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


    (T - lambda*I)*x = y   or   (T - lambda*I)**T*x = y,


 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.

JOB

          JOB is INTEGER


          Specifies the job to be performed by SLAGTS 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)**Tx = y  are to be solved,


                but diagonal elements of U are not to be perturbed.


          = -2: The equations  (T - lambda*I)**Tx = 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

          N is INTEGER


          The order of the matrix T.

A

          A is REAL array, dimension (N)


          On entry, A must contain the diagonal elements of U as


          returned from SLAGTF.

B

          B is REAL array, dimension (N-1)


          On entry, B must contain the first super-diagonal elements of


          U as returned from SLAGTF.

C

          C is REAL array, dimension (N-1)


          On entry, C must contain the sub-diagonal elements of L as


          returned from SLAGTF.

D

          D is REAL array, dimension (N-2)


          On entry, D must contain the second super-diagonal elements


          of U as returned from SLAGTF.

IN

          IN is INTEGER array, dimension (N)


          On entry, IN must contain details of the matrix P as returned


          from SLAGTF.

Y

          Y is REAL array, dimension (N)


          On entry, the right hand side vector y.


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

TOL

          TOL is REAL


          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

          INFO is INTEGER


          = 0   : successful exit


          .lt. 0: if INFO = -i, the i-th argument had an illegal value


          .gt. 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.

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December 2016