/*! \file
Copyright (c) 2003, The Regents of the University of California, through
Lawrence Berkeley National Laboratory (subject to receipt of any required 
approvals from U.S. Dept. of Energy) 

All rights reserved. 

The source code is distributed under BSD license, see the file License.txt
at the top-level directory.
*/

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


#include <math.h>
#include <stdlib.h>
#include "slu_zdefs.h"

#ifndef SGN
#define SGN(x) ((x)>=0?1:-1)
#endif

/*! \brief
 *
 * <pre>
 * 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.
 * </pre>
 */

int
ilu_zpivotL(
	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	   diagind,  /* diagonal of Pc*A*Pc' */
	int	   *swap,    /* in/out record the row permutation */
	int	   *iswap,   /* in/out inverse of swap, it is the same as
				perm_r after the factorization */
	int	   *marker,  /* in */
	int	   *pivrow,  /* in/out, as an input if *usepr!=0 */
	double	   fill_tol, /* in - fill tolerance of current column
			      * used for a singular column */
	milu_t	   milu,     /* in */
	doublecomplex	   drop_sum, /* in - computed in ilu_zcopy_to_ucol()
                                (MILU only) */
	GlobalLU_t *Glu,     /* modified - global LU data structures */
	SuperLUStat_t *stat  /* output */
       )
{

    int		 n;	 /* number of columns */
    int		 fsupc;  /* first column in the supernode */
    int		 nsupc;  /* no of columns in the supernode */
    int		 nsupr;  /* no of rows in the supernode */
    int_t	 lptr;	 /* points to the starting subscript of the supernode */
    register int	 pivptr;
    int		 old_pivptr, diag, ptr0;
    register double  pivmax, rtemp;
    double	 thresh;
    doublecomplex	 temp;
    doublecomplex	 *lu_sup_ptr;
    doublecomplex	 *lu_col_ptr;
    int_t	 *lsub_ptr;
    register int	 isub, icol, k, itemp;
    int_t	 *lsub, *xlsub;
    doublecomplex	 *lusup;
    int_t	 *xlusup;
    flops_t	 *ops = stat->ops;
    int		 info;
    doublecomplex one = {1.0, 0.0};

    /* Initialize pointers */
    n	       = Glu->n;
    lsub       = Glu->lsub;
    xlsub      = Glu->xlsub;
    lusup      = (doublecomplex *) 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 */

    /* Determine the largest abs numerical value for partial pivoting;
       Also search for user-specified pivot, and diagonal element. */
    pivmax = -1.0;
    pivptr = nsupc;
    diag = EMPTY;
    old_pivptr = nsupc;
    ptr0 = EMPTY;
    for (isub = nsupc; isub < nsupr; ++isub) {
        if (marker[lsub_ptr[isub]] > jcol)
            continue; /* do not overlap with a later relaxed supernode */

	switch (milu) {
	    case SMILU_1:
                z_add(&temp, &lu_col_ptr[isub], &drop_sum);
		rtemp = z_abs1(&temp);
		break;
	    case SMILU_2:
	    case SMILU_3:
                /* In this case, drop_sum contains the sum of the abs. value */
		rtemp = z_abs1(&lu_col_ptr[isub]);
		break;
	    case SILU:
	    default:
		rtemp = z_abs1(&lu_col_ptr[isub]);
		break;
	}
	if (rtemp > pivmax) { pivmax = rtemp; pivptr = isub; }
	if (*usepr && lsub_ptr[isub] == *pivrow) old_pivptr = isub;
	if (lsub_ptr[isub] == diagind) diag = isub;
	if (ptr0 == EMPTY) ptr0 = isub;
    }

    if (milu == SMILU_2 || milu == SMILU_3) pivmax += drop_sum.r;

    /* Test for singularity */
    if (pivmax < 0.0) {
#if SCIPY_FIX
	ABORT("[0]: matrix is singular");
#else
    	/*fprintf(stderr, "[0]: jcol=%d, SINGULAR!!!\n", jcol);
	fflush(stderr);
	exit(1); */
	*usepr = 0;
	return (jcol+1);
#endif
    }
    if ( pivmax == 0.0 ) {
	if (diag != EMPTY)
	    *pivrow = lsub_ptr[pivptr = diag];
	else if (ptr0 != EMPTY)
	    *pivrow = lsub_ptr[pivptr = ptr0];
	else {
	    /* look for the first row which does not
	       belong to any later supernodes */
	    for (icol = jcol; icol < n; icol++)
		if (marker[swap[icol]] <= jcol) break;
	    if (icol >= n) {
#if SCIPY_FIX
	ABORT("[1]: matrix is singular");
#else
		/* fprintf(stderr, "[1]: jcol=%d, SINGULAR!!!\n", jcol);
		fflush(stderr);
		exit(1); */
   	        *usepr = 0;
	        return (jcol+1);
#endif
	    }

	    *pivrow = swap[icol];

	    /* pick up the pivot row */
	    for (isub = nsupc; isub < nsupr; ++isub)
		if ( lsub_ptr[isub] == *pivrow ) { pivptr = isub; break; }
	}
	pivmax = fill_tol;
	lu_col_ptr[pivptr].r = pivmax;
	lu_col_ptr[pivptr].i = 0.0;
	*usepr = 0;
#ifdef DEBUG
	printf("[0] ZERO PIVOT: FILL (%d, %d).\n", *pivrow, jcol);
	fflush(stdout);
#endif
	info = jcol + 1;
    } /* end if (*pivrow == 0.0) */
    else {
	thresh = u * pivmax;

	/* Choose appropriate pivotal element by our policy. */
	if ( *usepr ) {
	    switch (milu) {
		case SMILU_1:
                    z_add(&temp, &lu_col_ptr[old_pivptr], &drop_sum);
		    rtemp = z_abs1(&temp);
		    break;
		case SMILU_2:
		case SMILU_3:
		    rtemp = z_abs1(&lu_col_ptr[old_pivptr]) + drop_sum.r;
		    break;
		case SILU:
		default:
		    rtemp = z_abs1(&lu_col_ptr[old_pivptr]);
		    break;
	    }
	    if ( rtemp != 0.0 && rtemp >= thresh ) pivptr = old_pivptr;
	    else *usepr = 0;
	}
	if ( *usepr == 0 ) {
	    /* Use diagonal pivot? */
	    if ( diag >= 0 ) { /* diagonal exists */
		switch (milu) {
		    case SMILU_1:
                        z_add(&temp, &lu_col_ptr[diag], &drop_sum);
         	        rtemp = z_abs1(&temp);
			break;
		    case SMILU_2:
		    case SMILU_3:
			rtemp = z_abs1(&lu_col_ptr[diag]) + drop_sum.r;
			break;
		    case SILU:
		    default:
			rtemp = z_abs1(&lu_col_ptr[diag]);
			break;
		}
		if ( rtemp != 0.0 && rtemp >= thresh ) pivptr = diag;
	    }
	    *pivrow = lsub_ptr[pivptr];
	}
	info = 0;

	/* Reset the diagonal */
	switch (milu) {
	    case SMILU_1:
		z_add(&lu_col_ptr[pivptr], &lu_col_ptr[pivptr], &drop_sum);
		break;
	    case SMILU_2:
	    case SMILU_3:
                temp = z_sgn(&lu_col_ptr[pivptr]);
                zz_mult(&temp, &temp, &drop_sum);
                z_add(&lu_col_ptr[pivptr], &lu_col_ptr[pivptr], &drop_sum);
		break;
	    case SILU:
	    default:
		break;
	}

    } /* end else */

    /* Record pivot row */
    perm_r[*pivrow] = jcol;
    if (jcol < n - 1) {
	register int t1, t2, t;
	t1 = iswap[*pivrow]; t2 = jcol;
	if (t1 != t2) {
	    t = swap[t1]; swap[t1] = swap[t2]; swap[t2] = t;
	    t1 = swap[t1]; t2 = t;
	    t = iswap[t1]; iswap[t1] = iswap[t2]; iswap[t2] = t;
	}
    } /* if (jcol < n - 1) */

    /* 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] += 10 * (nsupr - nsupc);
    z_div(&temp, &one, &lu_col_ptr[nsupc]);
    for (k = nsupc+1; k < nsupr; k++) 
	zz_mult(&lu_col_ptr[k], &lu_col_ptr[k], &temp);

    return info;
}
