cgeequ

NAME

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

SYNOPSIS

  SUBROUTINE CGEEQU( M, N, A, LDA, ROWSC, COLSC, ROWCND, COLCND, AMAX, 
 *      INFO)
  COMPLEX A(LDA,*)
  INTEGER M, N, LDA, INFO
  REAL ROWCND, COLCND, AMAX
  REAL ROWSC(*), COLSC(*)
 
  SUBROUTINE CGEEQU_64( M, N, A, LDA, ROWSC, COLSC, ROWCND, COLCND, 
 *      AMAX, INFO)
  COMPLEX A(LDA,*)
  INTEGER*8 M, N, LDA, INFO
  REAL ROWCND, COLCND, AMAX
  REAL ROWSC(*), COLSC(*)

F95 INTERFACE

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

C INTERFACE

#include <sunperf.h>

void cgeequ(int m, int n, complex *a, int lda, float *rowsc, float *colsc, float *rowcnd, float *colcnd, float *amax, int *info);

void cgeequ_64(long m, long n, complex *a, long lda, float *rowsc, float *colsc, float *rowcnd, float *colcnd, float *amax, long *info);

PURPOSE

cgeequ 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.
* ROWCND (output): If INFO = 0 or INFO > M, ROWCND contains the ratio of the smallest ROWSC(i) to the largest ROWSC(i). If ROWCND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by ROWSC.
* COLCND (output): If INFO = 0, COLCND contains the ratio of the smallest COLSC(i) to the largest COLSC(i). If COLCND >= 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)