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LAPACK version 3.0
zgttrf(3)

PURPOSE
  ZGTTRF - compute an LU factorization of a complex tridiagonal matrix A
  using elimination with partial pivoting and row interchanges

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

      INTEGER	     INFO, N

      INTEGER	     IPIV( * )

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

DESCRIPTION
  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.