int igraph_lapack_dsyevr(const igraph_matrix_t *A,
igraph_lapack_dsyev_which_t which,
igraph_real_t vl, igraph_real_t vu, int vestimate,
int il, int iu, igraph_real_t abstol,
igraph_vector_t *values, igraph_matrix_t *vectors,
igraph_vector_int_t *support) {
igraph_matrix_t Acopy;
char jobz = vectors ? 'V' : 'N', range, uplo='U';
int n=(int) igraph_matrix_nrow(A), lda=n, ldz=n;
int m, info;
igraph_vector_t *myvalues=values, vvalues;
igraph_vector_int_t *mysupport=support, vsupport;
igraph_vector_t work;
igraph_vector_int_t iwork;
int lwork=-1, liwork=-1;
if (n != igraph_matrix_ncol(A)) {
IGRAPH_ERROR("Cannot find eigenvalues/vectors", IGRAPH_NONSQUARE);
}
if (which==IGRAPH_LAPACK_DSYEV_INTERVAL &&
(vestimate < 1 || vestimate > n)) {
IGRAPH_ERROR("Estimated (upper bound) number of eigenvalues must be "
"between 1 and n", IGRAPH_EINVAL);
}
if (which==IGRAPH_LAPACK_DSYEV_SELECT && iu-il < 0) {
IGRAPH_ERROR("Invalid 'il' and/or 'iu' values", IGRAPH_EINVAL);
}
IGRAPH_CHECK(igraph_matrix_copy(&Acopy, A));
IGRAPH_FINALLY(igraph_matrix_destroy, &Acopy);
IGRAPH_VECTOR_INIT_FINALLY(&work, 1);
IGRAPH_CHECK(igraph_vector_int_init(&iwork, 1));
IGRAPH_FINALLY(igraph_vector_int_destroy, &iwork);
if (!values) {
IGRAPH_VECTOR_INIT_FINALLY(&vvalues, 0);
myvalues=&vvalues;
}
if (!support) {
IGRAPH_CHECK(igraph_vector_int_init(&vsupport, 0));
IGRAPH_FINALLY(igraph_vector_int_destroy, &vsupport);
mysupport=&vsupport;
}
switch (which) {
case IGRAPH_LAPACK_DSYEV_ALL:
range = 'A';
IGRAPH_CHECK(igraph_vector_resize(myvalues, n));
IGRAPH_CHECK(igraph_vector_int_resize(mysupport, 2*n));
if (vectors) { IGRAPH_CHECK(igraph_matrix_resize(vectors, n, n)); }
break;
case IGRAPH_LAPACK_DSYEV_INTERVAL:
range = 'V';
IGRAPH_CHECK(igraph_vector_resize(myvalues, vestimate));
IGRAPH_CHECK(igraph_vector_int_resize(mysupport, 2*vestimate));
if (vectors) { IGRAPH_CHECK(igraph_matrix_resize(vectors,n, vestimate)); }
break;
case IGRAPH_LAPACK_DSYEV_SELECT:
range = 'I';
IGRAPH_CHECK(igraph_vector_resize(myvalues, iu-il+1));
IGRAPH_CHECK(igraph_vector_int_resize(mysupport, 2*(iu-il+1)));
if (vectors) { IGRAPH_CHECK(igraph_matrix_resize(vectors, n, iu-il+1)); }
break;
}
igraphdsyevr_(&jobz, &range, &uplo, &n, &MATRIX(Acopy,0,0), &lda,
&vl, &vu, &il, &iu, &abstol, &m, VECTOR(*myvalues),
vectors ? &MATRIX(*vectors,0,0) : 0, &ldz, VECTOR(*mysupport),
VECTOR(work), &lwork, VECTOR(iwork), &liwork, &info);
lwork=(int) VECTOR(work)[0];
liwork=VECTOR(iwork)[0];
IGRAPH_CHECK(igraph_vector_resize(&work, lwork));
IGRAPH_CHECK(igraph_vector_int_resize(&iwork, liwork));
igraphdsyevr_(&jobz, &range, &uplo, &n, &MATRIX(Acopy,0,0), &lda,
&vl, &vu, &il, &iu, &abstol, &m, VECTOR(*myvalues),
vectors ? &MATRIX(*vectors,0,0) : 0, &ldz, VECTOR(*mysupport),
VECTOR(work), &lwork, VECTOR(iwork), &liwork, &info);
if (values) {
IGRAPH_CHECK(igraph_vector_resize(values, m));
}
if (vectors) {
IGRAPH_CHECK(igraph_matrix_resize(vectors, n, m));
}
if (support) {
IGRAPH_CHECK(igraph_vector_int_resize(support, m));
}
if (!support) {
igraph_vector_int_destroy(&vsupport);
IGRAPH_FINALLY_CLEAN(1);
}
if (!values) {
igraph_vector_destroy(&vvalues);
IGRAPH_FINALLY_CLEAN(1);
}
igraph_vector_int_destroy(&iwork);
igraph_vector_destroy(&work);
igraph_matrix_destroy(&Acopy);
IGRAPH_FINALLY_CLEAN(3);
return 0;
}
int igraph_i_vertex_coloring_greedy_cn(const igraph_t *graph, igraph_vector_int_t *colors) {
long i, vertex, maxdeg;
long vc = igraph_vcount(graph);
igraph_2wheap_t cn; /* indexed heap storing number of already coloured neighbours */
igraph_vector_int_t neigh_colors;
igraph_adjlist_t adjlist;
IGRAPH_CHECK(igraph_vector_int_resize(colors, vc));
igraph_vector_int_fill(colors, 0);
/* Nothing to do for 0 or 1 vertices.
* Remember that colours are integers starting from 0,
* and the 'colors' vector is already 0-initialized above.
*/
if (vc <= 1)
return IGRAPH_SUCCESS;
IGRAPH_CHECK(igraph_adjlist_init(graph, &adjlist, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_adjlist_destroy, &adjlist);
/* find maximum degree and a corresponding vertex */
{
igraph_vector_t degree;
IGRAPH_CHECK(igraph_vector_init(°ree, 0));
IGRAPH_FINALLY(igraph_vector_destroy, °ree);
IGRAPH_CHECK(igraph_degree(graph, °ree, igraph_vss_all(), IGRAPH_ALL, 0));
vertex = igraph_vector_which_max(°ree);
maxdeg = VECTOR(degree)[vertex];
igraph_vector_destroy(°ree);
IGRAPH_FINALLY_CLEAN(1);
}
IGRAPH_CHECK(igraph_vector_int_init(&neigh_colors, 0));
IGRAPH_CHECK(igraph_vector_int_reserve(&neigh_colors, maxdeg));
IGRAPH_FINALLY(igraph_vector_int_destroy, &neigh_colors);
IGRAPH_CHECK(igraph_2wheap_init(&cn, vc));
IGRAPH_FINALLY(igraph_2wheap_destroy, &cn);
for (i=0; i < vc; ++i)
if (i != vertex)
igraph_2wheap_push_with_index(&cn, i, 0); /* should not fail since memory was already reserved */
while (1) {
igraph_vector_int_t *neighbors = igraph_adjlist_get(&adjlist, vertex);
long neigh_count = igraph_vector_int_size(neighbors);
/* colour current vertex */
{
igraph_integer_t col;
IGRAPH_CHECK(igraph_vector_int_resize(&neigh_colors, neigh_count));
for (i=0; i < neigh_count; ++i)
VECTOR(neigh_colors)[i] = VECTOR(*colors)[ VECTOR(*neighbors)[i] ];
igraph_vector_int_sort(&neigh_colors);
i=0;
col = 0;
do {
while (i < neigh_count && VECTOR(neigh_colors)[i] == col)
i++;
col++;
} while (i < neigh_count && VECTOR(neigh_colors)[i] == col);
VECTOR(*colors)[vertex] = col;
}
/* increment number of coloured neighbours for each neighbour of vertex */
for (i=0; i < neigh_count; ++i) {
long idx = VECTOR(*neighbors)[i];
if (igraph_2wheap_has_elem(&cn, idx))
igraph_2wheap_modify(&cn, idx, igraph_2wheap_get(&cn, idx) + 1);
}
/* stop if no more vertices left to colour */
if (igraph_2wheap_empty(&cn))
break;
igraph_2wheap_delete_max_index(&cn, &vertex);
IGRAPH_ALLOW_INTERRUPTION();
}
/* subtract 1 from each colour value, so that colours start at 0 */
igraph_vector_int_add_constant(colors, -1);
/* free data structures */
igraph_vector_int_destroy(&neigh_colors);
igraph_adjlist_destroy(&adjlist);
igraph_2wheap_destroy(&cn);
IGRAPH_FINALLY_CLEAN(3);
return IGRAPH_SUCCESS;
}
