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/* -*- mode: C -*- */
/*
IGraph library.
Copyright (C) 2009-2012 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 <igraph_sparsemat.h>
#define EPS 1e-13
/* Generic test for 1x1 matrices */
void test_1x1(igraph_real_t value) {
igraph_sparsemat_t A, B;
igraph_matrix_t values, vectors;
igraph_vector_t values2;
igraph_arpack_options_t options;
igraph_arpack_options_init(&options);
igraph_sparsemat_init(&A, 1, 1, 1);
igraph_sparsemat_entry(&A, 0, 0, value);
igraph_sparsemat_compress(&A, &B);
igraph_sparsemat_destroy(&A);
igraph_matrix_init(&values, 0, 0);
igraph_matrix_init(&vectors, 0, 0);
options.mode=1;
igraph_sparsemat_arpack_rnsolve(&B, &options, /*storage=*/ 0,
&values, &vectors);
printf("rnsolve:\n - eigenvalues:\n "); igraph_matrix_print(&values);
printf(" - eigenvectors:\n "); igraph_matrix_print(&vectors);
igraph_matrix_destroy(&values);
igraph_matrix_destroy(&vectors);
igraph_vector_init(&values2, 0);
igraph_matrix_init(&vectors, 0, 0);
options.mode=1;
igraph_sparsemat_arpack_rssolve(&B, &options, /*storage=*/ 0,
&values2, &vectors, IGRAPH_SPARSEMAT_SOLVE_LU);
printf("rssolve:\n - eigenvalues:\n "); igraph_vector_print(&values2);
printf(" - eigenvectors:\n "); igraph_matrix_print(&vectors);
igraph_vector_destroy(&values2);
igraph_matrix_destroy(&vectors);
igraph_sparsemat_destroy(&B);
}
/* Generic test for 2x2 matrices */
void test_2x2(igraph_real_t a, igraph_real_t b, igraph_real_t c, igraph_real_t d) {
igraph_sparsemat_t A, B;
igraph_matrix_t values, vectors;
igraph_vector_t values2;
igraph_arpack_options_t options;
igraph_arpack_options_init(&options);
options.mode=1; options.nev=2;
igraph_sparsemat_init(&A, 2, 2, 4);
igraph_sparsemat_entry(&A, 0, 0, a);
igraph_sparsemat_entry(&A, 0, 1, b);
igraph_sparsemat_entry(&A, 1, 0, c);
igraph_sparsemat_entry(&A, 1, 1, d);
igraph_sparsemat_compress(&A, &B);
igraph_sparsemat_destroy(&A);
igraph_matrix_init(&values, 0, 0);
igraph_matrix_init(&vectors, 0, 0);
igraph_sparsemat_arpack_rnsolve(&B, &options, /*storage=*/ 0,
&values, &vectors);
printf("rnsolve:\n - eigenvalues:\n "); igraph_matrix_print(&values);
printf(" - eigenvectors:\n "); igraph_matrix_print(&vectors);
igraph_matrix_destroy(&values);
igraph_matrix_destroy(&vectors);
if (b == c) {
igraph_vector_init(&values2, 0);
igraph_matrix_init(&vectors, 0, 0);
igraph_sparsemat_arpack_rssolve(&B, &options, /*storage=*/ 0,
&values2, &vectors, IGRAPH_SPARSEMAT_SOLVE_QR);
printf("rssolve:\n - eigenvalues:\n "); igraph_vector_print(&values2);
printf(" - eigenvectors:\n "); igraph_matrix_print(&vectors);
igraph_vector_destroy(&values2);
igraph_matrix_destroy(&vectors);
}
igraph_sparsemat_destroy(&B);
}
int main() {
igraph_sparsemat_t A, B;
igraph_matrix_t vectors, values2;
igraph_vector_t values;
long int i;
igraph_arpack_options_t options;
igraph_real_t min, max;
igraph_t g1, g2, g3;
/***********************************************************************/
/* Identity matrix */
#define DIM 10
igraph_sparsemat_init(&A, DIM, DIM, DIM);
for (i=0; i<DIM; i++) {
igraph_sparsemat_entry(&A, i, i, 1.0);
}
igraph_sparsemat_compress(&A, &B);
igraph_sparsemat_destroy(&A);
igraph_vector_init(&values, 0);
igraph_arpack_options_init(&options);
options.mode=1;
igraph_sparsemat_arpack_rssolve(&B, &options, /*storage=*/ 0,
&values, /*vectors=*/ 0, /*solvemethod=*/0);
if (VECTOR(values)[0] != 1.0) { return 1; }
options.mode=3;
options.sigma=2;
igraph_sparsemat_arpack_rssolve(&B, &options, /*storage=*/ 0,
&values, /*vectors=*/ 0,
IGRAPH_SPARSEMAT_SOLVE_LU);
if (VECTOR(values)[0] != 1.0) { return 21; }
igraph_sparsemat_arpack_rssolve(&B, &options, /*storage=*/ 0,
&values, /*vectors=*/ 0,
IGRAPH_SPARSEMAT_SOLVE_QR);
if (VECTOR(values)[0] != 1.0) { return 31; }
igraph_vector_destroy(&values);
igraph_sparsemat_destroy(&B);
#undef DIM
/***********************************************************************/
/* Diagonal matrix */
#define DIM 10
igraph_sparsemat_init(&A, DIM, DIM, DIM);
for (i=0; i<DIM; i++) {
igraph_sparsemat_entry(&A, i, i, i+1.0);
}
igraph_sparsemat_compress(&A, &B);
igraph_sparsemat_destroy(&A);
igraph_vector_init(&values, 0);
igraph_matrix_init(&vectors, 0, 0);
options.mode=1;
igraph_sparsemat_arpack_rssolve(&B, &options, /*storage=*/ 0,
&values, /*vectors=*/ &vectors,
/*solvemethod=*/ 0);
if ( fabs(VECTOR(values)[0] - DIM) > EPS ) {
printf("VECTOR(values)[0] numerical precision is only %g, should be %g",
fabs((double)VECTOR(values)[0]-DIM), EPS);
return 2;
}
if ( fabs(fabs(MATRIX(vectors, DIM-1, 0)) - 1.0) > EPS) { return 3; }
MATRIX(vectors, DIM-1, 0) = 0.0;
igraph_matrix_minmax(&vectors, &min, &max);
if (fabs(min) > EPS) { return 3; }
if (fabs(max) > EPS) { return 3; }
options.mode=3;
options.sigma=11;
igraph_sparsemat_arpack_rssolve(&B, &options, /*storage=*/ 0,
&values, /*vectors=*/ &vectors,
IGRAPH_SPARSEMAT_SOLVE_LU);
if ( fabs(VECTOR(values)[0] - DIM) > EPS ) {
printf("VECTOR(values)[0] numerical precision is only %g, should be %g",
fabs((double)VECTOR(values)[0]-DIM), EPS);
return 22;
}
igraph_sparsemat_arpack_rssolve(&B, &options, /*storage=*/ 0,
&values, /*vectors=*/ &vectors,
IGRAPH_SPARSEMAT_SOLVE_QR);
if ( fabs(VECTOR(values)[0] - DIM) > EPS ) {
printf("VECTOR(values)[0] numerical precision is only %g, should be %g",
fabs((double)VECTOR(values)[0]-DIM), EPS);
return 32;
}
if ( fabs(fabs(MATRIX(vectors, DIM-1, 0)) - 1.0) > EPS) { return 23; }
MATRIX(vectors, DIM-1, 0) = 0.0;
igraph_matrix_minmax(&vectors, &min, &max);
if (fabs(min) > EPS) { return 23; }
if (fabs(max) > EPS) { return 23; }
igraph_vector_destroy(&values);
igraph_matrix_destroy(&vectors);
igraph_sparsemat_destroy(&B);
#undef DIM
/***********************************************************************/
/* A tree, plus a ring */
#define DIM 10
igraph_tree(&g1, DIM, /*children=*/ 2, IGRAPH_TREE_UNDIRECTED);
igraph_ring(&g2, DIM, IGRAPH_UNDIRECTED, /*mutual=*/ 0, /*circular=*/ 1);
igraph_union(&g3, &g1, &g2, /*edge_map1=*/ 0, /*edge_map1=*/ 0);
igraph_destroy(&g1);
igraph_destroy(&g2);
igraph_get_sparsemat(&g3, &A);
igraph_destroy(&g3);
igraph_sparsemat_compress(&A, &B);
igraph_sparsemat_destroy(&A);
igraph_vector_init(&values, 0);
igraph_matrix_init(&vectors, 0, 0);
options.mode=1;
igraph_sparsemat_arpack_rssolve(&B, &options, /*storage=*/ 0,
&values, &vectors, /*solvemethod=*/ 0);
if (MATRIX(vectors, 0, 0) < 0.0) {
igraph_matrix_scale(&vectors, -1.0);
}
igraph_vector_print(&values);
igraph_matrix_print(&vectors);
options.mode=3;
options.sigma=VECTOR(values)[0] * 1.1;
igraph_sparsemat_arpack_rssolve(&B, &options, /*storage=*/ 0,
&values, &vectors,
IGRAPH_SPARSEMAT_SOLVE_LU);
if (MATRIX(vectors, 0, 0) < 0.0) {
igraph_matrix_scale(&vectors, -1.0);
}
igraph_vector_print(&values);
igraph_matrix_print(&vectors);
igraph_sparsemat_arpack_rssolve(&B, &options, /*storage=*/ 0,
&values, &vectors,
IGRAPH_SPARSEMAT_SOLVE_QR);
if (MATRIX(vectors, 0, 0) < 0.0) {
igraph_matrix_scale(&vectors, -1.0);
}
igraph_vector_print(&values);
igraph_matrix_print(&vectors);
igraph_vector_destroy(&values);
igraph_matrix_destroy(&vectors);
igraph_sparsemat_destroy(&B);
#undef DIM
printf("--\n");
/***********************************************************************/
/* A directed tree and a directed, mutual ring */
#define DIM 10
igraph_tree(&g1, DIM, /*children=*/ 2, IGRAPH_TREE_OUT);
igraph_ring(&g2, DIM, IGRAPH_DIRECTED, /*mutual=*/ 1, /*circular=*/ 1);
igraph_union(&g3, &g1, &g2, /*edge_map1=*/ 0, /*edge_map2=*/ 0);
igraph_destroy(&g1);
igraph_destroy(&g2);
igraph_get_sparsemat(&g3, &A);
igraph_destroy(&g3);
igraph_sparsemat_compress(&A, &B);
igraph_sparsemat_destroy(&A);
igraph_matrix_init(&values2, 0, 0);
igraph_matrix_init(&vectors, 0, 0);
options.mode=1;
igraph_sparsemat_arpack_rnsolve(&B, &options, /*storage=*/ 0,
&values2, &vectors);
if (MATRIX(vectors, 0, 0) < 0.0) {
igraph_matrix_scale(&vectors, -1.0);
}
igraph_matrix_print(&values2);
igraph_matrix_print(&vectors);
igraph_matrix_destroy(&values2);
igraph_matrix_destroy(&vectors);
igraph_sparsemat_destroy(&B);
#undef DIM
/***********************************************************************/
/* A small test graph */
igraph_small(&g1, 11, IGRAPH_DIRECTED,
0, 1, 1, 3, 1, 8, 2, 10, 3, 6, 3, 10, 4, 2, 5, 4,
6, 1, 6, 4, 7, 9, 8, 5, 8, 7, 9, 8, 10, 0,
-1);
igraph_get_sparsemat(&g1, &A);
igraph_destroy(&g1);
igraph_sparsemat_compress(&A, &B);
igraph_sparsemat_destroy(&A);
igraph_matrix_init(&values2, 0, 0);
igraph_matrix_init(&vectors, 0, 0);
options.mode=1;
igraph_sparsemat_arpack_rnsolve(&B, &options, /*storage=*/ 0,
&values2, &vectors);
if (MATRIX(vectors, 0, 0) < 0.0) {
igraph_matrix_scale(&vectors, -1.0);
}
igraph_matrix_destroy(&values2);
igraph_matrix_destroy(&vectors);
igraph_sparsemat_destroy(&B);
/***********************************************************************/
/* Testing the special case solver for 1x1 matrices */
printf("--\n");
test_1x1(2);
test_1x1(0);
test_1x1(-3);
/***********************************************************************/
/* Testing the special case solver for 2x2 matrices */
printf("--\n");
test_2x2(1, 2, 2, 4); /* symmetric */
test_2x2(1, 2, 3, 4); /* non-symmetric, real eigenvalues */
test_2x2(1, -5, 10, 4); /* non-symmetric, complex eigenvalues */
test_2x2(0, 0, 0, 0); /* symmetric, pathological */
return 0;
}
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