NAME

ZPOCON - estimate 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

  —  LAPACK version 2.0  —  08 October 1994