
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 nonzero subdiagonal elements per column and U
is an upper triangular matrix with at most two nonzero superdiagonal elements per col
umn.
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 (N1)
On entry, B must contain the (n1) superdiagonal elements of T.
On exit, B is overwritten by the (n1) superdiagonal elements of the matrix U of
the factorization of T.
C (input/output) DOUBLE PRECISION array, dimension (N1)
On entry, C must contain the (n1) subdiagonal elements of T.
On exit, C is overwritten by the (n1) subdiagonal 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 (N2)
On exit, D is overwritten by the (n2) second superdiagonal 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) 
