zhpcon(3)

NAME

ZHPCON - estimate 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 ob

tained for norm(inv(A)), and the reciprocal of the condition num

ber 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

triangular, 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 struc

ture 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 ma

trix 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 ille

gal value

LAPACK version 3.0 15 June 2000

ZHPCON(3)