Contents
sppequ - compute row and column scalings intended to equili-
brate a symmetric positive definite matrix A in packed
storage and reduce its condition number (with respect to the
two-norm)
SUBROUTINE SPPEQU(UPLO, N, A, SCALE, SCOND, AMAX, INFO)
CHARACTER * 1 UPLO
INTEGER N, INFO
REAL SCOND, AMAX
REAL A(*), SCALE(*)
SUBROUTINE SPPEQU_64(UPLO, N, A, SCALE, SCOND, AMAX, INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, INFO
REAL SCOND, AMAX
REAL A(*), SCALE(*)
F95 INTERFACE
SUBROUTINE PPEQU(UPLO, [N], A, SCALE, SCOND, AMAX, [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, INFO
REAL :: SCOND, AMAX
REAL, DIMENSION(:) :: A, SCALE
SUBROUTINE PPEQU_64(UPLO, [N], A, SCALE, SCOND, AMAX, [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, INFO
REAL :: SCOND, AMAX
REAL, DIMENSION(:) :: A, SCALE
C INTERFACE
#include <sunperf.h>
void sppequ(char uplo, int n, float *a, float *scale, float
*scond, float *amax, int *info);
void sppequ_64(char uplo, long n, float *a, float *scale,
float *scond, float *amax, long *info);
sppequ computes row and column scalings intended to equili-
brate 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.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 0.
A (input) The upper or lower triangle of the symmetric
matrix A, packed columnwise in a linear array.
The j-th column of A is stored in the array A as
follows: if UPLO = 'U', A(i + (j-1)*j/2) = 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 (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.