/*! @file ilu_spanel_dfs.c

 * \brief Peforms a symbolic factorization on a panel of symbols and

 * record the entries with maximum absolute value in each column

 *

 * 

 * -- SuperLU routine (version 4.0) --

 * Lawrence Berkeley National Laboratory

 * June 30, 2009

 * 

 */

#include "slu_sdefs.h"

/*! \brief

 *

 * 

 * 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

 * 

 */

void

ilu_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 */

   float     *amax,	   /* out - max. abs. value of each column in panel */

   int	      *panel_lsub, /* out */

   int	      *segrep,	   /* out */

   int	      *repfnz,	   /* out */

   int	      *marker,	   /* out */

   int	      *parent,	   /* working array */

   int	      *xplore,	   /* working array */

   GlobalLU_t *Glu	   /* modified */

)

{

    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;

    float    *amax_col;

    register double tmp;

    /* 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;

    amax_col   = amax;

    *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

	*amax_col = 0.0;

	/* For each nonz in A[*,jj] do dfs */

	for (k = xa_begin[jj]; k < xa_end[jj]; k++) {

	    krow = asub[k];

	    tmp = fabs(a[k]);

	    if (tmp > *amax_col) *amax_col = tmp;

	    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[xsup[supno[krep]]];

		    maxdfs = xlsub[krep + 1];

#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[xsup[supno[krep]]];

					maxdfs = xlsub[krep + 1];

#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 = xlsub[krep + 1];

#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;

	amax_col++;

    } /* for jj ... */

}