cptcon(3)

NAME

CPTCON - compute the reciprocal of the condition number

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

onal matrix using the factorization A = L*D*L**H or A = U**H*D*U

computed by CPTTRF

SYNOPSIS

SUBROUTINE CPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )
    INTEGER        INFO, N
    REAL           ANORM, RCOND
    REAL           D( * ), RWORK( * )
    COMPLEX        E( * )

PURPOSE

CPTCON computes the reciprocal of the condition number (in

the 1-norm) of a complex Hermitian positive definite tridiagonal

matrix using the factorization A = L*D*L**H or A = U**H*D*U com

puted by CPTTRF. Norm(inv(A)) is computed by a direct method,

and the reciprocal of the condition number is computed as

RCOND = 1 / (ANORM * norm(inv(A))).

ARGUMENTS

N (input) INTEGER

The order of the matrix A. N >= 0.

D (input) REAL array, dimension (N)

The n diagonal elements of the diagonal matrix D

from the factorization of A, as computed by CPTTRF.

E (input) COMPLEX array, dimension (N-1)

The (n-1) off-diagonal elements of the unit bidi

agonal factor U or L from the factorization of A, as computed by

CPTTRF.

ANORM (input) REAL

The 1-norm of the original matrix A.

RCOND (output) REAL

The reciprocal of the condition number of the ma

trix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is

the 1-norm of inv(A) computed in this routine.

RWORK (workspace) REAL array, dimension (N)

INFO (output) INTEGER

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

gal value

FURTHER DETAILS

The method used is described in Nicholas J. Higham, "Effi

cient Algorithms for Computing the Condition Number of a Tridiag

onal Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January

1986.

LAPACK version 3.0 15 June 2000

CPTCON(3)