dlagts(3F)

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

     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 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
             overwritten by the solution vector x.

     TOL     (input/output) DOUBLE PRECISION
             On entry, with  JOB .lt. 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
             .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.