DLAGTS (3lapack)

may be used to solve one of the systems of equations (T - lambda*I)*x = y or (T (3lapack)
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.



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