dlagts(3)

NAME

DLAGTS - may be used to solve one of the systems of equa

tions (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 equa

tions (T - lambda*I)*x = y or (T - lambda*I)'*x = y, where T is

an n by n tridiagonal 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 op

tion to perturb zero or very small diagonal elements of U, this

option being intended for use in applications such as inverse it

eration.

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

overflow 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 di

agonal 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 overwritten by the solution vector x.

TOL (input/output) DOUBLE PRECISION

On entry, with JOB .lt. 0, TOL should be the min

imum perturbation 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 element 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(3)