DLAGTS(l) ) DLAGTS(l)NAME
DLAGTS - may be used to solve one of the systems of equations (T -
lambda*I)*x = y or (T - lambda*I)'*x = y,
SYNOPSIS
SUBROUTINE DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO )
INTEGER INFO, JOB, N
DOUBLE PRECISION TOL
INTEGER IN( * )
DOUBLE PRECISION A( * ), B( * ), C( * ), D( * ), Y( * )
PURPOSE
DLAGTS may be used to solve one of the systems of equations (T -
lambda*I)*x = y or (T - lambda*I)'*x = y, where T is an n by n tridiag‐
onal matrix, for x, following the factorization of (T - lambda*I) as
(T - lambda*I) = P*L*U ,
by routine DLAGTF. The choice of equation to be solved is controlled by
the argument JOB, and in each case there is an option to perturb zero
or very small diagonal elements of U, this option being intended for
use in applications such as inverse iteration.
ARGUMENTS
JOB (input) INTEGER
Specifies the job to be performed by DLAGTS as follows:
= 1: The equations (T - lambda*I)x = y are to be solved, but
diagonal elements of U are not to be perturbed. = -1: The
equations (T - lambda*I)x = y are to be solved and, if over‐
flow would otherwise occur, the diagonal elements of U are to
be perturbed. See argument TOL below. = 2: The equations (T
- lambda*I)'x = y are to be solved, but diagonal elements of U
are not to be perturbed. = -2: The equations (T - lambda*I)'x
= y are to be solved and, if overflow would otherwise occur,
the diagonal elements of U are to be perturbed. See argument
TOL below.
N (input) INTEGER
The order of the matrix T.
A (input) DOUBLE PRECISION array, dimension (N)
On entry, A must contain the diagonal elements of U as returned
from DLAGTF.
B (input) DOUBLE PRECISION array, dimension (N-1)
On entry, B must contain the first super-diagonal elements of U
as returned from DLAGTF.
C (input) DOUBLE PRECISION array, dimension (N-1)
On entry, C must contain the sub-diagonal elements of L as
returned from DLAGTF.
D (input) DOUBLE PRECISION array, dimension (N-2)
On entry, D must contain the second super-diagonal elements of
U as returned from DLAGTF.
IN (input) INTEGER array, dimension (N)
On entry, IN must contain details of the matrix P as returned
from DLAGTF.
Y (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the right hand side vector y. On exit, Y is over‐
written by the solution vector x.
TOL (input/output) DOUBLE PRECISION
On entry, with JOB .lt. 0, TOL should be the minimum perturba‐
tion to be made to very small diagonal elements of U. TOL
should normally be chosen as about eps*norm(U), where eps is
the relative machine precision, but if TOL is supplied as non-
positive, then it is reset to eps*max( abs( u(i,j) ) ). If
JOB .gt. 0 then TOL is not referenced.
On exit, TOL is changed as described above, only if TOL is non-
positive on entry. Otherwise TOL is unchanged.
INFO (output) INTEGER
= 0 : successful exit
element of the solution vector x. This can only occur when JOB
is supplied as positive and either means that a diagonal ele‐
ment of U is very small, or that the elements of the right-hand
side vector y are very large.
LAPACK version 3.0 15 June 2000 DLAGTS(l)
