/*! @file scolumn_dfs.c

 * \brief Performs a symbolic factorization

 *

 * 

 * -- 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.

 * 

*/

#include "slu_sdefs.h"

/*! \brief What type of supernodes we want */

#define T2_SUPER

/*! \brief

 *

 * 

 * Purpose

 * =======

 *   SCOLUMN_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.

 * 

 */

int

scolumn_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 = sLUMemXpand(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 =

					 sLUMemXpand(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;

}