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 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 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 oth
erwise 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.
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 diago
nal 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.
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