int igraph_dot_product_game(igraph_t *graph, const igraph_matrix_t *vecs,
igraph_bool_t directed) {
igraph_integer_t nrow=igraph_matrix_nrow(vecs);
igraph_integer_t ncol=igraph_matrix_ncol(vecs);
int i, j;
igraph_vector_t edges;
igraph_bool_t warned_neg=0, warned_big=0;
IGRAPH_VECTOR_INIT_FINALLY(&edges, 0);
RNG_BEGIN();
for (i = 0; i < ncol; i++) {
int from=directed ? 0 : i+1;
igraph_vector_t v1;
igraph_vector_view(&v1, &MATRIX(*vecs, 0, i), nrow);
for (j = from; j < ncol; j++) {
igraph_real_t prob;
igraph_vector_t v2;
if (i==j) { continue; }
igraph_vector_view(&v2, &MATRIX(*vecs, 0, j), nrow);
igraph_lapack_ddot(&v1, &v2, &prob);
if (prob < 0 && ! warned_neg) {
warned_neg=1;
IGRAPH_WARNING("Negative connection probability in "
"dot-product graph");
} else if (prob > 1 && ! warned_big) {
warned_big=1;
IGRAPH_WARNING("Greater than 1 connection probability in "
"dot-product graph");
IGRAPH_CHECK(igraph_vector_push_back(&edges, i));
IGRAPH_CHECK(igraph_vector_push_back(&edges, j));
} else if (RNG_UNIF01() < prob) {
IGRAPH_CHECK(igraph_vector_push_back(&edges, i));
IGRAPH_CHECK(igraph_vector_push_back(&edges, j));
}
}
}
RNG_END();
igraph_create(graph, &edges, ncol, directed);
igraph_vector_destroy(&edges);
IGRAPH_FINALLY_CLEAN(1);
return 0;
}
xmlEntityPtr igraph_i_graphml_sax_handler_get_entity(void *state0,
const xmlChar* name) {
xmlEntityPtr predef = xmlGetPredefinedEntity(name);
if (predef != NULL) return predef;
IGRAPH_WARNING("unknown XML entity found\n");
return blankEntity;
}
/**
* \function igraph_lazy_adjedgelist_init
* Initializes a lazy incidence list of edges
*
* This function was superseded by \ref igraph_lazy_inclist_init() in igraph 0.6.
* Please use \ref igraph_lazy_inclist_init() instead of this function.
*
* </para><para>
* Deprecated in version 0.6.
*/
int igraph_lazy_adjedgelist_init(const igraph_t *graph,
igraph_lazy_inclist_t *il,
igraph_neimode_t mode) {
IGRAPH_WARNING("igraph_lazy_adjedgelist_init() is deprecated, use "
"igraph_lazy_inclist_init() instead");
return igraph_lazy_inclist_init(graph, il, mode);
}
int igraph_i_weighted_cliques(const igraph_t *graph,
const igraph_vector_t *vertex_weights, igraph_vector_ptr_t *res,
igraph_real_t min_weight, igraph_real_t max_weight, igraph_bool_t maximal)
{
graph_t *g;
igraph_integer_t vcount = igraph_vcount(graph);
if (vcount == 0) {
igraph_vector_ptr_clear(res);
return IGRAPH_SUCCESS;
}
if (min_weight != (int) min_weight) {
IGRAPH_WARNING("Only integer vertex weights are supported; the minimum weight will be truncated to its integer part");
min_weight = (int) min_weight;
}
if (max_weight != (int) max_weight) {
IGRAPH_WARNING("Only integer vertex weights are supported; the maximum weight will be truncated to its integer part");
max_weight = (int) max_weight;
}
if (min_weight <= 0) min_weight = 1;
if (max_weight <= 0) max_weight = 0;
if (max_weight > 0 && max_weight < min_weight)
IGRAPH_ERROR("max_weight must not be smaller than min_weight", IGRAPH_EINVAL);
igraph_to_cliquer(graph, &g);
IGRAPH_FINALLY(graph_free, g);
IGRAPH_CHECK(set_weights(vertex_weights, g));
igraph_vector_ptr_clear(res);
igraph_cliquer_opt.user_data = res;
igraph_cliquer_opt.user_function = &collect_cliques_callback;
IGRAPH_FINALLY(free_clique_list, res);
CLIQUER_INTERRUPTABLE(clique_find_all(g, min_weight, max_weight, maximal, &igraph_cliquer_opt));
IGRAPH_FINALLY_CLEAN(1);
graph_free(g);
IGRAPH_FINALLY_CLEAN(1);
return IGRAPH_SUCCESS;
}
int igraph_i_maximal_or_largest_cliques_or_indsets(const igraph_t *graph,
igraph_vector_ptr_t *res,
igraph_integer_t *clique_number,
igraph_bool_t keep_only_largest,
igraph_bool_t complementer) {
igraph_i_max_ind_vsets_data_t clqdata;
long int no_of_nodes = igraph_vcount(graph), i;
if (igraph_is_directed(graph))
IGRAPH_WARNING("directionality of edges is ignored for directed graphs");
clqdata.matrix_size=no_of_nodes;
clqdata.keep_only_largest=keep_only_largest;
if (complementer)
IGRAPH_CHECK(igraph_adjlist_init_complementer(graph, &clqdata.adj_list, IGRAPH_ALL, 0));
else
IGRAPH_CHECK(igraph_adjlist_init(graph, &clqdata.adj_list, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_adjlist_destroy, &clqdata.adj_list);
clqdata.IS = igraph_Calloc(no_of_nodes, igraph_integer_t);
if (clqdata.IS == 0)
IGRAPH_ERROR("igraph_i_maximal_or_largest_cliques_or_indsets failed", IGRAPH_ENOMEM);
IGRAPH_FINALLY(igraph_free, clqdata.IS);
IGRAPH_VECTOR_INIT_FINALLY(&clqdata.deg, no_of_nodes);
for (i=0; i<no_of_nodes; i++)
VECTOR(clqdata.deg)[i] = igraph_vector_size(igraph_adjlist_get(&clqdata.adj_list, i));
clqdata.buckets = igraph_Calloc(no_of_nodes+1, igraph_set_t);
if (clqdata.buckets == 0)
IGRAPH_ERROR("igraph_maximal_or_largest_cliques_or_indsets failed", IGRAPH_ENOMEM);
IGRAPH_FINALLY(igraph_i_free_set_array, clqdata.buckets);
for (i=0; i<no_of_nodes; i++)
IGRAPH_CHECK(igraph_set_init(&clqdata.buckets[i], 0));
if (res) igraph_vector_ptr_clear(res);
/* Do the show */
clqdata.largest_set_size=0;
IGRAPH_CHECK(igraph_i_maximal_independent_vertex_sets_backtrack(graph, res, &clqdata, 0));
/* Cleanup */
for (i=0; i<no_of_nodes; i++) igraph_set_destroy(&clqdata.buckets[i]);
igraph_adjlist_destroy(&clqdata.adj_list);
igraph_vector_destroy(&clqdata.deg);
igraph_free(clqdata.IS);
igraph_free(clqdata.buckets);
IGRAPH_FINALLY_CLEAN(4);
if (clique_number) *clique_number = clqdata.largest_set_size;
return 0;
}
/* Checks if the community heap satisfies the heap property.
* Only useful for debugging. */
void igraph_i_fastgreedy_community_list_check_heap(
igraph_i_fastgreedy_community_list* list) {
long int i;
for (i=0; i<list->no_of_communities/2; i++) {
if ((2*i+1<list->no_of_communities && *list->heap[i]->maxdq->dq < *list->heap[2*i+1]->maxdq->dq) ||
(2*i+2<list->no_of_communities && *list->heap[i]->maxdq->dq < *list->heap[2*i+2]->maxdq->dq)) {
IGRAPH_WARNING("Heap property violated");
debug("Position: %ld, %ld and %ld\n", i, 2*i+1, 2*i+2);
igraph_i_fastgreedy_community_list_dump_heap(list);
}
}
}
int igraph_lapack_dgetrf(igraph_matrix_t *a, igraph_vector_int_t *ipiv,
int *info) {
int m=(int) igraph_matrix_nrow(a);
int n=(int) igraph_matrix_ncol(a);
int lda=m > 0 ? m : 1;
igraph_vector_int_t *myipiv=ipiv, vipiv;
if (!ipiv) {
IGRAPH_CHECK(igraph_vector_int_init(&vipiv, m<n ? m : n));
IGRAPH_FINALLY(igraph_vector_int_destroy, &vipiv);
myipiv=&vipiv;
}
igraphdgetrf_(&m, &n, VECTOR(a->data), &lda, VECTOR(*myipiv), info);
if (*info > 0) {
IGRAPH_WARNING("LU: factor is exactly singular");
} else if (*info < 0) {
switch(*info) {
case -1:
IGRAPH_ERROR("Invalid number of rows", IGRAPH_ELAPACK);
break;
case -2:
IGRAPH_ERROR("Invalid number of columns", IGRAPH_ELAPACK);
break;
case -3:
IGRAPH_ERROR("Invalid input matrix", IGRAPH_ELAPACK);
break;
case -4:
IGRAPH_ERROR("Invalid LDA parameter", IGRAPH_ELAPACK);
break;
case -5:
IGRAPH_ERROR("Invalid pivot vector", IGRAPH_ELAPACK);
break;
case -6:
IGRAPH_ERROR("Invalid info argument", IGRAPH_ELAPACK);
break;
default:
IGRAPH_ERROR("Unknown LAPACK error", IGRAPH_ELAPACK);
break;
}
}
if (!ipiv) {
igraph_vector_int_destroy(&vipiv);
IGRAPH_FINALLY_CLEAN(1);
}
return 0;
}
int igraph_create_bipartite(igraph_t *graph, const igraph_vector_bool_t *types,
const igraph_vector_t *edges,
igraph_bool_t directed) {
igraph_integer_t no_of_nodes=
(igraph_integer_t) igraph_vector_bool_size(types);
long int no_of_edges=igraph_vector_size(edges);
igraph_real_t min_edge=0, max_edge=0;
igraph_bool_t min_type=0, max_type=0;
long int i;
if (no_of_edges % 2 != 0) {
IGRAPH_ERROR("Invalid (odd) edges vector", IGRAPH_EINVEVECTOR);
}
no_of_edges /= 2;
if (no_of_edges != 0) {
igraph_vector_minmax(edges, &min_edge, &max_edge);
}
if (min_edge < 0 || max_edge >= no_of_nodes) {
IGRAPH_ERROR("Invalid (negative) vertex id", IGRAPH_EINVVID);
}
/* Check types vector */
if (no_of_nodes != 0) {
igraph_vector_bool_minmax(types, &min_type, &max_type);
if (min_type < 0 || max_type > 1) {
IGRAPH_WARNING("Non-binary type vector when creating a bipartite graph");
}
}
/* Check bipartiteness */
for (i=0; i<no_of_edges*2; i+=2) {
long int from=(long int) VECTOR(*edges)[i];
long int to=(long int) VECTOR(*edges)[i+1];
long int t1=VECTOR(*types)[from];
long int t2=VECTOR(*types)[to];
if ( (t1 && t2) || (!t1 && !t2) ) {
IGRAPH_ERROR("Invalid edges, not a bipartite graph", IGRAPH_EINVAL);
}
}
IGRAPH_CHECK(igraph_empty(graph, no_of_nodes, directed));
IGRAPH_FINALLY(igraph_destroy, graph);
IGRAPH_CHECK(igraph_add_edges(graph, edges, 0));
IGRAPH_FINALLY_CLEAN(1);
return 0;
}
/* Copy weights to a Cliquer graph */
static int set_weights(const igraph_vector_t *vertex_weights, graph_t *g) {
int i;
assert(vertex_weights != NULL);
if (igraph_vector_size(vertex_weights) != g->n)
IGRAPH_ERROR("Invalid vertex weight vector length", IGRAPH_EINVAL);
for (i=0; i < g->n; ++i) {
g->weights[i] = VECTOR(*vertex_weights)[i];
if (g->weights[i] != VECTOR(*vertex_weights)[i])
IGRAPH_WARNING("Only integer vertex weights are supported; weights will be truncated to their integer parts");
if (g->weights[i] <= 0)
IGRAPH_ERROR("Vertex weights must be positive", IGRAPH_EINVAL);
}
return IGRAPH_SUCCESS;
}
/* Convert an igraph graph to a Cliquer graph */
static void igraph_to_cliquer(const igraph_t *ig, graph_t **cg) {
igraph_integer_t vcount, ecount;
int i;
if (igraph_is_directed(ig))
IGRAPH_WARNING("Edge directions are ignored for clique calculations");
vcount = igraph_vcount(ig);
ecount = igraph_ecount(ig);
*cg = graph_new(vcount);
for (i=0; i < ecount; ++i) {
long s, t;
s = IGRAPH_FROM(ig, i);
t = IGRAPH_TO(ig, i);
if (s != t)
GRAPH_ADD_EDGE(*cg, s, t);
}
}
int igraph_forest_fire_game(igraph_t *graph, igraph_integer_t nodes,
igraph_real_t fw_prob, igraph_real_t bw_factor,
igraph_integer_t pambs, igraph_bool_t directed) {
igraph_vector_long_t visited;
long int no_of_nodes=nodes, actnode, i;
igraph_vector_t edges;
igraph_vector_t *inneis, *outneis;
igraph_i_forest_fire_data_t data;
igraph_dqueue_t neiq;
long int ambs=pambs;
igraph_real_t param_geom_out=1-fw_prob;
igraph_real_t param_geom_in=1-fw_prob*bw_factor;
if (fw_prob < 0) {
IGRAPH_ERROR("Forest fire model: 'fw_prob' should be between non-negative",
IGRAPH_EINVAL);
}
if (bw_factor < 0) {
IGRAPH_ERROR("Forest fire model: 'bw_factor' should be non-negative",
IGRAPH_EINVAL);
}
if (ambs < 0) {
IGRAPH_ERROR("Number of ambassadors ('ambs') should be non-negative",
IGRAPH_EINVAL);
}
if (fw_prob == 0 || ambs == 0) {
IGRAPH_WARNING("'fw_prob or ambs is zero, creating empty graph");
IGRAPH_CHECK(igraph_empty(graph, nodes, directed));
return 0;
}
IGRAPH_VECTOR_INIT_FINALLY(&edges, 0);
inneis=igraph_Calloc(no_of_nodes, igraph_vector_t);
if (!inneis) {
IGRAPH_ERROR("Cannot run forest fire model", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, inneis);
outneis=igraph_Calloc(no_of_nodes, igraph_vector_t);
if (!outneis) {
IGRAPH_ERROR("Cannot run forest fire model", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, outneis);
data.inneis=inneis;
data.outneis=outneis;
data.no_of_nodes=no_of_nodes;
IGRAPH_FINALLY(igraph_i_forest_fire_free, &data);
for (i=0; i<no_of_nodes; i++) {
IGRAPH_CHECK(igraph_vector_init(inneis+i, 0));
IGRAPH_CHECK(igraph_vector_init(outneis+i, 0));
}
IGRAPH_CHECK(igraph_vector_long_init(&visited, no_of_nodes));
IGRAPH_FINALLY(igraph_vector_long_destroy, &visited);
IGRAPH_DQUEUE_INIT_FINALLY(&neiq, 10);
RNG_BEGIN();
#define ADD_EDGE_TO(nei) \
if (VECTOR(visited)[(nei)] != actnode+1) { \
VECTOR(visited)[(nei)] = actnode+1; \
IGRAPH_CHECK(igraph_dqueue_push(&neiq, nei)); \
IGRAPH_CHECK(igraph_vector_push_back(&edges, actnode)); \
IGRAPH_CHECK(igraph_vector_push_back(&edges, nei)); \
IGRAPH_CHECK(igraph_vector_push_back(outneis+actnode, nei)); \
IGRAPH_CHECK(igraph_vector_push_back(inneis+nei, actnode)); \
}
IGRAPH_PROGRESS("Forest fire: ", 0.0, NULL);
for (actnode=1; actnode < no_of_nodes; actnode++) {
IGRAPH_PROGRESS("Forest fire: ", 100.0*actnode/no_of_nodes, NULL);
IGRAPH_ALLOW_INTERRUPTION();
/* We don't want to visit the current vertex */
VECTOR(visited)[actnode] = actnode+1;
/* Choose ambassador(s) */
for (i=0; i<ambs; i++) {
long int a=RNG_INTEGER(0, actnode-1);
ADD_EDGE_TO(a);
}
while (!igraph_dqueue_empty(&neiq)) {
long int actamb=(long int) igraph_dqueue_pop(&neiq);
igraph_vector_t *outv=outneis+actamb;
igraph_vector_t *inv=inneis+actamb;
long int no_in=igraph_vector_size(inv);
long int no_out=igraph_vector_size(outv);
long int neis_out=(long int) RNG_GEOM(param_geom_out);
long int neis_in=(long int) RNG_GEOM(param_geom_in);
/* outgoing neighbors */
if (neis_out >= no_out) {
for (i=0; i<no_out; i++) {
long int nei=(long int) VECTOR(*outv)[i];
ADD_EDGE_TO(nei);
}
} else {
long int oleft=no_out;
for (i=0; i<neis_out && oleft > 0; ) {
long int which=RNG_INTEGER(0, oleft-1);
long int nei=(long int) VECTOR(*outv)[which];
VECTOR(*outv)[which] = VECTOR(*outv)[oleft-1];
VECTOR(*outv)[oleft-1] = nei;
if (VECTOR(visited)[nei] != actnode+1) {
ADD_EDGE_TO(nei);
i++;
}
oleft--;
}
}
/* incoming neighbors */
if (neis_in >= no_in) {
for (i=0; i<no_in; i++) {
long int nei=(long int) VECTOR(*inv)[i];
ADD_EDGE_TO(nei);
}
} else {
long int ileft=no_in;
for (i=0; i<neis_in && ileft > 0; ) {
long int which=RNG_INTEGER(0, ileft-1);
long int nei=(long int) VECTOR(*inv)[which];
VECTOR(*inv)[which] = VECTOR(*inv)[ileft-1];
VECTOR(*inv)[ileft-1] = nei;
if (VECTOR(visited)[nei] != actnode+1) {
ADD_EDGE_TO(nei);
i++;
}
ileft--;
}
}
} /* while neiq not empty */
} /* actnode < no_of_nodes */
#undef ADD_EDGE_TO
RNG_END();
IGRAPH_PROGRESS("Forest fire: ", 100.0, NULL);
igraph_dqueue_destroy(&neiq);
igraph_vector_long_destroy(&visited);
igraph_i_forest_fire_free(&data);
igraph_free(outneis);
igraph_free(inneis);
IGRAPH_FINALLY_CLEAN(5);
IGRAPH_CHECK(igraph_create(graph, &edges, nodes, directed));
igraph_vector_destroy(&edges);
IGRAPH_FINALLY_CLEAN(1);
return 0;
}
int igraph_i_kleinberg(const igraph_t *graph, igraph_vector_t *vector,
igraph_real_t *value, igraph_bool_t scale,
igraph_arpack_options_t *options, int inout) {
igraph_adjlist_t myinadjlist, myoutadjlist;
igraph_adjlist_t *inadjlist, *outadjlist;
igraph_vector_t tmp;
igraph_vector_t values;
igraph_matrix_t vectors;
igraph_i_kleinberg_data_t extra;
long int i;
options->n=igraph_vcount(graph);
options->start=1;
IGRAPH_VECTOR_INIT_FINALLY(&values, 0);
IGRAPH_MATRIX_INIT_FINALLY(&vectors, options->n, 1);
IGRAPH_VECTOR_INIT_FINALLY(&tmp, options->n);
if (inout==0) {
inadjlist=&myinadjlist;
outadjlist=&myoutadjlist;
} else if (inout==1) {
inadjlist=&myoutadjlist;
outadjlist=&myinadjlist;
} else {
/* This should not happen */
IGRAPH_ERROR("Invalid 'inout' argument, plese do not call "
"this funtion directly", IGRAPH_FAILURE);
}
IGRAPH_CHECK(igraph_adjlist_init(graph, &myinadjlist, IGRAPH_IN));
IGRAPH_FINALLY(igraph_adjlist_destroy, &myinadjlist);
IGRAPH_CHECK(igraph_adjlist_init(graph, &myoutadjlist, IGRAPH_OUT));
IGRAPH_FINALLY(igraph_adjlist_destroy, &myoutadjlist);
IGRAPH_CHECK(igraph_degree(graph, &tmp, igraph_vss_all(), IGRAPH_ALL, 0));
for (i=0; i<options->n; i++) {
if (VECTOR(tmp)[i] != 0) {
MATRIX(vectors, i, 0) = VECTOR(tmp)[i];
} else {
MATRIX(vectors, i, 0) = 1.0;
}
}
extra.in=inadjlist; extra.out=outadjlist; extra.tmp=&tmp;
options->n = igraph_vcount(graph);
options->nev = 1;
options->ncv = 3;
options->which[0]='L'; options->which[1]='M';
options->start=1; /* no random start vector */
IGRAPH_CHECK(igraph_arpack_rssolve(igraph_i_kleinberg2, &extra,
options, 0, &values, &vectors));
igraph_adjlist_destroy(&myoutadjlist);
igraph_adjlist_destroy(&myinadjlist);
igraph_vector_destroy(&tmp);
IGRAPH_FINALLY_CLEAN(3);
if (value) {
*value = VECTOR(values)[0];
}
if (vector) {
igraph_real_t amax=0;
long int which=0;
long int i;
IGRAPH_CHECK(igraph_vector_resize(vector, options->n));
for (i=0; i<options->n; i++) {
igraph_real_t tmp;
VECTOR(*vector)[i] = MATRIX(vectors, i, 0);
tmp=fabs(VECTOR(*vector)[i]);
if (tmp>amax) { amax=tmp; which=i; }
}
if (scale && amax!=0) { igraph_vector_scale(vector, 1/VECTOR(*vector)[which]); }
}
if (options->info) {
IGRAPH_WARNING("Non-zero return code from ARPACK routine!");
}
igraph_matrix_destroy(&vectors);
igraph_vector_destroy(&values);
IGRAPH_FINALLY_CLEAN(2);
return 0;
}
int igraph_pagerank(const igraph_t *graph, igraph_vector_t *vector,
igraph_real_t *value, const igraph_vs_t vids,
igraph_bool_t directed, igraph_real_t damping,
const igraph_vector_t *weights,
igraph_arpack_options_t *options) {
igraph_matrix_t values;
igraph_matrix_t vectors;
igraph_integer_t dirmode;
igraph_vector_t outdegree;
igraph_vector_t tmp;
long int i;
long int no_of_nodes=igraph_vcount(graph);
long int no_of_edges=igraph_ecount(graph);
options->n = igraph_vcount(graph);
options->nev = 1;
options->ncv = 3;
options->which[0]='L'; options->which[1]='M';
options->start=1; /* no random start vector */
directed = directed && igraph_is_directed(graph);
if (weights && igraph_vector_size(weights) != igraph_ecount(graph))
{
IGRAPH_ERROR("Invalid length of weights vector when calculating "
"PageRank scores", IGRAPH_EINVAL);
}
IGRAPH_MATRIX_INIT_FINALLY(&values, 0, 0);
IGRAPH_MATRIX_INIT_FINALLY(&vectors, options->n, 1);
if (directed) { dirmode=IGRAPH_IN; } else { dirmode=IGRAPH_ALL; }
IGRAPH_VECTOR_INIT_FINALLY(&outdegree, options->n);
IGRAPH_VECTOR_INIT_FINALLY(&tmp, options->n);
RNG_BEGIN();
if (!weights) {
igraph_adjlist_t adjlist;
igraph_i_pagerank_data_t data = { graph, &adjlist, damping,
&outdegree, &tmp };
IGRAPH_CHECK(igraph_degree(graph, &outdegree, igraph_vss_all(),
directed ? IGRAPH_OUT : IGRAPH_ALL, /*loops=*/ 0));
/* Avoid division by zero */
for (i=0; i<options->n; i++) {
if (VECTOR(outdegree)[i]==0) {
VECTOR(outdegree)[i]=1;
}
MATRIX(vectors, i, 0) = VECTOR(outdegree)[i];
}
IGRAPH_CHECK(igraph_adjlist_init(graph, &adjlist, dirmode));
IGRAPH_FINALLY(igraph_adjlist_destroy, &adjlist);
IGRAPH_CHECK(igraph_arpack_rnsolve(igraph_i_pagerank,
&data, options, 0, &values, &vectors));
igraph_adjlist_destroy(&adjlist);
IGRAPH_FINALLY_CLEAN(1);
} else {
igraph_adjedgelist_t adjedgelist;
igraph_i_pagerank_data2_t data = { graph, &adjedgelist, weights,
damping, &outdegree, &tmp };
IGRAPH_CHECK(igraph_adjedgelist_init(graph, &adjedgelist, dirmode));
IGRAPH_FINALLY(igraph_adjedgelist_destroy, &adjedgelist);
/* Weighted degree */
for (i=0; i<no_of_edges; i++) {
long int from=IGRAPH_FROM(graph, i);
long int to=IGRAPH_TO(graph, i);
igraph_real_t weight=VECTOR(*weights)[i];
VECTOR(outdegree)[from] += weight;
if (!directed) {
VECTOR(outdegree)[to] += weight;
}
}
/* Avoid division by zero */
for (i=0; i<options->n; i++) {
if (VECTOR(outdegree)[i]==0) {
VECTOR(outdegree)[i]=1;
}
MATRIX(vectors, i, 0) = VECTOR(outdegree)[i];
}
IGRAPH_CHECK(igraph_arpack_rnsolve(igraph_i_pagerank2,
&data, options, 0, &values, &vectors));
igraph_adjedgelist_destroy(&adjedgelist);
IGRAPH_FINALLY_CLEAN(1);
}
RNG_END();
igraph_vector_destroy(&tmp);
igraph_vector_destroy(&outdegree);
IGRAPH_FINALLY_CLEAN(2);
if (value) {
*value=MATRIX(values, 0, 0);
}
if (vector) {
long int i;
igraph_vit_t vit;
long int nodes_to_calc;
igraph_real_t sum=0;
for (i=0; i<no_of_nodes; i++) {
sum += MATRIX(vectors, i, 0);
}
IGRAPH_CHECK(igraph_vit_create(graph, vids, &vit));
IGRAPH_FINALLY(igraph_vit_destroy, &vit);
nodes_to_calc=IGRAPH_VIT_SIZE(vit);
IGRAPH_CHECK(igraph_vector_resize(vector, nodes_to_calc));
for (IGRAPH_VIT_RESET(vit), i=0; !IGRAPH_VIT_END(vit);
IGRAPH_VIT_NEXT(vit), i++) {
VECTOR(*vector)[i] = MATRIX(vectors, (long int)IGRAPH_VIT_GET(vit), 0);
VECTOR(*vector)[i] /= sum;
}
igraph_vit_destroy(&vit);
IGRAPH_FINALLY_CLEAN(1);
}
if (options->info) {
IGRAPH_WARNING("Non-zero return code from ARPACK routine!");
}
igraph_matrix_destroy(&vectors);
igraph_matrix_destroy(&values);
IGRAPH_FINALLY_CLEAN(2);
return 0;
}
igraph_vector_t *igraph_lazy_adjedgelist_get_real(igraph_lazy_adjedgelist_t *il,
igraph_integer_t pno) {
IGRAPH_WARNING("igraph_lazy_adjedgelist_get_real() is deprecated, use "
"igraph_lazy_inclist_get_real() instead");
return igraph_lazy_inclist_get_real(il, pno);
}
/**
* \function igraph_lazy_adjedgelist_destroy
* Frees all memory allocated for an incidence list.
*
* This function was superseded by \ref igraph_lazy_inclist_destroy() in igraph 0.6.
* Please use \ref igraph_lazy_inclist_destroy() instead of this function.
*
* </para><para>
* Deprecated in version 0.6.
*/
void igraph_lazy_adjedgelist_destroy(igraph_lazy_inclist_t *il) {
IGRAPH_WARNING("igraph_lazy_adjedgelist_destroy() is deprecated, use "
"igraph_lazy_inclist_destroy() instead");
igraph_lazy_inclist_destroy(il);
}
int igraph_eigenvector_centrality(const igraph_t *graph, igraph_vector_t *vector,
igraph_real_t *value, igraph_bool_t scale,
const igraph_vector_t *weights,
igraph_arpack_options_t *options) {
igraph_vector_t values;
igraph_matrix_t vectors;
igraph_vector_t degree;
long int i;
options->n=igraph_vcount(graph);
options->start=1; /* no random start vector */
if (weights && igraph_vector_size(weights) != igraph_ecount(graph)) {
IGRAPH_ERROR("Invalid length of weights vector when calculating "
"eigenvector centrality", IGRAPH_EINVAL);
}
if (weights && igraph_is_directed(graph)) {
IGRAPH_WARNING("Weighted directed graph in eigenvector centrality");
}
IGRAPH_VECTOR_INIT_FINALLY(&values, 0);
IGRAPH_MATRIX_INIT_FINALLY(&vectors, options->n, 1);
IGRAPH_VECTOR_INIT_FINALLY(°ree, options->n);
IGRAPH_CHECK(igraph_degree(graph, °ree, igraph_vss_all(),
IGRAPH_ALL, /*loops=*/ 0));
for (i=0; i<options->n; i++) {
if (VECTOR(degree)[i]) {
MATRIX(vectors, i, 0) = VECTOR(degree)[i];
} else {
MATRIX(vectors, i, 0) = 1.0;
}
}
igraph_vector_destroy(°ree);
IGRAPH_FINALLY_CLEAN(1);
options->n = igraph_vcount(graph);
options->nev = 1;
options->ncv = 3;
options->which[0]='L'; options->which[1]='A';
options->start=1; /* no random start vector */
if (!weights) {
igraph_adjlist_t adjlist;
IGRAPH_CHECK(igraph_adjlist_init(graph, &adjlist, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_adjlist_destroy, &adjlist);
IGRAPH_CHECK(igraph_arpack_rssolve(igraph_i_eigenvector_centrality,
&adjlist, options, 0, &values, &vectors));
igraph_adjlist_destroy(&adjlist);
IGRAPH_FINALLY_CLEAN(1);
} else {
igraph_adjedgelist_t adjedgelist;
igraph_i_eigenvector_centrality_t data = { graph, &adjedgelist, weights };
IGRAPH_CHECK(igraph_adjedgelist_init(graph, &adjedgelist, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_adjedgelist_destroy, &adjedgelist);
IGRAPH_CHECK(igraph_arpack_rssolve(igraph_i_eigenvector_centrality2,
&data, options, 0, &values, &vectors));
igraph_adjedgelist_destroy(&adjedgelist);
IGRAPH_FINALLY_CLEAN(1);
}
if (value) {
*value=VECTOR(values)[0];
}
if (vector) {
igraph_real_t amax=0;
long int which=0;
long int i;
IGRAPH_CHECK(igraph_vector_resize(vector, options->n));
for (i=0; i<options->n; i++) {
igraph_real_t tmp;
VECTOR(*vector)[i] = MATRIX(vectors, i, 0);
tmp=fabs(VECTOR(*vector)[i]);
if (tmp>amax) { amax=tmp; which=i; }
}
if (scale && amax!=0) { igraph_vector_scale(vector, 1/VECTOR(*vector)[which]); }
}
if (options->info) {
IGRAPH_WARNING("Non-zero return code from ARPACK routine!");
}
igraph_matrix_destroy(&vectors);
igraph_vector_destroy(&values);
IGRAPH_FINALLY_CLEAN(2);
return 0;
}
void igraph_i_graphml_sax_handler_end_document(void *state0) {
struct igraph_i_graphml_parser_state *state=
(struct igraph_i_graphml_parser_state*)state0;
long i, l;
int r;
igraph_i_attribute_record_t idrec, eidrec;
const char *idstr="id";
igraph_bool_t already_has_vertex_id=0, already_has_edge_id=0;
if (!state->successful) return;
if (state->index<0) {
igraph_vector_ptr_t vattr, eattr, gattr;
long int esize=igraph_vector_ptr_size(&state->e_attrs);
const void **tmp;
r=igraph_vector_ptr_init(&vattr,
igraph_vector_ptr_size(&state->v_attrs)+1);
if (r) {
igraph_error("Cannot parse GraphML file", __FILE__, __LINE__, r);
igraph_i_graphml_sax_handler_error(state, "Cannot parse GraphML file");
return;
}
IGRAPH_FINALLY(igraph_vector_ptr_destroy, &vattr);
if (igraph_strvector_size(&state->edgeids) != 0) {
esize++;
}
r=igraph_vector_ptr_init(&eattr, esize);
if (r) {
igraph_error("Cannot parse GraphML file", __FILE__, __LINE__, r);
igraph_i_graphml_sax_handler_error(state, "Cannot parse GraphML file");
return;
}
IGRAPH_FINALLY(igraph_vector_ptr_destroy, &eattr);
r=igraph_vector_ptr_init(&gattr, igraph_vector_ptr_size(&state->g_attrs));
if (r) {
igraph_error("Cannot parse GraphML file", __FILE__, __LINE__, r);
igraph_i_graphml_sax_handler_error(state, "Cannot parse GraphML file");
return;
}
IGRAPH_FINALLY(igraph_vector_ptr_destroy, &gattr);
for (i=0; i<igraph_vector_ptr_size(&state->v_attrs); i++) {
igraph_i_graphml_attribute_record_t *graphmlrec=
VECTOR(state->v_attrs)[i];
igraph_i_attribute_record_t *rec=&graphmlrec->record;
/* Check that the name of the vertex attribute is not 'id'.
If it is then we cannot the complimentary 'id' attribute. */
if (! strcmp(rec->name, idstr)) {
already_has_vertex_id=1;
}
if (rec->type == IGRAPH_ATTRIBUTE_NUMERIC) {
igraph_vector_t *vec=(igraph_vector_t*)rec->value;
long int origsize=igraph_vector_size(vec);
long int nodes=igraph_trie_size(&state->node_trie);
igraph_vector_resize(vec, nodes);
for (l=origsize; l<nodes; l++) {
VECTOR(*vec)[l]=IGRAPH_NAN;
}
} else if (rec->type == IGRAPH_ATTRIBUTE_STRING) {
igraph_strvector_t *strvec=(igraph_strvector_t*)rec->value;
long int origsize=igraph_strvector_size(strvec);
long int nodes=igraph_trie_size(&state->node_trie);
igraph_strvector_resize(strvec, nodes);
for (l=origsize; l<nodes; l++) {
igraph_strvector_set(strvec, l, "");
}
}
VECTOR(vattr)[i]=rec;
}
if (!already_has_vertex_id) {
idrec.name=idstr;
idrec.type=IGRAPH_ATTRIBUTE_STRING;
tmp=&idrec.value;
igraph_trie_getkeys(&state->node_trie, (const igraph_strvector_t **)tmp);
VECTOR(vattr)[i]=&idrec;
} else {
igraph_vector_ptr_pop_back(&vattr);
IGRAPH_WARNING("Could not add vertex ids, "
"there is already an 'id' vertex attribute");
}
for (i=0; i<igraph_vector_ptr_size(&state->e_attrs); i++) {
igraph_i_graphml_attribute_record_t *graphmlrec=
VECTOR(state->e_attrs)[i];
igraph_i_attribute_record_t *rec=&graphmlrec->record;
if (! strcmp(rec->name, idstr)) {
already_has_edge_id=1;
}
if (rec->type == IGRAPH_ATTRIBUTE_NUMERIC) {
igraph_vector_t *vec=(igraph_vector_t*)rec->value;
long int origsize=igraph_vector_size(vec);
long int edges=igraph_vector_size(&state->edgelist)/2;
igraph_vector_resize(vec, edges);
for (l=origsize; l<edges; l++) {
VECTOR(*vec)[l]=IGRAPH_NAN;
}
} else if (rec->type == IGRAPH_ATTRIBUTE_STRING) {
igraph_strvector_t *strvec=(igraph_strvector_t*)rec->value;
long int origsize=igraph_strvector_size(strvec);
long int edges=igraph_vector_size(&state->edgelist)/2;
igraph_strvector_resize(strvec, edges);
for (l=origsize; l<edges; l++) {
igraph_strvector_set(strvec, l, "");
}
}
VECTOR(eattr)[i]=rec;
}
if (igraph_strvector_size(&state->edgeids) != 0) {
if (!already_has_edge_id) {
long int origsize=igraph_strvector_size(&state->edgeids);
eidrec.name=idstr;
eidrec.type=IGRAPH_ATTRIBUTE_STRING;
igraph_strvector_resize(&state->edgeids,
igraph_vector_size(&state->edgelist)/2);
for (; origsize < igraph_strvector_size(&state->edgeids); origsize++) {
igraph_strvector_set(&state->edgeids, origsize, "");
}
eidrec.value=&state->edgeids;
VECTOR(eattr)[(long int)igraph_vector_ptr_size(&eattr)-1]=&eidrec;
} else {
igraph_vector_ptr_pop_back(&eattr);
IGRAPH_WARNING("Could not add edge ids, "
"there is already an 'id' edge attribute");
}
}
for (i=0; i<igraph_vector_ptr_size(&state->g_attrs); i++) {
igraph_i_graphml_attribute_record_t *graphmlrec=
VECTOR(state->g_attrs)[i];
igraph_i_attribute_record_t *rec=&graphmlrec->record;
if (rec->type == IGRAPH_ATTRIBUTE_NUMERIC) {
igraph_vector_t *vec=(igraph_vector_t*)rec->value;
long int origsize=igraph_vector_size(vec);
igraph_vector_resize(vec, 1);
for (l=origsize; l<1; l++) {
VECTOR(*vec)[l]=IGRAPH_NAN;
}
} else if (rec->type == IGRAPH_ATTRIBUTE_STRING) {
igraph_strvector_t *strvec=(igraph_strvector_t*)rec->value;
long int origsize=igraph_strvector_size(strvec);
igraph_strvector_resize(strvec, 1);
for (l=origsize; l<1; l++) {
igraph_strvector_set(strvec, l, "");
}
}
VECTOR(gattr)[i]=rec;
}
igraph_empty_attrs(state->g, 0, state->edges_directed, &gattr);
igraph_add_vertices(state->g, igraph_trie_size(&state->node_trie),
&vattr);
igraph_add_edges(state->g, &state->edgelist, &eattr);
igraph_vector_ptr_destroy(&vattr);
igraph_vector_ptr_destroy(&eattr);
igraph_vector_ptr_destroy(&gattr);
IGRAPH_FINALLY_CLEAN(3);
}
igraph_i_graphml_destroy_state(state);
}
int igraph_lapack_dgesv(igraph_matrix_t *a, igraph_vector_int_t *ipiv,
igraph_matrix_t *b, int *info) {
int n=(int) igraph_matrix_nrow(a);
int nrhs=(int) igraph_matrix_ncol(b);
int lda= n > 0 ? n : 1;
int ldb= n > 0 ? n : 1;
igraph_vector_int_t *myipiv=ipiv, vipiv;
if (n != igraph_matrix_ncol(a)) {
IGRAPH_ERROR("Cannot LU solve matrix", IGRAPH_NONSQUARE);
}
if (n != igraph_matrix_nrow(b)) {
IGRAPH_ERROR("Cannot LU solve matrix, RHS of wrong size", IGRAPH_EINVAL);
}
if (!ipiv) {
IGRAPH_CHECK(igraph_vector_int_init(&vipiv, n));
IGRAPH_FINALLY(igraph_vector_int_destroy, &vipiv);
myipiv=&vipiv;
}
igraphdgesv_(&n, &nrhs, VECTOR(a->data), &lda, VECTOR(*myipiv),
VECTOR(b->data), &ldb, info);
if (*info > 0) {
IGRAPH_WARNING("LU: factor is exactly singular");
} else if (*info < 0) {
switch(*info) {
case -1:
IGRAPH_ERROR("Invalid number of rows/column", IGRAPH_ELAPACK);
break;
case -2:
IGRAPH_ERROR("Invalid number of RHS vectors", IGRAPH_ELAPACK);
break;
case -3:
IGRAPH_ERROR("Invalid input matrix", IGRAPH_ELAPACK);
break;
case -4:
IGRAPH_ERROR("Invalid LDA parameter", IGRAPH_ELAPACK);
break;
case -5:
IGRAPH_ERROR("Invalid pivot vector", IGRAPH_ELAPACK);
break;
case -6:
IGRAPH_ERROR("Invalid RHS matrix", IGRAPH_ELAPACK);
break;
case -7:
IGRAPH_ERROR("Invalid LDB parameter", IGRAPH_ELAPACK);
break;
case -8:
IGRAPH_ERROR("Invalid info argument", IGRAPH_ELAPACK);
break;
default:
IGRAPH_ERROR("Unknown LAPACK error", IGRAPH_ELAPACK);
break;
}
}
if (!ipiv) {
igraph_vector_int_destroy(&vipiv);
IGRAPH_FINALLY_CLEAN(1);
}
return 0;
}
int igraph_i_find_k_cliques(const igraph_t *graph,
long int size,
const igraph_real_t *member_storage,
igraph_real_t **new_member_storage,
long int old_clique_count,
long int *clique_count,
igraph_vector_t *neis,
igraph_bool_t independent_vertices) {
long int j, k, l, m, n, new_member_storage_size;
const igraph_real_t *c1, *c2;
igraph_real_t v1, v2;
igraph_bool_t ok;
/* Allocate the storage */
*new_member_storage=igraph_Realloc(*new_member_storage,
size*old_clique_count,
igraph_real_t);
if (*new_member_storage == 0) {
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
}
new_member_storage_size = size*old_clique_count;
IGRAPH_FINALLY(igraph_free, *new_member_storage);
m=n=0;
/* Now consider all pairs of i-1-cliques and see if they can be merged */
for (j=0; j<old_clique_count; j++) {
for (k=j+1; k<old_clique_count; k++) {
IGRAPH_ALLOW_INTERRUPTION();
/* Since cliques are represented by their vertex indices in increasing
* order, two cliques can be merged iff they have exactly the same
* indices excluding one AND there is an edge between the two different
* vertices */
c1 = member_storage+j*(size-1);
c2 = member_storage+k*(size-1);
/* Find the longest prefixes of c1 and c2 that are equal */
for (l=0; l<size-1 && c1[l] == c2[l]; l++)
(*new_member_storage)[m++]=c1[l];
/* Now, if l == size-1, the two vectors are totally equal.
This is a bug */
if (l == size-1) {
IGRAPH_WARNING("possible bug in igraph_cliques");
m=n;
} else {
/* Assuming that j<k, c1[l] is always less than c2[l], since cliques
* are ordered alphabetically. Now add c1[l] and store c2[l] in a
* dummy variable */
(*new_member_storage)[m++]=c1[l];
v1=c1[l];
v2=c2[l];
l++;
/* Copy the remaining part of the two vectors. Every member pair
* found in the remaining parts satisfies the following:
* 1. If they are equal, they should be added.
* 2. If they are not equal, the smaller must be equal to the
* one stored in the dummy variable. If not, the two vectors
* differ in more than one place. The larger will be stored in
* the dummy variable again.
*/
ok=1;
for (; l<size-1; l++) {
if (c1[l] == c2[l]) {
(*new_member_storage)[m++]=c1[l];
ok=0;
} else if (ok) {
if (c1[l] < c2[l]) {
if (c1[l] == v1) {
(*new_member_storage)[m++]=c1[l];
v2 = c2[l];
} else break;
} else {
if (ok && c2[l] == v1) {
(*new_member_storage)[m++]=c2[l];
v2 = c1[l];
} else break;
}
} else break;
}
/* Now, if l != size-1, the two vectors had a difference in more than
* one place, so the whole clique is invalid. */
if (l != size-1) {
/* Step back in new_member_storage */
m=n;
} else {
/* v1 and v2 are the two different vertices. Check for an edge
* if we are looking for cliques and check for the absence of an
* edge if we are looking for independent vertex sets */
IGRAPH_CHECK(igraph_neighbors(graph, neis, v1, IGRAPH_ALL));
l=igraph_vector_search(neis, 0, v2, 0);
if ((l && !independent_vertices) || (!l && independent_vertices)) {
/* Found a new clique, step forward in new_member_storage */
if (m==n || v2>(*new_member_storage)[m-1]) {
(*new_member_storage)[m++]=v2;
n=m;
} else {
m=n;
}
} else {
m=n;
}
}
/* See if new_member_storage is full. If so, reallocate */
if (m == new_member_storage_size) {
IGRAPH_FINALLY_CLEAN(1);
*new_member_storage = igraph_Realloc(*new_member_storage,
new_member_storage_size*2,
igraph_real_t);
if (*new_member_storage == 0)
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
new_member_storage_size *= 2;
IGRAPH_FINALLY(igraph_free, *new_member_storage);
}
}
}
}
/* Calculate how many cliques have we found */
*clique_count = n/size;
IGRAPH_FINALLY_CLEAN(1);
return 0;
}
/* Internal function for calculating cliques or independent vertex sets.
* They are practically the same except that the complementer of the graph
* should be used in the latter case.
*/
int igraph_i_cliques(const igraph_t *graph, igraph_vector_ptr_t *res,
igraph_integer_t min_size, igraph_integer_t max_size,
igraph_bool_t independent_vertices) {
igraph_integer_t no_of_nodes;
igraph_vector_t neis;
igraph_real_t *member_storage=0, *new_member_storage, *c1;
long int i, j, k, clique_count, old_clique_count;
if (igraph_is_directed(graph))
IGRAPH_WARNING("directionality of edges is ignored for directed graphs");
no_of_nodes = igraph_vcount(graph);
if (min_size < 0) { min_size = 0; }
if (max_size > no_of_nodes || max_size <= 0) { max_size = no_of_nodes; }
igraph_vector_ptr_clear(res);
IGRAPH_VECTOR_INIT_FINALLY(&neis, 0);
IGRAPH_FINALLY(igraph_i_cliques_free_res, res);
/* Will be resized later, if needed. */
member_storage=igraph_Calloc(1, igraph_real_t);
if (member_storage==0) {
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, member_storage);
/* Find all 1-cliques: every vertex will be a clique */
new_member_storage=igraph_Calloc(no_of_nodes, igraph_real_t);
if (new_member_storage==0) {
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, new_member_storage);
for (i=0; i<no_of_nodes; i++) {
new_member_storage[i] = i;
}
clique_count = no_of_nodes;
old_clique_count = 0;
/* Add size 1 cliques if requested */
if (min_size <= 1) {
IGRAPH_CHECK(igraph_vector_ptr_resize(res, no_of_nodes));
igraph_vector_ptr_null(res);
for (i=0; i<no_of_nodes; i++) {
igraph_vector_t *p=igraph_Calloc(1, igraph_vector_t);
if (p==0) {
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, p);
IGRAPH_CHECK(igraph_vector_init(p, 1));
VECTOR(*p)[0]=i;
VECTOR(*res)[i]=p;
IGRAPH_FINALLY_CLEAN(1);
}
}
for (i=2; i<=max_size && clique_count > 1; i++) {
/* Here new_member_storage contains the cliques found in the previous
iteration. Save this into member_storage, might be needed later */
c1=member_storage;
member_storage=new_member_storage;
new_member_storage=c1;
old_clique_count=clique_count;
IGRAPH_ALLOW_INTERRUPTION();
/* Calculate the cliques */
IGRAPH_FINALLY_CLEAN(2);
IGRAPH_CHECK(igraph_i_find_k_cliques(graph, i, member_storage,
&new_member_storage,
old_clique_count,
&clique_count,
&neis,
independent_vertices));
IGRAPH_FINALLY(igraph_free, member_storage);
IGRAPH_FINALLY(igraph_free, new_member_storage);
/* Add the cliques just found to the result if requested */
if (i>=min_size && i<=max_size) {
for (j=0, k=0; j<clique_count; j++, k+=i) {
igraph_vector_t *p=igraph_Calloc(1, igraph_vector_t);
if (p==0) {
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, p);
IGRAPH_CHECK(igraph_vector_init_copy(p, &new_member_storage[k], i));
IGRAPH_FINALLY(igraph_vector_destroy, p);
IGRAPH_CHECK(igraph_vector_ptr_push_back(res, p));
IGRAPH_FINALLY_CLEAN(2);
}
}
} /* i <= max_size && clique_count != 0 */
igraph_free(member_storage);
igraph_free(new_member_storage);
igraph_vector_destroy(&neis);
IGRAPH_FINALLY_CLEAN(4); /* 3 here, +1 is igraph_i_cliques_free_res */
return 0;
}
//_________________________________________________________________________
unsigned long graph_molloy_hash::shuffle(unsigned long times,
unsigned long maxtimes, int type) {
igraph_progress("Shuffle", 0, 0);
// assert(verify());
// counters
unsigned long nb_swaps = 0;
unsigned long all_swaps = 0;
unsigned long cost = 0;
// window
double T = double(min((unsigned long)(a),times)/10);
if(type==OPTIMAL_HEURISTICS) T=double(optimal_window());
if(type==BRUTE_FORCE_HEURISTICS) T=double(times*2);
// isolation test parameter, and buffers
double K = 2.4;
int *Kbuff = new int[int(K)+1];
bool *visited = new bool[n];
for(int i=0; i<n; i++) visited[i] = false;
// Used for monitoring , active only if VERBOSE()
int failures = 0;
int successes = 0;
double avg_K = 0;
double avg_T = 0;
unsigned long next = times;
next=0;
// Shuffle: while #edge swap attempts validated by connectivity < times ...
while(times>nb_swaps && maxtimes>all_swaps) {
// Backup graph
int *save = backup();
// Prepare counters, K, T
unsigned long swaps = 0;
int K_int = 0;
if(type == FINAL_HEURISTICS || type == BRUTE_FORCE_HEURISTICS) K_int=int(K);
unsigned long T_int = (unsigned long)(floor(T));
if(T_int<1) T_int=1;
// compute cost
cost += T_int;
if(K_int>2) cost += (unsigned long)(K_int)*(unsigned long)(T_int);
// Perform T edge swap attempts
for(int i=T_int; i>0; i--) {
// try one swap
swaps += (unsigned long)(random_edge_swap(K_int, Kbuff, visited));
all_swaps++;
// Verbose
if(nb_swaps+swaps>next) {
next = (nb_swaps+swaps)+max((unsigned long)(100),(unsigned long)(times/1000));
int progress = int(double(nb_swaps+swaps) / double(times));
igraph_progress("Shuffle", progress, 0);
}
}
// test connectivity
cost+=(unsigned long)(a/2);
bool ok = is_connected();
// performance monitor
{
avg_T += double(T_int); avg_K += double(K_int);
if(ok) successes++; else failures++;
}
// restore graph if needed, and count validated swaps
if(ok) nb_swaps += swaps;
else {
restore(save);
next=nb_swaps;
}
delete[] save;
// Adjust K and T following the heuristics.
switch(type) {
int steps;
case GKAN_HEURISTICS:
if (ok) T+=1.0; else T*=0.5;
break;
case FAB_HEURISTICS:
steps = 50 / (8+failures+successes);
if(steps<1) steps=1;
while(steps--) if(ok) T*=1.17182818; else T*=0.9;
if(T>double(5*a)) T=double(5*a);
break;
case FINAL_HEURISTICS:
if(ok) { if((K+10.0)*T>5.0*double(a)) K/=1.03; else T*=2; }
else { K*=1.35; delete[] Kbuff; Kbuff = new int[int(K)+1]; }
break;
case OPTIMAL_HEURISTICS:
if(ok) T=double(optimal_window());
break;
case BRUTE_FORCE_HEURISTICS:
K*=2; delete[] Kbuff; Kbuff = new int[int(K)+1];
break;
default:
IGRAPH_ERROR("Error in graph_molloy_hash::shuffle(): "
"Unknown heuristics type", IGRAPH_EINVAL);
return 0;
}
}
delete[] Kbuff;
delete[] visited;
if (maxtimes <= all_swaps) {
IGRAPH_WARNING("Cannot shuffle graph, maybe there is only a single one?");
}
// Status report
{
igraph_status("*** Shuffle Monitor ***\n", 0);
igraph_statusf(" - Average cost : %f / validated edge swap\n", 0,
double(cost)/double(nb_swaps));
igraph_statusf(" - Connectivity tests : %d (%d successes, %d failures)\n",
0, successes + failures, successes, failures);
igraph_statusf(" - Average window : %d\n", 0,
int(avg_T/double(successes+failures)));
if(type==FINAL_HEURISTICS || type==BRUTE_FORCE_HEURISTICS)
igraph_statusf(" - Average isolation test width : %f\n", 0,
avg_K/double(successes+failures));
}
return nb_swaps;
}
int igraph_i_maximal_cliques(const igraph_t *graph, igraph_i_maximal_clique_func_t func, void* data) {
int directed=igraph_is_directed(graph);
long int i, j, k, l;
igraph_integer_t no_of_nodes, nodes_to_check, nodes_done;
igraph_integer_t best_cand = 0, best_cand_degree = 0, best_fini_cand_degree;
igraph_adjlist_t adj_list;
igraph_stack_ptr_t stack;
igraph_i_maximal_cliques_stack_frame frame, *new_frame_ptr;
igraph_vector_t clique, new_cand, new_fini, cn, best_cand_nbrs, best_fini_cand_nbrs;
igraph_bool_t cont = 1;
int assret;
if (directed)
IGRAPH_WARNING("directionality of edges is ignored for directed graphs");
no_of_nodes = igraph_vcount(graph);
if (no_of_nodes == 0)
return IGRAPH_SUCCESS;
/* Construct an adjacency list representation */
IGRAPH_CHECK(igraph_adjlist_init(graph, &adj_list, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_adjlist_destroy, &adj_list);
IGRAPH_CHECK(igraph_adjlist_simplify(&adj_list));
igraph_adjlist_sort(&adj_list);
/* Initialize stack */
IGRAPH_CHECK(igraph_stack_ptr_init(&stack, 0));
IGRAPH_FINALLY(igraph_i_maximal_cliques_stack_destroy, &stack);
/* Create the initial (empty) clique */
IGRAPH_VECTOR_INIT_FINALLY(&clique, 0);
/* Initialize new_cand, new_fini, cn, best_cand_nbrs and best_fini_cand_nbrs (will be used later) */
IGRAPH_VECTOR_INIT_FINALLY(&new_cand, 0);
IGRAPH_VECTOR_INIT_FINALLY(&new_fini, 0);
IGRAPH_VECTOR_INIT_FINALLY(&cn, 0);
IGRAPH_VECTOR_INIT_FINALLY(&best_cand_nbrs, 0);
IGRAPH_VECTOR_INIT_FINALLY(&best_fini_cand_nbrs, 0);
/* Find the vertex with the highest degree */
best_cand = 0; best_cand_degree = igraph_vector_size(igraph_adjlist_get(&adj_list, 0));
for (i = 1; i < no_of_nodes; i++) {
j = igraph_vector_size(igraph_adjlist_get(&adj_list, i));
if (j > best_cand_degree) {
best_cand = i;
best_cand_degree = j;
}
}
/* Create the initial stack frame */
IGRAPH_CHECK(igraph_vector_init_seq(&frame.cand, 0, no_of_nodes-1));
IGRAPH_FINALLY(igraph_vector_destroy, &frame.cand);
IGRAPH_CHECK(igraph_vector_init(&frame.fini, 0));
IGRAPH_FINALLY(igraph_vector_destroy, &frame.fini);
IGRAPH_CHECK(igraph_vector_init(&frame.cand_filtered, 0));
IGRAPH_FINALLY(igraph_vector_destroy, &frame.cand_filtered);
IGRAPH_CHECK(igraph_vector_difference_sorted(&frame.cand,
igraph_adjlist_get(&adj_list, best_cand), &frame.cand_filtered));
IGRAPH_FINALLY_CLEAN(3);
IGRAPH_FINALLY(igraph_i_maximal_cliques_stack_frame_destroy, &frame);
/* TODO: frame.cand and frame.fini should be a set instead of a vector */
/* Main loop starts here */
nodes_to_check = igraph_vector_size(&frame.cand_filtered); nodes_done = 0;
while (!igraph_vector_empty(&frame.cand_filtered) || !igraph_stack_ptr_empty(&stack)) {
if (igraph_vector_empty(&frame.cand_filtered)) {
/* No candidates left to check in this stack frame, pop out the previous stack frame */
igraph_i_maximal_cliques_stack_frame *newframe = igraph_stack_ptr_pop(&stack);
igraph_i_maximal_cliques_stack_frame_destroy(&frame);
frame = *newframe;
free(newframe);
if (igraph_stack_ptr_size(&stack) == 1) {
/* We will be using the next candidate node in the next iteration, so we can increase
* nodes_done by 1 */
nodes_done++;
}
/* For efficiency reasons, we only check for interruption and show progress here */
IGRAPH_PROGRESS("Maximal cliques: ", 100.0 * nodes_done / nodes_to_check, NULL);
IGRAPH_ALLOW_INTERRUPTION();
igraph_vector_pop_back(&clique);
continue;
}
/* Try the next node in the clique */
i = igraph_vector_pop_back(&frame.cand_filtered);
IGRAPH_CHECK(igraph_vector_push_back(&clique, i));
/* Remove the node from the candidate list */
assret=igraph_vector_binsearch(&frame.cand, i, &j); assert(assret);
igraph_vector_remove(&frame.cand, j);
/* Add the node to the finished list */
assret = !igraph_vector_binsearch(&frame.fini, i, &j); assert(assret);
IGRAPH_CHECK(igraph_vector_insert(&frame.fini, j, i));
/* Create new_cand and new_fini */
IGRAPH_CHECK(igraph_vector_intersect_sorted(&frame.cand, igraph_adjlist_get(&adj_list, i), &new_cand));
IGRAPH_CHECK(igraph_vector_intersect_sorted(&frame.fini, igraph_adjlist_get(&adj_list, i), &new_fini));
/* Do we have anything more to search? */
if (igraph_vector_empty(&new_cand)) {
if (igraph_vector_empty(&new_fini)) {
/* We have a maximal clique here */
IGRAPH_CHECK(func(&clique, data, &cont));
if (!cont) {
/* The callback function requested to stop the search */
break;
}
}
igraph_vector_pop_back(&clique);
continue;
}
if (igraph_vector_empty(&new_fini) && igraph_vector_size(&new_cand) == 1) {
/* Shortcut: only one node left */
IGRAPH_CHECK(igraph_vector_push_back(&clique, VECTOR(new_cand)[0]));
IGRAPH_CHECK(func(&clique, data, &cont));
if (!cont) {
/* The callback function requested to stop the search */
break;
}
igraph_vector_pop_back(&clique);
igraph_vector_pop_back(&clique);
continue;
}
/* Find the next best candidate node in new_fini */
l = igraph_vector_size(&new_cand);
best_cand_degree = -1;
j = igraph_vector_size(&new_fini);
for (i = 0; i < j; i++) {
k = (long int)VECTOR(new_fini)[i];
IGRAPH_CHECK(igraph_vector_intersect_sorted(&new_cand, igraph_adjlist_get(&adj_list, k), &cn));
if (igraph_vector_size(&cn) > best_cand_degree) {
best_cand_degree = igraph_vector_size(&cn);
IGRAPH_CHECK(igraph_vector_update(&best_fini_cand_nbrs, &cn));
if (best_cand_degree == l) {
/* Cool, we surely have the best candidate node here as best_cand_degree can't get any better */
break;
}
}
}
/* Shortcut here: we don't have to examine new_cand */
if (best_cand_degree == l) {
igraph_vector_pop_back(&clique);
continue;
}
/* Still finding best candidate node */
best_fini_cand_degree = best_cand_degree;
best_cand_degree = -1;
j = igraph_vector_size(&new_cand);
l = l - 1;
for (i = 0; i < j; i++) {
k = (long int)VECTOR(new_cand)[i];
IGRAPH_CHECK(igraph_vector_intersect_sorted(&new_cand, igraph_adjlist_get(&adj_list, k), &cn));
if (igraph_vector_size(&cn) > best_cand_degree) {
best_cand_degree = igraph_vector_size(&cn);
IGRAPH_CHECK(igraph_vector_update(&best_cand_nbrs, &cn));
if (best_cand_degree == l) {
/* Cool, we surely have the best candidate node here as best_cand_degree can't get any better */
break;
}
}
}
/* Create a new stack frame in case we back out later */
new_frame_ptr = igraph_Calloc(1, igraph_i_maximal_cliques_stack_frame);
if (new_frame_ptr == 0) {
IGRAPH_ERROR("cannot allocate new stack frame", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, new_frame_ptr);
*new_frame_ptr = frame;
memset(&frame, 0, sizeof(frame));
IGRAPH_CHECK(igraph_stack_ptr_push(&stack, new_frame_ptr));
IGRAPH_FINALLY_CLEAN(1); /* ownership of new_frame_ptr taken by the stack */
/* Ownership of the current frame and its vectors (frame.cand, frame.done, frame.cand_filtered)
* is taken by the stack from now on. Vectors in frame must be re-initialized with new_cand,
* new_fini and stuff. The old frame.cand and frame.fini won't be leaked because they are
* managed by the stack now. */
frame.cand = new_cand;
frame.fini = new_fini;
IGRAPH_CHECK(igraph_vector_init(&new_cand, 0));
IGRAPH_CHECK(igraph_vector_init(&new_fini, 0));
IGRAPH_CHECK(igraph_vector_init(&frame.cand_filtered, 0));
/* Adjust frame.cand_filtered */
if (best_cand_degree < best_fini_cand_degree) {
IGRAPH_CHECK(igraph_vector_difference_sorted(&frame.cand, &best_fini_cand_nbrs, &frame.cand_filtered));
} else {
IGRAPH_CHECK(igraph_vector_difference_sorted(&frame.cand, &best_cand_nbrs, &frame.cand_filtered));
}
}
IGRAPH_PROGRESS("Maximal cliques: ", 100.0, NULL);
igraph_adjlist_destroy(&adj_list);
igraph_vector_destroy(&clique);
igraph_vector_destroy(&new_cand);
igraph_vector_destroy(&new_fini);
igraph_vector_destroy(&cn);
igraph_vector_destroy(&best_cand_nbrs);
igraph_vector_destroy(&best_fini_cand_nbrs);
igraph_i_maximal_cliques_stack_frame_destroy(&frame);
igraph_i_maximal_cliques_stack_destroy(&stack);
IGRAPH_FINALLY_CLEAN(9);
return IGRAPH_SUCCESS;
}
int igraph_adjedgelist_remove_duplicate(const igraph_t *graph,
igraph_inclist_t *al) {
IGRAPH_WARNING("igraph_adjedgelist_remove_duplicate() is deprecated, use "
"igraph_inclist_remove_duplicate() instead");
return igraph_inclist_remove_duplicate(graph, al);
}
int igraph_lapack_dgeev(const igraph_matrix_t *A,
igraph_vector_t *valuesreal,
igraph_vector_t *valuesimag,
igraph_matrix_t *vectorsleft,
igraph_matrix_t *vectorsright,
int *info) {
char jobvl= vectorsleft ? 'V' : 'N';
char jobvr= vectorsright ? 'V' : 'N';
int n=(int) igraph_matrix_nrow(A);
int lda=n, ldvl=n, ldvr=n, lwork=-1;
igraph_vector_t work;
igraph_vector_t *myreal=valuesreal, *myimag=valuesimag, vreal, vimag;
igraph_matrix_t Acopy;
int error=*info;
if (igraph_matrix_ncol(A) != n) {
IGRAPH_ERROR("Cannot calculate eigenvalues (dgeev)", IGRAPH_NONSQUARE);
}
IGRAPH_CHECK(igraph_matrix_copy(&Acopy, A));
IGRAPH_FINALLY(igraph_matrix_destroy, &Acopy);
IGRAPH_VECTOR_INIT_FINALLY(&work, 1);
if (!valuesreal) {
IGRAPH_VECTOR_INIT_FINALLY(&vreal, n);
myreal=&vreal;
} else {
IGRAPH_CHECK(igraph_vector_resize(myreal, n));
}
if (!valuesimag) {
IGRAPH_VECTOR_INIT_FINALLY(&vimag, n);
myimag=&vimag;
} else {
IGRAPH_CHECK(igraph_vector_resize(myimag, n));
}
if (vectorsleft) {
IGRAPH_CHECK(igraph_matrix_resize(vectorsleft, n, n));
}
if (vectorsright) {
IGRAPH_CHECK(igraph_matrix_resize(vectorsright, n, n));
}
igraphdgeev_(&jobvl, &jobvr, &n, &MATRIX(Acopy,0,0), &lda,
VECTOR(*myreal), VECTOR(*myimag),
vectorsleft ? &MATRIX(*vectorsleft ,0,0) : 0, &ldvl,
vectorsright ? &MATRIX(*vectorsright,0,0) : 0, &ldvr,
VECTOR(work), &lwork, info);
lwork=(int) VECTOR(work)[0];
IGRAPH_CHECK(igraph_vector_resize(&work, lwork));
igraphdgeev_(&jobvl, &jobvr, &n, &MATRIX(Acopy,0,0), &lda,
VECTOR(*myreal), VECTOR(*myimag),
vectorsleft ? &MATRIX(*vectorsleft ,0,0) : 0, &ldvl,
vectorsright ? &MATRIX(*vectorsright,0,0) : 0, &ldvr,
VECTOR(work), &lwork, info);
if (*info < 0) {
IGRAPH_ERROR("Cannot calculate eigenvalues (dgeev)", IGRAPH_ELAPACK);
} else if (*info > 0) {
if (error) {
IGRAPH_ERROR("Cannot calculate eigenvalues (dgeev)", IGRAPH_ELAPACK);
} else {
IGRAPH_WARNING("Cannot calculate eigenvalues (dgeev)");
}
}
if (!valuesimag) {
igraph_vector_destroy(&vimag);
IGRAPH_FINALLY_CLEAN(1);
}
if (!valuesreal) {
igraph_vector_destroy(&vreal);
IGRAPH_FINALLY_CLEAN(1);
}
igraph_vector_destroy(&work);
igraph_matrix_destroy(&Acopy);
IGRAPH_FINALLY_CLEAN(2);
return 0;
}
int igraph_adjedgelist_print(const igraph_inclist_t *al, FILE *outfile) {
IGRAPH_WARNING("igraph_adjedgelist_print() is deprecated, use "
"igraph_inclist_print() instead");
return igraph_inclist_print(al, outfile);
}
int igraph_lapack_dgeevx(igraph_lapack_dgeevx_balance_t balance,
const igraph_matrix_t *A,
igraph_vector_t *valuesreal,
igraph_vector_t *valuesimag,
igraph_matrix_t *vectorsleft,
igraph_matrix_t *vectorsright,
int *ilo, int *ihi, igraph_vector_t *scale,
igraph_real_t *abnrm,
igraph_vector_t *rconde,
igraph_vector_t *rcondv,
int *info) {
char balanc;
char jobvl= vectorsleft ? 'V' : 'N';
char jobvr= vectorsright ? 'V' : 'N';
char sense;
int n=(int) igraph_matrix_nrow(A);
int lda=n, ldvl=n, ldvr=n, lwork=-1;
igraph_vector_t work;
igraph_vector_int_t iwork;
igraph_matrix_t Acopy;
int error=*info;
igraph_vector_t *myreal=valuesreal, *myimag=valuesimag, vreal, vimag;
igraph_vector_t *myscale=scale, vscale;
if (igraph_matrix_ncol(A) != n) {
IGRAPH_ERROR("Cannot calculate eigenvalues (dgeevx)", IGRAPH_NONSQUARE);
}
switch (balance) {
case IGRAPH_LAPACK_DGEEVX_BALANCE_NONE:
balanc='N';
break;
case IGRAPH_LAPACK_DGEEVX_BALANCE_PERM:
balanc='P';
break;
case IGRAPH_LAPACK_DGEEVX_BALANCE_SCALE:
balanc='S';
break;
case IGRAPH_LAPACK_DGEEVX_BALANCE_BOTH:
balanc='B';
break;
default:
IGRAPH_ERROR("Invalid 'balance' argument", IGRAPH_EINVAL);
break;
}
if (!rconde && !rcondv) {
sense='N';
} else if (rconde && !rcondv) {
sense='E';
} else if (!rconde && rcondv) {
sense='V';
} else {
sense='B';
}
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, n));
IGRAPH_FINALLY(igraph_vector_int_destroy, &iwork);
if (!valuesreal) {
IGRAPH_VECTOR_INIT_FINALLY(&vreal, n);
myreal=&vreal;
} else {
IGRAPH_CHECK(igraph_vector_resize(myreal, n));
}
if (!valuesimag) {
IGRAPH_VECTOR_INIT_FINALLY(&vimag, n);
myimag=&vimag;
} else {
IGRAPH_CHECK(igraph_vector_resize(myimag, n));
}
if (!scale) {
IGRAPH_VECTOR_INIT_FINALLY(&vscale, n);
myscale=&vscale;
} else {
IGRAPH_CHECK(igraph_vector_resize(scale, n));
}
if (vectorsleft) {
IGRAPH_CHECK(igraph_matrix_resize(vectorsleft, n, n));
}
if (vectorsright) {
IGRAPH_CHECK(igraph_matrix_resize(vectorsright, n, n));
}
igraphdgeevx_(&balanc, &jobvl, &jobvr, &sense, &n, &MATRIX(Acopy,0,0),
&lda, VECTOR(*myreal), VECTOR(*myimag),
vectorsleft ? &MATRIX(*vectorsleft ,0,0) : 0, &ldvl,
vectorsright ? &MATRIX(*vectorsright,0,0) : 0, &ldvr,
ilo, ihi, VECTOR(*myscale), abnrm,
rconde ? VECTOR(*rconde) : 0,
rcondv ? VECTOR(*rcondv) : 0,
VECTOR(work), &lwork, VECTOR(iwork), info);
lwork=(int) VECTOR(work)[0];
IGRAPH_CHECK(igraph_vector_resize(&work, lwork));
igraphdgeevx_(&balanc, &jobvl, &jobvr, &sense, &n, &MATRIX(Acopy,0,0),
&lda, VECTOR(*myreal), VECTOR(*myimag),
vectorsleft ? &MATRIX(*vectorsleft ,0,0) : 0, &ldvl,
vectorsright ? &MATRIX(*vectorsright,0,0) : 0, &ldvr,
ilo, ihi, VECTOR(*myscale), abnrm,
rconde ? VECTOR(*rconde) : 0,
rcondv ? VECTOR(*rcondv) : 0,
VECTOR(work), &lwork, VECTOR(iwork), info);
if (*info < 0) {
IGRAPH_ERROR("Cannot calculate eigenvalues (dgeev)", IGRAPH_ELAPACK);
} else if (*info > 0) {
if (error) {
IGRAPH_ERROR("Cannot calculate eigenvalues (dgeev)", IGRAPH_ELAPACK);
} else {
IGRAPH_WARNING("Cannot calculate eigenvalues (dgeev)");
}
}
if (!scale) {
igraph_vector_destroy(&vscale);
IGRAPH_FINALLY_CLEAN(1);
}
if (!valuesimag) {
igraph_vector_destroy(&vimag);
IGRAPH_FINALLY_CLEAN(1);
}
if (!valuesreal) {
igraph_vector_destroy(&vreal);
IGRAPH_FINALLY_CLEAN(1);
}
igraph_vector_int_destroy(&iwork);
igraph_vector_destroy(&work);
igraph_matrix_destroy(&Acopy);
IGRAPH_FINALLY_CLEAN(3);
return 0;
}
/**
* Finding maximum bipartite matchings on bipartite graphs using the
* Hungarian algorithm (a.k.a. Kuhn-Munkres algorithm).
*
* The algorithm uses a maximum cardinality matching on a subset of
* tight edges as a starting point. This is achieved by
* \c igraph_i_maximum_bipartite_matching_unweighted on the restricted
* graph.
*
* The algorithm works reliably only if the weights are integers. The
* \c eps parameter should specity a very small number; if the slack on
* an edge falls below \c eps, it will be considered tight. If all your
* weights are integers, you can safely set \c eps to zero.
*/
int igraph_i_maximum_bipartite_matching_weighted(const igraph_t* graph,
const igraph_vector_bool_t* types, igraph_integer_t* matching_size,
igraph_real_t* matching_weight, igraph_vector_long_t* matching,
const igraph_vector_t* weights, igraph_real_t eps) {
long int i, j, k, n, no_of_nodes, no_of_edges;
igraph_integer_t u, v, w, msize;
igraph_t newgraph;
igraph_vector_long_t match; /* will store the matching */
igraph_vector_t slack; /* will store the slack on each edge */
igraph_vector_t parent; /* parent vertices during a BFS */
igraph_vector_t vec1, vec2; /* general temporary vectors */
igraph_vector_t labels; /* will store the labels */
igraph_dqueue_long_t q; /* a FIFO for BST */
igraph_bool_t smaller_set; /* denotes which part of the bipartite graph is smaller */
long int smaller_set_size; /* size of the smaller set */
igraph_real_t dual; /* solution of the dual problem */
igraph_adjlist_t tight_phantom_edges; /* adjacency list to manage tight phantom edges */
igraph_integer_t alternating_path_endpoint;
igraph_vector_t* neis;
igraph_vector_int_t *neis2;
igraph_inclist_t inclist; /* incidence list of the original graph */
/* The Hungarian algorithm is originally for complete bipartite graphs.
* For non-complete bipartite graphs, a phantom edge of weight zero must be
* added between every pair of non-connected vertices. We don't do this
* explicitly of course. See the comments below about how phantom edges
* are taken into account. */
no_of_nodes = igraph_vcount(graph);
no_of_edges = igraph_ecount(graph);
if (eps < 0) {
IGRAPH_WARNING("negative epsilon given, clamping to zero");
eps = 0;
}
/* (1) Initialize data structures */
IGRAPH_CHECK(igraph_vector_long_init(&match, no_of_nodes));
IGRAPH_FINALLY(igraph_vector_long_destroy, &match);
IGRAPH_CHECK(igraph_vector_init(&slack, no_of_edges));
IGRAPH_FINALLY(igraph_vector_destroy, &slack);
IGRAPH_VECTOR_INIT_FINALLY(&vec1, 0);
IGRAPH_VECTOR_INIT_FINALLY(&vec2, 0);
IGRAPH_VECTOR_INIT_FINALLY(&labels, no_of_nodes);
IGRAPH_CHECK(igraph_dqueue_long_init(&q, 0));
IGRAPH_FINALLY(igraph_dqueue_long_destroy, &q);
IGRAPH_VECTOR_INIT_FINALLY(&parent, no_of_nodes);
IGRAPH_CHECK(igraph_adjlist_init_empty(&tight_phantom_edges,
(igraph_integer_t) no_of_nodes));
IGRAPH_FINALLY(igraph_adjlist_destroy, &tight_phantom_edges);
IGRAPH_CHECK(igraph_inclist_init(graph, &inclist, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_inclist_destroy, &inclist);
/* (2) Find which set is the smaller one */
j = 0;
for (i = 0; i < no_of_nodes; i++) {
if (VECTOR(*types)[i] == 0)
j++;
}
smaller_set = (j > no_of_nodes / 2);
smaller_set_size = smaller_set ? (no_of_nodes - j) : j;
/* (3) Calculate the initial labeling and the set of tight edges. Use the
* smaller set only. Here we can assume that there are no phantom edges
* among the tight ones. */
dual = 0;
for (i = 0; i < no_of_nodes; i++) {
igraph_real_t max_weight = 0;
if (VECTOR(*types)[i] != smaller_set) {
VECTOR(labels)[i] = 0;
continue;
}
neis = igraph_inclist_get(&inclist, i);
n = igraph_vector_size(neis);
for (j = 0, k = 0; j < n; j++) {
if (VECTOR(*weights)[(long int)VECTOR(*neis)[j]] > max_weight) {
k = (long int) VECTOR(*neis)[j];
max_weight = VECTOR(*weights)[k];
}
}
VECTOR(labels)[i] = max_weight;
dual += max_weight;
}
igraph_vector_clear(&vec1);
IGRAPH_CHECK(igraph_get_edgelist(graph, &vec2, 0));
#define IS_TIGHT(i) (VECTOR(slack)[i] <= eps)
for (i = 0, j = 0; i < no_of_edges; i++, j+=2) {
u = (igraph_integer_t) VECTOR(vec2)[j];
v = (igraph_integer_t) VECTOR(vec2)[j+1];
VECTOR(slack)[i] = VECTOR(labels)[u] + VECTOR(labels)[v] - VECTOR(*weights)[i];
if (IS_TIGHT(i)) {
IGRAPH_CHECK(igraph_vector_push_back(&vec1, u));
IGRAPH_CHECK(igraph_vector_push_back(&vec1, v));
}
}
igraph_vector_clear(&vec2);
/* (4) Construct a temporary graph on which the initial maximum matching
* will be calculated (only on the subset of tight edges) */
IGRAPH_CHECK(igraph_create(&newgraph, &vec1,
(igraph_integer_t) no_of_nodes, 0));
IGRAPH_FINALLY(igraph_destroy, &newgraph);
IGRAPH_CHECK(igraph_maximum_bipartite_matching(&newgraph, types, &msize, 0, &match, 0, 0));
igraph_destroy(&newgraph);
IGRAPH_FINALLY_CLEAN(1);
/* (5) Main loop until the matching becomes maximal */
while (msize < smaller_set_size) {
igraph_real_t min_slack, min_slack_2;
igraph_integer_t min_slack_u, min_slack_v;
/* (7) Fill the push queue with the unmatched nodes from the smaller set. */
igraph_vector_clear(&vec1);
igraph_vector_clear(&vec2);
igraph_vector_fill(&parent, -1);
for (i = 0; i < no_of_nodes; i++) {
if (UNMATCHED(i) && VECTOR(*types)[i] == smaller_set) {
IGRAPH_CHECK(igraph_dqueue_long_push(&q, i));
VECTOR(parent)[i] = i;
IGRAPH_CHECK(igraph_vector_push_back(&vec1, i));
}
}
#ifdef MATCHING_DEBUG
debug("Matching:");
igraph_vector_long_print(&match);
debug("Unmatched vertices are marked by non-negative numbers:\n");
igraph_vector_print(&parent);
debug("Labeling:");
igraph_vector_print(&labels);
debug("Slacks:");
igraph_vector_print(&slack);
#endif
/* (8) Run the BFS */
alternating_path_endpoint = -1;
while (!igraph_dqueue_long_empty(&q)) {
v = (int) igraph_dqueue_long_pop(&q);
debug("Considering vertex %ld\n", (long int)v);
/* v is always in the smaller set. Find the neighbors of v, which
* are all in the larger set. Find the pairs of these nodes in
* the smaller set and push them to the queue. Mark the traversed
* nodes as seen.
*
* Here we have to be careful as there are two types of incident
* edges on v: real edges and phantom ones. Real edges are
* given by igraph_inclist_get. Phantom edges are not given so we
* (ab)use an adjacency list data structure that lists the
* vertices connected to v by phantom edges only. */
neis = igraph_inclist_get(&inclist, v);
n = igraph_vector_size(neis);
for (i = 0; i < n; i++) {
j = (long int) VECTOR(*neis)[i];
/* We only care about tight edges */
if (!IS_TIGHT(j))
continue;
/* Have we seen the other endpoint already? */
u = IGRAPH_OTHER(graph, j, v);
if (VECTOR(parent)[u] >= 0)
continue;
debug(" Reached vertex %ld via edge %ld\n", (long)u, (long)j);
VECTOR(parent)[u] = v;
IGRAPH_CHECK(igraph_vector_push_back(&vec2, u));
w = (int) VECTOR(match)[u];
if (w == -1) {
/* u is unmatched and it is in the larger set. Therefore, we
* could improve the matching by following the parents back
* from u to the root.
*/
alternating_path_endpoint = u;
break; /* since we don't need any more endpoints that come from v */
} else {
IGRAPH_CHECK(igraph_dqueue_long_push(&q, w));
VECTOR(parent)[w] = u;
}
IGRAPH_CHECK(igraph_vector_push_back(&vec1, w));
}
/* Now do the same with the phantom edges */
neis2 = igraph_adjlist_get(&tight_phantom_edges, v);
n = igraph_vector_int_size(neis2);
for (i = 0; i < n; i++) {
u = (igraph_integer_t) VECTOR(*neis2)[i];
/* Have we seen u already? */
if (VECTOR(parent)[u] >= 0)
continue;
/* Check if the edge is really tight; it might have happened that the
* edge became non-tight in the meanwhile. We do not remove these from
* tight_phantom_edges at the moment, so we check them once again here.
*/
if (fabs(VECTOR(labels)[(long int)v] + VECTOR(labels)[(long int)u]) > eps)
continue;
debug(" Reached vertex %ld via tight phantom edge\n", (long)u);
VECTOR(parent)[u] = v;
IGRAPH_CHECK(igraph_vector_push_back(&vec2, u));
w = (int) VECTOR(match)[u];
if (w == -1) {
/* u is unmatched and it is in the larger set. Therefore, we
* could improve the matching by following the parents back
* from u to the root.
*/
alternating_path_endpoint = u;
break; /* since we don't need any more endpoints that come from v */
} else {
IGRAPH_CHECK(igraph_dqueue_long_push(&q, w));
VECTOR(parent)[w] = u;
}
IGRAPH_CHECK(igraph_vector_push_back(&vec1, w));
}
}
/* Okay; did we have an alternating path? */
if (alternating_path_endpoint != -1) {
#ifdef MATCHING_DEBUG
debug("BFS parent tree:");
igraph_vector_print(&parent);
#endif
/* Increase the size of the matching with the alternating path. */
v = alternating_path_endpoint;
u = (igraph_integer_t) VECTOR(parent)[v];
debug("Extending matching with alternating path ending in %ld.\n", (long int)v);
while (u != v) {
w = (int) VECTOR(match)[v];
if (w != -1)
VECTOR(match)[w] = -1;
VECTOR(match)[v] = u;
VECTOR(match)[v] = u;
w = (int) VECTOR(match)[u];
if (w != -1)
VECTOR(match)[w] = -1;
VECTOR(match)[u] = v;
v = (igraph_integer_t) VECTOR(parent)[u];
u = (igraph_integer_t) VECTOR(parent)[v];
}
msize++;
#ifdef MATCHING_DEBUG
debug("New matching after update:");
igraph_vector_long_print(&match);
debug("Matching size is now: %ld\n", (long)msize);
#endif
continue;
}
#ifdef MATCHING_DEBUG
debug("Vertices reachable from unmatched ones via tight edges:\n");
igraph_vector_print(&vec1);
igraph_vector_print(&vec2);
#endif
/* At this point, vec1 contains the nodes in the smaller set (A)
* reachable from unmatched nodes in A via tight edges only, while vec2
* contains the nodes in the larger set (B) reachable from unmatched
* nodes in A via tight edges only. Also, parent[i] >= 0 if node i
* is reachable */
/* Check the edges between reachable nodes in A and unreachable
* nodes in B, and find the minimum slack on them.
*
* Since the weights are positive, we do no harm if we first
* assume that there are no "real" edges between the two sets
* mentioned above and determine an upper bound for min_slack
* based on this. */
min_slack = IGRAPH_INFINITY;
min_slack_u = min_slack_v = 0;
n = igraph_vector_size(&vec1);
for (i = 0; i < no_of_nodes; i++) {
if (VECTOR(*types)[i] == smaller_set)
continue;
if (VECTOR(labels)[i] < min_slack) {
min_slack = VECTOR(labels)[i];
min_slack_v = (igraph_integer_t) i;
}
}
min_slack_2 = IGRAPH_INFINITY;
for (i = 0; i < n; i++) {
u = (igraph_integer_t) VECTOR(vec1)[i];
/* u is surely from the smaller set, but we are interested in it
* only if it is reachable from an unmatched vertex */
if (VECTOR(parent)[u] < 0)
continue;
if (VECTOR(labels)[u] < min_slack_2) {
min_slack_2 = VECTOR(labels)[u];
min_slack_u = u;
}
}
min_slack += min_slack_2;
debug("Starting approximation for min_slack = %.4f (based on vertex pair %ld--%ld)\n",
min_slack, (long int)min_slack_u, (long int)min_slack_v);
n = igraph_vector_size(&vec1);
for (i = 0; i < n; i++) {
u = (igraph_integer_t) VECTOR(vec1)[i];
/* u is a reachable node in A; get its incident edges.
*
* There are two types of incident edges: 1) real edges,
* 2) phantom edges. Phantom edges were treated earlier
* when we determined the initial value for min_slack. */
debug("Trying to expand along vertex %ld\n", (long int)u);
neis = igraph_inclist_get(&inclist, u);
k = igraph_vector_size(neis);
for (j = 0; j < k; j++) {
/* v is the vertex sitting at the other end of an edge incident
* on u; check whether it was reached */
v = IGRAPH_OTHER(graph, VECTOR(*neis)[j], u);
debug(" Edge %ld -- %ld (ID=%ld)\n", (long int)u, (long int)v, (long int)VECTOR(*neis)[j]);
if (VECTOR(parent)[v] >= 0) {
/* v was reached, so we are not interested in it */
debug(" %ld was reached, so we are not interested in it\n", (long int)v);
continue;
}
/* v is the ID of the edge from now on */
v = (igraph_integer_t) VECTOR(*neis)[j];
if (VECTOR(slack)[v] < min_slack) {
min_slack = VECTOR(slack)[v];
min_slack_u = u;
min_slack_v = IGRAPH_OTHER(graph, v, u);
}
debug(" Slack of this edge: %.4f, min slack is now: %.4f\n",
VECTOR(slack)[v], min_slack);
}
}
debug("Minimum slack: %.4f on edge %d--%d\n", min_slack, (int)min_slack_u, (int)min_slack_v);
if (min_slack > 0) {
/* Decrease the label of reachable nodes in A by min_slack.
* Also update the dual solution */
n = igraph_vector_size(&vec1);
for (i = 0; i < n; i++) {
u = (igraph_integer_t) VECTOR(vec1)[i];
VECTOR(labels)[u] -= min_slack;
neis = igraph_inclist_get(&inclist, u);
k = igraph_vector_size(neis);
for (j = 0; j < k; j++) {
debug(" Decreasing slack of edge %ld (%ld--%ld) by %.4f\n",
(long)VECTOR(*neis)[j], (long)u,
(long)IGRAPH_OTHER(graph, VECTOR(*neis)[j], u), min_slack);
VECTOR(slack)[(long int)VECTOR(*neis)[j]] -= min_slack;
}
dual -= min_slack;
}
/* Increase the label of reachable nodes in B by min_slack.
* Also update the dual solution */
n = igraph_vector_size(&vec2);
for (i = 0; i < n; i++) {
u = (igraph_integer_t) VECTOR(vec2)[i];
VECTOR(labels)[u] += min_slack;
neis = igraph_inclist_get(&inclist, u);
k = igraph_vector_size(neis);
for (j = 0; j < k; j++) {
debug(" Increasing slack of edge %ld (%ld--%ld) by %.4f\n",
(long)VECTOR(*neis)[j], (long)u,
(long)IGRAPH_OTHER(graph, (long)VECTOR(*neis)[j], u), min_slack);
VECTOR(slack)[(long int)VECTOR(*neis)[j]] += min_slack;
}
dual += min_slack;
}
}
/* Update the set of tight phantom edges.
* Note that we must do it even if min_slack is zero; the reason is that
* it can happen that min_slack is zero in the first step if there are
* isolated nodes in the input graph.
*
* TODO: this is O(n^2) here. Can we do it faster? */
for (u = 0; u < no_of_nodes; u++) {
if (VECTOR(*types)[u] != smaller_set)
continue;
for (v = 0; v < no_of_nodes; v++) {
if (VECTOR(*types)[v] == smaller_set)
continue;
if (VECTOR(labels)[(long int)u] + VECTOR(labels)[(long int)v] <= eps) {
/* Tight phantom edge found. Note that we don't have to check whether
* u and v are connected; if they were, then the slack of this edge
* would be negative. */
neis2 = igraph_adjlist_get(&tight_phantom_edges, u);
if (!igraph_vector_int_binsearch(neis2, v, &i)) {
debug("New tight phantom edge: %ld -- %ld\n", (long)u, (long)v);
IGRAPH_CHECK(igraph_vector_int_insert(neis2, i, v));
}
}
}
}
#ifdef MATCHING_DEBUG
debug("New labels:");
igraph_vector_print(&labels);
debug("Slacks after updating with min_slack:");
igraph_vector_print(&slack);
#endif
}
/* Cleanup: remove phantom edges from the matching */
for (i = 0; i < no_of_nodes; i++) {
if (VECTOR(*types)[i] != smaller_set)
continue;
if (VECTOR(match)[i] != -1) {
j = VECTOR(match)[i];
neis2 = igraph_adjlist_get(&tight_phantom_edges, i);
if (igraph_vector_int_binsearch(neis2, j, 0)) {
VECTOR(match)[i] = VECTOR(match)[j] = -1;
msize--;
}
}
}
/* Fill the output parameters */
if (matching != 0) {
IGRAPH_CHECK(igraph_vector_long_update(matching, &match));
}
if (matching_size != 0) {
*matching_size = msize;
}
if (matching_weight != 0) {
*matching_weight = 0;
for (i = 0; i < no_of_edges; i++) {
if (IS_TIGHT(i)) {
IGRAPH_CHECK(igraph_edge(graph, (igraph_integer_t) i, &u, &v));
if (VECTOR(match)[u] == v)
*matching_weight += VECTOR(*weights)[i];
}
}
}
/* Release everything */
#undef IS_TIGHT
igraph_inclist_destroy(&inclist);
igraph_adjlist_destroy(&tight_phantom_edges);
igraph_vector_destroy(&parent);
igraph_dqueue_long_destroy(&q);
igraph_vector_destroy(&labels);
igraph_vector_destroy(&vec1);
igraph_vector_destroy(&vec2);
igraph_vector_destroy(&slack);
igraph_vector_long_destroy(&match);
IGRAPH_FINALLY_CLEAN(9);
return IGRAPH_SUCCESS;
}
