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

#include "slu_sdefs.h"


/*! \brief
 *
 * <pre>
 * Purpose
 * =======
 *   ILU_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.
 * </pre>
 */
int
ilu_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	      *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; 	/* 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(7);
	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 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 = 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[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 = 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[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;
}
