spanel_dfs.c

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/*
 * -- SuperLU routine (version 2.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * November 15, 1997
 *
 */
/*
  Copyright (c) 1994 by Xerox Corporation.  All rights reserved.
 
  THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
  EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.
 
  Permission is hereby granted to use or copy this program for any
  purpose, provided the above notices are retained on all copies.
  Permission to modify the code and to distribute modified code is
  granted, provided the above notices are retained, and a notice that
  the code was modified is included with the above copyright notice.
*/

#include "ssp_defs.h"
#include "util.h"

void
spanel_dfs (
       const int  m,           /* in - number of rows in the matrix */
       const int  w,           /* in */
       const int  jcol,        /* in */
       SuperMatrix *A,       /* in - original matrix */
       int        *perm_r,     /* in */
       int        *nseg,       /* out */
       float     *dense,      /* out */
       int        *panel_lsub, /* out */
       int        *segrep,     /* out */
       int        *repfnz,     /* out */
       int        *xprune,     /* out */
       int        *marker,     /* out */     
       int        *parent,     /* working array */
       int        *xplore,     /* working array */
       GlobalLU_t *Glu         /* modified */
       )
{
/*
 * Purpose
 * =======
 *
 *   Performs a symbolic factorization on a panel of columns [jcol, jcol+w).
 *
 *   A supernode representative is the last column of a supernode.
 *   The nonzeros in U[*,j] are segments that end at supernodal
 *   representatives.
 *
 *   The routine returns one list of the supernodal representatives
 *   in topological order of the dfs that generates them. This list is
 *   a superset of the topological order of each individual column within
 *   the panel. 
 *   The location of the first nonzero in each supernodal segment
 *   (supernodal entry location) is also returned. Each column has a 
 *   separate list for this purpose.
 *
 *   Two marker arrays are used for dfs:
 *     marker[i] == jj, if i was visited during dfs of current column jj;
 *     marker1[i] >= jcol, if i was visited by earlier columns in this panel;
 *
 *   marker: A-row --> A-row/col (0/1)
 *   repfnz: SuperA-col --> PA-row
 *   parent: SuperA-col --> SuperA-col
 *   xplore: SuperA-col --> index to L-structure
 *
 */
    NCPformat *Astore;
    float    *a;
    int       *asub;
    int       *xa_begin, *xa_end;
    int       krep, chperm, chmark, chrep, oldrep, kchild, myfnz;
    int       k, krow, kmark, kperm;
    int       xdfs, maxdfs, kpar;
    int       jj;      /* index through each column in the panel */
    int       *marker1;    /* marker1[jj] >= jcol if vertex jj was visited 
                  by a previous column within this panel.   */
    int       *repfnz_col; /* start of each column in the panel */
    float    *dense_col;  /* start of each column in the panel */
    int       nextl_col;   /* next available position in panel_lsub[*,jj] */
    int       *xsup, *supno;
    int       *lsub, *xlsub;

    /* Initialize pointers */
    Astore     = A->Store;
    a          = Astore->nzval;
    asub       = Astore->rowind;
    xa_begin   = Astore->colbeg;
    xa_end     = Astore->colend;
    marker1    = marker + m;
    repfnz_col = repfnz;
    dense_col  = dense;
    *nseg      = 0;
    xsup       = Glu->xsup;
    supno      = Glu->supno;
    lsub       = Glu->lsub;
    xlsub      = Glu->xlsub;

    /* For each column in the panel */
    for (jj = jcol; jj < jcol + w; jj++) {
    nextl_col = (jj - jcol) * m;

#ifdef CHK_DFS
    printf("\npanel col %d: ", jj);
#endif

    /* For each nonz in A[*,jj] do dfs */
    for (k = xa_begin[jj]; k < xa_end[jj]; k++) {
        krow = asub[k];
            dense_col[krow] = a[k];
        kmark = marker[krow];       
        if ( kmark == jj ) 
        continue;     /* krow visited before, go to the next nonzero */

        /* For each unmarked nbr krow of jj
         * krow is in L: place it in structure of L[*,jj]
         */
        marker[krow] = jj;
        kperm = perm_r[krow];
        
        if ( kperm == EMPTY ) {
        panel_lsub[nextl_col++] = krow; /* krow is indexed into A */
        }
        /* 
         * krow is in U: if its supernode-rep krep
         * has been explored, update repfnz[*]
         */
        else {
        
        krep = xsup[supno[kperm]+1] - 1;
        myfnz = repfnz_col[krep];
        
#ifdef CHK_DFS
        printf("krep %d, myfnz %d, perm_r[%d] %d\n", krep, myfnz, krow, kperm);
#endif
        if ( myfnz != EMPTY ) { /* Representative visited before */
            if ( myfnz > kperm ) repfnz_col[krep] = kperm;
            /* continue; */
        }
        else {
            /* Otherwise, perform dfs starting at krep */
            oldrep = EMPTY;
            parent[krep] = oldrep;
            repfnz_col[krep] = kperm;
            xdfs = xlsub[krep];
            maxdfs = xprune[krep];
            
#ifdef CHK_DFS 
            printf("  xdfs %d, maxdfs %d: ", xdfs, maxdfs);
            for (i = xdfs; i < maxdfs; i++) printf(" %d", lsub[i]);
            printf("\n");
#endif
            do {
            /* 
             * For each unmarked kchild of krep 
             */
            while ( xdfs < maxdfs ) {
                
                kchild = lsub[xdfs];
                xdfs++;
                chmark = marker[kchild];
                
                if ( chmark != jj ) { /* Not reached yet */
                marker[kchild] = jj;
                chperm = perm_r[kchild];
                  
                /* Case kchild is in L: place it in L[*,j] */
                if ( chperm == EMPTY ) {
                    panel_lsub[nextl_col++] = kchild;
                } 
                /* Case kchild is in U: 
                 *   chrep = its supernode-rep. If its rep has 
                 *   been explored, update its repfnz[*]
                 */
                else {
                    
                    chrep = xsup[supno[chperm]+1] - 1;
                    myfnz = repfnz_col[chrep];
#ifdef CHK_DFS
                    printf("chrep %d,myfnz %d,perm_r[%d] %d\n",chrep,myfnz,kchild,chperm);
#endif
                    if ( myfnz != EMPTY ) { /* Visited before */
                    if ( myfnz > chperm )
                        repfnz_col[chrep] = chperm;
                    }
                    else {
                    /* Cont. dfs at snode-rep of kchild */
                    xplore[krep] = xdfs;    
                    oldrep = krep;
                    krep = chrep; /* Go deeper down G(L) */
                    parent[krep] = oldrep;
                    repfnz_col[krep] = chperm;
                    xdfs = xlsub[krep];     
                    maxdfs = xprune[krep];
#ifdef CHK_DFS 
                    printf("  xdfs %d, maxdfs %d: ", xdfs, maxdfs);
                    for (i = xdfs; i < maxdfs; i++) printf(" %d", lsub[i]); 
                    printf("\n");
#endif
                    } /* else */
                  
                } /* else */
                  
                } /* if... */
                
            } /* while xdfs < maxdfs */
            
            /* krow has no more unexplored nbrs:
             *    Place snode-rep krep in postorder DFS, if this 
             *    segment is seen for the first time. (Note that
             *    "repfnz[krep]" may change later.)
             *    Backtrack dfs to its parent.
             */
            if ( marker1[krep] < jcol ) {
                segrep[*nseg] = krep;
                ++(*nseg);
                marker1[krep] = jj;
            }
            
            kpar = parent[krep]; /* Pop stack, mimic recursion */
            if ( kpar == EMPTY ) break; /* dfs done */
            krep = kpar;
            xdfs = xplore[krep];
            maxdfs = xprune[krep];
            
#ifdef CHK_DFS 
            printf("  pop stack: krep %d,xdfs %d,maxdfs %d: ", krep,xdfs,maxdfs);
            for (i = xdfs; i < maxdfs; i++) printf(" %d", lsub[i]);
            printf("\n");
#endif
            } while ( kpar != EMPTY ); /* do-while - until empty stack */
            
        } /* else */
        
        } /* else */
        
    } /* for each nonz in A[*,jj] */
    
    repfnz_col += m;    /* Move to next column */
        dense_col += m;
    
    } /* for jj ... */
    
}