CPPEQU(l) ) CPPEQU(l)NAME
CPPEQU - 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, AP, S, SCOND, AMAX, INFO )
CHARACTER UPLO
INTEGER INFO, N
REAL AMAX, SCOND
REAL S( * )
COMPLEX AP( * )
PURPOSE
CPPEQU 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 fac‐
tors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix B with ele‐
ments 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 pos‐
sible condition number over all possible diagonal scalings.
ARGUMENTS
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (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 AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) =
A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) =
A(i,j) for j<=i<=n.
S (output) REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.
SCOND (output) REAL
If INFO = 0, S contains the ratio of the smallest S(i) to the
largest S(i). If SCOND >= 0.1 and AMAX is neither too large
nor too small, it is not worth scaling by S.
AMAX (output) REAL
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) INTEGER
= 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.
LAPACK version 3.0 15 June 2000 CPPEQU(l)