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dptcon

 NAME
      DPTCON - compute the reciprocal of the condition number (in
      the 1-norm) of a real symmetric positive definite tridiago-
      nal 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 tridiago-
      nal 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 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 DPTTRF.

      E       (input) DOUBLE PRECISION array, dimension (N-1)
              The (n-1) off-diagonal elements of the unit bidiago-
              nal 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 rou-
              tine.

      WORK    (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, "Effi-
      cient Algorithms for Computing the Condition Number of a
      Tridiagonal Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No.
      1, January 1986.