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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 piv‐
       oting 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 nor‐
	       mally be chose as approximately the largest relative  error  in
	       the  elements  of T. For example, if the elements of T are cor‐
	       rect 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 singular or nearly singular,

       INFO    (output) INTEGER
	       = 0   : successful exit

LAPACK version 3.0		 15 June 2000			     DLAGTF(l)
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