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/*! @file slaqgs.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 SLAQGE
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*
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*/
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/*
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* File name: slaqgs.c
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* History: Modified from LAPACK routine SLAQGE
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*/
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#include <math.h></math.h>
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#include "slu_sdefs.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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* SLAQGS 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_S; Mtype = GE.
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*
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* R (input) float*, dimension (A->nrow)
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* The row scale factors for A.
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*
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* C (input) float*, dimension (A->ncol)
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* The column scale factors for A.
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*
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* ROWCND (input) float
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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) float
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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) float
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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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slaqgs(SuperMatrix *A, float *r, float *c,
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float rowcnd, float colcnd, float 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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float *Aval;
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int i, j, irow;
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float large, small, cj;
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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 = slamch_("Safe minimum") / slamch_("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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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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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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Aval[i] *= cj * r[irow];
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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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} /* slaqgs */
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