Lines 1-385
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/* |
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* Copyright 1997, Regents of the University of Minnesota |
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* |
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* smbfactor.c |
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* |
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* This file performs the symbolic factorization of a matrix |
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* |
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* Started 8/1/97 |
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* George |
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* |
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* $Id: smbfactor.c,v 1.2 2002/08/10 06:02:55 karypis Exp $ |
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* |
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*/ |
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#include <metisbin.h> |
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|
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/************************************************************************* |
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* This function sets up data structures for fill-in computations |
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**************************************************************************/ |
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void ComputeFillIn(GraphType *graph, idxtype *iperm) |
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{ |
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idxtype i, j, k, nvtxs, maxlnz, maxsub; |
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idxtype *xadj, *adjncy; |
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idxtype *perm, *xlnz, *xnzsub, *nzsub; |
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double opc; |
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|
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/* |
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mprintf("\nSymbolic factorization... --------------------------------------------\n"); |
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*/ |
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|
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nvtxs = graph->nvtxs; |
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xadj = graph->xadj; |
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adjncy = graph->adjncy; |
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|
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maxsub = 4*xadj[nvtxs]; |
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|
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/* Relabel the vertices so that it starts from 1 */ |
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k = xadj[nvtxs]; |
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for (i=0; i<k; i++) |
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adjncy[i]++; |
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for (i=0; i<nvtxs+1; i++) |
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xadj[i]++; |
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|
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/* Allocate the required memory */ |
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perm = idxmalloc(nvtxs+1, "ComputeFillIn: perm"); |
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xlnz = idxmalloc(nvtxs+1, "ComputeFillIn: xlnz"); |
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xnzsub = idxmalloc(nvtxs+1, "ComputeFillIn: xnzsub"); |
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nzsub = idxmalloc(maxsub, "ComputeFillIn: nzsub"); |
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|
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/* Construct perm from iperm and change the numbering of iperm */ |
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for (i=0; i<nvtxs; i++) |
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perm[iperm[i]] = i; |
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for (i=0; i<nvtxs; i++) { |
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iperm[i]++; |
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perm[i]++; |
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} |
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|
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/* |
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* Call sparspak routine. |
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*/ |
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if (smbfct(nvtxs, xadj, adjncy, perm, iperm, xlnz, &maxlnz, xnzsub, nzsub, &maxsub)) { |
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gk_free((void **)&nzsub, LTERM); |
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|
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maxsub = 4*maxsub; |
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nzsub = idxmalloc(maxsub, "ComputeFillIn: nzsub"); |
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if (smbfct(nvtxs, xadj, adjncy, perm, iperm, xlnz, &maxlnz, xnzsub, nzsub, &maxsub)) |
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errexit("MAXSUB is too small!"); |
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} |
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|
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opc = 0; |
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for (i=0; i<nvtxs; i++) |
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xlnz[i]--; |
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for (i=0; i<nvtxs; i++) |
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opc += (xlnz[i+1]-xlnz[i])*(xlnz[i+1]-xlnz[i]) - (xlnz[i+1]-xlnz[i]); |
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|
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mprintf(" Nonzeros: %D, \tOperation Count: %6.4le\n", maxlnz, opc); |
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|
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gk_free((void **)&perm, &xlnz, &xnzsub, &nzsub, LTERM); |
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|
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|
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/* Relabel the vertices so that it starts from 0 */ |
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for (i=0; i<nvtxs; i++) |
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iperm[i]--; |
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for (i=0; i<nvtxs+1; i++) |
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xadj[i]--; |
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k = xadj[nvtxs]; |
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for (i=0; i<k; i++) |
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adjncy[i]--; |
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|
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} |
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|
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|
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/************************************************************************* |
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* This function sets up data structures for fill-in computations |
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**************************************************************************/ |
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idxtype ComputeFillIn2(GraphType *graph, idxtype *iperm) |
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{ |
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idxtype i, j, k, nvtxs, maxlnz, maxsub; |
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idxtype *xadj, *adjncy; |
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idxtype *perm, *xlnz, *xnzsub, *nzsub; |
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double opc; |
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|
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nvtxs = graph->nvtxs; |
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xadj = graph->xadj; |
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adjncy = graph->adjncy; |
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|
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maxsub = 4*xadj[nvtxs]; |
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|
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/* Relabel the vertices so that it starts from 1 */ |
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k = xadj[nvtxs]; |
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for (i=0; i<k; i++) |
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adjncy[i]++; |
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for (i=0; i<nvtxs+1; i++) |
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xadj[i]++; |
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|
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/* Allocate the required memory */ |
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perm = idxmalloc(nvtxs+1, "ComputeFillIn: perm"); |
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xlnz = idxmalloc(nvtxs+1, "ComputeFillIn: xlnz"); |
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xnzsub = idxmalloc(nvtxs+1, "ComputeFillIn: xnzsub"); |
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nzsub = idxmalloc(maxsub, "ComputeFillIn: nzsub"); |
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|
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/* Construct perm from iperm and change the numbering of iperm */ |
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for (i=0; i<nvtxs; i++) |
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perm[iperm[i]] = i; |
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for (i=0; i<nvtxs; i++) { |
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iperm[i]++; |
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perm[i]++; |
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} |
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|
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/* |
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* Call sparspak routine. |
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*/ |
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if (smbfct(nvtxs, xadj, adjncy, perm, iperm, xlnz, &maxlnz, xnzsub, nzsub, &maxsub)) { |
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gk_free((void **)&nzsub, LTERM); |
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|
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maxsub = 4*maxsub; |
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nzsub = idxmalloc(maxsub, "ComputeFillIn: nzsub"); |
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if (smbfct(nvtxs, xadj, adjncy, perm, iperm, xlnz, &maxlnz, xnzsub, nzsub, &maxsub)) |
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errexit("MAXSUB is too small!"); |
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} |
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|
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opc = 0; |
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for (i=0; i<nvtxs; i++) |
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xlnz[i]--; |
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for (i=0; i<nvtxs; i++) |
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opc += (xlnz[i+1]-xlnz[i])*(xlnz[i+1]-xlnz[i]) - (xlnz[i+1]-xlnz[i]); |
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|
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gk_free((void **)&perm, &xlnz, &xnzsub, &nzsub, LTERM); |
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|
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/* Relabel the vertices so that it starts from 0 */ |
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for (i=0; i<nvtxs; i++) |
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iperm[i]--; |
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for (i=0; i<nvtxs+1; i++) |
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xadj[i]--; |
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k = xadj[nvtxs]; |
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for (i=0; i<k; i++) |
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adjncy[i]--; |
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|
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return maxlnz; |
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|
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} |
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|
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/***************************************************************** |
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********** SMBFCT ..... SYMBOLIC FACTORIZATION ********* |
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****************************************************************** |
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* PURPOSE - THIS ROUTINE PERFORMS SYMBOLIC FACTORIZATION |
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* ON A PERMUTED LINEAR SYSTEM AND IT ALSO SETS UP THE |
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* COMPRESSED DATA STRUCTURE FOR THE SYSTEM. |
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* |
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* INPUT PARAMETERS - |
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* NEQNS - NUMBER OF EQUATIONS. |
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* (XADJ, ADJNCY) - THE ADJACENCY STRUCTURE. |
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* (PERM, INVP) - THE PERMUTATION VECTOR AND ITS INVERSE. |
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* |
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* UPDATED PARAMETERS - |
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* MAXSUB - SIZE OF THE SUBSCRIPT ARRAY NZSUB. ON RETURN, |
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* IT CONTAINS THE NUMBER OF SUBSCRIPTS USED |
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* |
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* OUTPUT PARAMETERS - |
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* XLNZ - INDEX INTO THE NONZERO STORAGE VECTOR LNZ. |
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* (XNZSUB, NZSUB) - THE COMPRESSED SUBSCRIPT VECTORS. |
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* MAXLNZ - THE NUMBER OF NONZEROS FOUND. |
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* |
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*******************************************************************/ |
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idxtype smbfct(idxtype neqns, idxtype *xadj, idxtype *adjncy, idxtype *perm, idxtype *invp, |
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idxtype *xlnz, idxtype *maxlnz, idxtype *xnzsub, idxtype *nzsub, idxtype *maxsub) |
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{ |
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/* Local variables */ |
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idxtype node, rchm, mrgk, lmax, i, j, k, m, nabor, nzbeg, nzend; |
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idxtype kxsub, jstop, jstrt, mrkflg, inz, knz, flag; |
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idxtype *mrglnk, *marker, *rchlnk; |
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|
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rchlnk = idxmalloc(neqns+1, "smbfct: rchlnk"); |
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marker = idxsmalloc(neqns+1, 0, "smbfct: marker"); |
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mrglnk = idxsmalloc(neqns+1, 0, "smbfct: mgrlnk"); |
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|
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/* Parameter adjustments */ |
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--marker; |
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--mrglnk; |
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--rchlnk; |
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--nzsub; |
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--xnzsub; |
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--xlnz; |
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--invp; |
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--perm; |
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--adjncy; |
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--xadj; |
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|
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/* Function Body */ |
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flag = 0; |
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nzbeg = 1; |
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nzend = 0; |
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xlnz[1] = 1; |
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|
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/* FOR EACH COLUMN KNZ COUNTS THE NUMBER OF NONZEROS IN COLUMN K ACCUMULATED IN RCHLNK. */ |
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for (k = 1; k <= neqns; ++k) { |
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knz = 0; |
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mrgk = mrglnk[k]; |
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mrkflg = 0; |
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marker[k] = k; |
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if (mrgk != 0) |
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marker[k] = marker[mrgk]; |
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xnzsub[k] = nzend; |
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node = perm[k]; |
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|
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if (xadj[node] >= xadj[node+1]) { |
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xlnz[k+1] = xlnz[k]; |
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continue; |
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} |
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|
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/* USE RCHLNK TO LINK THROUGH THE STRUCTURE OF A(*,K) BELOW DIAGONAL */ |
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rchlnk[k] = neqns+1; |
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for (j=xadj[node]; j<xadj[node+1]; j++) { |
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nabor = invp[adjncy[j]]; |
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if (nabor <= k) |
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continue; |
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rchm = k; |
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|
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do { |
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m = rchm; |
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rchm = rchlnk[m]; |
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} while (rchm <= nabor); |
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|
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knz++; |
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rchlnk[m] = nabor; |
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rchlnk[nabor] = rchm; |
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if (marker[nabor] != marker[k]) |
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mrkflg = 1; |
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} |
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|
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/* TEST FOR MASS SYMBOLIC ELIMINATION */ |
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lmax = 0; |
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if (mrkflg != 0 || mrgk == 0 || mrglnk[mrgk] != 0) |
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goto L350; |
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xnzsub[k] = xnzsub[mrgk] + 1; |
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knz = xlnz[mrgk + 1] - (xlnz[mrgk] + 1); |
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goto L1400; |
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|
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/* LINK THROUGH EACH COLUMN I THAT AFFECTS L(*,K) */ |
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L350: |
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i = k; |
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while ((i = mrglnk[i]) != 0) { |
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inz = xlnz[i+1] - (xlnz[i]+1); |
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jstrt = xnzsub[i] + 1; |
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jstop = xnzsub[i] + inz; |
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|
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if (inz > lmax) { |
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lmax = inz; |
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xnzsub[k] = jstrt; |
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} |
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|
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/* MERGE STRUCTURE OF L(*,I) IN NZSUB INTO RCHLNK. */ |
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rchm = k; |
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for (j = jstrt; j <= jstop; ++j) { |
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nabor = nzsub[j]; |
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do { |
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m = rchm; |
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rchm = rchlnk[m]; |
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} while (rchm < nabor); |
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|
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if (rchm != nabor) { |
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knz++; |
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rchlnk[m] = nabor; |
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rchlnk[nabor] = rchm; |
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rchm = nabor; |
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} |
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} |
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} |
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|
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/* CHECK IF SUBSCRIPTS DUPLICATE THOSE OF ANOTHER COLUMN */ |
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if (knz == lmax) |
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goto L1400; |
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|
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/* OR IF TAIL OF K-1ST COLUMN MATCHES HEAD OF KTH */ |
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if (nzbeg > nzend) |
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goto L1200; |
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|
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i = rchlnk[k]; |
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for (jstrt = nzbeg; jstrt <= nzend; ++jstrt) { |
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if (nzsub[jstrt] < i) |
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continue; |
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|
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if (nzsub[jstrt] == i) |
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goto L1000; |
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else |
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goto L1200; |
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} |
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goto L1200; |
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|
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L1000: |
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xnzsub[k] = jstrt; |
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for (j = jstrt; j <= nzend; ++j) { |
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if (nzsub[j] != i) |
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goto L1200; |
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i = rchlnk[i]; |
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if (i > neqns) |
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goto L1400; |
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} |
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nzend = jstrt - 1; |
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|
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/* COPY THE STRUCTURE OF L(*,K) FROM RCHLNK TO THE DATA STRUCTURE (XNZSUB, NZSUB) */ |
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L1200: |
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nzbeg = nzend + 1; |
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nzend += knz; |
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|
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if (nzend > *maxsub) { |
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flag = 1; /* Out of memory */ |
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break; |
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} |
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|
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i = k; |
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for (j=nzbeg; j<=nzend; ++j) { |
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i = rchlnk[i]; |
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nzsub[j] = i; |
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marker[i] = k; |
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} |
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xnzsub[k] = nzbeg; |
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marker[k] = k; |
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|
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/* |
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* UPDATE THE VECTOR MRGLNK. NOTE COLUMN L(*,K) JUST FOUND |
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* IS REQUIRED TO DETERMINE COLUMN L(*,J), WHERE |
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* L(J,K) IS THE FIRST NONZERO IN L(*,K) BELOW DIAGONAL. |
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*/ |
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L1400: |
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if (knz > 1) { |
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kxsub = xnzsub[k]; |
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i = nzsub[kxsub]; |
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mrglnk[k] = mrglnk[i]; |
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mrglnk[i] = k; |
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} |
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|
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xlnz[k + 1] = xlnz[k] + knz; |
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} |
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|
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if (flag == 0) { |
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*maxlnz = xlnz[neqns] - 1; |
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*maxsub = xnzsub[neqns]; |
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xnzsub[neqns + 1] = xnzsub[neqns]; |
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} |
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|
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marker++; |
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mrglnk++; |
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rchlnk++; |
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nzsub++; |
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xnzsub++; |
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xlnz++; |
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invp++; |
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perm++; |
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adjncy++; |
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xadj++; |
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gk_free((void **)&rchlnk, &mrglnk, &marker, LTERM); |
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|
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return flag; |
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|
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} |
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