public static void coarsen1(vtx_data **graph, /* array of vtx data for graph */
int nvtxs, /* number of vertices in graph */
int nedges, /* number of edges in graph */
vtx_data ***pcgraph, /* coarsened version of graph */
int *pcnvtxs, /* number of vtxs in coarsened graph */
int *pcnedges, /* number of edges in coarsened graph */
int **pv2cv, /* pointer to v2cv */
int igeom, /* dimension for geometric information */
float **coords, /* coordinates for vertices */
float **ccoords, /* coordinates for coarsened vertices */
bool useEdgeWeights /* are edge weights being used? */
)
{
double time; /* time routine is entered */
int * v2cv; /* maps from vtxs to cvtxs */
int * mflag; /* flag indicating vtx matched or not */
int cnvtxs; /* number of vtxs in coarse graph */
int nmerged; /* number of edges contracted */
time = seconds();
/* Allocate and initialize space. */
v2cv = (int *)Marshal.AllocHGlobal((nvtxs + 1) * sizeof(int));
mflag = (int *)Marshal.AllocHGlobal((nvtxs + 1) * sizeof(int));
/* Find a maximal matching in the graph. */
nmerged = maxmatch(graph, nvtxs, nedges, mflag, useEdgeWeights, igeom, coords);
match_time += seconds() - time;
/* Now construct coarser graph by contracting along matching edges. */
/* Pairs of values in mflag array indicate matched vertices. */
/* A zero value indicates that vertex is unmatched. */
/*
* makecgraph(graph, nvtxs, pcgraph, pcnvtxs, pcnedges, mflag, *pv2cv, nmerged, useEdgeWeights, igeom, coords, ccoords);
* makecgraph2(graph, nvtxs, nedges, pcgraph, pcnvtxs, pcnedges, mflag, *pv2cv, nmerged, useEdgeWeights, igeom, coords, ccoords);
*/
makev2cv(mflag, nvtxs, v2cv);
Marshal.FreeHGlobal((IntPtr)mflag);
cnvtxs = nvtxs - nmerged;
makefgraph(graph, nvtxs, nedges, pcgraph, cnvtxs, pcnedges, v2cv, useEdgeWeights, igeom, coords,
ccoords);
*pcnvtxs = cnvtxs;
*pv2cv = v2cv;
coarsen_time += seconds() - time;
}
public static bool flatten(vtx_data **graph, /* array of vtx data for graph */
int nvtxs, /* number of vertices in graph */
int nedges, /* number of edges in graph */
vtx_data ***pcgraph, /* coarsened version of graph */
int *pcnvtxs, /* number of vtxs in coarsened graph */
int *pcnedges, /* number of edges in coarsened graph */
int **pv2cv, /* pointer to v2cv */
bool useEdgeWeights, /* are edge weights being used? */
int igeom, /* dimensions of geometric data */
float **coords, /* coordinates for vertices */
float **ccoords /* coordinates for coarsened vertices */
)
{
double Thresh; /* minimal acceptable size reduction */
int * v2cv; /* map from vtxs to coarse vtxs */
int cnvtxs; /* number of vertices in flattened graph */
Thresh = .9;
v2cv = (int *)Marshal.AllocHGlobal((nvtxs + 1) * sizeof(int));
find_flat(graph, nvtxs, &cnvtxs, v2cv);
if (cnvtxs <= Thresh * nvtxs) /* Sufficient shrinkage? */
{
makefgraph(graph, nvtxs, nedges, pcgraph, cnvtxs, pcnedges, v2cv, useEdgeWeights, igeom, coords,
ccoords);
*pcnvtxs = cnvtxs;
*pv2cv = v2cv;
return(true);
}
/* Not worth bothering */
Marshal.FreeHGlobal((IntPtr)v2cv);
return(false);
}
/* Change from a FORTRAN graph style to our graph data structure. */
public static bool reformat(int *start, /* start of edge list for each vertex */
int *adjacency, /* edge list data */
int nvtxs, /* number of vertices in graph */
int *pnedges, /* ptr to number of edges in graph */
int *vwgts, /* weights for all vertices */
float *ewgts, /* weights for all edges */
vtx_data ***pgraph /* ptr to array of vtx data for graph */
)
{
Trace.WriteLine($"<Entering {nameof(reformat)}>");
vtx_data **graph = null; /* array of vtx data for graph */
vtx_data * links = null; /* space for data for all vtxs */
int * edges = null; /* space for all adjacency lists */
float * eweights = null; /* space for all edge weights */
int * eptr = null; /* steps through adjacency list */
int * eptr_save = null; /* saved index into adjacency list */
float * wptr = null; /* steps through edge weights list */
int self_edge; /* number of self loops detected */
int size; /* length of all edge lists */
double sum; /* sum of edge weights for a vtx */
int i, j; /* loop counters */
var useEdgeWeights = (ewgts != null); /* are edge weights being used? */
var using_vwgts = (vwgts != null); /* are vertex weights being used? */
graph = (vtx_data **)Marshal.AllocHGlobal((nvtxs + 1) * sizeof(vtx_data *));
*pgraph = graph;
if (graph == null)
{
return(true);
}
graph[1] = null;
/* Set up all the basic data structure for the vertices. */
/* Replace many small mallocs by a few large ones. */
links = (vtx_data *)Marshal.AllocHGlobal((nvtxs) * sizeof(vtx_data));
if (links == null)
{
return(true);
}
for (i = 1; i <= nvtxs; i++)
{
graph[i] = links++;
}
graph[1]->edges = null;
graph[1]->ewgts = null;
/* Now fill in all the data fields. */
if (start != null)
{
*pnedges = start[nvtxs] / 2;
}
else
{
*pnedges = 0;
}
size = 2 * (*pnedges) + nvtxs;
edges = (int *)Marshal.AllocHGlobal(size * sizeof(int));
if (edges == null)
{
return(true);
}
if (useEdgeWeights)
{
eweights = (float *)Marshal.AllocHGlobal(size * sizeof(float));
if (eweights == null)
{
return(true);
}
}
if (start != null)
{
eptr = adjacency + start[0];
wptr = ewgts;
}
self_edge = 0;
for (i = 1; i <= nvtxs; i++)
{
if (using_vwgts)
{
graph[i]->vwgt = *(vwgts++);
}
else
{
graph[i]->vwgt = 1;
}
if (start != null)
{
size = start[i] - start[i - 1];
}
else
{
size = 0;
}
graph[i]->nedges = size + 1;
graph[i]->edges = edges;
*edges++ = i;
eptr_save = eptr;
for (j = size; j != 0; j--)
{
if (*eptr != i)
{
*edges++ = *eptr++;
}
else
{
/* Self edge, skip it. */
//if (self_edge == 0)
{
Trace.WriteLine($"WARNING: Self edge ({i:d},{i:d}) being ignored");
}
++self_edge;
eptr++;
--(graph[i]->nedges);
--(*pnedges);
}
}
if (useEdgeWeights)
{
graph[i]->ewgts = eweights;
eweights++;
sum = 0;
for (j = size; j != 0; j--)
{
if (*eptr_save++ != i)
{
sum += *wptr;
*eweights++ = *wptr++;
}
else
{
wptr++;
}
}
graph[i]->ewgts[0] = (float)-sum;
}
else
{
graph[i]->ewgts = null;
}
}
if (self_edge > 1)
{
Trace.WriteLine($"WARNING: {self_edge:d} self edges were detected and ignored");
}
return(false);
}
/* Construct a weighted quotient graph representing the inter-set communication. */
public static bool make_comm_graph(vtx_data ***pcomm_graph, /* graph for communication requirements */
vtx_data **graph, /* graph data structure */
int nvtxs, /* number of vertices in graph */
bool useEdgeWeights, /* are edge weights being used? */
int *assign, /* current assignment */
int nsets_tot /* total number of sets */
)
{
float ewgt; /* edge weight in graph */
int ** edges_list = null; /* lists of edges */
int ** ewgts_list = null; /* lists of edge weights */
int * edges = null; /* edges in communication graph */
int * ewgts = null; /* edge weights in communication graph */
float *float_ewgts = null; /* edge weights in floating point */
int * adj_sets = null; /* weights connecting sets */
int * order = null; /* ordering of vertices by set */
int * sizes = null; /* sizes of different sets */
int * start = null; /* pointers into adjacency data */
int * adjacency = null; /* array with all the edge info */
int * eptr = null; /* loops through edges in graph */
int * ewptr = null; /* loop through edge weights */
int set, set2; /* sets two vertices belong to */
int vertex; /* vertex in graph */
int ncomm_edges; /* number of edges in communication graph */
bool error; /* out of space? */
int i, j; /* loop counters */
error = true;
*pcomm_graph = null;
/* First construct some mappings to ease later manipulations. */
sizes = (int *)Marshal.AllocHGlobal(nsets_tot * sizeof(int));
if (sizes == null)
{
goto skip;
}
for (i = 0; i < nsets_tot; i++)
{
sizes[i] = 0;
}
for (i = 1; i <= nvtxs; i++)
{
++(sizes[assign[i]]);
}
/* Now make sizes reflect the start index for each set. */
for (i = 1; i < nsets_tot - 1; i++)
{
sizes[i] += sizes[i - 1];
}
for (i = nsets_tot - 1; i != 0; i--)
{
sizes[i] = sizes[i - 1];
}
sizes[0] = 0;
/* Now construct list of all vertices in set 0, all in set 1, etc. */
order = (int *)Marshal.AllocHGlobal(nvtxs * sizeof(int));
if (order == null)
{
goto skip;
}
for (i = 1; i <= nvtxs; i++)
{
set = assign[i];
order[sizes[set]] = i;
++sizes[set];
}
/* For each set, find total weight to all neighbors. */
adj_sets = (int *)Marshal.AllocHGlobal(nsets_tot * sizeof(int));
edges_list = (int **)Marshal.AllocHGlobal(nsets_tot * sizeof(int *));
ewgts_list = (int **)Marshal.AllocHGlobal(nsets_tot * sizeof(int *));
start = (int *)Marshal.AllocHGlobal((nsets_tot + 1) * sizeof(int));
if (adj_sets == null || edges_list == null || ewgts_list == null || start == null)
{
goto skip;
}
start[0] = 0;
ewgt = 1;
ncomm_edges = 0;
for (set = 0; set < nsets_tot; set++)
{
edges_list[set] = null;
ewgts_list[set] = null;
}
for (set = 0; set < nsets_tot; set++)
{
for (i = 0; i < nsets_tot; i++)
{
adj_sets[i] = 0;
}
for (i = (set != 0 ? sizes[set - 1] : 0); i < sizes[set]; i++)
{
vertex = order[i];
for (j = 1; j < graph[vertex]->nedges; j++)
{
set2 = assign[graph[vertex]->edges[j]];
if (set2 != set)
{
if (useEdgeWeights)
{
ewgt = graph[vertex]->ewgts[j];
}
adj_sets[set2] += (int)ewgt;
}
}
}
/* Now save adj_sets data to later construct graph. */
j = 0;
for (i = 0; i < nsets_tot; i++)
{
if (adj_sets[i] != 0)
{
j++;
}
}
ncomm_edges += j;
start[set + 1] = ncomm_edges;
if (j != 0)
{
edges_list[set] = edges = (int *)Marshal.AllocHGlobal(j * sizeof(int));
ewgts_list[set] = ewgts = (int *)Marshal.AllocHGlobal(j * sizeof(int));
if (edges == null || ewgts == null)
{
goto skip;
}
}
j = 0;
for (i = 0; i < nsets_tot; i++)
{
if (adj_sets[i] != 0)
{
edges[j] = i + 1;
ewgts[j] = adj_sets[i];
j++;
}
}
}
Marshal.FreeHGlobal((IntPtr)adj_sets);
Marshal.FreeHGlobal((IntPtr)order);
Marshal.FreeHGlobal((IntPtr)sizes);
adj_sets = order = sizes = null;
/* I now need to pack the edge and weight data into single arrays. */
adjacency = (int *)Marshal.AllocHGlobal((ncomm_edges + 1) * sizeof(int));
float_ewgts = (float *)Marshal.AllocHGlobal((ncomm_edges + 1) * sizeof(float));
if (adjacency == null || float_ewgts == null)
{
goto skip;
}
for (set = 0; set < nsets_tot; set++)
{
j = start[set];
eptr = edges_list[set];
ewptr = ewgts_list[set];
for (i = start[set]; i < start[set + 1]; i++)
{
adjacency[i] = eptr[i - j];
float_ewgts[i] = ewptr[i - j];
}
if (start[set] != start[set + 1])
{
Marshal.FreeHGlobal((IntPtr)edges_list[set]);
Marshal.FreeHGlobal((IntPtr)ewgts_list[set]);
}
}
Marshal.FreeHGlobal((IntPtr)edges_list);
Marshal.FreeHGlobal((IntPtr)ewgts_list);
edges_list = ewgts_list = null;
error =
reformat(start, adjacency, nsets_tot, &ncomm_edges, (int *)null, float_ewgts, pcomm_graph);
skip:
Marshal.FreeHGlobal((IntPtr)adj_sets);
Marshal.FreeHGlobal((IntPtr)order);
Marshal.FreeHGlobal((IntPtr)sizes);
if (edges_list != null)
{
for (set = nsets_tot - 1; set >= 0; set--)
{
if (edges_list[set] != null)
{
Marshal.FreeHGlobal((IntPtr)edges_list[set]);
}
}
Marshal.FreeHGlobal((IntPtr)edges_list);
}
if (ewgts_list != null)
{
for (set = nsets_tot - 1; set >= 0; set--)
{
if (ewgts_list[set] != null)
{
Marshal.FreeHGlobal((IntPtr)ewgts_list[set]);
}
}
Marshal.FreeHGlobal((IntPtr)ewgts_list);
}
Marshal.FreeHGlobal((IntPtr)float_ewgts);
Marshal.FreeHGlobal((IntPtr)adjacency);
Marshal.FreeHGlobal((IntPtr)start);
return(error);
}
public static void makefgraph(vtx_data **graph, /* array of vtx data for graph */
int nvtxs, /* number of vertices in graph */
int nedges, /* number of edges in graph */
vtx_data ***pcgraph, /* coarsened version of graph */
int cnvtxs, /* number of vtxs in coarsened graph */
int *pcnedges, /* number of edges in coarsened graph */
int *v2cv, /* mapping from vtxs to coarsened vtxs */
bool useEdgeWeights, /* are edge weights being used? */
int igeom, /* dimensions of geometric data */
float **coords, /* coordinates for vertices */
float **ccoords /* coordinates for coarsened vertices */
)
{
vtx_data **cgraph = null; /* coarsened version of graph */
vtx_data * links = null; /* space for all the vertex data */
vtx_data **gptr = null; /* loops through cgraph */
vtx_data * cgptr = null; /* loops through cgraph */
int * iptr = null; /* loops through integer arrays */
int * seenflag = null; /* flags for vtxs already put in edge list */
int * sptr = null; /* loops through seenflags */
int * cv2v_vals = null; /* vtxs corresponding to each cvtx */
int * cv2v_ptrs = null; /* indices into cv2v_vals */
float * eweights = null; /* space for edge weights in coarsened graph */
float * ewptr = null; /* loops through eweights */
float * fptr = null; /* loops through eweights */
float ewgt; /* edge weight */
double ewgt_sum; /* sum of edge weights */
double time; /* timing parameters */
int nseen; /* number of edges of coarse graph seen so far */
int vtx; /* vertex in original graph */
int cvtx; /* vertex in coarse graph */
int cnedges; /* twice number of edges in coarsened graph */
int neighbor; /* neighboring vertex */
int size; /* space needed for coarsened graph */
int * edges = null; /* space for edges in coarsened graph */
int * eptr = null; /* loops through edges data structure */
int cneighbor; /* neighboring vertex number in coarsened graph */
int i, j; /* loop counters */
/* Compute the number of vertices and edges in the coarsened graph, */
/* and construct start pointers into coarsened edge array. */
time = seconds();
/* Construct mapping from original graph vtxs to coarsened graph vtxs. */
cv2v_vals = (int *)Marshal.AllocHGlobal(nvtxs * sizeof(int));
cv2v_ptrs = (int *)Marshal.AllocHGlobal((cnvtxs + 2) * sizeof(int));
makecv2v(nvtxs, cnvtxs, v2cv, cv2v_vals, cv2v_ptrs);
/* Compute an upper bound on the number of coarse graph edges. */
cnedges = nedges - (nvtxs - cnvtxs);
/* Now allocate space for the new graph. Overallocate and realloc later. */
*pcgraph = cgraph = (vtx_data **)Marshal.AllocHGlobal((cnvtxs + 1) * sizeof(vtx_data *));
links = (vtx_data *)Marshal.AllocHGlobal(cnvtxs * sizeof(vtx_data));
size = 2 * cnedges + cnvtxs;
edges = (int *)Marshal.AllocHGlobal(size * sizeof(int));
if (COARSEN_EWGTS)
{
ewptr = eweights = (float *)Marshal.AllocHGlobal(size * sizeof(float));
}
/* Zero all the seen flags. */
seenflag = (int *)Marshal.AllocHGlobal((cnvtxs + 1) * sizeof(int));
sptr = seenflag;
for (i = cnvtxs; i != 0; i--)
{
*(++sptr) = 0;
}
/* Use the renumbering to fill in the edge lists for the new graph. */
cnedges = 0;
eptr = edges;
ewgt = 1;
sptr = cv2v_vals;
for (cvtx = 1; cvtx <= cnvtxs; cvtx++)
{
nseen = 1;
cgptr = cgraph[cvtx] = links++;
if (COARSEN_VWGTS)
{
cgptr->vwgt = 0;
}
else
{
cgptr->vwgt = 1;
}
eptr[0] = cvtx;
cgptr->edges = eptr;
if (COARSEN_EWGTS)
{
cgptr->ewgts = ewptr;
}
else
{
cgptr->ewgts = null;
}
ewgt_sum = 0;
for (i = cv2v_ptrs[cvtx + 1] - cv2v_ptrs[cvtx]; i != 0; i--)
{
vtx = *sptr++;
iptr = graph[vtx]->edges;
if (useEdgeWeights)
{
fptr = graph[vtx]->ewgts;
}
for (j = graph[vtx]->nedges - 1; j != 0; j--)
{
neighbor = *(++iptr);
cneighbor = v2cv[neighbor];
if (cneighbor != cvtx)
{
if (useEdgeWeights)
{
ewgt = *(++fptr);
}
ewgt_sum += ewgt;
/* Seenflags being used as map from cvtx to index. */
if (seenflag[cneighbor] == 0)
{
/* New neighbor. */
cgptr->edges[nseen] = cneighbor;
if (COARSEN_EWGTS)
{
cgptr->ewgts[nseen] = ewgt;
}
seenflag[cneighbor] = nseen++;
}
else
{
/* Already seen neighbor. */
if (COARSEN_EWGTS)
{
cgptr->ewgts[seenflag[cneighbor]] += ewgt;
}
}
}
else if (useEdgeWeights)
{
++fptr;
}
}
}
/* Now clear the seenflag values. */
iptr = cgptr->edges;
for (j = nseen - 1; j != 0; j--)
{
seenflag[*(++iptr)] = 0;
}
if (COARSEN_EWGTS)
{
cgptr->ewgts[0] = (float)-ewgt_sum;
}
/* Increment pointers into edges list. */
cgptr->nedges = nseen;
eptr += nseen;
if (COARSEN_EWGTS)
{
ewptr += nseen;
}
cnedges += nseen - 1;
}
Marshal.FreeHGlobal((IntPtr)seenflag);
/* Form new vertex weights by adding those from contracted edges. */
if (COARSEN_VWGTS)
{
gptr = graph;
for (i = 1; i <= nvtxs; i++)
{
cgraph[v2cv[i]]->vwgt += (*(++gptr))->vwgt;
}
}
/* Reduce arrays to actual sizes */
cnedges /= 2;
size = 2 * cnedges + cnvtxs;
eptr = edges;
edges = (int *)Marshal.ReAllocHGlobal((IntPtr)edges, (IntPtr)(size * sizeof(int)));
if (eptr != edges)
{
/* Need to reset pointers in graph. */
for (i = 1; i <= cnvtxs; i++)
{
cgraph[i]->edges = edges;
edges += cgraph[i]->nedges;
}
}
if (COARSEN_EWGTS)
{
ewptr = eweights;
eweights = (float *)Marshal.ReAllocHGlobal((IntPtr)eweights, (IntPtr)(size * sizeof(float)));
if (ewptr != eweights)
{
/* Need to reset pointers in graph. */
for (i = 1; i <= cnvtxs; i++)
{
cgraph[i]->ewgts = eweights;
eweights += cgraph[i]->nedges;
}
}
}
/* If desired, make new vtx coordinates = center-of-mass of their parents. */
if (coords != null && ccoords != null && igeom > 0)
{
makeccoords(graph, cnvtxs, cv2v_ptrs, cv2v_vals, igeom, coords, ccoords);
}
*pcnedges = cnedges;
Marshal.FreeHGlobal((IntPtr)cv2v_ptrs);
Marshal.FreeHGlobal((IntPtr)cv2v_vals);
if (DEBUG_COARSEN)
{
Trace.WriteLine($" Coarse graph has {cnvtxs:D} vertices and {cnedges:D} edges");
}
make_cgraph_time += seconds() - time;
}