kusano 7d535a
kusano 7d535a
/*! @file dlaqgs.c
kusano 7d535a
 * \brief Equlibrates a general sprase matrix
kusano 7d535a
 *
kusano 7d535a
 * 
kusano 7d535a
 * -- SuperLU routine (version 2.0) --
kusano 7d535a
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
kusano 7d535a
 * and Lawrence Berkeley National Lab.
kusano 7d535a
 * November 15, 1997
kusano 7d535a
 * 
kusano 7d535a
 * Modified from LAPACK routine DLAQGE
kusano 7d535a
 * 
kusano 7d535a
 */
kusano 7d535a
/*
kusano 7d535a
 * File name:	dlaqgs.c
kusano 7d535a
 * History:     Modified from LAPACK routine DLAQGE
kusano 7d535a
 */
kusano 7d535a
#include <math.h></math.h>
kusano 7d535a
#include "slu_ddefs.h"
kusano 7d535a
kusano 7d535a
/*! \brief
kusano 7d535a
 *
kusano 7d535a
 * 
kusano 7d535a
 *   Purpose   
kusano 7d535a
 *   =======   
kusano 7d535a
 *
kusano 7d535a
 *   DLAQGS equilibrates a general sparse M by N matrix A using the row and   
kusano 7d535a
 *   scaling factors in the vectors R and C.   
kusano 7d535a
 *
kusano 7d535a
 *   See supermatrix.h for the definition of 'SuperMatrix' structure.
kusano 7d535a
 *
kusano 7d535a
 *   Arguments   
kusano 7d535a
 *   =========   
kusano 7d535a
 *
kusano 7d535a
 *   A       (input/output) SuperMatrix*
kusano 7d535a
 *           On exit, the equilibrated matrix.  See EQUED for the form of 
kusano 7d535a
 *           the equilibrated matrix. The type of A can be:
kusano 7d535a
 *	    Stype = NC; Dtype = SLU_D; Mtype = GE.
kusano 7d535a
 *	    
kusano 7d535a
 *   R       (input) double*, dimension (A->nrow)
kusano 7d535a
 *           The row scale factors for A.
kusano 7d535a
 *	    
kusano 7d535a
 *   C       (input) double*, dimension (A->ncol)
kusano 7d535a
 *           The column scale factors for A.
kusano 7d535a
 *	    
kusano 7d535a
 *   ROWCND  (input) double
kusano 7d535a
 *           Ratio of the smallest R(i) to the largest R(i).
kusano 7d535a
 *	    
kusano 7d535a
 *   COLCND  (input) double
kusano 7d535a
 *           Ratio of the smallest C(i) to the largest C(i).
kusano 7d535a
 *	    
kusano 7d535a
 *   AMAX    (input) double
kusano 7d535a
 *           Absolute value of largest matrix entry.
kusano 7d535a
 *	    
kusano 7d535a
 *   EQUED   (output) char*
kusano 7d535a
 *           Specifies the form of equilibration that was done.   
kusano 7d535a
 *           = 'N':  No equilibration   
kusano 7d535a
 *           = 'R':  Row equilibration, i.e., A has been premultiplied by  
kusano 7d535a
 *                   diag(R).   
kusano 7d535a
 *           = 'C':  Column equilibration, i.e., A has been postmultiplied  
kusano 7d535a
 *                   by diag(C).   
kusano 7d535a
 *           = 'B':  Both row and column equilibration, i.e., A has been
kusano 7d535a
 *                   replaced by diag(R) * A * diag(C).   
kusano 7d535a
 *
kusano 7d535a
 *   Internal Parameters   
kusano 7d535a
 *   ===================   
kusano 7d535a
 *
kusano 7d535a
 *   THRESH is a threshold value used to decide if row or column scaling   
kusano 7d535a
 *   should be done based on the ratio of the row or column scaling   
kusano 7d535a
 *   factors.  If ROWCND < THRESH, row scaling is done, and if   
kusano 7d535a
 *   COLCND < THRESH, column scaling is done.   
kusano 7d535a
 *
kusano 7d535a
 *   LARGE and SMALL are threshold values used to decide if row scaling   
kusano 7d535a
 *   should be done based on the absolute size of the largest matrix   
kusano 7d535a
 *   element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.   
kusano 7d535a
 *
kusano 7d535a
 *   ===================================================================== 
kusano 7d535a
 * 
kusano 7d535a
 */
kusano 7d535a
kusano 7d535a
void
kusano 7d535a
dlaqgs(SuperMatrix *A, double *r, double *c, 
kusano 7d535a
	double rowcnd, double colcnd, double amax, char *equed)
kusano 7d535a
{
kusano 7d535a
kusano 7d535a
kusano 7d535a
#define THRESH    (0.1)
kusano 7d535a
    
kusano 7d535a
    /* Local variables */
kusano 7d535a
    NCformat *Astore;
kusano 7d535a
    double   *Aval;
kusano 7d535a
    int i, j, irow;
kusano 7d535a
    double large, small, cj;
kusano 7d535a
kusano 7d535a
kusano 7d535a
    /* Quick return if possible */
kusano 7d535a
    if (A->nrow <= 0 || A->ncol <= 0) {
kusano 7d535a
	*(unsigned char *)equed = 'N';
kusano 7d535a
	return;
kusano 7d535a
    }
kusano 7d535a
kusano 7d535a
    Astore = A->Store;
kusano 7d535a
    Aval = Astore->nzval;
kusano 7d535a
    
kusano 7d535a
    /* Initialize LARGE and SMALL. */
kusano 7d535a
    small = dlamch_("Safe minimum") / dlamch_("Precision");
kusano 7d535a
    large = 1. / small;
kusano 7d535a
kusano 7d535a
    if (rowcnd >= THRESH && amax >= small && amax <= large) {
kusano 7d535a
	if (colcnd >= THRESH)
kusano 7d535a
	    *(unsigned char *)equed = 'N';
kusano 7d535a
	else {
kusano 7d535a
	    /* Column scaling */
kusano 7d535a
	    for (j = 0; j < A->ncol; ++j) {
kusano 7d535a
		cj = c[j];
kusano 7d535a
		for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
kusano 7d535a
		    Aval[i] *= cj;
kusano 7d535a
                }
kusano 7d535a
	    }
kusano 7d535a
	    *(unsigned char *)equed = 'C';
kusano 7d535a
	}
kusano 7d535a
    } else if (colcnd >= THRESH) {
kusano 7d535a
	/* Row scaling, no column scaling */
kusano 7d535a
	for (j = 0; j < A->ncol; ++j)
kusano 7d535a
	    for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
kusano 7d535a
		irow = Astore->rowind[i];
kusano 7d535a
		Aval[i] *= r[irow];
kusano 7d535a
	    }
kusano 7d535a
	*(unsigned char *)equed = 'R';
kusano 7d535a
    } else {
kusano 7d535a
	/* Row and column scaling */
kusano 7d535a
	for (j = 0; j < A->ncol; ++j) {
kusano 7d535a
	    cj = c[j];
kusano 7d535a
	    for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
kusano 7d535a
		irow = Astore->rowind[i];
kusano 7d535a
		Aval[i] *= cj * r[irow];
kusano 7d535a
	    }
kusano 7d535a
	}
kusano 7d535a
	*(unsigned char *)equed = 'B';
kusano 7d535a
    }
kusano 7d535a
kusano 7d535a
    return;
kusano 7d535a
kusano 7d535a
} /* dlaqgs */
kusano 7d535a