zpoequb (3p)

Name

zpoequb - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number with respect to the two-norm

Synopsis

SUBROUTINE ZPOEQUB(N, A, LDA, S, SCOND, AMAX, INFO)


INTEGER INFO, LDA, N

DOUBLE PRECISION AMAX, SCOND

DOUBLE COMPLEX A(LDA,*)

DOUBLE PRECISION S(*)


SUBROUTINE ZPOEQUB_64(N, A, LDA, S, SCOND, AMAX, INFO)


INTEGER*8 INFO, LDA, N

DOUBLE PRECISION AMAX, SCOND

DOUBLE COMPLEX A(LDA,*)

DOUBLE PRECISION S(*)


F95 INTERFACE
SUBROUTINE POEQUB(N, A, LDA, S, SCOND, AMAX, INFO)


INTEGER :: N, LDA, INFO

REAL(8), DIMENSION(:) :: S

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

REAL(8) :: SCOND, AMAX


SUBROUTINE POEQUB_64(N, A, LDA, S, SCOND, AMAX, INFO)


INTEGER(8) :: N, LDA, INFO

REAL(8), DIMENSION(:) :: S

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

REAL(8) :: SCOND, AMAX


C INTERFACE
#include <sunperf.h>

void  zpoequb  (int  n,  doublecomplex  *a,  int lda, double *s, double
*scond, double *amax, int *info);


void zpoequb_64 (long n, doublecomplex *a, long lda, double *s,  double
*scond, double *amax, long *info);

Description

Oracle Solaris Studio Performance Library                          zpoequb(3P)



NAME
       zpoequb  -  compute  row  and column scalings intended to equilibrate a
       symmetric positive definite matrix A and reduce  its  condition  number
       with respect to the two-norm


SYNOPSIS
       SUBROUTINE ZPOEQUB(N, A, LDA, S, SCOND, AMAX, INFO)


       INTEGER INFO, LDA, N

       DOUBLE PRECISION AMAX, SCOND

       DOUBLE COMPLEX A(LDA,*)

       DOUBLE PRECISION S(*)


       SUBROUTINE ZPOEQUB_64(N, A, LDA, S, SCOND, AMAX, INFO)


       INTEGER*8 INFO, LDA, N

       DOUBLE PRECISION AMAX, SCOND

       DOUBLE COMPLEX A(LDA,*)

       DOUBLE PRECISION S(*)


   F95 INTERFACE
       SUBROUTINE POEQUB(N, A, LDA, S, SCOND, AMAX, INFO)


       INTEGER :: N, LDA, INFO

       REAL(8), DIMENSION(:) :: S

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

       REAL(8) :: SCOND, AMAX


       SUBROUTINE POEQUB_64(N, A, LDA, S, SCOND, AMAX, INFO)


       INTEGER(8) :: N, LDA, INFO

       REAL(8), DIMENSION(:) :: S

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

       REAL(8) :: SCOND, AMAX


   C INTERFACE
       #include <sunperf.h>

       void  zpoequb  (int  n,  doublecomplex  *a,  int lda, double *s, double
                 *scond, double *amax, int *info);


       void zpoequb_64 (long n, doublecomplex *a, long lda, double *s,  double
                 *scond, double *amax, long *info);


PURPOSE
       zpoequb computes row and column scalings intended to equilibrate a sym-
       metric positive definite matrix A and reduce its condition number (with
       respect  to  the  two-norm).   S  contains  the  scale  factors, S(i) =
       1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j)
       = S(i)*A(i,j)*S(j) has ones on the diagonal.  This choice of S puts the
       condition number of B within a factor N of the smallest possible condi-
       tion number over all possible diagonal scalings.


ARGUMENTS
       N (input)
                 N is INTEGER
                 The order of the matrix A.  N >= 0.


       A (input)
                 A is COMPLEX*16 array, dimension (LDA,N)
                 The  N-by-N  symmetric positive definite matrix whose scaling
                 factors are to be computed.  Only the diagonal elements of  A
                 are referenced.


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


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


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


       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, the i-th diagonal element is nonpositive.



                                  7 Nov 2015                       zpoequb(3P)