 CGTTRF(3) computes an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges

## SYNOPSIS

SUBROUTINE CGTTRF(
N, DL, D, DU, DU2, IPIV, INFO )

INTEGER INFO, N

INTEGER IPIV( * )

COMPLEX D( * ), DL( * ), DU( * ), DU2( * )

## PURPOSE

CGTTRF computes an LU factorization of a complex 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) COMPLEX 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) COMPLEX 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) COMPLEX 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) COMPLEX 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.