Contents
zpoequ - compute row and column scalings intended to equili-
brate a Hermitian positive definite matrix A and reduce its
condition number (with respect to the two-norm)
SUBROUTINE ZPOEQU(N, A, LDA, SCALE, SCOND, AMAX, INFO)
DOUBLE COMPLEX A(LDA,*)
INTEGER N, LDA, INFO
DOUBLE PRECISION SCOND, AMAX
DOUBLE PRECISION SCALE(*)
SUBROUTINE ZPOEQU_64(N, A, LDA, SCALE, SCOND, AMAX, INFO)
DOUBLE COMPLEX A(LDA,*)
INTEGER*8 N, LDA, INFO
DOUBLE PRECISION SCOND, AMAX
DOUBLE PRECISION SCALE(*)
F95 INTERFACE
SUBROUTINE POEQU([N], A, [LDA], SCALE, SCOND, AMAX, [INFO])
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER :: N, LDA, INFO
REAL(8) :: SCOND, AMAX
REAL(8), DIMENSION(:) :: SCALE
SUBROUTINE POEQU_64([N], A, [LDA], SCALE, SCOND, AMAX, [INFO])
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER(8) :: N, LDA, INFO
REAL(8) :: SCOND, AMAX
REAL(8), DIMENSION(:) :: SCALE
C INTERFACE
#include <sunperf.h>
void zpoequ(int n, doublecomplex *a, int lda, double *scale,
double *scond, double *amax, int *info);
void zpoequ_64(long n, doublecomplex *a, long lda, double
*scale, double *scond, double *amax, long *info);
zpoequ computes row and column scalings intended to
equilibrate a Hermitian 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 condition number over all possible diago-
nal scalings.
N (input) The order of the matrix A. N >= 0.
A (input) The N-by-N Hermitian positive definite matrix
whose scaling factors are to be computed. Only
the diagonal elements of A are referenced.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,N).
SCALE (output)
If INFO = 0, SCALE contains the scale factors for
A.
SCOND (output)
If INFO = 0, SCALE contains the ratio of the smal-
lest 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 under-
flow, the matrix should be scaled.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
> 0: if INFO = i, the i-th diagonal element is
nonpositive.