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dpttrf

 NAME
      DPTTRF - compute the factorization of a real symmetric posi-
      tive definite tridiagonal matrix A

 SYNOPSIS
      SUBROUTINE DPTTRF( N, D, E, INFO )

          INTEGER        INFO, N

          DOUBLE         PRECISION D( * ), E( * )

 PURPOSE
      DPTTRF computes the factorization of a real symmetric posi-
      tive definite tridiagonal matrix A.

      If the subdiagonal elements of A are supplied in the array
      E, the factorization has the form A = L*D*L**T, where D is
      diagonal and L is unit lower bidiagonal; if the superdiago-
      nal elements of A are supplied, it has the form A =
      U**T*D*U, where U is unit upper bidiagonal.  (The two forms
      are equivalent if A is real.)

 ARGUMENTS
      N       (input) INTEGER
              The order of the matrix A.  N >= 0.

      D       (input/output) DOUBLE PRECISION array, dimension (N)
              On entry, the n diagonal elements of the tridiagonal
              matrix A.  On exit, the n diagonal elements of the
              diagonal matrix D from the L*D*L**T factorization of
              A.

      E       (input/output) DOUBLE PRECISION array, dimension (N-
              1)
              On entry, the (n-1) off-diagonal elements of the
              tridiagonal matrix A.  On exit, the (n-1) off-
              diagonal elements of the unit bidiagonal factor L or
              U from the factorization of A.

      INFO    (output) INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal
              value
              > 0:  if INFO = i, the leading minor of order i is
              not positive definite; if i < N, the factorization
              could not be completed, while if i = N, the factori-
              zation was completed, but D(N) = 0.