi_dim(m11, 2 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi m(1,1)");
s += f;
f = test_SV_decomp_jacobi_dim(m51, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi m(5,1)");
s += f;
/* M<N not implemented yet */
#if 0
f = test_SV_decomp_jacobi_dim(m35, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi m(3,5)");
s += f;
#endif
f = test_SV_decomp_jacobi_dim(m53, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi m(5,3)");
s += f;
f = test_SV_decomp_jacobi_dim(moler10, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi moler(10)");
s += f;
f = test_SV_decomp_jacobi_dim(hilb2, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi hilbert(2)");
s += f;
f = test_SV_decomp_jacobi_dim(hilb3, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi hilbert(3)");
s += f;
f = test_SV_decomp_jacobi_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi hilbert(4)");
s += f;
f = test_SV_decomp_jacobi_dim(hilb12, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi hilbert(12)");
s += f;
f = test_SV_decomp_jacobi_dim(vander2, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi vander(2)");
s += f;
f = test_SV_decomp_jacobi_dim(vander3, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi vander(3)");
s += f;
f = test_SV_decomp_jacobi_dim(vander4, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi vander(4)");
s += f;
f = test_SV_decomp_jacobi_dim(vander12, 1e-4);
gsl_test(f, " SV_decomp_jacobi vander(12)");
s += f;
f = test_SV_decomp_jacobi_dim(row3, 10 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi row3");
s += f;
f = test_SV_decomp_jacobi_dim(row5, 128 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi row5");
s += f;
f = test_SV_decomp_jacobi_dim(row12, 1024 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi row12");
s += f;
#ifdef TEST_JACOBI_INF
f = test_SV_decomp_jacobi_dim(inf5, 1024 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi inf5");
s += f;
f = test_SV_decomp_jacobi_dim(nan5, 1024 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi nan5");
s += f;
#endif
{
double i1, i2, i3, i4;
double lower = -2, upper = 2;
for (i1 = lower; i1 <= upper; i1++)
{
for (i2 = lower; i2 <= upper; i2++)
{
for (i3 = lower; i3 <= upper; i3++)
{
for (i4 = lower; i4 <= upper; i4++)
{
gsl_matrix_set (A22, 0,0, i1);
gsl_matrix_set (A22, 0,1, i2);
gsl_matrix_set (A22, 1,0, i3);
gsl_matrix_set (A22, 1,1, i4);
f = test_SV_decomp_jacobi_dim(A22, 16 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi (2x2) A=[%g, %g; %g, %g]", i1,i2,i3,i4);
s += f;
}
}
}
}
}
{
int i;
double carry = 0, lower = 0, upper = 1;
double *a = A33->data;
for (i=0; i<9; i++) {
a[i] = lower;
}
while (carry == 0.0) {
f = test_SV_decomp_jacobi_dim(A33, 64 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi (3x3) A=[ %g, %g, %g; %g, %g, %g; %g, %g, %g]",
a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8]);
/* increment */
carry=1.0;
for (i=9; carry > 0.0 && i>0 && i--;)
{
double v=a[i]+carry;
carry = (v>upper) ? 1.0 : 0.0;
a[i] = (v>upper) ? lower : v;
}
}
}
#ifdef TEST_SVD_4X4
{
int i;
unsigned long k = 0;
double carry = 0, lower = 0, upper = 1;
double *a = A44->data;
for (i=0; i<16; i++) {
a[i] = lower;
}
while (carry == 0.0) {
k++;
f = test_SV_decomp_jacobi_dim(A44, 64 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi (4x4) A=[ %g, %g, %g, %g; %g, %g, %g, %g; %g, %g, %g, %g; %g, %g, %g, %g] %lu",
a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9],
a[10], a[11], a[12], a[13], a[14], a[15], k);
/* increment */
carry=1.0;
for (i=16; carry > 0.0 && i>0 && i--;)
{
double v=a[i]+carry;
carry = (v>upper) ? 1.0 : 0.0;
a[i] = (v>upper) ? lower : v;
}
}
}
#endif
{
int i;
unsigned long k = 0;
double carry = 0, lower = 0, upper = 1;
double *a = A55->data;
for (i=0; i<25; i++) {
a[i] = lower;
}
while (carry == 0.0) {
k++;
if (k % 1001 == 0)
{
f = test_SV_decomp_jacobi_dim(A55, 64 * GSL_DBL_EPSILON);
gsl_test(f, " SV_decomp_jacobi (5x5) case=%lu",k);
}
/* increment */
carry=1.0;
for (i=25; carry >0.0 && i>0 && i--;)
{
double v=a[i]+carry;
carry = (v>upper) ? 1.0 : 0.0;
a[i] = (v>upper) ? lower : v;
}
}
}
return s;
}
int
test_cholesky_solve_dim(const gsl_matrix * m, const double * actual, double eps)
{
int s = 0;
unsigned long i, dim = m->size1;
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_matrix * u = gsl_matrix_alloc(dim,dim);
gsl_vector * x = gsl_vector_calloc(dim);
gsl_matrix_memcpy(u,m);
for(i=0; i<dim; i++) gsl_vector_set(rhs, i, i+1.0);
s += gsl_linalg_cholesky_decomp(u);
s += gsl_linalg_cholesky_solve(u, rhs, x);
for(i=0; i<dim; i++) {
int foo = check(gsl_vector_get(x, i), actual[i], eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(x);
gsl_matrix_free(u);
gsl_vector_free(rhs);
return s;
}
int test_cholesky_solve(void)
{
int f;
int s = 0;
f = test_cholesky_solve_dim(hilb2, hilb2_solution, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " cholesky_solve hilbert(2)");
s += f;
f = test_cholesky_solve_dim(hilb3, hilb3_solution, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " cholesky_solve hilbert(3)");
s += f;
f = test_cholesky_solve_dim(hilb4, hilb4_solution, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " cholesky_solve hilbert(4)");
s += f;
f = test_cholesky_solve_dim(hilb12, hilb12_solution, 0.5);
gsl_test(f, " cholesky_solve hilbert(12)");
s += f;
return s;
}
int
test_cholesky_decomp_dim(const gsl_matrix * m, double eps)
{
int s = 0;
unsigned long i,j, M = m->size1, N = m->size2;
gsl_matrix * v = gsl_matrix_alloc(M,N);
gsl_matrix * a = gsl_matrix_alloc(M,N);
gsl_matrix * l = gsl_matrix_alloc(M,N);
gsl_matrix * lt = gsl_matrix_alloc(N,N);
gsl_matrix_memcpy(v,m);
s += gsl_linalg_cholesky_decomp(v);
/* Compute L LT */
for (i = 0; i < N ; i++)
{
for (j = 0; j < N; j++)
{
double vij = gsl_matrix_get(v, i, j);
gsl_matrix_set (l, i, j, i>=j ? vij : 0);
gsl_matrix_set (lt, i, j, i<=j ? vij : 0);
}
}
/* compute a = l lt */
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, l, lt, 0.0, a);
for(i=0; i<M; i++) {
for(j=0; j<N; j++) {
double aij = gsl_matrix_get(a, i, j);
double mij = gsl_matrix_get(m, i, j);
int foo = check(aij, mij, eps);
if(foo) {
printf("(%3lu,%3lu)[%lu,%lu]: %22.18g %22.18g\n", M, N, i,j, aij, mij);
}
s += foo;
}
}
gsl_matrix_free(v);
gsl_matrix_free(a);
gsl_matrix_free(l);
gsl_matrix_free(lt);
return s;
}
int test_cholesky_decomp(void)
{
int f;
int s = 0;
f = test_cholesky_decomp_dim(hilb2, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " cholesky_decomp hilbert(2)");
s += f;
f = test_cholesky_decomp_dim(hilb3, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " cholesky_decomp hilbert(3)");
s += f;
f = test_cholesky_decomp_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " cholesky_decomp hilbert(4)");
s += f;
f = test_cholesky_decomp_dim(hilb12, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " cholesky_decomp hilbert(12)");
s += f;
return s;
}
int
test_cholesky_decomp_unit_dim(const gsl_matrix * m, double eps)
{
int s = 0;
const unsigned long M = m->size1;
const unsigned long N = m->size2;
unsigned long i,j;
gsl_matrix * v = gsl_matrix_alloc(M,N);
gsl_matrix * a = gsl_matrix_alloc(M,N);
gsl_matrix * l = gsl_matrix_alloc(M,N);
gsl_matrix * lt = gsl_matrix_alloc(N,N);
gsl_matrix * dm = gsl_matrix_alloc(M,N);
gsl_vector * dv = gsl_vector_alloc(M);
gsl_matrix_memcpy(v,m);
s += gsl_linalg_cholesky_decomp_unit(v, dv);
/*
for(i = 0; i < M; i++)
{
for(j = 0; j < N; j++)
{
printf("v[%lu,%lu]: %22.18e\n", i,j, gsl_matrix_get(v, i, j));
}
}
for(i = 0; i < M; i++)
{
printf("d[%lu]: %22.18e\n", i, gsl_vector_get(dv, i));
}
*/
/* put L and transpose(L) into separate matrices */
for(i = 0; i < N ; i++)
{
for(j = 0; j < N; j++)
{
const double vij = gsl_matrix_get(v, i, j);
gsl_matrix_set (l, i, j, i>=j ? vij : 0);
gsl_matrix_set (lt, i, j, i<=j ? vij : 0);
}
}
/* put D into its own matrix */
gsl_matrix_set_zero(dm);
for(i = 0; i < M; ++i) gsl_matrix_set(dm, i, i, gsl_vector_get(dv, i));
/* compute a = L * D * transpose(L); uses v for temp space */
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, dm, lt, 0.0, v);
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, l, v, 0.0, a);
for(i = 0; i < M; i++)
{
for(j = 0; j < N; j++)
{
const double aij = gsl_matrix_get(a, i, j);
const double mij = gsl_matrix_get(m, i, j);
int foo = check(aij, mij, eps);
if(foo)
{
printf("(%3lu,%3lu)[%lu,%lu]: %22.18g %22.18g\n", M, N, i,j, aij, mij);
}
s += foo;
}
}
gsl_vector_free(dv);
gsl_matrix_free(dm);
gsl_matrix_free(lt);
gsl_matrix_free(l);
gsl_matrix_free(v);
gsl_matrix_free(a);
return s;
}
int test_cholesky_decomp_unit(void)
{
int f;
int s = 0;
f = test_cholesky_decomp_unit_dim(hilb2, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " cholesky_decomp_unit hilbert(2)");
s += f;
f = test_cholesky_decomp_unit_dim(hilb3, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " cholesky_decomp_unit hilbert(3)");
s += f;
f = test_cholesky_decomp_unit_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " cholesky_decomp_unit hilbert(4)");
s += f;
f = test_cholesky_decomp_unit_dim(hilb12, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " cholesky_decomp_unit hilbert(12)");
s += f;
return s;
}
int
test_HH_solve_dim(const gsl_matrix * m, const double * actual, double eps)
{
int s = 0;
unsigned long i, dim = m->size1;
gsl_permutation * perm = gsl_permutation_alloc(dim);
gsl_matrix * hh = gsl_matrix_alloc(dim,dim);
gsl_vector * d = gsl_vector_alloc(dim);
gsl_vector * x = gsl_vector_alloc(dim);
gsl_matrix_memcpy(hh,m);
for(i=0; i<dim; i++) gsl_vector_set(x, i, i+1.0);
s += gsl_linalg_HH_svx(hh, x);
for(i=0; i<dim; i++) {
int foo = check(gsl_vector_get(x, i),actual[i],eps);
if( foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(x);
gsl_vector_free(d);
gsl_matrix_free(hh);
gsl_permutation_free(perm);
return s;
}
int test_HH_solve(void)
{
int f;
int s = 0;
f = test_HH_solve_dim(hilb2, hilb2_solution, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " HH_solve hilbert(2)");
s += f;
f = test_HH_solve_dim(hilb3, hilb3_solution, 128.0 * GSL_DBL_EPSILON);
gsl_test(f, " HH_solve hilbert(3)");
s += f;
f = test_HH_solve_dim(hilb4, hilb4_solution, 2.0 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " HH_solve hilbert(4)");
s += f;
f = test_HH_solve_dim(hilb12, hilb12_solution, 0.5);
gsl_test(f, " HH_solve hilbert(12)");
s += f;
f = test_HH_solve_dim(vander2, vander2_solution, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " HH_solve vander(2)");
s += f;
f = test_HH_solve_dim(vander3, vander3_solution, 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " HH_solve vander(3)");
s += f;
f = test_HH_solve_dim(vander4, vander4_solution, 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " HH_solve vander(4)");
s += f;
f = test_HH_solve_dim(vander12, vander12_solution, 0.05);
gsl_test(f, " HH_solve vander(12)");
s += f;
return s;
}
int
test_TDS_solve_dim(unsigned long dim, double d, double od, const double * actual, double eps)
{
int s = 0;
unsigned long i;
gsl_vector * offdiag = gsl_vector_alloc(dim-1);
gsl_vector * diag = gsl_vector_alloc(dim);
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_vector * x = gsl_vector_alloc(dim);
for(i=0; i<dim; i++) {
gsl_vector_set(diag, i, d);
gsl_vector_set(rhs, i, i + 1.0);
}
for(i=0; i<dim-1; i++) {
gsl_vector_set(offdiag, i, od);
}
s += gsl_linalg_solve_symm_tridiag(diag, offdiag, rhs, x);
for(i=0; i<dim; i++) {
double si = gsl_vector_get(x, i);
double ai = actual[i];
int foo = check(si, ai, eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(x);
gsl_vector_free(rhs);
gsl_vector_free(diag);
gsl_vector_free(offdiag);
return s;
}
int test_TDS_solve(void)
{
int f;
int s = 0;
{
double actual[] = {0.0, 2.0};
f = test_TDS_solve_dim(2, 1.0, 0.5, actual, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " solve_TDS dim=2 A");
s += f;
}
{
double actual[] = {3.0/8.0, 15.0/8.0};
f = test_TDS_solve_dim(2, 1.0, 1.0/3.0, actual, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " solve_TDS dim=2 B");
s += f;
}
{
double actual[] = {5.0/8.0, 9.0/8.0, 2.0, 15.0/8.0, 35.0/8.0};
f = test_TDS_solve_dim(5, 1.0, 1.0/3.0, actual, 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " solve_TDS dim=5");
s += f;
}
return s;
}
int
test_TDS_cyc_solve_one(const unsigned long dim, const double * d, const double * od,
const double * r, const double * actual, double eps)
{
int s = 0;
unsigned long i;
gsl_vector * offdiag = gsl_vector_alloc(dim);
gsl_vector * diag = gsl_vector_alloc(dim);
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_vector * x = gsl_vector_alloc(dim);
for(i=0; i<dim; i++) {
gsl_vector_set(diag, i, d[i]);
gsl_vector_set(rhs, i, r[i]);
gsl_vector_set(offdiag, i, od[i]);
}
s += gsl_linalg_solve_symm_cyc_tridiag(diag, offdiag, rhs, x);
for(i=0; i<dim; i++) {
double si = gsl_vector_get(x, i);
double ai = actual[i];
int foo = check(si, ai, eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(x);
gsl_vector_free(rhs);
gsl_vector_free(diag);
gsl_vector_free(offdiag);
return s;
}
int test_TDS_cyc_solve(void)
{
int f;
int s = 0;
#ifdef SUPPORT_UNDERSIZE_CYC
{
unsigned long dim = 1;
double diag[] = { 2 };
double offdiag[] = { 3 };
double rhs[] = { 7 };
double actual[] = { 3.5 };
f = test_TDS_cyc_solve_one(dim, diag, offdiag, rhs, actual, 28.0 * GSL_DBL_EPSILON);
gsl_test(f, " solve_TDS_cyc dim=%lu A", dim);
s += f;
}
{
unsigned long dim = 2;
double diag[] = { 1, 2 };
double offdiag[] = { 3, 4 };
double rhs[] = { 7, -7 };
double actual[] = { -5, 4 };
f = test_TDS_cyc_solve_one(dim, diag, offdiag, rhs, actual, 28.0 * GSL_DBL_EPSILON);
gsl_test(f, " solve_TDS_cyc dim=%lu A", dim);
s += f;
}
#endif
{
unsigned long dim = 3;
double diag[] = { 1, 1, 1 };
double offdiag[] = { 3, 3, 3 };
double rhs[] = { 7, -7, 7 };
double actual[] = { -2, 5, -2 };
f = test_TDS_cyc_solve_one(dim, diag, offdiag, rhs, actual, 28.0 * GSL_DBL_EPSILON);
gsl_test(f, " solve_TDS_cyc dim=%lu A", dim);
s += f;
}
{
unsigned long dim = 5;
double diag[] = { 4, 2, 1, 2, 4 };
double offdiag[] = { 1, 1, 1, 1, 1 };
double rhs[] = { 30, -24, 3, 21, -30 };
double actual[] = { 12, 3, -42, 42, -21 };
/* f = test_TDS_cyc_solve_one(dim, diag, offdiag, rhs, actual, 7.0 * GSL_DBL_EPSILON);
FIXME: bad accuracy */
f = test_TDS_cyc_solve_one(dim, diag, offdiag, rhs, actual, 35.0 * GSL_DBL_EPSILON);
gsl_test(f, " solve_TDS_cyc dim=%lu B", dim);
s += f;
}
return s;
}
int
test_TDN_solve_dim(unsigned long dim, double d, double a, double b, const double * actual, double eps)
{
int s = 0;
unsigned long i;
gsl_vector * abovediag = gsl_vector_alloc(dim-1);
gsl_vector * belowdiag = gsl_vector_alloc(dim-1);
gsl_vector * diag = gsl_vector_alloc(dim);
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_vector * x = gsl_vector_alloc(dim);
for(i=0; i<dim; i++) {
gsl_vector_set(diag, i, d);
gsl_vector_set(rhs, i, i + 1.0);
}
for(i=0; i<dim-1; i++) {
gsl_vector_set(abovediag, i, a);
gsl_vector_set(belowdiag, i, b);
}
s += gsl_linalg_solve_tridiag(diag, abovediag, belowdiag, rhs, x);
for(i=0; i<dim; i++) {
double si = gsl_vector_get(x, i);
double ai = actual[i];
int foo = check(si, ai, eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(x);
gsl_vector_free(rhs);
gsl_vector_free(diag);
gsl_vector_free(abovediag);
gsl_vector_free(belowdiag);
return s;
}
int test_TDN_solve(void)
{
int f;
int s = 0;
double actual[16];
actual[0] = -7.0/3.0;
actual[1] = 5.0/3.0;
actual[2] = 4.0/3.0;
f = test_TDN_solve_dim(3, 1.0, 2.0, 1.0, actual, 2.0 * GSL_DBL_EPSILON);
gsl_test(f, " solve_TDN dim=2 A");
s += f;
actual[0] = 0.75;
actual[1] = 0.75;
actual[2] = 2.625;
f = test_TDN_solve_dim(3, 1.0, 1.0/3.0, 1.0/2.0, actual, 2.0 * GSL_DBL_EPSILON);
gsl_test(f, " solve_TDN dim=2 B");
s += f;
actual[0] = 99.0/140.0;
actual[1] = 41.0/35.0;
actual[2] = 19.0/10.0;
actual[3] = 72.0/35.0;
actual[4] = 139.0/35.0;
f = test_TDN_solve_dim(5, 1.0, 1.0/4.0, 1.0/2.0, actual, 35.0/8.0 * GSL_DBL_EPSILON);
gsl_test(f, " solve_TDN dim=5");
s += f;
return s;
}
int
test_TDN_cyc_solve_dim(unsigned long dim, double d, double a, double b, const double * actual, double eps)
{
int s = 0;
unsigned long i;
gsl_vector * abovediag = gsl_vector_alloc(dim);
gsl_vector * belowdiag = gsl_vector_alloc(dim);
gsl_vector * diag = gsl_vector_alloc(dim);
gsl_vector * rhs = gsl_vector_alloc(dim);
gsl_vector * x = gsl_vector_alloc(dim);
for(i=0; i<dim; i++) {
gsl_vector_set(diag, i, d);
gsl_vector_set(rhs, i, i + 1.0);
}
for(i=0; i<dim; i++) {
gsl_vector_set(abovediag, i, a);
gsl_vector_set(belowdiag, i, b);
}
s += gsl_linalg_solve_cyc_tridiag(diag, abovediag, belowdiag, rhs, x);
for(i=0; i<dim; i++) {
double si = gsl_vector_get(x, i);
double ai = actual[i];
int foo = check(si, ai, eps);
if(foo) {
printf("%3lu[%lu]: %22.18g %22.18g\n", dim, i, gsl_vector_get(x, i), actual[i]);
}
s += foo;
}
gsl_vector_free(x);
gsl_vector_free(rhs);
gsl_vector_free(diag);
gsl_vector_free(abovediag);
gsl_vector_free(belowdiag);
return s;
}
int test_TDN_cyc_solve(void)
{
int f;
int s = 0;
double actual[16];
actual[0] = 3.0/2.0;
actual[1] = -1.0/2.0;
actual[2] = 1.0/2.0;
f = test_TDN_cyc_solve_dim(3, 1.0, 2.0, 1.0, actual, 32.0 * GSL_DBL_EPSILON);
gsl_test(f, " solve_TDN_cyc dim=2 A");
s += f;
actual[0] = -5.0/22.0;
actual[1] = -3.0/22.0;
actual[2] = 29.0/22.0;
actual[3] = -9.0/22.0;
actual[4] = 43.0/22.0;
f = test_TDN_cyc_solve_dim(5, 3.0, 2.0, 1.0, actual, 66.0 * GSL_DBL_EPSILON);
gsl_test(f, " solve_TDN_cyc dim=5");
s += f;
return s;
}
int
test_bidiag_decomp_dim(const gsl_matrix * m, double eps)
{
int s = 0;
unsigned long i,j,k,r, M = m->size1, N = m->size2;
gsl_matrix * A = gsl_matrix_alloc(M,N);
gsl_matrix * a = gsl_matrix_alloc(M,N);
gsl_matrix * b = gsl_matrix_alloc(N,N);
gsl_matrix * u = gsl_matrix_alloc(M,N);
gsl_matrix * v = gsl_matrix_alloc(N,N);
gsl_vector * tau1 = gsl_vector_alloc(N);
gsl_vector * tau2 = gsl_vector_alloc(N-1);
gsl_vector * d = gsl_vector_alloc(N);
gsl_vector * sd = gsl_vector_alloc(N-1);
gsl_matrix_memcpy(A,m);
s += gsl_linalg_bidiag_decomp(A, tau1, tau2);
s += gsl_linalg_bidiag_unpack(A, tau1, u, tau2, v, d, sd);
gsl_matrix_set_zero(b);
for (i = 0; i < N; i++) gsl_matrix_set(b, i,i, gsl_vector_get(d,i));
for (i = 0; i < N-1; i++) gsl_matrix_set(b, i,i+1, gsl_vector_get(sd,i));
/* Compute A = U B V^T */
for (i = 0; i < M ; i++)
{
for (j = 0; j < N; j++)
{
double sum = 0;
for (k = 0; k < N; k++)
{
for (r = 0; r < N; r++)
{
sum += gsl_matrix_get(u, i, k) * gsl_matrix_get (b, k, r)
* gsl_matrix_get(v, j, r);
}
}
gsl_matrix_set (a, i, j, sum);
}
}
for(i=0; i<M; i++) {
for(j=0; j<N; j++) {
double aij = gsl_matrix_get(a, i, j);
double mij = gsl_matrix_get(m, i, j);
int foo = check(aij, mij, eps);
if(foo) {
printf("(%3lu,%3lu)[%lu,%lu]: %22.18g %22.18g\n", M, N, i,j, aij, mij);
}
s += foo;
}
}
gsl_matrix_free(A);
gsl_matrix_free(a);
gsl_matrix_free(u);
gsl_matrix_free(v);
gsl_matrix_free(b);
gsl_vector_free(tau1);
gsl_vector_free(tau2);
gsl_vector_free(d);
gsl_vector_free(sd);
return s;
}
int test_bidiag_decomp(void)
{
int f;
int s = 0;
f = test_bidiag_decomp_dim(m53, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " bidiag_decomp m(5,3)");
s += f;
f = test_bidiag_decomp_dim(m97, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " bidiag_decomp m(9,7)");
s += f;
f = test_bidiag_decomp_dim(hilb2, 2 * 8.0 * GSL_DBL_EPSILON);
gsl_test(f, " bidiag_decomp hilbert(2)");
s += f;
f = test_bidiag_decomp_dim(hilb3, 2 * 64.0 * GSL_DBL_EPSILON);
gsl_test(f, " bidiag_decomp hilbert(3)");
s += f;
f = test_bidiag_decomp_dim(hilb4, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " bidiag_decomp hilbert(4)");
s += f;
f = test_bidiag_decomp_dim(hilb12, 2 * 1024.0 * GSL_DBL_EPSILON);
gsl_test(f, " bidiag_decomp hilbert(12)");
s += f;
return s;
}
void
my_error_handler (const char *reason, const char *file, int line, int err)
{
if (0) printf ("(caught [%s:%d: %s (%d)])\n", file, line, reason, err) ;
}
int main(void)
{
gsl_ieee_env_setup ();
gsl_set_error_handler (&my_error_handler);
m11 = create_general_matrix(1,1);
m51 = create_general_matrix(5,1);
m35 = create_general_matrix(3,5);
m53 = create_general_matrix(5,3);
m97 = create_general_matrix(9,7);
s35 = create_singular_matrix(3,5);
s53 = create_singular_matrix(5,3);
hilb2 = create_hilbert_matrix(2);
hilb3 = create_hilbert_matrix(3);
hilb4 = create_hilbert_matrix(4);
hilb12 = create_hilbert_matrix(12);
vander2 = create_vandermonde_matrix(2);
vander3 = create_vandermonde_matrix(3);
vander4 = create_vandermonde_matrix(4);
vander12 = create_vandermonde_matrix(12);
moler10 = create_moler_matrix(10);
c7 = create_complex_matrix(7);
row3 = create_row_matrix(3,3);
row5 = create_row_matrix(5,5);
row12 = create_row_matrix(12,12);
A22 = create_2x2_matrix (0.0, 0.0, 0.0, 0.0);
A33 = gsl_matrix_alloc(3,3);
A44 = gsl_matrix_alloc(4,4);
A55 = gsl_matrix_alloc(5,5);
inf5 = create_diagonal_matrix (inf5_data, 5);
gsl_matrix_set(inf5, 3, 3, GSL_POSINF);
nan5 = create_diagonal_matrix (inf5_data, 5);
gsl_matrix_set(nan5, 3, 3, GSL_NAN);
/* Matmult now obsolete */
#ifdef MATMULT
gsl_test(test_matmult(), "Matrix Multiply");
gsl_test(test_matmult_mod(), "Matrix Multiply with Modification");
#endif
gsl_test(test_bidiag_decomp(), "Bidiagonal Decomposition");
gsl_test(test_LU_solve(), "LU Decomposition and Solve");
gsl_test(test_LUc_solve(), "Complex LU Decomposition and Solve");
gsl_test(test_QR_decomp(), "QR Decomposition");
gsl_test(test_QR_solve(), "QR Solve");
gsl_test(test_LQ_solve(), "LQ Solve");
gsl_test(test_PTLQ_solve(), "PTLQ Solve");
gsl_test(test_LQ_decomp(), "LQ Decomposition");
gsl_test(test_LQ_LQsolve(), "LQ LQ Solve");
gsl_test(test_LQ_lssolve(), "LQ LS Solve");
gsl_test(test_LQ_update(), "LQ Rank-1 Update");
gsl_test(test_QRPT_decomp(), "PTLQ Decomposition");
gsl_test(test_PTLQ_solve(), "PTLQ Solve");
gsl_test(test_QR_QRsolve(), "QR QR Solve");
gsl_test(test_QR_lssolve(), "QR LS Solve");
gsl_test(test_QR_update(), "QR Rank-1 Update");
gsl_test(test_QRPT_decomp(), "QRPT Decomposition");
gsl_test(test_QRPT_solve(), "QRPT Solve");
gsl_test(test_QRPT_QRsolve(), "QRPT QR Solve");
gsl_test(test_SV_decomp(), "Singular Value Decomposition");
gsl_test(test_SV_decomp_jacobi(), "Singular Value Decomposition (Jacobi)");
gsl_test(test_SV_decomp_mod(), "Singular Value Decomposition (Mod)");
gsl_test(test_SV_solve(), "SVD Solve");
gsl_test(test_cholesky_decomp(), "Cholesky Decomposition");
gsl_test(test_cholesky_decomp_unit(), "Cholesky Decomposition [unit triangular]");
gsl_test(test_cholesky_solve(), "Cholesky Solve");
gsl_test(test_HH_solve(), "Householder solve");
gsl_test(test_TDS_solve(), "Tridiagonal symmetric solve");
gsl_test(test_TDS_cyc_solve(), "Tridiagonal symmetric cyclic solve");
gsl_test(test_TDN_solve(), "Tridiagonal nonsymmetric solve");
gsl_test(test_TDN_cyc_solve(), "Tridiagonal nonsymmetric cyclic solve");
gsl_matrix_free(m11);
gsl_matrix_free(m35);
gsl_matrix_free(m51);
gsl_matrix_free(m53);
gsl_matrix_free(m97);
gsl_matrix_free(s35);
gsl_matrix_free(s53);
gsl_matrix_free(hilb2);
gsl_matrix_free(hilb3);
gsl_matrix_free(hilb4);
gsl_matrix_free(hilb12);
gsl_matrix_free(vander2);
gsl_matrix_free(vander3);
gsl_matrix_free(vander4);
gsl_matrix_free(vander12);
gsl_matrix_free(moler10);
gsl_matrix_complex_free(c7);
gsl_matrix_free(row3);
gsl_matrix_free(row5);
gsl_matrix_free(row12);
gsl_matrix_free(A22);
gsl_matrix_free(A33);
gsl_matrix_free(A44);
gsl_matrix_free(A55);
gsl_matrix_free (inf5);
gsl_matrix_free (nan5);
exit (gsl_test_summary());
}