DGTTRF(3)      LAPACK routine of NEC Numeric Library Collection      DGTTRF(3)



NAME
       DGTTRF

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



PURPOSE
            DGTTRF computes an LU factorization of a real 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)
                     N is INTEGER
                     The order of the matrix A.

           DL        (input/output)
                     DL is DOUBLE PRECISION 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)
                     D is DOUBLE PRECISION 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)
                     DU is DOUBLE PRECISION 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)
                     DU2 is DOUBLE PRECISION array, dimension (N-2)
                     On exit, DU2 is overwritten by the (n-2) elements of the
                     second super-diagonal of U.

           IPIV      (output)
                     IPIV is 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)
                     INFO is 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                  31 October 2017                      DGTTRF(3)