cgeequb (3p)

Name

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

Synopsis

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


INTEGER INFO, LDA, M, N

REAL AMAX, COLCND, ROWCND

REAL C(*), R(*)

COMPLEX A(LDA,*)


SUBROUTINE CGEEQUB_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO)


INTEGER*8 INFO, LDA, M, N

REAL AMAX, COLCND, ROWCND

REAL C(*), R(*)

COMPLEX A(LDA,*)


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


INTEGER :: M, N, LDA, INFO

REAL, DIMENSION(:) :: R, C

COMPLEX, DIMENSION(:,:) :: A

REAL :: ROWCND, COLCND, AMAX


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


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

REAL, DIMENSION(:) :: R, C

COMPLEX, DIMENSION(:,:) :: A

REAL :: ROWCND, COLCND, AMAX


C INTERFACE
#include <sunperf.h>

void cgeequb (int m, int n, floatcomplex *a, int lda, float  *r,  float
*c, float *rowcnd, float *colcnd, float *amax, int *info);


void  cgeequb_64  (long m, long n, floatcomplex *a, long lda, float *r,
float *c, float *rowcnd, float  *colcnd,  float  *amax,  long
*info);

Description

Oracle Solaris Studio Performance Library                          cgeequb(3P)



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


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


       INTEGER INFO, LDA, M, N

       REAL AMAX, COLCND, ROWCND

       REAL C(*), R(*)

       COMPLEX A(LDA,*)


       SUBROUTINE CGEEQUB_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO)


       INTEGER*8 INFO, LDA, M, N

       REAL AMAX, COLCND, ROWCND

       REAL C(*), R(*)

       COMPLEX A(LDA,*)


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


       INTEGER :: M, N, LDA, INFO

       REAL, DIMENSION(:) :: R, C

       COMPLEX, DIMENSION(:,:) :: A

       REAL :: ROWCND, COLCND, AMAX


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


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

       REAL, DIMENSION(:) :: R, C

       COMPLEX, DIMENSION(:,:) :: A

       REAL :: ROWCND, COLCND, AMAX


   C INTERFACE
       #include <sunperf.h>

       void cgeequb (int m, int n, floatcomplex *a, int lda, float  *r,  float
                 *c, float *rowcnd, float *colcnd, float *amax, int *info);


       void  cgeequb_64  (long m, long n, floatcomplex *a, long lda, float *r,
                 float *c, float *rowcnd, float  *colcnd,  float  *amax,  long
                 *info);


PURPOSE
       cgeequb  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 CGEEQU 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 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 REAL array, dimension (M)
                 If INFO = 0 or INFO > M, R contains the row scale factors for
                 A.


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


       ROWCND (output)
                 ROWCND is REAL
                 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 REAL
                 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)
                 AMAX is REAL
                 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                       cgeequb(3P)