SYNOPSIS
 SUBROUTINE DGTTRF(
 N, DL, D, DU, DU2, IPIV, INFO )
 INTEGER INFO, N
 INTEGER IPIV( * )
 DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * )
PURPOSE
DGTTRF computes an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges. The factorization has the formA = L * U
where L is a product of permutation and unit lower bidiagonal matrices and U is upper triangular with nonzeros in only the main diagonal and first two superdiagonals.
ARGUMENTS
 N (input) INTEGER
 The order of the matrix A.
 DL (input/output) DOUBLE PRECISION array, dimension (N1)
 On entry, DL must contain the (n1) subdiagonal elements of A. On exit, DL is overwritten by the (n1) multipliers that define the matrix L from the LU factorization of A.
 D (input/output) DOUBLE PRECISION array, dimension (N)
 On entry, D must contain the diagonal elements of A. On exit, D is overwritten by the n diagonal elements of the upper triangular matrix U from the LU factorization of A.
 DU (input/output) DOUBLE PRECISION array, dimension (N1)
 On entry, DU must contain the (n1) superdiagonal elements of A. On exit, DU is overwritten by the (n1) elements of the first superdiagonal of U.
 DU2 (output) DOUBLE PRECISION array, dimension (N2)
 On exit, DU2 is overwritten by the (n2) elements of the second superdiagonal of U.
 IPIV (output) INTEGER array, dimension (N)
 The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = k, the kth argument had an illegal value
> 0: if INFO = k, U(k,k) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.