sgeequ

NAME

sgeequ - compute row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number

SYNOPSIS

  SUBROUTINE SGEEQU( M, N, A, LDA, ROWSC, COLSC, ROWCN, COLCN, AMAX, 
 *      INFO)
  INTEGER M, N, LDA, INFO
  REAL ROWCN, COLCN, AMAX
  REAL A(LDA,*), ROWSC(*), COLSC(*)
 
  SUBROUTINE SGEEQU_64( M, N, A, LDA, ROWSC, COLSC, ROWCN, COLCN, 
 *      AMAX, INFO)
  INTEGER*8 M, N, LDA, INFO
  REAL ROWCN, COLCN, AMAX
  REAL A(LDA,*), ROWSC(*), COLSC(*)

F95 INTERFACE

  SUBROUTINE GEEQU( [M], [N], A, [LDA], ROWSC, COLSC, ROWCN, COLCN, 
 *       AMAX, [INFO])
  INTEGER :: M, N, LDA, INFO
  REAL :: ROWCN, COLCN, AMAX
  REAL, DIMENSION(:) :: ROWSC, COLSC
  REAL, DIMENSION(:,:) :: A
 
  SUBROUTINE GEEQU_64( [M], [N], A, [LDA], ROWSC, COLSC, ROWCN, COLCN, 
 *       AMAX, [INFO])
  INTEGER(8) :: M, N, LDA, INFO
  REAL :: ROWCN, COLCN, AMAX
  REAL, DIMENSION(:) :: ROWSC, COLSC
  REAL, DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

void sgeequ(int m, int n, float *a, int lda, float *rowsc, float *colsc, float *rowcn, float *colcn, float *amax, int *info);

void sgeequ_64(long m, long n, float *a, long lda, float *rowsc, float *colsc, float *rowcn, float *colcn, float *amax, long *info);

PURPOSE

sgeequ computes row and column scalings intended to equilibrate an M-by-N matrix A and reduce its condition number. R returns the row scale factors and C the column scale factors, chosen to try to make the largest element in each row and column of the matrix B with elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.

R(i) and C(j) are restricted to be between SMLNUM = smallest safe number and BIGNUM = largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of A but works well in practice.

ARGUMENTS

* M (input): The number of rows of the matrix A. M >= 0.
* N (input): The number of columns of the matrix A. N >= 0.
* A (input): The M-by-N matrix whose equilibration factors are to be computed.
* LDA (input): The leading dimension of the array A. LDA >= max(1,M).
* ROWSC (output): If INFO = 0 or INFO > M, ROWSC contains the row scale factors for A.
* COLSC (output): If INFO = 0, COLSC contains the column scale factors for A.
* ROWCN (output): If INFO = 0 or INFO > M, ROWCN contains the ratio of the smallest ROWSC(i) to the largest ROWSC(i). If ROWCN >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by ROWSC.
* COLCN (output): If INFO = 0, COLCN contains the ratio of the smallest COLSC(i) to the largest COLSC(i). If COLCN >= 0.1, it is not worth scaling by COLSC.
* AMAX (output): Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
* INFO (output)