dppequ - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
SUBROUTINE DPPEQU( UPLO, N, A, SCALE, SCOND, AMAX, INFO) CHARACTER * 1 UPLO INTEGER N, INFO DOUBLE PRECISION SCOND, AMAX DOUBLE PRECISION A(*), SCALE(*)
SUBROUTINE DPPEQU_64( UPLO, N, A, SCALE, SCOND, AMAX, INFO) CHARACTER * 1 UPLO INTEGER*8 N, INFO DOUBLE PRECISION SCOND, AMAX DOUBLE PRECISION A(*), SCALE(*)
SUBROUTINE PPEQU( UPLO, [N], A, SCALE, SCOND, AMAX, [INFO]) CHARACTER(LEN=1) :: UPLO INTEGER :: N, INFO REAL(8) :: SCOND, AMAX REAL(8), DIMENSION(:) :: A, SCALE
SUBROUTINE PPEQU_64( UPLO, [N], A, SCALE, SCOND, AMAX, [INFO]) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, INFO REAL(8) :: SCOND, AMAX REAL(8), DIMENSION(:) :: A, SCALE
#include <sunperf.h>
void dppequ(char uplo, int n, double *a, double *scale, double *scond, double *amax, int *info);
void dppequ_64(char uplo, long n, double *a, double *scale, double *scond, double *amax, long *info);
dppequ computes row and column scalings intended to equilibrate a
symmetric positive definite matrix A in packed storage 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 diagonal
scalings.
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
A(i,j)
for 1 < =i < =j;
if UPLO = 'L', A(i + (j-1)*(2n-j)/2) = A(i,j)
for j < =i < =n.
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.
= 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.