[PATCH] use a different starting vector for igraph_community_leading_eigenvector...

Gbp-Pq: Name different_starting_vector.patch

diff --git a/src/community.c b/src/community.c
index 337067934c8b31236579719eebd9dd7b117b9c5d..5e836dcbcb3d4d3c569a6b60a270c3944b3fd1a9 100644 (file)
--- a/src/community.c
+++ b/src/community.c
@@ -1736,13 +1736,19 @@ int igraph_community_leading_eigenvector(const igraph_t *graph,
       igraph_set_error_handler(errh);
       igraph_set_warning_handler(warnh);
       if (options->nconv < 1) {
-       /* Call again, from a fixed starting point */
+       /* Call again from a fixed starting point. Note that we cannot use a
+        * fixed all-1 starting vector as sometimes ARPACK would return a
+        * 'starting vector is zero' error -- this is of course not true but
+        * it's a result of ARPACK >= 3.6.3 trying to force the starting vector
+        * into the range of OP (i.e. the matrix being solved). The initial
+        * vector we use here seems to work, but I have no theoretical argument
+        * for its usage; it just happens to work. */
        options->start=1;
        options->info=0;
        options->ncv=0;
        options->lworkl = 0;    /* we surely have enough space */
        for (i=0; i < options->n ; i++) {
-         storage.resid[i] = 1;
+         storage.resid[i] = i % 2 ? 1 : -1;
        }
        IGRAPH_CHECK(igraph_arpack_rssolve(arpcb2, &extra, options, &storage,
                                           /*values=*/ 0, /*vectors=*/ 0));
@@ -1774,12 +1780,13 @@ int igraph_community_leading_eigenvector(const igraph_t *graph,
                            /*values=*/ 0, /*vectors=*/ 0);
       igraph_set_error_handler(errh);
       if (options->nconv < 1) {
-       /* Call again from a fixed starting point */
+       /* Call again from a fixed starting point. See the comment a few lines
+        * above about the exact choice of this starting vector */
        options->start=1;
        options->info=0;
        options->ncv=0;
        options->lworkl = 0;    /* we surely have enough space */
-       for (i=0; i < options->n; i++) { storage.resid[i] = 1; }
+       for (i=0; i < options->n; i++) { storage.resid[i] = i % 2 ? 1 : -1; }
        IGRAPH_CHECK(igraph_arpack_rssolve(arpcb1, &extra, options, &storage, 
                                           /*values=*/ 0, /*vectors=*/ 0));
        options->start=0;