DPTCON  -  compute  the reciprocal of the condition number
       (in the 1-norm) of  a  real  symmetric  positive  definite
       tridiagonal matrix using the factorization A = L*D*L**T or
       A = U**T*D*U computed by DPTTRF


SYNOPSIS

       SUBROUTINE DPTCON( N, D, E, ANORM, RCOND, WORK, INFO )

           INTEGER        INFO, N

           DOUBLE         PRECISION ANORM, RCOND

           DOUBLE         PRECISION D( * ), E( * ), WORK( * )


PURPOSE

       DPTCON computes the reciprocal of the condition number (in
       the 1-norm) of a real symmetric positive definite tridiag­
       onal matrix using the factorization A = L*D*L**T  or  A  =
       U**T*D*U  computed by DPTTRF.  Norm(inv(A)) is computed by
       a direct method, and the reciprocal of the condition  num­
       ber 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  DPT­
               TRF.

       E       (input) DOUBLE PRECISION 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 DPTTRF.

       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.

       WORK    (workspace) DOUBLE PRECISION array, dimension (N)

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

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


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