/*! \file
Copyright (c) 2003, The Regents of the University of California, through
Lawrence Berkeley National Laboratory (subject to receipt of any required 
approvals from U.S. Dept. of Energy) 

All rights reserved. 

The source code is distributed under BSD license, see the file License.txt
at the top-level directory.
*/

/*! @file ilu_dcolumn_dfs.c
 * \brief Performs a symbolic factorization
 *
 * <pre>
 * -- SuperLU routine (version 4.0) --
 * Lawrence Berkeley National Laboratory
 * June 30, 2009
 * </pre>
*/

#include "slu_ddefs.h"


/*! \brief
 *
 * <pre>
 * Purpose
 * =======
 *   ILU_DCOLUMN_DFS performs a symbolic factorization on column jcol, and
 *   decide the supernode boundary.
 *
 *   This routine does not use numeric values, but only use the RHS
 *   row indices to start the dfs.
 *
 *   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 a list of such supernodal
 *   representatives in topological order of the dfs that generates them.
 *   The location of the first nonzero in each such supernodal segment
 *   (supernodal entry location) is also returned.
 *
 * Local parameters
 * ================
 *   nseg: no of segments in current U[*,j]
 *   jsuper: jsuper=EMPTY if column j does not belong to the same
 *	supernode as j-1. Otherwise, jsuper=nsuper.
 *
 *   marker2: A-row --> A-row/col (0/1)
 *   repfnz: SuperA-col --> PA-row
 *   parent: SuperA-col --> SuperA-col
 *   xplore: SuperA-col --> index to L-structure
 *
 * Return value
 * ============
 *     0  success;
 *   > 0  number of bytes allocated when run out of space.
 * </pre>
 */
int
ilu_dcolumn_dfs(
	   const int  m,	 /* in - number of rows in the matrix */
	   const int  jcol,	 /* in */
	   int	      *perm_r,	 /* in */
	   int	      *nseg,	 /* modified - with new segments appended */
	   int	      *lsub_col, /* in - defines the RHS vector to start the
				    dfs */
	   int	      *segrep,	 /* modified - with new segments appended */
	   int	      *repfnz,	 /* modified */
	   int	      *marker,	 /* modified */
	   int	      *parent,	 /* working array */
	   int_t      *xplore,	 /* working array */
	   GlobalLU_t *Glu	 /* modified */
	   )
{

    int     jcolp1, jcolm1, jsuper, nsuper;
    int     k, krep, krow, kmark, kperm;
    int     *marker2;		/* Used for small panel LU */
    int     fsupc;		/* First column of a snode */
    int     myfnz;		/* First nonz column of a U-segment */
    int     chperm, chmark, chrep, kchild, kpar, oldrep;
    int_t   xdfs, maxdfs; 
    int_t   jptr, jm1ptr;
    int_t   ito, ifrom; 	/* Used to compress row subscripts */
    int_t   mem_error, nextl;
    int     *xsup, *supno;
    int_t   *lsub, *xlsub;
    int_t   nzlmax;
    int     maxsuper;

    xsup    = Glu->xsup;
    supno   = Glu->supno;
    lsub    = Glu->lsub;
    xlsub   = Glu->xlsub;
    nzlmax  = Glu->nzlmax;

    maxsuper = sp_ienv(7);
    jcolp1  = jcol + 1;
    jcolm1  = jcol - 1;
    nsuper  = supno[jcol];
    jsuper  = nsuper;
    nextl   = xlsub[jcol];
    marker2 = &marker[2*m];


    /* For each nonzero in A[*,jcol] do dfs */
    for (k = 0; lsub_col[k] != EMPTY; k++) {

	krow = lsub_col[k];
	lsub_col[k] = EMPTY;
	kmark = marker2[krow];

	/* krow was visited before, go to the next nonzero */
	if ( kmark == jcol ) continue;

	/* For each unmarked nbr krow of jcol
	 *	krow is in L: place it in structure of L[*,jcol]
	 */
	marker2[krow] = jcol;
	kperm = perm_r[krow];

	if ( kperm == EMPTY ) {
	    lsub[nextl++] = krow;	/* krow is indexed into A */
	    if ( nextl >= nzlmax ) {
		if ((mem_error = dLUMemXpand(jcol, nextl, LSUB, &nzlmax, Glu)))
		    return (mem_error);
		lsub = Glu->lsub;
	    }
	    if ( kmark != jcolm1 ) jsuper = EMPTY;/* Row index subset testing */
	} else {
	    /*	krow is in U: if its supernode-rep krep
	     *	has been explored, update repfnz[*]
	     */
	    krep = xsup[supno[kperm]+1] - 1;
	    myfnz = repfnz[krep];

	    if ( myfnz != EMPTY ) {	/* Visited before */
		if ( myfnz > kperm ) repfnz[krep] = kperm;
		/* continue; */
	    }
	    else {
		/* Otherwise, perform dfs starting at krep */
		oldrep = EMPTY;
		parent[krep] = oldrep;
		repfnz[krep] = kperm;
		xdfs = xlsub[xsup[supno[krep]]];
		maxdfs = xlsub[krep + 1];

		do {
		    /*
		     * For each unmarked kchild of krep
		     */
		    while ( xdfs < maxdfs ) {

			kchild = lsub[xdfs];
			xdfs++;
			chmark = marker2[kchild];

			if ( chmark != jcol ) { /* Not reached yet */
			    marker2[kchild] = jcol;
			    chperm = perm_r[kchild];

			    /* Case kchild is in L: place it in L[*,k] */
			    if ( chperm == EMPTY ) {
				lsub[nextl++] = kchild;
				if ( nextl >= nzlmax ) {
				    if ( (mem_error = dLUMemXpand(jcol,nextl,
					    LSUB,&nzlmax,Glu)) )
					return (mem_error);
				    lsub = Glu->lsub;
				}
				if ( chmark != jcolm1 ) jsuper = EMPTY;
			    } else {
				/* Case kchild is in U:
				 *   chrep = its supernode-rep. If its rep has
				 *   been explored, update its repfnz[*]
				 */
				chrep = xsup[supno[chperm]+1] - 1;
				myfnz = repfnz[chrep];
				if ( myfnz != EMPTY ) { /* Visited before */
				    if ( myfnz > chperm )
					repfnz[chrep] = chperm;
				} else {
				    /* Continue dfs at super-rep of kchild */
				    xplore[krep] = xdfs;
				    oldrep = krep;
				    krep = chrep; /* Go deeper down G(L^t) */
				    parent[krep] = oldrep;
				    repfnz[krep] = chperm;
				    xdfs = xlsub[xsup[supno[krep]]];
				    maxdfs = xlsub[krep + 1];
				} /* else */

			   } /* else */

			} /* if */

		    } /* while */

		    /* krow has no more unexplored nbrs;
		     *	  place supernode-rep krep in postorder DFS.
		     *	  backtrack dfs to its parent
		     */
		    segrep[*nseg] = krep;
		    ++(*nseg);
		    kpar = parent[krep]; /* Pop from stack, mimic recursion */
		    if ( kpar == EMPTY ) break; /* dfs done */
		    krep = kpar;
		    xdfs = xplore[krep];
		    maxdfs = xlsub[krep + 1];

		} while ( kpar != EMPTY );	/* Until empty stack */

	    } /* else */

	} /* else */

    } /* for each nonzero ... */

    /* Check to see if j belongs in the same supernode as j-1 */
    if ( jcol == 0 ) { /* Do nothing for column 0 */
	nsuper = supno[0] = 0;
    } else {
	fsupc = xsup[nsuper];
	jptr = xlsub[jcol];	/* Not compressed yet */
	jm1ptr = xlsub[jcolm1];

	if ( (nextl-jptr != jptr-jm1ptr-1) ) jsuper = EMPTY;

	/* Always start a new supernode for a singular column */
	if ( nextl == jptr ) jsuper = EMPTY;

	/* Make sure the number of columns in a supernode doesn't
	   exceed threshold. */
	if ( jcol - fsupc >= maxsuper ) jsuper = EMPTY;

	/* If jcol starts a new supernode, reclaim storage space in
	 * lsub from the previous supernode. Note we only store
	 * the subscript set of the first columns of the supernode.
	 */
	if ( jsuper == EMPTY ) {	/* starts a new supernode */
	    if ( (fsupc < jcolm1) ) { /* >= 2 columns in nsuper */
#ifdef CHK_COMPRESS
		printf("  Compress lsub[] at super %d-%d\n", fsupc, jcolm1);
#endif
		ito = xlsub[fsupc+1];
		xlsub[jcolm1] = ito;
		xlsub[jcol] = ito;
		for (ifrom = jptr; ifrom < nextl; ++ifrom, ++ito)
		    lsub[ito] = lsub[ifrom];
		nextl = ito;
	    }
	    nsuper++;
	    supno[jcol] = nsuper;
	} /* if a new supernode */

    }	/* else: jcol > 0 */

    /* Tidy up the pointers before exit */
    xsup[nsuper+1] = jcolp1;
    supno[jcolp1]  = nsuper;
    xlsub[jcolp1]  = nextl;

    return 0;
}
