zppcon(3)

NAME

ZPPCON - estimate the reciprocal of the condition number

(in the 1-norm) of a complex Hermitian positive definite packed

matrix using the Cholesky factorization A = U**H*U or A = L*L**H

computed by ZPPTRF

SYNOPSIS

SUBROUTINE ZPPCON( UPLO, N, AP, ANORM, RCOND, WORK, RWORK,
INFO )
    CHARACTER      UPLO
    INTEGER        INFO, N
    DOUBLE         PRECISION ANORM, RCOND
    DOUBLE         PRECISION RWORK( * )
    COMPLEX*16     AP( * ), WORK( * )

PURPOSE

ZPPCON estimates the reciprocal of the condition number

(in the 1-norm) of a complex Hermitian positive definite packed

matrix using the Cholesky factorization A = U**H*U or A = L*L**H

computed by ZPPTRF. 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

= '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*16 array, dimension (N*(N+1)/2)

The triangular factor U or L from the Cholesky

factorization A = U**H*U or A = L*L**H, packed columnwise in a

linear array. The j-th column of U or L is stored in the array

AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for

1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for

j<=i<=n.

ANORM (input) DOUBLE PRECISION

The 1-norm (or infinity-norm) of the Hermitian ma

trix 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)

RWORK (workspace) DOUBLE PRECISION array, dimension (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

ZPPCON(3)