ZHPCON(1) LAPACK routine (version 3.2) ZHPCON(1)NAME
ZHPCON - estimates the reciprocal of the condition number of a complex
Hermitian packed matrix A using the factorization A = U*D*U**H or A =
L*D*L**H computed by ZHPTRF
SYNOPSIS
SUBROUTINE ZHPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
CHARACTER UPLO
INTEGER INFO, N
DOUBLE PRECISION ANORM, RCOND
INTEGER IPIV( * )
COMPLEX*16 AP( * ), WORK( * )
PURPOSE
ZHPCON estimates the reciprocal of the condition number of a complex
Hermitian packed matrix A using the factorization A = U*D*U**H or A =
L*D*L**H computed by ZHPTRF. An estimate is obtained for norm(inv(A)),
and the reciprocal of the condition number is computed as RCOND = 1 /
(ANORM * norm(inv(A))).
ARGUMENTS
UPLO (input) CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix. = 'U': Upper triangu‐
lar, form is A = U*D*U**H;
= 'L': Lower triangular, form is A = L*D*L**H.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
The block diagonal matrix D and the multipliers used to obtain
the factor U or L as computed by ZHPTRF, stored as a packed
triangular matrix.
IPIV (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D as
determined by ZHPTRF.
ANORM (input) DOUBLE PRECISION
The 1-norm of the original matrix A.
RCOND (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A, com‐
puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti‐
mate of the 1-norm of inv(A) computed in this routine.
WORK (workspace) COMPLEX*16 array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
LAPACK routine (version 3.2) November 2008 ZHPCON(1)
