Contents
dpoequ - compute row and column scalings intended to equili-
brate a symmetric positive definite matrix A and reduce its
condition number (with respect to the two-norm)
SUBROUTINE DPOEQU(N, A, LDA, SCALE, SCOND, AMAX, INFO)
INTEGER N, LDA, INFO
DOUBLE PRECISION SCOND, AMAX
DOUBLE PRECISION A(LDA,*), SCALE(*)
SUBROUTINE DPOEQU_64(N, A, LDA, SCALE, SCOND, AMAX, INFO)
INTEGER*8 N, LDA, INFO
DOUBLE PRECISION SCOND, AMAX
DOUBLE PRECISION A(LDA,*), SCALE(*)
F95 INTERFACE
SUBROUTINE POEQU([N], A, [LDA], SCALE, SCOND, AMAX, [INFO])
INTEGER :: N, LDA, INFO
REAL(8) :: SCOND, AMAX
REAL(8), DIMENSION(:) :: SCALE
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE POEQU_64([N], A, [LDA], SCALE, SCOND, AMAX, [INFO])
INTEGER(8) :: N, LDA, INFO
REAL(8) :: SCOND, AMAX
REAL(8), DIMENSION(:) :: SCALE
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dpoequ(int n, double *a, int lda, double *scale, double
*scond, double *amax, int *info);
void dpoequ_64(long n, double *a, long lda, double *scale,
double *scond, double *amax, long *info);
dpoequ computes row and column scalings intended to equili-
brate a symmetric 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 con-
dition number over all possible diagonal scalings.
N (input) The order of the matrix A. N >= 0.
A (input) 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)
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.