146 lines
3.9 KiB
C
146 lines
3.9 KiB
C
|
|
||
|
|
/*! @file slaqgs.c
|
||
|
|
* \brief Equlibrates a general sprase matrix
|
||
|
|
*
|
||
|
|
* <pre>
|
||
|
|
* -- SuperLU routine (version 2.0) --
|
||
|
|
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
|
||
|
|
* and Lawrence Berkeley National Lab.
|
||
|
|
* November 15, 1997
|
||
|
|
*
|
||
|
|
* Modified from LAPACK routine SLAQGE
|
||
|
|
* </pre>
|
||
|
|
*/
|
||
|
|
/*
|
||
|
|
* File name: slaqgs.c
|
||
|
|
* History: Modified from LAPACK routine SLAQGE
|
||
|
|
*/
|
||
|
|
#include <math.h>
|
||
|
|
#include "slu_sdefs.h"
|
||
|
|
|
||
|
|
/*! \brief
|
||
|
|
*
|
||
|
|
* <pre>
|
||
|
|
* Purpose
|
||
|
|
* =======
|
||
|
|
*
|
||
|
|
* SLAQGS 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 = NC; Dtype = SLU_S; Mtype = 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) char*
|
||
|
|
* Specifies the form of equilibration that was done.
|
||
|
|
* = 'N': No equilibration
|
||
|
|
* = 'R': Row equilibration, i.e., A has been premultiplied by
|
||
|
|
* diag(R).
|
||
|
|
* = 'C': Column equilibration, i.e., A has been postmultiplied
|
||
|
|
* by diag(C).
|
||
|
|
* = 'B': 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.
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
* </pre>
|
||
|
|
*/
|
||
|
|
|
||
|
|
void
|
||
|
|
slaqgs(SuperMatrix *A, float *r, float *c,
|
||
|
|
float rowcnd, float colcnd, float amax, char *equed)
|
||
|
|
{
|
||
|
|
|
||
|
|
|
||
|
|
#define THRESH (0.1)
|
||
|
|
|
||
|
|
/* Local variables */
|
||
|
|
NCformat *Astore;
|
||
|
|
float *Aval;
|
||
|
|
int i, j, irow;
|
||
|
|
float large, small, cj;
|
||
|
|
|
||
|
|
|
||
|
|
/* Quick return if possible */
|
||
|
|
if (A->nrow <= 0 || A->ncol <= 0) {
|
||
|
|
*(unsigned char *)equed = 'N';
|
||
|
|
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)
|
||
|
|
*(unsigned char *)equed = 'N';
|
||
|
|
else {
|
||
|
|
/* Column scaling */
|
||
|
|
for (j = 0; j < A->ncol; ++j) {
|
||
|
|
cj = c[j];
|
||
|
|
for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
|
||
|
|
Aval[i] *= cj;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
*(unsigned char *)equed = 'C';
|
||
|
|
}
|
||
|
|
} 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];
|
||
|
|
Aval[i] *= r[irow];
|
||
|
|
}
|
||
|
|
*(unsigned char *)equed = 'R';
|
||
|
|
} 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];
|
||
|
|
Aval[i] *= cj * r[irow];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
*(unsigned char *)equed = 'B';
|
||
|
|
}
|
||
|
|
|
||
|
|
return;
|
||
|
|
|
||
|
|
} /* slaqgs */
|
||
|
|
|