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dlagtf.f(3)				      LAPACK				      dlagtf.f(3)

NAME
       dlagtf.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dlagtf (N, A, LAMBDA, B, C, TOL, D, IN, INFO)
	   DLAGTF computes an LU factorization of a matrix T-\I, where T is a general tridiagonal
	   matrix, and \ a scalar, using partial pivoting with row interchanges.

Function/Subroutine Documentation
   subroutine dlagtf (integerN, double precision, dimension( * )A, double precisionLAMBDA, double
       precision, dimension( * )B, double precision, dimension( * )C, double precisionTOL, double
       precision, dimension( * )D, integer, dimension( * )IN, integerINFO)
       DLAGTF computes an LU factorization of a matrix T-\I, where T is a general tridiagonal
       matrix, and \ a scalar, using partial pivoting with row interchanges.

       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.

       Parameters:
	   N

		     N is INTEGER
		     The order of the matrix T.

	   A

		     A is 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

		     LAMBDA is DOUBLE PRECISION
		     On entry, the scalar lambda.

	   B

		     B is 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

		     C is 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

		     TOL is 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

		     D is 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

		     IN is 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

		     INFO is INTEGER
		     = 0   : successful exit
		     .lt. 0: if INFO = -k, the kth argument had an illegal value

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Definition at line 157 of file dlagtf.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dlagtf.f(3)
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