sgeequb (3p)

Name

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

Synopsis

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


INTEGER INFO, LDA, M, N

REAL AMAX, COLCND, ROWCND

REAL A(LDA,*), C(*), R(*)


SUBROUTINE SGEEQUB_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO)


INTEGER*8 INFO, LDA, M, N

REAL AMAX, COLCND, ROWCND

REAL A(LDA,*), C(*), R(*)


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


REAL, DIMENSION(:,:) :: A

INTEGER :: M, N, LDA, INFO

REAL, DIMENSION(:) :: R, C

REAL :: ROWCND, COLCND, AMAX


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


REAL, DIMENSION(:,:) :: A

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

REAL, DIMENSION(:) :: R, C

REAL :: ROWCND, COLCND, AMAX


C INTERFACE
#include <sunperf.h>

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


void  sgeequb_64  (long  m, long n, float *a, long lda, float *r, float
*c, float *rowcnd, float *colcnd, float *amax, long *info);

Description

Oracle Solaris Studio Performance Library                          sgeequb(3P)



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


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


       INTEGER INFO, LDA, M, N

       REAL AMAX, COLCND, ROWCND

       REAL A(LDA,*), C(*), R(*)


       SUBROUTINE SGEEQUB_64(M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO)


       INTEGER*8 INFO, LDA, M, N

       REAL AMAX, COLCND, ROWCND

       REAL A(LDA,*), C(*), R(*)


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


       REAL, DIMENSION(:,:) :: A

       INTEGER :: M, N, LDA, INFO

       REAL, DIMENSION(:) :: R, C

       REAL :: ROWCND, COLCND, AMAX


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


       REAL, DIMENSION(:,:) :: A

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

       REAL, DIMENSION(:) :: R, C

       REAL :: ROWCND, COLCND, AMAX


   C INTERFACE
       #include <sunperf.h>

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


       void  sgeequb_64  (long  m, long n, float *a, long lda, float *r, float
                 *c, float *rowcnd, float *colcnd, float *amax, long *info);


PURPOSE
       sgeequb 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 SGEEQU 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 REAL array, dimension (LDA,N)
                 The  M-by-N matrix whose equilibration factors are to be com-
                 puted.


       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                       sgeequb(3P)