# ?lagts

Solves the system of equations (T - lambda*I)*x = y or (T - lambda*I)T*x = y ,where T is a general tridiagonal matrix and lambda is a scalar, using the LU factorization computed by ?lagtf.

## Syntax

call slagts( job, n, a, b, c, d, in, y, tol, info )

call dlagts( job, n, a, b, c, d, in, y, tol, info )

## Description

This routine may be used to solve for x one of the systems of equations:

`(T - lambda*I)*x = y` or `(T - lambda*I)'*x = y`,

where T is an n-by-n tridiagonal matrix, following the factorization of (`T - lambda*I`) as

`T - lambda*I = P*L*U`,

computed by the routine ?lagtf.

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.

## Input Parameters

job

  INTEGER. Specifies the job to be performed by ?lagts 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 diagonal elements of U are to be perturbed. See argument tol below.

n

  INTEGER. The order of the matrix T (`n ≥ 0`).

a, b, c, d

  REAL for slagts

  DOUBLE PRECISION for dlagts

  Arrays, dimension a(n), b(n-1), c(n-1), d(n-2):

  On entry, a(*) must contain the diagonal elements of U as returned from ?lagtf.

  On entry, b(*) must contain the first super-diagonal elements of U as returned from ?lagtf.

  On entry, c(*) must contain the sub-diagonal elements of L as returned from ?lagtf.

  On entry, d(*) must contain the second super-diagonal elements of U as returned from ?lagtf.

in

  INTEGER.

  Array, dimension (n).

  On entry, in(*) must contain details of the matrix p as returned from ?lagtf.

y

  REAL for slagts

  DOUBLE PRECISION for dlagts

  Array, dimension (n). On entry, the right hand side vector y.

tol

  REAL for slagtf

  DOUBLE PRECISION for dlagtf.

  On entry, with `job < 0`, tol should be the minimum 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 > 0` then tol is not referenced.

## Output Parameters

y

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

tol

  On exit, tol is changed as described in Input Parameters section above, only if tol is non-positive on entry. Otherwise tol is unchanged.

info

  INTEGER.

  If `info = 0`, the execution is successful.

  If `info = -i`, the i-th parameter had an illegal value. If `info = i >0`, overflow would occur when computing the ith 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.

Parent topic: Auxiliary Routines