NAME

cpocon - 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 CPOTRF

SYNOPSIS

SUBROUTINE CPOCON(
UPLO, N, A, LDA, ANORM, RCOND, WORK, RWORK, INFO )

void cpocon(char uplo, long int n, complex ∗ca, long int lda,
float anorm, float ∗srcond, long int ∗info)

CHARACTER UPLO

INTEGER INFO, LDA, N

REAL ANORM, RCOND

REAL RWORK( ∗ )

COMPLEX A( LDA, ∗ ), WORK( ∗ )

PURPOSE

CPOCON 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 CPOTRF. 
 
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 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 CPOTRF.

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

ANORM   (input) REAL
The 1-norm (or infinity-norm) of the Hermitian matrix A.

RCOND   (output) REAL
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 array, dimension (2∗N)

RWORK   (workspace) REAL array, dimension (N)

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

Sun, Inc.  —  Last change: 20 Sep 1996