/** \file opennl/superlu/spivotL.c
 *  \ingroup opennl
 */

/*
 * -- 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 <math.h>
#include <stdlib.h>
#include "ssp_defs.h"

#undef DEBUG

int
spivotL(
        const int  jcol,     /* in */
        const double u,      /* in - diagonal pivoting threshold */
        int        *usepr,   /* re-use the pivot sequence given by perm_r/iperm_r */
        int        *perm_r,  /* may be modified */
        int        *iperm_r, /* in - inverse of perm_r */
        int        *iperm_c, /* in - used to find diagonal of Pc*A*Pc' */
        int        *pivrow,  /* out */
        GlobalLU_t *Glu,     /* modified - global LU data structures */
	SuperLUStat_t *stat  /* output */
       )
{
/*
 * Purpose
 * =======
 *   Performs the numerical pivoting on the current column of L,
 *   and the CDIV operation.
 *
 *   Pivot policy:
 *   (1) Compute thresh = u * max_(i>=j) abs(A_ij);
 *   (2) IF user specifies pivot row k and abs(A_kj) >= thresh THEN
 *           pivot row = k;
 *       ELSE IF abs(A_jj) >= thresh THEN
 *           pivot row = j;
 *       ELSE
 *           pivot row = m;
 * 
 *   Note: If you absolutely want to use a given pivot order, then set u=0.0.
 *
 *   Return value: 0      success;
 *                 i > 0  U(i,i) is exactly zero.
 *
 */
    int          fsupc;	    /* first column in the supernode */
    int          nsupc;	    /* no of columns in the supernode */
    int          nsupr;     /* no of rows in the supernode */
    int          lptr;	    /* points to the starting subscript of the supernode */
    int          pivptr, old_pivptr, diag, diagind;
    double       pivmax, rtemp, thresh;
    double       temp;
    double       *lu_sup_ptr; 
    double       *lu_col_ptr;
    int          *lsub_ptr;
    int          isub, icol, k, itemp;
    int          *lsub, *xlsub;
    double       *lusup;
    int          *xlusup;
    flops_t      *ops = stat->ops;

    /* Initialize pointers */
    lsub       = Glu->lsub;
    xlsub      = Glu->xlsub;
    lusup      = Glu->lusup;
    xlusup     = Glu->xlusup;
    fsupc      = (Glu->xsup)[(Glu->supno)[jcol]];
    nsupc      = jcol - fsupc;	        /* excluding jcol; nsupc >= 0 */
    lptr       = xlsub[fsupc];
    nsupr      = xlsub[fsupc+1] - lptr;
    lu_sup_ptr = &lusup[xlusup[fsupc]];	/* start of the current supernode */
    lu_col_ptr = &lusup[xlusup[jcol]];	/* start of jcol in the supernode */
    lsub_ptr   = &lsub[lptr];	/* start of row indices of the supernode */

#ifdef DEBUG
if ( jcol == MIN_COL ) {
    printf("Before cdiv: col %d\n", jcol);
    for (k = nsupc; k < nsupr; k++) 
	printf("  lu[%d] %f\n", lsub_ptr[k], lu_col_ptr[k]);
}
#endif
    
    /* Determine the largest abs numerical value for partial pivoting;
       Also search for user-specified pivot, and diagonal element. */
    if ( *usepr ) *pivrow = iperm_r[jcol];
    diagind = iperm_c[jcol];
    pivmax = 0.0;
    pivptr = nsupc;
    diag = EMPTY;
    old_pivptr = nsupc;
    for (isub = nsupc; isub < nsupr; ++isub) {
	rtemp = fabs (lu_col_ptr[isub]);
	if ( rtemp > pivmax ) {
	    pivmax = rtemp;
	    pivptr = isub;
	}
	if ( *usepr && lsub_ptr[isub] == *pivrow ) old_pivptr = isub;
	if ( lsub_ptr[isub] == diagind ) diag = isub;
    }

    /* Test for singularity */
    if ( pivmax == 0.0 ) {
	*pivrow = lsub_ptr[pivptr];
	perm_r[*pivrow] = jcol;
	*usepr = 0;
	return (jcol+1);
    }

    thresh = u * pivmax;
    
    /* Choose appropriate pivotal element by our policy. */
    if ( *usepr ) {
        rtemp = fabs (lu_col_ptr[old_pivptr]);
	if ( rtemp != 0.0 && rtemp >= thresh )
	    pivptr = old_pivptr;
	else
	    *usepr = 0;
    }
    if ( *usepr == 0 ) {
	/* Use diagonal pivot? */
	if ( diag >= 0 ) { /* diagonal exists */
	    rtemp = fabs (lu_col_ptr[diag]);
	    if ( rtemp != 0.0 && rtemp >= thresh ) pivptr = diag;
        }
	*pivrow = lsub_ptr[pivptr];
    }
    
    /* Record pivot row */
    perm_r[*pivrow] = jcol;
    
    /* Interchange row subscripts */
    if ( pivptr != nsupc ) {
	itemp = lsub_ptr[pivptr];
	lsub_ptr[pivptr] = lsub_ptr[nsupc];
	lsub_ptr[nsupc] = itemp;

	/* Interchange numerical values as well, for the whole snode, such 
	 * that L is indexed the same way as A.
 	 */
	for (icol = 0; icol <= nsupc; icol++) {
	    itemp = pivptr + icol * nsupr;
	    temp = lu_sup_ptr[itemp];
	    lu_sup_ptr[itemp] = lu_sup_ptr[nsupc + icol*nsupr];
	    lu_sup_ptr[nsupc + icol*nsupr] = temp;
	}
    } /* if */

    /* cdiv operation */
    ops[FACT] += nsupr - nsupc;

    temp = 1.0 / lu_col_ptr[nsupc];
    for (k = nsupc+1; k < nsupr; k++) 
	lu_col_ptr[k] *= temp;

    return 0;
}

