• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

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

SYNOPSIS

  SUBROUTINE ZGEEQU( M, N, A, LDA, ROWSC, COLSC, ROWCN, COLCN, AMAX, 
 *      INFO)
  DOUBLE COMPLEX A(LDA,*)
  INTEGER M, N, LDA, INFO
  DOUBLE PRECISION ROWCN, COLCN, AMAX
  DOUBLE PRECISION ROWSC(*), COLSC(*)

  SUBROUTINE ZGEEQU_64( M, N, A, LDA, ROWSC, COLSC, ROWCN, COLCN, 
 *      AMAX, INFO)
  DOUBLE COMPLEX A(LDA,*)
  INTEGER*8 M, N, LDA, INFO
  DOUBLE PRECISION ROWCN, COLCN, AMAX
  DOUBLE PRECISION ROWSC(*), COLSC(*)

F95 INTERFACE

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

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

C INTERFACE

#include <sunperf.h>

void zgeequ(int m, int n, doublecomplex *a, int lda, double *rowsc, double *colsc, double *rowcn, double *colcn, double *amax, int *info);

void zgeequ_64(long m, long n, doublecomplex *a, long lda, double *rowsc, double *colsc, double *rowcn, double *colcn, double *amax, long *info);

PURPOSE

zgeequ 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)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value

   > 0:  if INFO  = i,  and i is

   < = M:  the i-th row of A is exactly zero

   >  M:  the (i-M)-th column of A is exactly zero