ZPTCON(3f)               LAPACK routine (version 3.1)               ZPTCON(3f)



NAME
       ZPTCON - 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 computed by ZPTTRF

SYNOPSIS
       SUBROUTINE ZPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )

           INTEGER        INFO, N

           DOUBLE         PRECISION ANORM, RCOND

           DOUBLE         PRECISION D( * ), RWORK( * )

           COMPLEX*16     E( * )

PURPOSE
       ZPTCON 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 computed by ZPTTRF.

       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) DOUBLE PRECISION array, dimension (N)
               The n diagonal elements of the diagonal matrix D from the
               factorization of A, as computed by ZPTTRF.

       E       (input) COMPLEX*16 array, dimension (N-1)
               The (n-1) off-diagonal elements of the unit bidiagonal factor U
               or L from the factorization of A, as computed by ZPTTRF.

       ANORM   (input) DOUBLE PRECISION
               The 1-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 the
               1-norm of inv(A) computed in this routine.

       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

FURTHER DETAILS
       The method used is described in Nicholas J. Higham, "Efficient
       Algorithms for Computing the Condition Number of a Tridiagonal Matrix",
       SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.




 LAPACK routine (version 3.1)    November 2006                      ZPTCON(3f)
