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NAME
     dgttrf - compute an LU factorization of a  real  tridiagonal
     matrix  A  using  elimination  with partial pivoting and row
     interchanges

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

     INTEGER INFO, N

     INTEGER IPIV( * )

     DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * )



     #include <sunperf.h>

     void dgttrf(int n, double *dl, double *d, double *du, double
               *du2, int *ipivot, int *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  bidiago-
     nal 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) DOUBLE PRECISION  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) 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) DOUBLE PRECISION  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) DOUBLE PRECISION 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  indi-
               cates a row interchange was not required.

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

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