NAME¶

ZPOCON - estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF

SYNOPSIS¶

SUBROUTINE ZPOCON(

UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK, INFO )

CHARACTER UPLO INTEGER INFO, LDA, N DOUBLE PRECISION ANORM, RCOND DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( LDA, * ), WORK( * )

PURPOSE¶

ZPOCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF. 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.

A (input) COMPLEX*16 array, dimension (LDA,N)

The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by ZPOTRF.

LDA (input) INTEGER

The leading dimension of the array A. LDA >= max(1,N).

ANORM (input) DOUBLE PRECISION

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

RWORK (workspace) DOUBLE PRECISION array, dimension (N)

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value