zgeequb (3p)

Name

zgeequb - computes row and column scalings intended to equilibrate an M-by-N matrix A and redu ce its condition number

Synopsis

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


INTEGER INFO, LDA, M, N

DOUBLE PRECISION AMAX, COLCND, ROWCND

DOUBLE PRECISION C(*),R(*)


SUBROUTINE ZGEEQUB_64( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO )


INTEGER*8 INFO, LDA, M, N

DOUBLE PRECISION AMAX, COLCND, ROWCND

DOUBLE PRECISION C(*),R(*)


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


INTEGER :: M, N, LDA, INFO

REAL(8), DIMENSION(:) :: R, C

COMPLEX(8), DIMENSION(:,:) :: A

REAL(8) :: ROWCND, COLCND, AMAX


SUBROUTINE GEEQUB_64( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO )


INTEGER(8) :: M, N, LDA, INFO

REAL(8), DIMENSION(:) :: R, C

COMPLEX(8), DIMENSION(:,:) :: A

REAL(8) :: ROWCND, COLCND, AMAX


C INTERFACE
#include <sunperf.h>

void  zgeequb (int m, int n, doublecomplex *a, int lda, double *r, dou-
ble *c, double *rowcnd, double  *colcnd,  double  *amax,  int
*info);


void zgeequb_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                          zgeequb(3P)



NAME
       zgeequb  -  computes row and column scalings intended to equilibrate an
       M-by-N matrix A and redu ce its condition number


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


       INTEGER INFO, LDA, M, N

       DOUBLE PRECISION AMAX, COLCND, ROWCND

       DOUBLE PRECISION C(*),R(*)


       SUBROUTINE ZGEEQUB_64( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO )


       INTEGER*8 INFO, LDA, M, N

       DOUBLE PRECISION AMAX, COLCND, ROWCND

       DOUBLE PRECISION C(*),R(*)


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


       INTEGER :: M, N, LDA, INFO

       REAL(8), DIMENSION(:) :: R, C

       COMPLEX(8), DIMENSION(:,:) :: A

       REAL(8) :: ROWCND, COLCND, AMAX


       SUBROUTINE GEEQUB_64( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO )


       INTEGER(8) :: M, N, LDA, INFO

       REAL(8), DIMENSION(:) :: R, C

       COMPLEX(8), DIMENSION(:,:) :: A

       REAL(8) :: ROWCND, COLCND, AMAX


   C INTERFACE
       #include <sunperf.h>

       void  zgeequb (int m, int n, doublecomplex *a, int lda, double *r, dou-
                 ble *c, double *rowcnd, double  *colcnd,  double  *amax,  int
                 *info);


       void zgeequb_64 (long m, long n, doublecomplex *a, long lda, double *r,
                 double *c, double *rowcnd, double *colcnd, double *amax, long
                 *info);


PURPOSE
       zgeequb  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 an absolute value of at most the radix.

       R(i)  and C(j) are restricted to be a power of the radix 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.

       This routine differs from ZGEEQU by restricting the scaling factors  to
       a  power  of  the  radix.  Baring over- and underflow, scaling by these
       factors introduces no additional rounding errors.  However, the  scaled
       entries'  magnitured  are  no  longer  approximately  1 but lie between
       sqrt(radix) and 1/sqrt(radix).


ARGUMENTS
       M (input)
                 M is INTEGER
                 The number of rows of the matrix A.  M >= 0.


       N (input)
                 N is INTEGER
                 The number of columns of the matrix A.  N >= 0.


       A (input)
                 A is COMPLEX*16 array, dimension (LDA,N)
                 The M-by-N matrix whose equilibration factors are
                 to be computed.


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


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


       C (output)
                 C is DOUBLE PRECISION array, dimension (N)
                 If INFO = 0,  C contains the column scale factors for A.


       ROWCND (output)
                 ROWCND is DOUBLE PRECISION
                 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)
                 COLCND is DOUBLE PRECISION
                 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 scaling by C.


       AMAX (output)
                 AMAX is DOUBLE PRECISION
                 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)
                 INFO is INTEGER
                 = 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                       zgeequb(3P)