DLAGTF(l)								 )								 DLAGTF(l)

NAME

       DLAGTF - factorize the matrix (T - lambda*I), where T is an n by n tridiagonal matrix and lambda is a scalar, as  T - lambda*I = PLU,

SYNOPSIS

       SUBROUTINE DLAGTF( N, A, LAMBDA, B, C, TOL, D, IN, INFO )

	   INTEGER	  INFO, N

	   DOUBLE	  PRECISION LAMBDA, TOL

	   INTEGER	  IN( * )

	   DOUBLE	  PRECISION A( * ), B( * ), C( * ), D( * )

PURPOSE

       DLAGTF factorizes the matrix (T - lambda*I), where T is an n by n tridiagonal matrix and lambda is a scalar, as T - lambda*I = PLU, where P
       is a permutation matrix, L is a unit lower tridiagonal matrix with at most one non-zero sub-diagonal elements per column and U is an  upper
       triangular matrix with at most two non-zero super-diagonal elements per column.

       The factorization is obtained by Gaussian elimination with partial pivoting and implicit row scaling.

       The  parameter  LAMBDA  is  included  in the routine so that DLAGTF may be used, in conjunction with DLAGTS, to obtain eigenvectors of T by
       inverse iteration.

ARGUMENTS

       N       (input) INTEGER
	       The order of the matrix T.

       A       (input/output) DOUBLE PRECISION array, dimension (N)
	       On entry, A must contain the diagonal elements of T.

	       On exit, A is overwritten by the n diagonal elements of the upper triangular matrix U of the factorization of T.

       LAMBDA  (input) DOUBLE PRECISION
	       On entry, the scalar lambda.

       B       (input/output) DOUBLE PRECISION array, dimension (N-1)
	       On entry, B must contain the (n-1) super-diagonal elements of T.

	       On exit, B is overwritten by the (n-1) super-diagonal elements of the matrix U of the factorization of T.

       C       (input/output) DOUBLE PRECISION array, dimension (N-1)
	       On entry, C must contain the (n-1) sub-diagonal elements of T.

	       On exit, C is overwritten by the (n-1) sub-diagonal elements of the matrix L of the factorization of T.

       TOL     (input) DOUBLE PRECISION
	       On entry, a relative tolerance used to indicate whether or not the matrix (T - lambda*I) is nearly singular. TOL should normally be
	       chose  as  approximately  the largest relative error in the elements of T. For example, if the elements of T are correct to about 4
	       significant figures, then TOL should be set to about 5*10**(-4). If TOL is supplied as less than eps, where  eps  is  the  relative
	       machine precision, then the value eps is used in place of TOL.

       D       (output) DOUBLE PRECISION array, dimension (N-2)
	       On exit, D is overwritten by the (n-2) second super-diagonal elements of the matrix U of the factorization of T.

       IN      (output) INTEGER array, dimension (N)
	       On exit, IN contains details of the permutation matrix P. If an interchange occurred at the kth step of the elimination, then IN(k)
	       = 1, otherwise IN(k) = 0. The element IN(n) returns the smallest positive integer j such that

	       abs( u(j,j) ).le. norm( (T - lambda*I)(j) )*TOL,

	       where norm( A(j) ) denotes the sum of the absolute values of the jth row of the matrix A.  If  no  such	j  exists  then  IN(n)	is
	       returned as zero. If IN(n) is returned as positive, then a diagonal element of U is small, indicating that (T - lambda*I) is singu-
	       lar or nearly singular,

       INFO    (output) INTEGER
	       = 0   : successful exit

LAPACK version 3.0						   15 June 2000 							 DLAGTF(l)