zpbequ (3p)

Name

zpbequ - mitian positive definite band matrix A and reduce its condition number (with respect to the two-norm)

Synopsis

SUBROUTINE ZPBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO)

CHARACTER*1 UPLO
DOUBLE COMPLEX A(LDA,*)
INTEGER N, KD, LDA, INFO
DOUBLE PRECISION SCOND, AMAX
DOUBLE PRECISION SCALE(*)

SUBROUTINE ZPBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX,
INFO)

CHARACTER*1 UPLO
DOUBLE COMPLEX A(LDA,*)
INTEGER*8 N, KD, LDA, INFO
DOUBLE PRECISION SCOND, AMAX
DOUBLE PRECISION SCALE(*)




F95 INTERFACE
SUBROUTINE PBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX,
INFO)

CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER :: N, KD, LDA, INFO
REAL(8) :: SCOND, AMAX
REAL(8), DIMENSION(:) :: SCALE

SUBROUTINE PBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX,
INFO)

CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER(8) :: N, KD, LDA, INFO
REAL(8) :: SCOND, AMAX
REAL(8), DIMENSION(:) :: SCALE




C INTERFACE
#include <sunperf.h>

void zpbequ(char uplo, int n, int kd, doublecomplex *a, int lda, double
*scale, double *scond, double *amax, int *info);

void zpbequ_64(char uplo, long n, long kd, doublecomplex *a, long  lda,
double *scale, double *scond, double *amax, long *info);

Description

Oracle Solaris Studio Performance Library                           zpbequ(3P)



NAME
       zpbequ - compute row and column scalings intended to equilibrate a Her-
       mitian positive definite band matrix A and reduce its condition  number
       (with respect to the two-norm)


SYNOPSIS
       SUBROUTINE ZPBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO)

       CHARACTER*1 UPLO
       DOUBLE COMPLEX A(LDA,*)
       INTEGER N, KD, LDA, INFO
       DOUBLE PRECISION SCOND, AMAX
       DOUBLE PRECISION SCALE(*)

       SUBROUTINE ZPBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX,
             INFO)

       CHARACTER*1 UPLO
       DOUBLE COMPLEX A(LDA,*)
       INTEGER*8 N, KD, LDA, INFO
       DOUBLE PRECISION SCOND, AMAX
       DOUBLE PRECISION SCALE(*)




   F95 INTERFACE
       SUBROUTINE PBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX,
              INFO)

       CHARACTER(LEN=1) :: UPLO
       COMPLEX(8), DIMENSION(:,:) :: A
       INTEGER :: N, KD, LDA, INFO
       REAL(8) :: SCOND, AMAX
       REAL(8), DIMENSION(:) :: SCALE

       SUBROUTINE PBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX,
              INFO)

       CHARACTER(LEN=1) :: UPLO
       COMPLEX(8), DIMENSION(:,:) :: A
       INTEGER(8) :: N, KD, LDA, INFO
       REAL(8) :: SCOND, AMAX
       REAL(8), DIMENSION(:) :: SCALE




   C INTERFACE
       #include <sunperf.h>

       void zpbequ(char uplo, int n, int kd, doublecomplex *a, int lda, double
                 *scale, double *scond, double *amax, int *info);

       void zpbequ_64(char uplo, long n, long kd, doublecomplex *a, long  lda,
                 double *scale, double *scond, double *amax, long *info);



PURPOSE
       zpbequ  computes row and column scalings intended to equilibrate a Her-
       mitian positive definite band 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
       UPLO (input)
                 = 'U':  Upper triangular of A is stored;
                 = 'L':  Lower triangular of A is stored.


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


       KD (input)
                 The  number  of superdiagonals of the matrix A if UPLO = 'U',
                 or the number of subdiagonals if UPLO = 'L'.  KD >= 0.


       A (input) The upper or lower triangle of the Hermitian band  matrix  A,
                 stored  in the first KD+1 rows of the array.  The j-th column
                 of A is stored in the j-th column of the array A as  follows:
                 if  UPLO = 'U', A(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
                 if UPLO = 'L', A(1+i-j,j)    = A(i,j) for  j<=i<=min(n,j+kd).


       LDA (input)
                 The leading dimension of the array A.  LDA >= KD+1.


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


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


       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, the i-th diagonal element is  nonpositive.




                                  7 Nov 2015                        zpbequ(3P)