dgttrf(3)

NAME

DGTTRF - compute an LU factorization of a real tridiagonal

matrix A using elimination with partial pivoting and row inter

changes

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 inter

changes. The factorization has the form

A = L * U

where L is a product of permutation and unit lower bidiag

onal 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) multipli

ers 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 ele

ments 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 ille

gal 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.

LAPACK version 3.0 15 June 2000

DGTTRF(3)