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/* -*- mode: C -*- */
/*
IGraph library.
Copyright (C) 2010-2012 Gabor Csardi <csardi.gabor@gmail.com>
334 Harvard st, Cambridge MA, 02139 USA
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
*/
#include <igraph.h>
#include <time.h>
#define DIM 10
igraph_bool_t check_ev(const igraph_matrix_t *A,
const igraph_vector_t *values,
const igraph_matrix_t *vectors, igraph_real_t tol) {
igraph_vector_t v, y;
int i, j;
int m=igraph_matrix_ncol(vectors);
int n=igraph_matrix_nrow(A);
if (igraph_matrix_ncol(A) != n) { return 1; }
if (igraph_vector_size(values) != m) { return 1; }
if (igraph_matrix_nrow(vectors) != n) { return 1; }
igraph_vector_init(&y, n);
for (i=0; i<m; i++) {
igraph_vector_view(&v, &MATRIX(*vectors, 0, i), n);
igraph_vector_update(&y, &v);
igraph_blas_dgemv(/*transpose=*/ 0, /*alpha=*/ 1.0, A, &v,
/*beta=*/ -VECTOR(*values)[i], &y);
for (j=0; j<n; j++) {
if (fabs(VECTOR(y)[i]) > tol) {
printf("Matrix:\n"); igraph_matrix_print(A);
printf("lambda= %g\n", VECTOR(*values)[i]);
printf("v= "); igraph_vector_print(&v);
printf("residual: "); igraph_vector_print(&y);
return 1;
}
}
}
igraph_vector_destroy(&y);
return 0;
}
int main() {
igraph_matrix_t A;
igraph_matrix_t vectors, vectors2;
igraph_vector_t values, values2;
int i, j;
int il, iu;
igraph_real_t vl, vu;
igraph_rng_seed(igraph_rng_default(), 42);
igraph_matrix_init(&A, DIM, DIM);
igraph_matrix_init(&vectors, 0, 0);
igraph_vector_init(&values, 0);
/* All eigenvalues and eigenvectors */
for (i=0; i<DIM; i++) {
for (j=i; j<DIM; j++) {
MATRIX(A, i, j) = MATRIX(A, j, i) =
igraph_rng_get_integer(igraph_rng_default(), 1, 10);
}
}
igraph_lapack_dsyevr(&A, IGRAPH_LAPACK_DSYEV_ALL, /*vl=*/ 0, /*vu=*/ 0,
/*vestimate=*/ 0, /*il=*/ 0, /*iu=*/ 0,
/*abstol=*/ 1e-10, &values, &vectors, /*support=*/ 0);
if (igraph_vector_size(&values) != DIM) { return 1; }
if (igraph_matrix_nrow(&vectors) != DIM ||
igraph_matrix_ncol(&vectors) != DIM) { return 2; }
if (check_ev(&A, &values, &vectors, /*tol=*/ 1e-8)) { return 3; }
/* Only a subset */
igraph_matrix_init(&vectors2, 0, 0);
igraph_vector_init(&values2, 0);
il=2; iu=5;
igraph_lapack_dsyevr(&A, IGRAPH_LAPACK_DSYEV_SELECT, /*vl=*/ 0, /*vu=*/ 0,
/*vestimate=*/ 0, /*il=*/ il, /*iu=*/ iu,
/*abstol=*/ 1e-10, &values2, &vectors2,
/*support=*/ 0);
if (igraph_vector_size(&values2) != iu-il+1) { return 4; }
if (igraph_matrix_nrow(&vectors2) != DIM ||
igraph_matrix_ncol(&vectors2) != iu-il+1) { return 5; }
for (i=0; i<iu-il+1; i++) {
igraph_real_t m1=1.0;
if (fabs(VECTOR(values)[il+i-1] - VECTOR(values2)[i]) > 1e-8) {
printf("Full: "); igraph_vector_print(&values);
printf("Subset: "); igraph_vector_print(&values2);
return 6;
}
if (MATRIX(vectors, 0, il+i-1) * MATRIX(vectors2, 0, i) < 0) {
m1=-1.0;
} else {
m1=1.0;
}
for (j=0; j<DIM; j++) {
if (fabs(MATRIX(vectors, j, il+i-1) -
m1 * MATRIX(vectors2, j, i)) > 1e-8) {
printf("Full:\n"); igraph_matrix_print(&vectors);
printf("Subset:\n"); igraph_matrix_print(&vectors2);
return 7;
}
}
}
igraph_vector_destroy(&values2);
igraph_matrix_destroy(&vectors2);
/* Subset based on an interval */
igraph_matrix_init(&vectors2, 0, 0);
igraph_vector_init(&values2, 0);
il=2; iu=5;
vl = (VECTOR(values)[il-1] + VECTOR(values)[il-2]) / 2.0;
vu = (VECTOR(values)[iu] + VECTOR(values)[iu-1]) / 2.0;
igraph_lapack_dsyevr(&A, IGRAPH_LAPACK_DSYEV_INTERVAL, vl, vu,
/*vestimate=*/ iu-il+1, /*il=*/ 0, /*iu=*/ 0,
/*abstol=*/ 1e-10, &values2, &vectors2,
/*support=*/ 0);
if (igraph_vector_size(&values2) != iu-il+1) { return 4; }
if (igraph_matrix_nrow(&vectors2) != DIM ||
igraph_matrix_ncol(&vectors2) != iu-il+1) { return 5; }
for (i=0; i<iu-il+1; i++) {
igraph_real_t m1=1.0;
if (fabs(VECTOR(values)[il+i-1] - VECTOR(values2)[i]) > 1e-8) {
printf("Full: "); igraph_vector_print(&values);
printf("Subset: "); igraph_vector_print(&values2);
return 6;
}
if (MATRIX(vectors, 0, il+i-1) * MATRIX(vectors2, 0, i) < 0) {
m1=-1.0;
} else {
m1=1.0;
}
for (j=0; j<DIM; j++) {
if (fabs(MATRIX(vectors, j, il+i-1) -
m1 * MATRIX(vectors2, j, i)) > 1e-8) {
printf("Full:\n"); igraph_matrix_print(&vectors);
printf("Subset:\n"); igraph_matrix_print(&vectors2);
return 7;
}
}
}
igraph_vector_destroy(&values2);
igraph_matrix_destroy(&vectors2);
igraph_vector_destroy(&values);
igraph_matrix_destroy(&vectors);
igraph_matrix_destroy(&A);
return 0;
}
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