DPTCON (3lapack)

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 tridiagonal 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 bidiagonal 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 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.