CGTTRF - compute an LU factorization of a complex tridiag­
       onal 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 tridiago­
       nal 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 bidiag­
       onal 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)  multipli­
               ers  that  define the matrix L from the LU factor­
               ization 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 ele­
               ments 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.

               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  indi­
               cates a row interchange was not required.

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -k, the k-th argument had an ille­
               gal 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 equa­
               tions.


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