.TH ZPPEQU l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
ZPPEQU - compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)
.SH SYNOPSIS
.TP 19
SUBROUTINE ZPPEQU(
UPLO, N, AP, S, SCOND, AMAX, INFO )
.TP 19
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CHARACTER
UPLO
.TP 19
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INTEGER
INFO, N
.TP 19
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DOUBLE
PRECISION AMAX, SCOND
.TP 19
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DOUBLE
PRECISION S( * )
.TP 19
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COMPLEX*16
AP( * )
.SH PURPOSE
ZPPEQU computes row and column scalings intended to equilibrate a Hermitian 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.
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.SH ARGUMENTS
.TP 8
UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
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= 'L':  Lower triangle of A is stored.
.TP 8
N       (input) INTEGER
The order of the matrix A.  N >= 0.
.TP 8
AP      (input) COMPLEX*16 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.
.TP 8
S       (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, S contains the scale factors for A.
.TP 8
SCOND   (output) DOUBLE PRECISION
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.
.TP 8
AMAX    (output) DOUBLE PRECISION
Absolute value of largest matrix element.  If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.
.TP 8
INFO    (output) INTEGER
= 0:  successful exit
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< 0:  if INFO = -i, the i-th argument had an illegal value
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> 0:  if INFO = i, the i-th diagonal element is nonpositive.