NAME

       slagts.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slagts (JOB, N, A, B, C, D, IN, Y, TOL, INFO)
           SLAGTS solves the system of equations (T-λI)x = y or (T-λI)Tx = y,where T is a general
           tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf.

Function/Subroutine Documentation

   subroutine slagts (integerJOB, integerN, real, dimension( * )A, real, dimension( * )B, real,
       dimension( * )C, real, dimension( * )D, integer, dimension( * )IN, real, dimension( * )Y,
       realTOL, integerINFO)
       SLAGTS solves the system of equations (T-λI)x = y or (T-λI)Tx = y,where T is a general
       tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf.

       Purpose:

            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.

       Parameters:
           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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Definition at line 162 of file slagts.f.

Author

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