
/*! @file zcolumn_dfs.c
 * \brief Performs a symbolic factorization
 *
 * <pre>
 * -- SuperLU routine (version 3.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * October 15, 2003
 *
 * 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.
 * </pre>
*/

#include "slu_zdefs.h"

/*! \brief What type of supernodes we want */
#define T2_SUPER


/*! \brief
 *
 * <pre>
 * Purpose
 * =======
 *   ZCOLUMN_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
zcolumn_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        *xprune,   /* modified */
	   int        *marker,   /* modified */
	   int        *parent,	 /* working array */
	   int        *xplore,   /* working array */
	   GlobalLU_t *Glu       /* modified */
	   )
{

    int     jcolp1, jcolm1, jsuper, nsuper, nextl;
    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;
    int     xdfs, maxdfs, kpar, oldrep;
    int     jptr, jm1ptr;
    int     ito, ifrom, istop;	/* Used to compress row subscripts */
    int     mem_error;
    int     *xsup, *supno, *lsub, *xlsub;
    int     nzlmax;
    static  int  first = 1, maxsuper;
    
    xsup    = Glu->xsup;
    supno   = Glu->supno;
    lsub    = Glu->lsub;
    xlsub   = Glu->xlsub;
    nzlmax  = Glu->nzlmax;

    if ( first ) {
	maxsuper = sp_ienv(3);
	first = 0;
    }
    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 nonz */
        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 = zLUMemXpand(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[krep];
	  	maxdfs = xprune[krep];

		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 =
					 zLUMemXpand(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[krep];     
				    maxdfs = xprune[krep];
				} /* 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 = xprune[krep];

		} 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];

#ifdef T2_SUPER
	if ( (nextl-jptr != jptr-jm1ptr-1) ) jsuper = EMPTY;
#endif
	/* 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 and last columns of
   	 * a supernode. (first for num values, last for pruning)
	 */
	if ( jsuper == EMPTY ) {	/* starts a new supernode */
	    if ( (fsupc < jcolm1-1) ) {	/* >= 3 columns in nsuper */
#ifdef CHK_COMPRESS
		printf("  Compress lsub[] at super %d-%d\n", fsupc, jcolm1);
#endif
	        ito = xlsub[fsupc+1];
		xlsub[jcolm1] = ito;
		istop = ito + jptr - jm1ptr;
		xprune[jcolm1] = istop; /* Initialize xprune[jcol-1] */
		xlsub[jcol] = istop;
		for (ifrom = jm1ptr; ifrom < nextl; ++ifrom, ++ito)
		    lsub[ito] = lsub[ifrom];
		nextl = ito;            /* = istop + length(jcol) */
	    }
	    nsuper++;
	    supno[jcol] = nsuper;
	} /* if a new supernode */

    }	/* else: jcol > 0 */ 
    
    /* Tidy up the pointers before exit */
    xsup[nsuper+1] = jcolp1;
    supno[jcolp1]  = nsuper;
    xprune[jcol]   = nextl;	/* Initialize upper bound for pruning */
    xlsub[jcolp1]  = nextl;

    return 0;
}
