sp_coletree.c

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/*  Elimination tree computation and layout routines */

#include <stdio.h>
#include <stdlib.h>
#include "ssp_defs.h"

/* 
 *  Implementation of disjoint set union routines.
 *  Elements are integers in 0..n-1, and the 
 *  names of the sets themselves are of type int.
 *  
 *  Calls are:
 *  initialize_disjoint_sets (n) initial call.
 *  s = make_set (i)             returns a set containing only i.
 *  s = link (t, u)      returns s = t union u, destroying t and u.
 *  s = find (i)         return name of set containing i.
 *  finalize_disjoint_sets   final call.
 *
 *  This implementation uses path compression but not weighted union.
 *  See Tarjan's book for details.
 *  John Gilbert, CMI, 1987.
 *
 *  Implemented path-halving by XSL 07/05/95.
 */

static int  *pp;        /* parent array for sets */

static 
int *mxCallocInt(int n)
{
    register int i;
    int *buf;

    buf = (int *) SUPERLU_MALLOC( n * sizeof(int) );
    if ( !buf ) {
         ABORT("SUPERLU_MALLOC fails for buf in mxCallocInt()");
       }
    for (i = 0; i < n; i++) buf[i] = 0;
    return (buf);
}
      
static
void initialize_disjoint_sets (
    int n
    )
{
    pp = mxCallocInt(n);
}


static
int make_set (
    int i
    )
{
    pp[i] = i;
    return i;
}


static
int link (
    int s,
    int t
    )
{
    pp[s] = t;
    return t;
}


/* PATH HALVING */
static
int find (int i)
{
    register int p, gp;
    
    p = pp[i];
    gp = pp[p];
    while (gp != p) {
    pp[i] = gp;
    i = gp;
    p = pp[i];
    gp = pp[p];
    }
    return (p);
}

#if 0
/* PATH COMPRESSION */
static
int find (
    int i
    )
{
    if (pp[i] != i) 
        pp[i] = find (pp[i]);
    return pp[i];
}
#endif

static
void finalize_disjoint_sets (
    void
    )
{
    SUPERLU_FREE(pp);
}


/*
 *      Find the elimination tree for A'*A.
 *      This uses something similar to Liu's algorithm. 
 *      It runs in time O(nz(A)*log n) and does not form A'*A.
 *
 *      Input:
 *        Sparse matrix A.  Numeric values are ignored, so any
 *        explicit zeros are treated as nonzero.
 *      Output:
 *        Integer array of parents representing the elimination
 *        tree of the symbolic product A'*A.  Each vertex is a
 *        column of A, and nc means a root of the elimination forest.
 *
 *      John R. Gilbert, Xerox, 10 Dec 1990
 *      Based on code by JRG dated 1987, 1988, and 1990.
 */

/*
 * Nonsymmetric elimination tree
 */
int
sp_coletree(
        int *acolst, int *acolend, /* column start and end past 1 */
        int *arow,                 /* row indices of A */
        int nr, int nc,            /* dimension of A */
        int *parent                /* parent in elim tree */
        )
{
    int *root;          /* root of subtee of etree  */
    int     *firstcol;      /* first nonzero col in each row*/
    int rset, cset;             
    int row, col;
    int rroot;
    int p;

    root = mxCallocInt (nc);
    initialize_disjoint_sets (nc);

    /* Compute firstcol[row] = first nonzero column in row */

    firstcol = mxCallocInt (nr);
    for (row = 0; row < nr; firstcol[row++] = nc);
    for (col = 0; col < nc; col++) 
        for (p = acolst[col]; p < acolend[col]; p++) {
            row = arow[p];
            firstcol[row] = SUPERLU_MIN(firstcol[row], col);
        }

    /* Compute etree by Liu's algorithm for symmetric matrices,
           except use (firstcol[r],c) in place of an edge (r,c) of A.
       Thus each row clique in A'*A is replaced by a star
       centered at its first vertex, which has the same fill. */

    for (col = 0; col < nc; col++) {
        cset = make_set (col);
        root[cset] = col;
        parent[col] = nc; /* Matlab */
        for (p = acolst[col]; p < acolend[col]; p++) {
            row = firstcol[arow[p]];
            if (row >= col) continue;
            rset = find (row);
            rroot = root[rset];
            if (rroot != col) {
                parent[rroot] = col;
                cset = link (cset, rset);
                root[cset] = col;
            }
        }
    }

    SUPERLU_FREE (root);
    SUPERLU_FREE (firstcol);
    finalize_disjoint_sets ();
    return 0;
}

/*
 *  q = TreePostorder (n, p);
 *
 *  Postorder a tree.
 *  Input:
 *    p is a vector of parent pointers for a forest whose
 *        vertices are the integers 0 to n-1; p[root]==n.
 *  Output:
 *    q is a vector indexed by 0..n-1 such that q[i] is the
 *    i-th vertex in a postorder numbering of the tree.
 *
 *        ( 2/7/95 modified by X.Li:
 *          q is a vector indexed by 0:n-1 such that vertex i is the
 *          q[i]-th vertex in a postorder numbering of the tree.
 *          That is, this is the inverse of the previous q. )
 *
 *  In the child structure, lower-numbered children are represented
 *  first, so that a tree which is already numbered in postorder
 *  will not have its order changed.
 *    
 *  Written by John Gilbert, Xerox, 10 Dec 1990.
 *  Based on code written by John Gilbert at CMI in 1987.
 */

static int  *first_kid, *next_kid;  /* Linked list of children. */
static int  *post, postnum;

static
/*
 * Depth-first search from vertex v.
 */
void etdfs (
    int v
    )
{
    int w;

    for (w = first_kid[v]; w != -1; w = next_kid[w]) {
        etdfs (w);
    }
    /* post[postnum++] = v; in Matlab */
    post[v] = postnum++;    /* Modified by X.Li on 2/14/95 */
}


/*
 * Post order a tree
 */
int *TreePostorder(
    int n,
    int *parent
)
{
    int v, dad;

    /* Allocate storage for working arrays and results  */
    first_kid =     mxCallocInt (n+1);
    next_kid  =     mxCallocInt (n+1);
    post      =     mxCallocInt (n+1);

    /* Set up structure describing children */
    for (v = 0; v <= n; first_kid[v++] = -1);
    for (v = n-1; v >= 0; v--) {
        dad = parent[v];
        next_kid[v] = first_kid[dad];
        first_kid[dad] = v;
    }

    /* Depth-first search from dummy root vertex #n */
    postnum = 0;
    etdfs (n);

    SUPERLU_FREE (first_kid);
    SUPERLU_FREE (next_kid);
    return post;
}


/*
 *      p = spsymetree (A);
 *
 *      Find the elimination tree for symmetric matrix A.
 *      This uses Liu's algorithm, and runs in time O(nz*log n).
 *
 *      Input:
 *        Square sparse matrix A.  No check is made for symmetry;
 *        elements below and on the diagonal are ignored.
 *        Numeric values are ignored, so any explicit zeros are 
 *        treated as nonzero.
 *      Output:
 *        Integer array of parents representing the etree, with n
 *        meaning a root of the elimination forest.
 *      Note:  
 *        This routine uses only the upper triangle, while sparse
 *        Cholesky (as in spchol.c) uses only the lower.  Matlab's
 *        dense Cholesky uses only the upper.  This routine could
 *        be modified to use the lower triangle either by transposing
 *        the matrix or by traversing it by rows with auxiliary
 *        pointer and link arrays.
 *
 *      John R. Gilbert, Xerox, 10 Dec 1990
 *      Based on code by JRG dated 1987, 1988, and 1990.
 *      Modified by X.S. Li, November 1999.
 */

/*
 * Symmetric elimination tree
 */
int
sp_symetree(
        int *acolst, int *acolend, /* column starts and ends past 1 */
        int *arow,            /* row indices of A */
        int n,                /* dimension of A */
        int *parent     /* parent in elim tree */
        )
{
    int *root;          /* root of subtree of etree     */
    int rset, cset;             
    int row, col;
    int rroot;
    int p;

    root = mxCallocInt (n);
    initialize_disjoint_sets (n);

    for (col = 0; col < n; col++) {
        cset = make_set (col);
        root[cset] = col;
        parent[col] = n; /* Matlab */
        for (p = acolst[col]; p < acolend[col]; p++) {
            row = arow[p];
            if (row >= col) continue;
            rset = find (row);
            rroot = root[rset];
            if (rroot != col) {
                parent[rroot] = col;
                cset = link (cset, rset);
                root[cset] = col;
            }
        }
    }
    SUPERLU_FREE (root);
    finalize_disjoint_sets ();
    return 0;
} /* SP_SYMETREE */