zgttrf(3F)

NAME
     ZGTTRF - compute 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.  N >= 0.

     DL      (input/output) COMPLEX*16 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) 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) superdiagonal elements of A.
             On exit, DU is overwritten by the (n-1) elements of the first
             superdiagonal of U.

     DU2     (output) COMPLEX*16 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.