int test_unnormalized_laplacian(igraph_bool_t dir) {
igraph_t g;
igraph_matrix_t m;
igraph_vector_t vec;
igraph_matrix_init(&m, 1, 1);
/* No loop or multiple edges */
igraph_ring(&g, 5, dir, 0, 1);
igraph_laplacian(&g, &m, 0);
print_matrix(&m);
printf("===\n");
/* Add some loop edges */
igraph_vector_init_real(&vec, 4, 1.0, 1.0, 2.0, 2.0);
igraph_add_edges(&g, &vec, 0);
igraph_vector_destroy(&vec);
igraph_laplacian(&g, &m, 0);
print_matrix(&m);
printf("===\n");
/* Duplicate some edges */
igraph_vector_init_real(&vec, 4, 1.0, 2.0, 3.0, 4.0);
igraph_add_edges(&g, &vec, 0);
igraph_vector_destroy(&vec);
igraph_laplacian(&g, &m, 0);
print_matrix(&m);
igraph_destroy(&g);
igraph_matrix_destroy(&m);
return 0;
}
int test_normalized_laplacian(igraph_bool_t dir) {
igraph_t g;
igraph_matrix_t m;
igraph_vector_t vec;
igraph_matrix_init(&m, 1, 1);
igraph_bool_t ok = 1;
/* Undirected graph, no loop or multiple edges */
igraph_ring(&g, 5, dir, 0, 1);
igraph_laplacian(&g, &m, 1);
ok = ok && check_laplacian(&g, &m);
/* Add some loop edges */
igraph_vector_init_real(&vec, 4, 1.0, 1.0, 2.0, 2.0);
igraph_add_edges(&g, &vec, 0);
igraph_vector_destroy(&vec);
igraph_laplacian(&g, &m, 1);
ok = ok && check_laplacian(&g, &m);
/* Duplicate some edges */
igraph_vector_init_real(&vec, 4, 1.0, 2.0, 3.0, 4.0);
igraph_add_edges(&g, &vec, 0);
igraph_vector_destroy(&vec);
igraph_laplacian(&g, &m, 1);
ok = ok && check_laplacian(&g, &m);
igraph_destroy(&g);
igraph_matrix_destroy(&m);
if (ok)
printf("OK\n");
return !ok;
}
int main() {
int nodes=10;
igraph_t g;
igraph_matrix_t L, R;
igraph_sparsemat_t Lsparse, Rsparse;
igraph_matrix_t V;
igraph_matrix_complex_t V2;
igraph_sparsemat_t laplacian;
igraph_vector_t groups;
igraph_eigen_which_t which;
igraph_matrix_init(&L, 0, 0);
igraph_matrix_init(&R, 0, 0);
igraph_matrix_init(&V, 0, 0);
igraph_matrix_complex_init(&V2, 0, 0);
igraph_vector_init(&groups, 0);
igraph_rng_seed(igraph_rng_default(), 42);
igraph_tree(&g, 10, /* children= */ 3, IGRAPH_TREE_UNDIRECTED);
igraph_sparsemat_init(&laplacian, nodes, nodes, igraph_ecount(&g)*2);
igraph_rng_seed(igraph_rng_default(), 42);
igraph_laplacian(&g, /*res=*/ 0, /*sparseres=*/ &laplacian,
/*normalized=*/ 0, /*weights=*/ 0);
which.pos=IGRAPH_EIGEN_LM;
which.howmany=1;
igraph_eigen_matrix(/*matrix=*/ 0, &laplacian, /*fun=*/ 0, 10,
/*extra=*/ 0, /*algorithm=*/ IGRAPH_EIGEN_LAPACK,
&which, /*options=*/ 0, /*storage=*/ 0,
/*values=*/ 0, &V2);
igraph_matrix_complex_real(&V2, &V);
#define SEMI() \
do { \
igraph_scg_semiprojectors(&groups, IGRAPH_SCG_LAPLACIAN, &L, &R, \
&Lsparse, &Rsparse, /*p=*/ 0, \
IGRAPH_SCG_NORM_ROW); \
} while(0)
#define PRINTRES() \
do { \
printf("----------------------\n"); \
igraph_matrix_print(&L); \
printf("---\n"); \
igraph_matrix_print(&R); \
printf("---\n"); \
igraph_sparsemat_destroy(&Lsparse); \
igraph_sparsemat_destroy(&Rsparse); \
} while (0)
/* -------------- */
igraph_scg_grouping(&V, &groups, /*intervals=*/ 3,
/*intervals_vector=*/ 0, IGRAPH_SCG_LAPLACIAN,
IGRAPH_SCG_OPTIMUM, /*p=*/ 0, /*maxiter=*/ 10000);
SEMI();
PRINTRES();
/* -------------- */
igraph_scg_grouping(&V, &groups, /*intervals=*/ 2,
/*intervals_vector=*/ 0, IGRAPH_SCG_LAPLACIAN,
IGRAPH_SCG_INTERV_KM, /*p=*/ 0, /*maxiter=*/ 10000);
SEMI();
PRINTRES();
/* -------------- */
igraph_scg_grouping(&V, &groups, /*intervals=*/ 2,
/*intervals_vector=*/ 0, IGRAPH_SCG_LAPLACIAN,
IGRAPH_SCG_INTERV, /*p=*/ 0, /*maxiter=*/ 10000);
SEMI();
PRINTRES();
/* -------------- */
igraph_scg_grouping(&V, &groups, /*(ignored) intervals=*/ 0,
/*intervals_vector=*/ 0, IGRAPH_SCG_LAPLACIAN,
IGRAPH_SCG_EXACT, /*p=*/ 0, /*maxiter=*/ 10000);
SEMI();
PRINTRES();
/* -------------- */
igraph_matrix_destroy(&L);
igraph_matrix_destroy(&R);
igraph_matrix_destroy(&V);
igraph_matrix_complex_destroy(&V2);
igraph_vector_destroy(&groups);
igraph_sparsemat_destroy(&laplacian);
igraph_destroy(&g);
return 0;
}
int main() {
const int nodes=10;
igraph_t g;
igraph_matrix_t V;
igraph_matrix_complex_t V2;
igraph_sparsemat_t laplacian;
igraph_vector_t groups;
igraph_eigen_which_t which;
igraph_tree(&g, nodes, /* children= */ 3, IGRAPH_TREE_UNDIRECTED);
igraph_sparsemat_init(&laplacian, nodes, nodes, igraph_ecount(&g)*2);
igraph_matrix_complex_init(&V2, 0, 0);
igraph_matrix_init(&V, 0, 0);
igraph_vector_init(&groups, 0);
igraph_rng_seed(igraph_rng_default(), 42);
igraph_sparsemat_init(&laplacian, 0, 0, 0);
igraph_laplacian(&g, /*res=*/ 0, /*sparseres=*/ &laplacian,
/*normalized=*/ 0, /*weights=*/ 0);
which.pos=IGRAPH_EIGEN_LR;
which.howmany=1;
igraph_eigen_matrix(/*matrix=*/ 0, &laplacian, /*fun=*/ 0, nodes,
/*extra=*/ 0, /*algorithm=*/ IGRAPH_EIGEN_LAPACK,
&which, /*options=*/ 0, /*storage=*/ 0,
/*values=*/ 0, &V2);
igraph_matrix_complex_real(&V2, &V);
/* ------------ */
igraph_scg_grouping(&V, &groups, /*intervals=*/ 3,
/*intervals_vector=*/ 0, IGRAPH_SCG_LAPLACIAN,
IGRAPH_SCG_OPTIMUM, /*p=*/ 0, /*maxiter=*/ 10000);
igraph_vector_print(&groups);
/* ------------ */
igraph_scg_grouping(&V, &groups, /*intervals=*/ 3,
/*intervals_vector=*/ 0, IGRAPH_SCG_LAPLACIAN,
IGRAPH_SCG_INTERV_KM, /*p=*/ 0, /*maxiter=*/ 10000);
igraph_vector_print(&groups);
/* ------------ */
igraph_scg_grouping(&V, &groups, /*intervals=*/ 3,
/*intervals_vector=*/ 0, IGRAPH_SCG_LAPLACIAN,
IGRAPH_SCG_INTERV, /*p=*/ 0, /*maxiter=*/ 10000);
igraph_vector_print(&groups);
/* ------------ */
igraph_scg_grouping(&V, &groups, /*(ignored) intervals=*/ 0,
/*intervals_vector=*/ 0, IGRAPH_SCG_LAPLACIAN,
IGRAPH_SCG_EXACT, /*p=*/ 0, /*maxiter=*/ 10000);
igraph_vector_print(&groups);
/* ------------ */
igraph_vector_destroy(&groups);
igraph_matrix_destroy(&V);
igraph_matrix_complex_destroy(&V2);
igraph_sparsemat_destroy(&laplacian);
igraph_destroy(&g);
#ifdef __APPLE__
return 0;
#else
return 77;
#endif
}
int test_unnormalized_laplacian(igraph_vector_t* w, igraph_bool_t dir) {
igraph_t g;
igraph_matrix_t m, m2;
igraph_sparsemat_t sm;
igraph_vector_t vec, *weights = 0;
igraph_matrix_init(&m, 1, 1);
igraph_sparsemat_init(&sm, 0, 0, 0);
if (w) {
weights = (igraph_vector_t*)calloc(1, sizeof(igraph_vector_t));
igraph_vector_copy(weights, w);
}
/* No loop or multiple edges */
igraph_ring(&g, 5, dir, 0, 1);
igraph_laplacian(&g, &m, &sm, 0, weights);
igraph_matrix_init(&m2, 0, 0);
igraph_sparsemat_as_matrix(&m2, &sm);
if (!igraph_matrix_all_e_tol(&m, &m2, 0)) {
return 41;
}
igraph_matrix_destroy(&m2);
igraph_matrix_print(&m);
printf("===\n");
/* Add some loop edges */
igraph_vector_init_real(&vec, 4, 1.0, 1.0, 2.0, 2.0);
igraph_add_edges(&g, &vec, 0);
igraph_vector_destroy(&vec);
if (weights) {
igraph_vector_push_back(weights, 2);
igraph_vector_push_back(weights, 2);
}
igraph_laplacian(&g, &m, &sm, 0, weights);
igraph_matrix_init(&m2, 0, 0);
igraph_sparsemat_as_matrix(&m2, &sm);
if (!igraph_matrix_all_e_tol(&m, &m2, 0)) {
return 42;
}
igraph_matrix_destroy(&m2);
igraph_matrix_print(&m);
printf("===\n");
/* Duplicate some edges */
igraph_vector_init_real(&vec, 4, 1.0, 2.0, 3.0, 4.0);
igraph_add_edges(&g, &vec, 0);
igraph_vector_destroy(&vec);
if (weights) {
igraph_vector_push_back(weights, 3);
igraph_vector_push_back(weights, 3);
}
igraph_laplacian(&g, &m, &sm, 0, weights);
igraph_matrix_init(&m2, 0, 0);
igraph_sparsemat_as_matrix(&m2, &sm);
if (!igraph_matrix_all_e_tol(&m, &m2, 0)) {
return 43;
}
igraph_matrix_destroy(&m2);
igraph_matrix_print(&m);
igraph_destroy(&g);
igraph_matrix_destroy(&m);
if (weights) {
igraph_vector_destroy(weights); free(weights);
}
return 0;
}
int test_normalized_laplacian(igraph_vector_t *w, igraph_bool_t dir) {
igraph_t g;
igraph_matrix_t m, m2;
igraph_sparsemat_t sm;
igraph_vector_t vec, *weights = 0;
igraph_bool_t ok = 1;
igraph_matrix_init(&m, 1, 1);
igraph_sparsemat_init(&sm, 0, 0, 0);
if (w) {
weights = (igraph_vector_t*)calloc(1, sizeof(igraph_vector_t));
igraph_vector_copy(weights, w);
}
/* Undirected graph, no loop or multiple edges */
igraph_ring(&g, 5, dir, 0, 1);
igraph_laplacian(&g, &m, &sm, 1, weights);
igraph_matrix_init(&m2, 0, 0);
igraph_sparsemat_as_matrix(&m2, &sm);
if (!igraph_matrix_all_e_tol(&m, &m2, 0)) {
return 44;
}
igraph_matrix_destroy(&m2);
ok = ok && check_laplacian(&g, &m, weights);
/* Add some loop edges */
igraph_vector_init_real(&vec, 4, 1.0, 1.0, 2.0, 2.0);
igraph_add_edges(&g, &vec, 0);
igraph_vector_destroy(&vec);
if (weights) {
igraph_vector_push_back(weights, 2);
igraph_vector_push_back(weights, 2);
}
igraph_laplacian(&g, &m, &sm, 1, weights);
igraph_matrix_init(&m2, 0, 0);
igraph_sparsemat_as_matrix(&m2, &sm);
if (!igraph_matrix_all_e_tol(&m, &m2, 0)) {
return 45;
}
igraph_matrix_destroy(&m2);
ok = ok && check_laplacian(&g, &m, weights);
/* Duplicate some edges */
igraph_vector_init_real(&vec, 4, 1.0, 2.0, 3.0, 4.0);
igraph_add_edges(&g, &vec, 0);
igraph_vector_destroy(&vec);
if (weights) {
igraph_vector_push_back(weights, 3);
igraph_vector_push_back(weights, 3);
}
igraph_laplacian(&g, &m, &sm, 1, weights);
igraph_matrix_init(&m2, 0, 0);
igraph_sparsemat_as_matrix(&m2, &sm);
if (!igraph_matrix_all_e_tol(&m, &m2, 0)) {
return 46;
}
igraph_matrix_destroy(&m2);
ok = ok && check_laplacian(&g, &m, weights);
igraph_destroy(&g);
igraph_matrix_destroy(&m);
if (weights) {
igraph_vector_destroy(weights); free(weights);
}
if (ok)
printf("OK\n");
return !ok;
}