DLAGTF(1) LAPACK routine (version 3.2) DLAGTF(1)NAME
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,
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 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 trian‐
gular 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 ele‐
ments 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 routine (version 3.2) November 2008 DLAGTF(1)
