ZGTCON(3f)

NAME
ZGTCON - 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 computed 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 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)

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