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 form

   A = 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 (N-1)

On entry, DL must contain the (n-1) sub-diagonal elements of A. On exit, DL is overwritten by the (n-1) 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 (N-1)

On entry, DU must contain the (n-1) super-diagonal elements of A. On exit, DU is overwritten by the (n-1) elements of the first super-diagonal of U.

DU2 (output) DOUBLE PRECISION array, dimension (N-2)

On exit, DU2 is overwritten by the (n-2) elements of the second super-diagonal 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 k-th 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.