/*! \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.
*/

/*
 * -- SuperLU routine (version 3.0) --
 * Lawrence Berkeley National Lab, Univ. of California Berkeley,
 * and Xerox Palo Alto Research Center.
 * September 10, 2007
 *
 */
/*
 * File name:	claqgs.c
 * History:     Modified from LAPACK routine CLAQGE
 */
#include <math.h>
#include "slu_mt_cdefs.h"

void claqgs(SuperMatrix* A, float* r, float* c, float rowcnd, float colcnd, float amax, equed_t* equed) {
    /*
        Purpose
        =======

        claqgs() equilibrates a general sparse M by N matrix A using the row and
        scaling factors in the vectors R and C.

        See supermatrix.h for the definition of 'SuperMatrix' structure.

        Arguments
        =========

        A       (input/output) SuperMatrix*
                On exit, the equilibrated matrix.  See EQUED for the form of
                the equilibrated matrix. The type of A can be:
            Stype = SLU_NC; Dtype = SLU_C; Mtype = SLU_GE.

        R       (input) float*, dimension (A->nrow)
                The row scale factors for A.

        C       (input) float*, dimension (A->ncol)
                The column scale factors for A.

        ROWCND  (input) float
                Ratio of the smallest R(i) to the largest R(i).

        COLCND  (input) float
                Ratio of the smallest C(i) to the largest C(i).

        AMAX    (input) float
                Absolute value of largest matrix entry.

        EQUED   (output) equed_t*
                Specifies the form of equilibration that was done.
                = NOEQUIL: No equilibration
                = ROW:  Row equilibration, i.e., A has been premultiplied by
                        diag(R).
                = COL:  Column equilibration, i.e., A has been postmultiplied
                        by diag(C).
                = BOTH: Both row and column equilibration, i.e., A has been
                        replaced by diag(R) * A * diag(C).

        Internal Parameters
        ===================

        THRESH is a threshold value used to decide if row or column scaling
        should be done based on the ratio of the row or column scaling
        factors.  If ROWCND < THRESH, row scaling is done, and if
        COLCND < THRESH, column scaling is done.

        LARGE and SMALL are threshold values used to decide if row scaling
        should be done based on the absolute size of the largest matrix
        element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.

        =====================================================================
    */

#define THRESH (0.1)

    /* Local variables */
    NCformat* Astore;
    complex* Aval;
    int_t i, j, irow;
    float large, small, cj;
    extern double slamch_(char*);
    float temp;

    /* Quick return if possible */
    if(A->nrow <= 0 || A->ncol <= 0) {
        *equed = NOEQUIL;
        return;
    }

    Astore = A->Store;
    Aval = Astore->nzval;

    /* Initialize LARGE and SMALL. */
    small = slamch_("Safe minimum") / slamch_("Precision");
    large = 1. / small;

    if(rowcnd >= THRESH && amax >= small && amax <= large) {
        if(colcnd >= THRESH)
            *equed = NOEQUIL;
        else {
            /* Column scaling */
            for(j = 0; j < A->ncol; ++j) {
                cj = c[j];
                for(i = Astore->colptr[j]; i < Astore->colptr[j + 1]; ++i) {
                    cs_mult(&Aval[i], &Aval[i], cj);
                }
            }
            *equed = COL;
        }
    }
    else if(colcnd >= THRESH) {
        /* Row scaling, no column scaling */
        for(j = 0; j < A->ncol; ++j)
            for(i = Astore->colptr[j]; i < Astore->colptr[j + 1]; ++i) {
                irow = Astore->rowind[i];
                cs_mult(&Aval[i], &Aval[i], r[irow]);
            }
        *equed = ROW;
    }
    else {
        /* Row and column scaling */
        for(j = 0; j < A->ncol; ++j) {
            cj = c[j];
            for(i = Astore->colptr[j]; i < Astore->colptr[j + 1]; ++i) {
                irow = Astore->rowind[i];
                temp = cj * r[irow];
                cs_mult(&Aval[i], &Aval[i], temp);
            }
        }
        *equed = BOTH;
    }

    return;

} /* claqgs */
