zgeequ (3p)

Name

zgeequ - by-N matrix A and reduce its condition number

Synopsis

SUBROUTINE ZGEEQU(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
INFO)

DOUBLE COMPLEX A(LDA,*)
INTEGER M, N, LDA, INFO
DOUBLE PRECISION ROWCND, COLCND, AMAX
DOUBLE PRECISION R(*), C(*)

SUBROUTINE ZGEEQU_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
INFO)

DOUBLE COMPLEX A(LDA,*)
INTEGER*8 M, N, LDA, INFO
DOUBLE PRECISION ROWCND, COLCND, AMAX
DOUBLE PRECISION R(*), C(*)




F95 INTERFACE
SUBROUTINE GEEQU(M, N, A, LDA, R, C, ROWCND, COLCND,
AMAX, INFO)

COMPLEX(8), DIMENSION(:,:) :: A
INTEGER :: M, N, LDA, INFO
REAL(8) :: ROWCND, COLCND, AMAX
REAL(8), DIMENSION(:) :: R, C

SUBROUTINE GEEQU_64(M, N, A, LDA, R, C, ROWCND, COLCND,
AMAX, INFO)

COMPLEX(8), DIMENSION(:,:) :: A
INTEGER(8) :: M, N, LDA, INFO
REAL(8) :: ROWCND, COLCND, AMAX
REAL(8), DIMENSION(:) :: R, C




C INTERFACE
#include <sunperf.h>

void zgeequ(int m, int n, doublecomplex *a, int lda, double *r,  double
*c, double *rowcnd, double *colcnd, double *amax, int *info);

void zgeequ_64(long m, long n, doublecomplex *a, long lda,  double  *r,
double *c, double *rowcnd, double *colcnd, double *amax, long
*info);

Description

Oracle Solaris Studio Performance Library                           zgeequ(3P)



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, R, C, ROWCND, COLCND, AMAX,
             INFO)

       DOUBLE COMPLEX A(LDA,*)
       INTEGER M, N, LDA, INFO
       DOUBLE PRECISION ROWCND, COLCND, AMAX
       DOUBLE PRECISION R(*), C(*)

       SUBROUTINE ZGEEQU_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
             INFO)

       DOUBLE COMPLEX A(LDA,*)
       INTEGER*8 M, N, LDA, INFO
       DOUBLE PRECISION ROWCND, COLCND, AMAX
       DOUBLE PRECISION R(*), C(*)




   F95 INTERFACE
       SUBROUTINE GEEQU(M, N, A, LDA, R, C, ROWCND, COLCND,
              AMAX, INFO)

       COMPLEX(8), DIMENSION(:,:) :: A
       INTEGER :: M, N, LDA, INFO
       REAL(8) :: ROWCND, COLCND, AMAX
       REAL(8), DIMENSION(:) :: R, C

       SUBROUTINE GEEQU_64(M, N, A, LDA, R, C, ROWCND, COLCND,
              AMAX, INFO)

       COMPLEX(8), DIMENSION(:,:) :: A
       INTEGER(8) :: M, N, LDA, INFO
       REAL(8) :: ROWCND, COLCND, AMAX
       REAL(8), DIMENSION(:) :: R, C




   C INTERFACE
       #include <sunperf.h>

       void zgeequ(int m, int n, doublecomplex *a, int lda, double *r,  double
                 *c, double *rowcnd, double *colcnd, double *amax, int *info);

       void zgeequ_64(long m, long n, doublecomplex *a, long lda,  double  *r,
                 double *c, double *rowcnd, double *colcnd, 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  num-
       ber  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 com-
                 puted.


       LDA (input)
                 The leading dimension of the array A.  LDA >= max(1,M).


       R (output)
                 If INFO = 0 or INFO > M, R contains the row scale factors for
                 A.


       C (output)
                 If INFO = 0,  C contains the column scale factors for A.


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


       COLCND (output)
                 If INFO = 0, COLCND contains the ratio of the  smallest  C(i)
                 to the largest C(i).  If COLCND >= 0.1, it is not worth scal-
                 ing by C.


       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




                                  7 Nov 2015                        zgeequ(3P)