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dlagts

 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 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 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) 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 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.