/*! @file ilu_heap_relax_snode.c

 * \brief Identify the initial relaxed supernodes

 *

 * 

 * -- SuperLU routine (version 4.0) --

 * Lawrence Berkeley National Laboratory

 * June 1, 2009

 * 

 */

#include "slu_ddefs.h"

/*! \brief

 *

 * 

 * Purpose

 * =======

 *    ilu_heap_relax_snode() - Identify the initial relaxed supernodes,

 *    assuming that the matrix has been reordered according to the postorder

 *    of the etree.

 * 

 */

void

ilu_heap_relax_snode (

	     const     int n,

	     int       *et,	      /* column elimination tree */

	     const int relax_columns, /* max no of columns allowed in a

					 relaxed snode */

	     int       *descendants,  /* no of descendants of each node

					 in the etree */

	     int       *relax_end,    /* last column in a supernode

				       * if j-th column starts a relaxed

				       * supernode, relax_end[j] represents

				       * the last column of this supernode */

	     int       *relax_fsupc   /* first column in a supernode

				       * relax_fsupc[j] represents the first

				       * column of j-th supernode */

	     )

{

    register int i, j, k, l, f, parent;

    register int snode_start;	/* beginning of a snode */

    int *et_save, *post, *inv_post, *iwork;

    int nsuper_et = 0, nsuper_et_post = 0;

    /* The etree may not be postordered, but is heap ordered. */

    iwork = (int*) intMalloc(3*n+2);

    if ( !iwork ) ABORT("SUPERLU_MALLOC fails for iwork[]");

    inv_post = iwork + n+1;

    et_save = inv_post + n+1;

    /* Post order etree */

    post = (int *) TreePostorder(n, et);

    for (i = 0; i < n+1; ++i) inv_post[post[i]] = i;

    /* Renumber etree in postorder */

    for (i = 0; i < n; ++i) {

	iwork[post[i]] = post[et[i]];

	et_save[i] = et[i]; /* Save the original etree */

    }

    for (i = 0; i < n; ++i) et[i] = iwork[i];

    /* Compute the number of descendants of each node in the etree */

    ifill (relax_end, n, EMPTY);

    ifill (relax_fsupc, n, EMPTY);

    for (j = 0; j < n; j++) descendants[j] = 0;

    for (j = 0; j < n; j++) {

	parent = et[j];

	if ( parent != n )  /* not the dummy root */

	    descendants[parent] += descendants[j] + 1;

    }

    /* Identify the relaxed supernodes by postorder traversal of the etree. */

    for ( f = j = 0; j < n; ) {

	parent = et[j];

	snode_start = j;

	while ( parent != n && descendants[parent] < relax_columns ) {

	    j = parent;

	    parent = et[j];

	}

	/* Found a supernode in postordered etree; j is the last column. */

	++nsuper_et_post;

	k = n;

	for (i = snode_start; i <= j; ++i)

	    k = SUPERLU_MIN(k, inv_post[i]);

	l = inv_post[j];

	if ( (l - k) == (j - snode_start) ) {

	    /* It's also a supernode in the original etree */

	    relax_end[k] = l;		/* Last column is recorded */

	    relax_fsupc[f++] = k;

	    ++nsuper_et;

	} else {

	    for (i = snode_start; i <= j; ++i) {

		l = inv_post[i];

		if ( descendants[i] == 0 ) {

		    relax_end[l] = l;

		    relax_fsupc[f++] = l;

		    ++nsuper_et;

		}

	    }

	}

	j++;

	/* Search for a new leaf */

	while ( descendants[j] != 0 && j < n ) j++;

    }

#if ( PRNTlevel>=1 )

    printf(".. heap_snode_relax:\n"

	   "\tNo of relaxed snodes in postordered etree:\t%d\n"

	   "\tNo of relaxed snodes in original etree:\t%d\n",

	   nsuper_et_post, nsuper_et);

#endif

    /* Recover the original etree */

    for (i = 0; i < n; ++i) et[i] = et_save[i];

    SUPERLU_FREE(post);

    SUPERLU_FREE(iwork);

}