/*! @file heap_relax_snode.c
 * \brief Identify the initial relaxed supernodes
 *
 * <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_ddefs.h"

/*! \brief
 *
 * <pre>
 * Purpose
 * =======
 *    relax_snode() - Identify the initial relaxed supernodes, assuming that 
 *    the matrix has been reordered according to the postorder of the etree.
 * </pre>
 */ 

void
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 */
	     )
{
    register int i, j, k, l, 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);
    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 (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 */
	    ++nsuper_et;
	} else {
	    for (i = snode_start; i <= j; ++i) {
	        l = inv_post[i];
	        if ( descendants[i] == 0 ) {
		    relax_end[l] = 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);
}