195 lines
5.6 KiB
C
195 lines
5.6 KiB
C
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/*! @file cgsequ.c
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* \brief Computes row and column scalings
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*
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* <pre>
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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 CGEEQU
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* </pre>
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*/
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/*
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* File name: cgsequ.c
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* History: Modified from LAPACK routine CGEEQU
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*/
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#include <math.h>
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#include "slu_cdefs.h"
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/*! \brief
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*
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* <pre>
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* Purpose
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* =======
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*
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* CGSEQU computes row and column scalings intended to equilibrate an
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* M-by-N sparse matrix A and reduce its condition number. R returns the row
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* scale factors and C the column scale factors, chosen to try to make
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* the largest element in each row and column of the matrix B with
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* elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
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*
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* R(i) and C(j) are restricted to be between SMLNUM = smallest safe
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* number and BIGNUM = largest safe number. Use of these scaling
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* factors is not guaranteed to reduce the condition number of A but
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* works well in practice.
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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) SuperMatrix*
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* The matrix of dimension (A->nrow, A->ncol) whose equilibration
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* factors are to be computed. The type of A can be:
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* Stype = SLU_NC; Dtype = SLU_C; Mtype = SLU_GE.
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*
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* R (output) float*, size A->nrow
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* If INFO = 0 or INFO > M, R contains the row scale factors
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* for A.
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*
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* C (output) float*, size A->ncol
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* If INFO = 0, C contains the column scale factors for A.
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*
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* ROWCND (output) float*
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* If INFO = 0 or INFO > M, ROWCND contains the ratio of the
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* smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
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* AMAX is neither too large nor too small, it is not worth
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* scaling by R.
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*
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* COLCND (output) float*
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* If INFO = 0, COLCND contains the ratio of the smallest
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* C(i) to the largest C(i). If COLCND >= 0.1, it is not
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* worth scaling by C.
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*
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* AMAX (output) float*
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* Absolute value of largest matrix element. If AMAX is very
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* close to overflow or very close to underflow, the matrix
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* should be scaled.
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*
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* INFO (output) int*
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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* > 0: if INFO = i, and i is
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* <= A->nrow: the i-th row of A is exactly zero
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* > A->ncol: the (i-M)-th column of A is exactly zero
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*
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* =====================================================================
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* </pre>
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*/
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void
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cgsequ(SuperMatrix *A, float *r, float *c, float *rowcnd,
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float *colcnd, float *amax, int *info)
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{
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/* Local variables */
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NCformat *Astore;
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complex *Aval;
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int i, j, irow;
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float rcmin, rcmax;
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float bignum, smlnum;
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extern float slamch_(char *);
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/* Test the input parameters. */
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*info = 0;
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if ( A->nrow < 0 || A->ncol < 0 ||
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A->Stype != SLU_NC || A->Dtype != SLU_C || A->Mtype != SLU_GE )
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*info = -1;
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if (*info != 0) {
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i = -(*info);
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xerbla_("cgsequ", &i);
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return;
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}
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/* Quick return if possible */
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if ( A->nrow == 0 || A->ncol == 0 ) {
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*rowcnd = 1.;
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*colcnd = 1.;
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*amax = 0.;
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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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/* Get machine constants. */
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smlnum = slamch_("S");
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bignum = 1. / smlnum;
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/* Compute row scale factors. */
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for (i = 0; i < A->nrow; ++i) r[i] = 0.;
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/* Find the maximum element in each row. */
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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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r[irow] = SUPERLU_MAX( r[irow], c_abs1(&Aval[i]) );
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}
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/* Find the maximum and minimum scale factors. */
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rcmin = bignum;
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rcmax = 0.;
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for (i = 0; i < A->nrow; ++i) {
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rcmax = SUPERLU_MAX(rcmax, r[i]);
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rcmin = SUPERLU_MIN(rcmin, r[i]);
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}
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*amax = rcmax;
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if (rcmin == 0.) {
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/* Find the first zero scale factor and return an error code. */
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for (i = 0; i < A->nrow; ++i)
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if (r[i] == 0.) {
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*info = i + 1;
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return;
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}
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} else {
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/* Invert the scale factors. */
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for (i = 0; i < A->nrow; ++i)
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r[i] = 1. / SUPERLU_MIN( SUPERLU_MAX( r[i], smlnum ), bignum );
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/* Compute ROWCND = min(R(I)) / max(R(I)) */
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*rowcnd = SUPERLU_MAX( rcmin, smlnum ) / SUPERLU_MIN( rcmax, bignum );
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}
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/* Compute column scale factors */
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for (j = 0; j < A->ncol; ++j) c[j] = 0.;
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/* Find the maximum element in each column, assuming the row
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scalings computed above. */
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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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c[j] = SUPERLU_MAX( c[j], c_abs1(&Aval[i]) * r[irow] );
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}
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/* Find the maximum and minimum scale factors. */
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rcmin = bignum;
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rcmax = 0.;
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for (j = 0; j < A->ncol; ++j) {
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rcmax = SUPERLU_MAX(rcmax, c[j]);
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rcmin = SUPERLU_MIN(rcmin, c[j]);
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}
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if (rcmin == 0.) {
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/* Find the first zero scale factor and return an error code. */
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for (j = 0; j < A->ncol; ++j)
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if ( c[j] == 0. ) {
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*info = A->nrow + j + 1;
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return;
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}
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} else {
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/* Invert the scale factors. */
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for (j = 0; j < A->ncol; ++j)
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c[j] = 1. / SUPERLU_MIN( SUPERLU_MAX( c[j], smlnum ), bignum);
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/* Compute COLCND = min(C(J)) / max(C(J)) */
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*colcnd = SUPERLU_MAX( rcmin, smlnum ) / SUPERLU_MIN( rcmax, bignum );
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}
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return;
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} /* cgsequ */
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