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/*! @file zlaqgs.c
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 * \brief Equlibrates a general sprase matrix
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 *
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 * 
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 * -- SuperLU routine (version 2.0) --
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 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
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 * and Lawrence Berkeley National Lab.
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 * November 15, 1997
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 * 
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 * Modified from LAPACK routine ZLAQGE
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 * 
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 */
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/*
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 * File name:	zlaqgs.c
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 * History:     Modified from LAPACK routine ZLAQGE
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 */
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#include <math.h></math.h>
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#include "slu_zdefs.h"
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/*! \brief
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 *
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 * 
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 *   Purpose   
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 *   =======   
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 *
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 *   ZLAQGS equilibrates a general sparse M by N matrix A using the row and   
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 *   scaling factors in the vectors R and C.   
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 *
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 *   See supermatrix.h for the definition of 'SuperMatrix' structure.
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 *
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 *   Arguments   
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 *   =========   
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 *
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 *   A       (input/output) SuperMatrix*
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 *           On exit, the equilibrated matrix.  See EQUED for the form of 
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 *           the equilibrated matrix. The type of A can be:
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 *	    Stype = NC; Dtype = SLU_Z; Mtype = GE.
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 *	    
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 *   R       (input) double*, dimension (A->nrow)
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 *           The row scale factors for A.
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 *	    
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 *   C       (input) double*, dimension (A->ncol)
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 *           The column scale factors for A.
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 *	    
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 *   ROWCND  (input) double
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 *           Ratio of the smallest R(i) to the largest R(i).
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 *	    
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 *   COLCND  (input) double
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 *           Ratio of the smallest C(i) to the largest C(i).
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 *	    
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 *   AMAX    (input) double
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 *           Absolute value of largest matrix entry.
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 *	    
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 *   EQUED   (output) char*
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 *           Specifies the form of equilibration that was done.   
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 *           = 'N':  No equilibration   
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 *           = 'R':  Row equilibration, i.e., A has been premultiplied by  
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 *                   diag(R).   
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 *           = 'C':  Column equilibration, i.e., A has been postmultiplied  
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 *                   by diag(C).   
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 *           = 'B':  Both row and column equilibration, i.e., A has been
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 *                   replaced by diag(R) * A * diag(C).   
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 *
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 *   Internal Parameters   
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 *   ===================   
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 *
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 *   THRESH is a threshold value used to decide if row or column scaling   
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 *   should be done based on the ratio of the row or column scaling   
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 *   factors.  If ROWCND < THRESH, row scaling is done, and if   
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 *   COLCND < THRESH, column scaling is done.   
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 *
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 *   LARGE and SMALL are threshold values used to decide if row scaling   
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 *   should be done based on the absolute size of the largest matrix   
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 *   element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.   
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 *
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 *   ===================================================================== 
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 * 
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 */
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void
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zlaqgs(SuperMatrix *A, double *r, double *c, 
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	double rowcnd, double colcnd, double amax, char *equed)
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{
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#define THRESH    (0.1)
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    /* Local variables */
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    NCformat *Astore;
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    doublecomplex   *Aval;
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    int i, j, irow;
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    double large, small, cj;
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    double temp;
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    /* Quick return if possible */
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    if (A->nrow <= 0 || A->ncol <= 0) {
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	*(unsigned char *)equed = 'N';
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	return;
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    }
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    Astore = A->Store;
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    Aval = Astore->nzval;
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    /* Initialize LARGE and SMALL. */
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    small = dlamch_("Safe minimum") / dlamch_("Precision");
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    large = 1. / small;
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    if (rowcnd >= THRESH && amax >= small && amax <= large) {
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	if (colcnd >= THRESH)
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	    *(unsigned char *)equed = 'N';
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	else {
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	    /* Column scaling */
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	    for (j = 0; j < A->ncol; ++j) {
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		cj = c[j];
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		for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
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		    zd_mult(&Aval[i], &Aval[i], cj);
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                }
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	    }
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	    *(unsigned char *)equed = 'C';
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	}
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    } else if (colcnd >= THRESH) {
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	/* Row scaling, no column scaling */
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	for (j = 0; j < A->ncol; ++j)
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	    for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
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		irow = Astore->rowind[i];
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		zd_mult(&Aval[i], &Aval[i], r[irow]);
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	    }
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	*(unsigned char *)equed = 'R';
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    } else {
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	/* Row and column scaling */
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	for (j = 0; j < A->ncol; ++j) {
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	    cj = c[j];
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	    for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
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		irow = Astore->rowind[i];
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		temp = cj * r[irow];
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		zd_mult(&Aval[i], &Aval[i], temp);
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	    }
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	}
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	*(unsigned char *)equed = 'B';
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    }
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    return;
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} /* zlaqgs */
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