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# slagts

```
NAME
SLAGTS - 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 SLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO )

INTEGER        INFO, JOB, N

REAL           TOL

INTEGER        IN( * )

REAL           A( * ), B( * ), C( * ), D( * ), Y( * )

PURPOSE
SLAGTS may be used to solve one of the systems of equations

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 SLAGTF. 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 SLAGTS as fol-
lows:
=  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 per-
turbed. 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) REAL array, dimension (N)
On entry, A must contain the diagonal elements of U

as returned from SLAGTF.

B       (input) REAL array, dimension (N-1)
On entry, B must contain the first super-diagonal
elements of U as returned from SLAGTF.

C       (input) REAL array, dimension (N-1)
On entry, C must contain the sub-diagonal elements
of L as returned from SLAGTF.

D       (input) REAL array, dimension (N-2)
On entry, D must contain the second super-diagonal
elements of U as returned from SLAGTF.

IN      (input) INTEGER array, dimension (N)
On entry, IN must contain details of the matrix P as
returned from SLAGTF.

Y       (input/output) REAL array, dimension (N)
On entry, the right hand side vector y.

On exit, Y is overwritten by the solution vector x.

TOL     (input/output) REAL
On entry with  JOB .lt. 0, TOL should be the minimum
perturbation to be made to very small diagonal ele-
ments of U.  TOL should normally be chosen as about
eps*norm(U), where eps is the relative machine pre-
cision, 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)
= 0   : successful exit
< 0: if INFO = -k, the kth argument had an illegal
value
> 0: overflow would occur when computing the
INFO(th) 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.
```