cppequ(3P) Sun Performance Library cppequ(3P)NAMEcppequ - compute row and column scalings intended to equilibrate a Her‐
mitian positive definite matrix A in packed storage and reduce its con‐
dition number (with respect to the two-norm)
SYNOPSIS
SUBROUTINE CPPEQU(UPLO, N, A, SCALE, SCOND, AMAX, INFO)
CHARACTER * 1 UPLO
COMPLEX A(*)
INTEGER N, INFO
REAL SCOND, AMAX
REAL SCALE(*)
SUBROUTINE CPPEQU_64(UPLO, N, A, SCALE, SCOND, AMAX, INFO)
CHARACTER * 1 UPLO
COMPLEX A(*)
INTEGER*8 N, INFO
REAL SCOND, AMAX
REAL SCALE(*)
F95 INTERFACE
SUBROUTINE PPEQU(UPLO, [N], A, SCALE, SCOND, AMAX, [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: A
INTEGER :: N, INFO
REAL :: SCOND, AMAX
REAL, DIMENSION(:) :: SCALE
SUBROUTINE PPEQU_64(UPLO, [N], A, SCALE, SCOND, AMAX, [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: A
INTEGER(8) :: N, INFO
REAL :: SCOND, AMAX
REAL, DIMENSION(:) :: SCALE
C INTERFACE
#include <sunperf.h>
void cppequ(char uplo, int n, complex *a, float *scale, float *scond,
float *amax, int *info);
void cppequ_64(char uplo, long n, complex *a, float *scale, float
*scond, float *amax, long *info);
PURPOSEcppequ computes row and column scalings intended to equilibrate a Her‐
mitian 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) COMPLEX array, dimension (N*(N+1)/2)
The upper or lower triangle of the Hermitian 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) REAL 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 cppequ(3P)
