dppequ(3P) Sun Performance Library dppequ(3P)NAMEdppequ - compute row and column scalings intended to equilibrate a sym‐
metric positive definite matrix A in packed storage and reduce its con‐
dition number (with respect to the two-norm)
SYNOPSIS
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(*)
F95 INTERFACE
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
C INTERFACE
#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);
PURPOSEdppequ computes row and column scalings intended to equilibrate a sym‐
metric positive definite matrix A in packed storage and reduce its con‐
dition 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.
ARGUMENTS
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) DOUBLE PRECISION array, dimension (N*(N+1)/2)
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) DOUBLE PRECISION array, dimension (N)
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.
6 Mar 2009 dppequ(3P)
