# zhpcon (l) - Linux Manuals

## 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. = aqUaq: Upper triangular, form is A = U*D*U**H;
= aqLaq: 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, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate 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