Homepage > Man Pages > Category > Subroutines
Homepage > Man Pages > Name > L

# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: computes an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row

```NAME
LAPACK-3 - computes an LU factorization of a complex tridiagonal matrix
A using elimination with partial pivoting and row interchanges

SYNOPSIS
SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO )

INTEGER        INFO, N

INTEGER        IPIV( * )

COMPLEX*16     D( * ), DL( * ), DU( * ), DU2( * )

PURPOSE
ZGTTRF 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*16 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*16 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*16 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*16 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.

LAPACK routine (version 3.2)     March 2011                       LAPACK-3(3)
```