ZGTTRF (3lapack)

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.