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/*
* Copyright 1997, Regents of the University of Minnesota
*
* smbfactor.c
*
* This file performs the symbolic factorization of a matrix
*
* Started 8/1/97
* George
*
* $Id: smbfactor.c 10154 2011-06-09 21:27:35Z karypis $
*
*/
#include "metisbin.h"
/*************************************************************************/
/*! This function sets up data structures for fill-in computations */
/*************************************************************************/
void ComputeFillIn(graph_t *graph, idx_t *perm, idx_t *iperm,
size_t *r_maxlnz, size_t *r_opc)
{
idx_t i, j, k, nvtxs, maxlnz, maxsub;
idx_t *xadj, *adjncy;
idx_t *xlnz, *xnzsub, *nzsub;
size_t opc;
/*
printf("\nSymbolic factorization... --------------------------------------------\n");
*/
nvtxs = graph->nvtxs;
xadj = graph->xadj;
adjncy = graph->adjncy;
maxsub = 8*(nvtxs+xadj[nvtxs]);
/* Relabel the vertices so that it starts from 1 */
for (i=0; i<xadj[nvtxs]; i++)
adjncy[i]++;
for (i=0; i<nvtxs+1; i++)
xadj[i]++;
for (i=0; i<nvtxs; i++) {
iperm[i]++;
perm[i]++;
}
/* Allocate the required memory */
xlnz = imalloc(nvtxs+2, "ComputeFillIn: xlnz");
xnzsub = imalloc(nvtxs+2, "ComputeFillIn: xnzsub");
nzsub = imalloc(maxsub+1, "ComputeFillIn: nzsub");
/* Call sparspak's routine. */
if (smbfct(nvtxs, xadj, adjncy, perm, iperm, xlnz, &maxlnz, xnzsub, nzsub, &maxsub)) {
printf("Realocating nzsub...\n");
gk_free((void **)&nzsub, LTERM);
maxsub *= 2;
nzsub = imalloc(maxsub+1, "ComputeFillIn: nzsub");
if (smbfct(nvtxs, xadj, adjncy, perm, iperm, xlnz, &maxlnz, xnzsub, nzsub, &maxsub))
errexit("MAXSUB is too small!");
}
for (i=0; i<nvtxs; i++)
xlnz[i]--;
for (opc=0, i=0; i<nvtxs; i++)
opc += (xlnz[i+1]-xlnz[i])*(xlnz[i+1]-xlnz[i]) - (xlnz[i+1]-xlnz[i]);
*r_maxlnz = maxlnz;
*r_opc = opc;
gk_free((void **)&xlnz, &xnzsub, &nzsub, LTERM);
/* Relabel the vertices so that it starts from 0 */
for (i=0; i<nvtxs; i++) {
iperm[i]--;
perm[i]--;
}
for (i=0; i<nvtxs+1; i++)
xadj[i]--;
for (i=0; i<xadj[nvtxs]; i++)
adjncy[i]--;
}
/*************************************************************************/
/*!
PURPOSE - THIS ROUTINE PERFORMS SYMBOLIC FACTORIZATION
ON A PERMUTED LINEAR SYSTEM AND IT ALSO SETS UP THE
COMPRESSED DATA STRUCTURE FOR THE SYSTEM.
INPUT PARAMETERS -
NEQNS - NUMBER OF EQUATIONS.
(XADJ, ADJNCY) - THE ADJACENCY STRUCTURE.
(PERM, INVP) - THE PERMUTATION VECTOR AND ITS INVERSE.
UPDATED PARAMETERS -
MAXSUB - SIZE OF THE SUBSCRIPT ARRAY NZSUB. ON RETURN,
IT CONTAINS THE NUMBER OF SUBSCRIPTS USED
OUTPUT PARAMETERS -
XLNZ - INDEX INTO THE NONZERO STORAGE VECTOR LNZ.
(XNZSUB, NZSUB) - THE COMPRESSED SUBSCRIPT VECTORS.
MAXLNZ - THE NUMBER OF NONZEROS FOUND.
*/
/*************************************************************************/
idx_t smbfct(idx_t neqns, idx_t *xadj, idx_t *adjncy, idx_t *perm, idx_t *invp,
idx_t *xlnz, idx_t *maxlnz, idx_t *xnzsub, idx_t *nzsub,
idx_t *maxsub)
{
/* Local variables */
idx_t node, rchm, mrgk, lmax, i, j, k, m, nabor, nzbeg, nzend;
idx_t kxsub, jstop, jstrt, mrkflg, inz, knz, flag;
idx_t *mrglnk, *marker, *rchlnk;
rchlnk = ismalloc(neqns+1, 0, "smbfct: rchlnk");
marker = ismalloc(neqns+1, 0, "smbfct: marker");
mrglnk = ismalloc(neqns+1, 0, "smbfct: mgrlnk");
/* Parameter adjustments */
--marker;
--mrglnk;
--rchlnk;
--nzsub;
--xnzsub;
--xlnz;
--invp;
--perm;
--adjncy;
--xadj;
/* Function Body */
flag = 0;
nzbeg = 1;
nzend = 0;
xlnz[1] = 1;
/* FOR EACH COLUMN KNZ COUNTS THE NUMBER OF NONZEROS IN COLUMN K ACCUMULATED IN RCHLNK. */
for (k=1; k<=neqns; k++) {
xnzsub[k] = nzend;
node = perm[k];
knz = 0;
mrgk = mrglnk[k];
mrkflg = 0;
marker[k] = k;
if (mrgk != 0) {
assert(mrgk > 0 && mrgk <= neqns);
marker[k] = marker[mrgk];
}
if (xadj[node] >= xadj[node+1]) {
xlnz[k+1] = xlnz[k];
continue;
}
/* USE RCHLNK TO LINK THROUGH THE STRUCTURE OF A(*,K) BELOW DIAGONAL */
assert(k <= neqns && k > 0);
rchlnk[k] = neqns+1;
for (j=xadj[node]; j<xadj[node+1]; j++) {
nabor = invp[adjncy[j]];
if (nabor <= k)
continue;
rchm = k;
do {
m = rchm;
assert(m > 0 && m <= neqns);
rchm = rchlnk[m];
} while (rchm <= nabor);
knz++;
assert(m > 0 && m <= neqns);
rchlnk[m] = nabor;
assert(nabor > 0 && nabor <= neqns);
rchlnk[nabor] = rchm;
assert(k > 0 && k <= neqns);
if (marker[nabor] != marker[k])
mrkflg = 1;
}
/* TEST FOR MASS SYMBOLIC ELIMINATION */
lmax = 0;
assert(mrgk >= 0 && mrgk <= neqns);
if (mrkflg != 0 || mrgk == 0 || mrglnk[mrgk] != 0)
goto L350;
xnzsub[k] = xnzsub[mrgk] + 1;
knz = xlnz[mrgk + 1] - (xlnz[mrgk] + 1);
goto L1400;
L350:
/* LINK THROUGH EACH COLUMN I THAT AFFECTS L(*,K) */
i = k;
assert(i > 0 && i <= neqns);
while ((i = mrglnk[i]) != 0) {
assert(i > 0 && i <= neqns);
inz = xlnz[i+1] - (xlnz[i]+1);
jstrt = xnzsub[i] + 1;
jstop = xnzsub[i] + inz;
if (inz > lmax) {
lmax = inz;
xnzsub[k] = jstrt;
}
/* MERGE STRUCTURE OF L(*,I) IN NZSUB INTO RCHLNK. */
rchm = k;
for (j=jstrt; j<=jstop; j++) {
nabor = nzsub[j];
do {
m = rchm;
assert(m > 0 && m <= neqns);
rchm = rchlnk[m];
} while (rchm < nabor);
if (rchm != nabor) {
knz++;
assert(m > 0 && m <= neqns);
rchlnk[m] = nabor;
assert(nabor > 0 && nabor <= neqns);
rchlnk[nabor] = rchm;
rchm = nabor;
}
}
}
/* CHECK IF SUBSCRIPTS DUPLICATE THOSE OF ANOTHER COLUMN */
if (knz == lmax)
goto L1400;
/* OR IF TAIL OF K-1ST COLUMN MATCHES HEAD OF KTH */
if (nzbeg > nzend)
goto L1200;
assert(k > 0 && k <= neqns);
i = rchlnk[k];
for (jstrt = nzbeg; jstrt <= nzend; ++jstrt) {
if (nzsub[jstrt] < i)
continue;
if (nzsub[jstrt] == i)
goto L1000;
else
goto L1200;
}
goto L1200;
L1000:
xnzsub[k] = jstrt;
for (j = jstrt; j <= nzend; ++j) {
if (nzsub[j] != i)
goto L1200;
assert(i > 0 && i <= neqns);
i = rchlnk[i];
if (i > neqns)
goto L1400;
}
nzend = jstrt - 1;
/* COPY THE STRUCTURE OF L(*,K) FROM RCHLNK TO THE DATA STRUCTURE (XNZSUB, NZSUB) */
L1200:
nzbeg = nzend + 1;
nzend += knz;
if (nzend >= *maxsub) {
flag = 1; /* Out of memory */
break;
}
i = k;
for (j=nzbeg; j<=nzend; j++) {
assert(i > 0 && i <= neqns);
i = rchlnk[i];
nzsub[j] = i;
assert(i > 0 && i <= neqns);
marker[i] = k;
}
xnzsub[k] = nzbeg;
assert(k > 0 && k <= neqns);
marker[k] = k;
/*
* UPDATE THE VECTOR MRGLNK. NOTE COLUMN L(*,K) JUST FOUND
* IS REQUIRED TO DETERMINE COLUMN L(*,J), WHERE
* L(J,K) IS THE FIRST NONZERO IN L(*,K) BELOW DIAGONAL.
*/
L1400:
if (knz > 1) {
kxsub = xnzsub[k];
i = nzsub[kxsub];
assert(i > 0 && i <= neqns);
assert(k > 0 && k <= neqns);
mrglnk[k] = mrglnk[i];
mrglnk[i] = k;
}
xlnz[k + 1] = xlnz[k] + knz;
}
if (flag == 0) {
*maxlnz = xlnz[neqns] - 1;
*maxsub = xnzsub[neqns];
xnzsub[neqns + 1] = xnzsub[neqns];
}
marker++;
mrglnk++;
rchlnk++;
nzsub++;
xnzsub++;
xlnz++;
invp++;
perm++;
adjncy++;
xadj++;
gk_free((void **)&rchlnk, &mrglnk, &marker, LTERM);
return flag;
}
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