static Multilevel Multilevel_establish(Multilevel grid, Multilevel_control ctrl){
Multilevel cgrid;
int coarsen_scheme_used;
real *cnode_weights = NULL;
SparseMatrix P, R, A, cA, D, cD;
#ifdef DEBUG_PRINT
if (Verbose) {
print_padding(grid->level);
fprintf(stderr, "level -- %d, n = %d, nz = %d nz/n = %f\n", grid->level, grid->n, grid->A->nz, grid->A->nz/(double) grid->n);
}
#endif
A = grid->A;
D = grid->D;
if (grid->level >= ctrl->maxlevel - 1) {
#ifdef DEBUG_PRINT
if (Verbose) {
print_padding(grid->level);
fprintf(stderr, " maxlevel reached, coarsening stops\n");
}
#endif
return grid;
}
Multilevel_coarsen(A, &cA, D, &cD, grid->node_weights, &cnode_weights, &P, &R, ctrl, &coarsen_scheme_used);
if (!cA) return grid;
cgrid = Multilevel_init(cA, cD, cnode_weights);
grid->next = cgrid;
cgrid->coarsen_scheme_used = coarsen_scheme_used;
cgrid->level = grid->level + 1;
cgrid->n = cA->m;
cgrid->A = cA;
cgrid->D = cD;
cgrid->P = P;
grid->R = R;
cgrid->prev = grid;
cgrid = Multilevel_establish(cgrid, ctrl);
return grid;
}
static void Multilevel_coarsen(SparseMatrix A, SparseMatrix *cA, real *node_wgt, real **cnode_wgt,
SparseMatrix *P, SparseMatrix *R, Multilevel_control ctrl, int *coarsen_scheme_used){
int *matching = NULL, nmatch, nc, nzc, n, i;
int *irn = NULL, *jcn = NULL, *ia = NULL, *ja = NULL;
real *val = NULL;
SparseMatrix B = NULL;
int *vset = NULL, nvset, ncov, j;
int *cluster, *clusterp, ncluster;
assert(A->m == A->n);
*cA = NULL;
*P = NULL;
*R = NULL;
n = A->m;
*coarsen_scheme_used = ctrl->coarsen_scheme;
switch (ctrl->coarsen_scheme){
case COARSEN_HYBRID:
#ifdef DEBUG_PRINT
if (Verbose)
fprintf(stderr, "hybrid scheme, try COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_EDGE_PERNODE_LEAVES_FIRST first\n");
#endif
*coarsen_scheme_used = ctrl->coarsen_scheme = COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_EDGE_PERNODE_LEAVES_FIRST;
Multilevel_coarsen(A, cA, node_wgt, cnode_wgt, P, R, ctrl, coarsen_scheme_used);
if (!(*cA)) {
#ifdef DEBUG_PRINT
if (Verbose)
fprintf(stderr, "switching to COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_EDGE_PERNODE_SUPERNODES_FIRST\n");
#endif
*coarsen_scheme_used = ctrl->coarsen_scheme = COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_EDGE_PERNODE_SUPERNODES_FIRST;
Multilevel_coarsen(A, cA, node_wgt, cnode_wgt, P, R, ctrl, coarsen_scheme_used);
}
if (!(*cA)) {
#ifdef DEBUG_PRINT
if (Verbose)
fprintf(stderr, "switching to COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_CLUSTER_PERNODE_LEAVES_FIRST\n");
#endif
*coarsen_scheme_used = ctrl->coarsen_scheme = COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_CLUSTER_PERNODE_LEAVES_FIRST;
Multilevel_coarsen(A, cA, node_wgt, cnode_wgt, P, R, ctrl, coarsen_scheme_used);
}
if (!(*cA)) {
#ifdef DEBUG_PRINT
if (Verbose)
fprintf(stderr, "switching to COARSEN_INDEPENDENT_VERTEX_SET\n");
#endif
*coarsen_scheme_used = ctrl->coarsen_scheme = COARSEN_INDEPENDENT_VERTEX_SET;
Multilevel_coarsen(A, cA, node_wgt, cnode_wgt, P, R, ctrl, coarsen_scheme_used);
}
if (!(*cA)) {
#ifdef DEBUG_PRINT
if (Verbose)
fprintf(stderr, "switching to COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_EDGE_PERNODE\n");
#endif
*coarsen_scheme_used = ctrl->coarsen_scheme = COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_EDGE_PERNODE;
Multilevel_coarsen(A, cA, node_wgt, cnode_wgt, P, R, ctrl, coarsen_scheme_used);
}
ctrl->coarsen_scheme = COARSEN_HYBRID;
break;
case COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_EDGE_PERNODE_SUPERNODES_FIRST:
case COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_CLUSTER_PERNODE_LEAVES_FIRST:
case COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_EDGE_PERNODE_LEAVES_FIRST:
if (ctrl->coarsen_scheme == COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_EDGE_PERNODE_LEAVES_FIRST) {
maximal_independent_edge_set_heavest_edge_pernode_leaves_first(A, ctrl->randomize, &cluster, &clusterp, &ncluster);
} else if (ctrl->coarsen_scheme == COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_EDGE_PERNODE_SUPERNODES_FIRST) {
maximal_independent_edge_set_heavest_edge_pernode_supernodes_first(A, ctrl->randomize, &cluster, &clusterp, &ncluster);
} else {
maximal_independent_edge_set_heavest_cluster_pernode_leaves_first(A, 4, ctrl->randomize, &cluster, &clusterp, &ncluster);
}
assert(ncluster <= n);
nc = ncluster;
if (nc > ctrl->min_coarsen_factor*n || nc < ctrl->minsize) {
#ifdef DEBUG_PRINT
if (Verbose)
fprintf(stderr, "nc = %d, nf = %d, minsz = %d, coarsen_factor = %f coarsening stops\n",nc, n, ctrl->minsize, ctrl->min_coarsen_factor);
#endif
goto RETURN;
}
irn = N_GNEW(n,int);
jcn = N_GNEW(n,int);
val = N_GNEW(n,real);
nzc = 0;
for (i = 0; i < ncluster; i++){
for (j = clusterp[i]; j < clusterp[i+1]; j++){
assert(clusterp[i+1] > clusterp[i]);
irn[nzc] = cluster[j];
jcn[nzc] = i;
val[nzc++] = 1.;
}
}
assert(nzc == n);
*P = SparseMatrix_from_coordinate_arrays(nzc, n, nc, irn, jcn, (void *) val, MATRIX_TYPE_REAL);
*R = SparseMatrix_transpose(*P);
B = SparseMatrix_multiply(*R, A);
if (!B) goto RETURN;
*cA = SparseMatrix_multiply(B, *P);
if (!*cA) goto RETURN;
SparseMatrix_multiply_vector(*R, node_wgt, cnode_wgt, FALSE);
*R = SparseMatrix_divide_row_by_degree(*R);
SparseMatrix_set_symmetric(*cA);
SparseMatrix_set_pattern_symmetric(*cA);
*cA = SparseMatrix_remove_diagonal(*cA);
break;
case COARSEN_INDEPENDENT_EDGE_SET:
maximal_independent_edge_set(A, ctrl->randomize, &matching, &nmatch);
case COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_EDGE_PERNODE:
if (ctrl->coarsen_scheme == COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_EDGE_PERNODE)
maximal_independent_edge_set_heavest_edge_pernode(A, ctrl->randomize, &matching, &nmatch);
case COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_EDGE_PERNODE_DEGREE_SCALED:
if (ctrl->coarsen_scheme == COARSEN_INDEPENDENT_EDGE_SET_HEAVEST_EDGE_PERNODE_DEGREE_SCALED)
maximal_independent_edge_set_heavest_edge_pernode_scaled(A, ctrl->randomize, &matching, &nmatch);
nc = nmatch;
if (nc > ctrl->min_coarsen_factor*n || nc < ctrl->minsize) {
#ifdef DEBUG_PRINT
if (Verbose)
fprintf(stderr, "nc = %d, nf = %d, minsz = %d, coarsen_factor = %f coarsening stops\n",nc, n, ctrl->minsize, ctrl->min_coarsen_factor);
#endif
goto RETURN;
}
irn = N_GNEW(n,int);
jcn = N_GNEW(n,int);
val = N_GNEW(n,real);
nzc = 0; nc = 0;
for (i = 0; i < n; i++){
if (matching[i] >= 0){
if (matching[i] == i){
irn[nzc] = i;
jcn[nzc] = nc;
val[nzc++] = 1.;
} else {
irn[nzc] = i;
jcn[nzc] = nc;
val[nzc++] = 1;
irn[nzc] = matching[i];
jcn[nzc] = nc;
val[nzc++] = 1;
matching[matching[i]] = -1;
}
nc++;
matching[i] = -1;
}
}
assert(nc == nmatch);
assert(nzc == n);
*P = SparseMatrix_from_coordinate_arrays(nzc, n, nc, irn, jcn, (void *) val, MATRIX_TYPE_REAL);
*R = SparseMatrix_transpose(*P);
B = SparseMatrix_multiply(*R, A);
if (!B) goto RETURN;
*cA = SparseMatrix_multiply(B, *P);
if (!*cA) goto RETURN;
SparseMatrix_multiply_vector(*R, node_wgt, cnode_wgt, FALSE);
*R = SparseMatrix_divide_row_by_degree(*R);
SparseMatrix_set_symmetric(*cA);
SparseMatrix_set_pattern_symmetric(*cA);
*cA = SparseMatrix_remove_diagonal(*cA);
break;
case COARSEN_INDEPENDENT_VERTEX_SET:
case COARSEN_INDEPENDENT_VERTEX_SET_RS:
if (ctrl->coarsen_scheme == COARSEN_INDEPENDENT_VERTEX_SET){
maximal_independent_vertex_set(A, ctrl->randomize, &vset, &nvset, &nzc);
} else {
maximal_independent_vertex_set_RS(A, ctrl->randomize, &vset, &nvset, &nzc);
}
ia = A->ia;
ja = A->ja;
nc = nvset;
if (nc > ctrl->min_coarsen_factor*n || nc < ctrl->minsize) {
#ifdef DEBUG_PRINT
if (Verbose)
fprintf(stderr, "nc = %d, nf = %d, minsz = %d, coarsen_factor = %f coarsening stops\n",nc, n, ctrl->minsize, ctrl->min_coarsen_factor);
#endif
goto RETURN;
}
irn = N_GNEW(nzc,int);
jcn = N_GNEW(nzc,int);
val = N_GNEW(nzc,real);
nzc = 0;
for (i = 0; i < n; i++){
if (vset[i] == MAX_IND_VTX_SET_F){
ncov = 0;
for (j = ia[i]; j < ia[i+1]; j++){
if (vset[ja[j]] >= MAX_IND_VTX_SET_C){
ncov++;
}
}
assert(ncov > 0);
for (j = ia[i]; j < ia[i+1]; j++){
if (vset[ja[j]] >= MAX_IND_VTX_SET_C){
irn[nzc] = i;
jcn[nzc] = vset[ja[j]];
val[nzc++] = 1./(double) ncov;
}
}
} else {
assert(vset[i] >= MAX_IND_VTX_SET_C);
irn[nzc] = i;
jcn[nzc] = vset[i];
val[nzc++] = 1.;
}
}
*P = SparseMatrix_from_coordinate_arrays(nzc, n, nc, irn, jcn, (void *) val, MATRIX_TYPE_REAL);
*R = SparseMatrix_transpose(*P);
B = SparseMatrix_multiply(*R, A);
if (!B) goto RETURN;
*cA = SparseMatrix_multiply(B, *P);
if (!*cA) goto RETURN;
SparseMatrix_multiply_vector(*R, node_wgt, cnode_wgt, FALSE);
SparseMatrix_set_symmetric(*cA);
SparseMatrix_set_pattern_symmetric(*cA);
*cA = SparseMatrix_remove_diagonal(*cA);
break;
default:
goto RETURN;
}
RETURN:
if (matching) FREE(matching);
if (vset) FREE(vset);
if (irn) FREE(irn);
if (jcn) FREE(jcn);
if (val) FREE(val);
if (B) SparseMatrix_delete(B);
}
