NAME

DGTTRF - compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges

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.  N >= 0.

DL      (input/output) DOUBLE PRECISION array, dimension (N-1)
On entry, DL must contain the (n-1) subdiagonal 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) superdiagonal elements of A. On exit, DU is overwritten by the (n-1) elements of the first superdiagonal of U.

DU2     (output) DOUBLE PRECISION array, dimension (N-2)
On exit, DU2 is overwritten by the (n-2) 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 = -i, the i-th argument had an illegal value
> 0:  if INFO = i, U(i,i) 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 2.0  —  08 October 1994