zgtcon(3)

NAME

ZGTCON - estimate the reciprocal of the condition number

of a complex tridiagonal matrix A using the LU factorization as

computed by ZGTTRF

SYNOPSIS

SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2,  IPIV,  ANORM,
RCOND, WORK, INFO )
    CHARACTER      NORM
    INTEGER        INFO, N
    DOUBLE         PRECISION ANORM, RCOND
    INTEGER        IPIV( * )
    COMPLEX*16      D(  *  ),  DL( * ), DU( * ), DU2( * ),
WORK( * )

PURPOSE

ZGTCON estimates the reciprocal of the condition number of

a complex tridiagonal matrix A using the LU factorization as com

puted by ZGTTRF. 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

NORM (input) CHARACTER*1

Specifies whether the 1-norm condition number or

the infinity-norm condition number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.

N (input) INTEGER

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

DL (input) COMPLEX*16 array, dimension (N-1)

The (n-1) multipliers that define the matrix L

from the LU factorization of A as computed by ZGTTRF.

D (input) COMPLEX*16 array, dimension (N)

The n diagonal elements of the upper triangular

matrix U from the LU factorization of A.

DU (input) COMPLEX*16 array, dimension (N-1)

The (n-1) elements of the first superdiagonal of

U.

DU2 (input) COMPLEX*16 array, dimension (N-2)

The (n-2) elements of the second superdiagonal of

U.

IPIV (input) INTEGER array, dimension (N)

The pivot indices; for 1 <= i <= n, row i of the

matrix was interchanged with row IPIV(i). IPIV(i) will always be

either i or i+1; IPIV(i) = i indicates a row interchange was not

required.

ANORM (input) DOUBLE PRECISION

If NORM = '1' or 'O', the 1-norm of the original

matrix A. If NORM = 'I', the infinity-norm of the original 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)

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

ZGTCON(3)