cpoequ(3P) Sun Performance Library cpoequ(3P)NAMEcpoequ - compute row and column scalings intended to equilibrate a Her‐
mitian positive definite matrix A and reduce its condition number (with
respect to the two-norm)
SYNOPSIS
SUBROUTINE CPOEQU(N, A, LDA, SCALE, SCOND, AMAX, INFO)
COMPLEX A(LDA,*)
INTEGER N, LDA, INFO
REAL SCOND, AMAX
REAL SCALE(*)
SUBROUTINE CPOEQU_64(N, A, LDA, SCALE, SCOND, AMAX, INFO)
COMPLEX A(LDA,*)
INTEGER*8 N, LDA, INFO
REAL SCOND, AMAX
REAL SCALE(*)
F95 INTERFACE
SUBROUTINE POEQU([N], A, [LDA], SCALE, SCOND, AMAX, [INFO])
COMPLEX, DIMENSION(:,:) :: A
INTEGER :: N, LDA, INFO
REAL :: SCOND, AMAX
REAL, DIMENSION(:) :: SCALE
SUBROUTINE POEQU_64([N], A, [LDA], SCALE, SCOND, AMAX, [INFO])
COMPLEX, DIMENSION(:,:) :: A
INTEGER(8) :: N, LDA, INFO
REAL :: SCOND, AMAX
REAL, DIMENSION(:) :: SCALE
C INTERFACE
#include <sunperf.h>
void cpoequ(int n, complex *a, int lda, float *scale, float *scond,
float *amax, int *info);
void cpoequ_64(long n, complex *a, long lda, float *scale, float
*scond, float *amax, long *info);
PURPOSEcpoequ computes row and column scalings intended to equilibrate a Her‐
mitian 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 condi‐
tion number over all possible diagonal scalings.
ARGUMENTS
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 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 cpoequ(3P)
