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version 1.8, 2011/07/22 07:38:06 version 1.9, 2011/11/21 20:42:55
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   *> \brief \b DLAGTS
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLAGTS + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlagts.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlagts.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlagts.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, JOB, N
   *       DOUBLE PRECISION   TOL
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IN( * )
   *       DOUBLE PRECISION   A( * ), B( * ), C( * ), D( * ), Y( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLAGTS 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 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.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] JOB
   *> \verbatim
   *>          JOB is 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)**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.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix T.
   *> \endverbatim
   *>
   *> \param[in] A
   *> \verbatim
   *>          A is DOUBLE PRECISION array, dimension (N)
   *>          On entry, A must contain the diagonal elements of U as
   *>          returned from DLAGTF.
   *> \endverbatim
   *>
   *> \param[in] B
   *> \verbatim
   *>          B is DOUBLE PRECISION array, dimension (N-1)
   *>          On entry, B must contain the first super-diagonal elements of
   *>          U as returned from DLAGTF.
   *> \endverbatim
   *>
   *> \param[in] C
   *> \verbatim
   *>          C is DOUBLE PRECISION array, dimension (N-1)
   *>          On entry, C must contain the sub-diagonal elements of L as
   *>          returned from DLAGTF.
   *> \endverbatim
   *>
   *> \param[in] D
   *> \verbatim
   *>          D is DOUBLE PRECISION array, dimension (N-2)
   *>          On entry, D must contain the second super-diagonal elements
   *>          of U as returned from DLAGTF.
   *> \endverbatim
   *>
   *> \param[in] IN
   *> \verbatim
   *>          IN is INTEGER array, dimension (N)
   *>          On entry, IN must contain details of the matrix P as returned
   *>          from DLAGTF.
   *> \endverbatim
   *>
   *> \param[in,out] Y
   *> \verbatim
   *>          Y is DOUBLE PRECISION array, dimension (N)
   *>          On entry, the right hand side vector y.
   *>          On exit, Y is overwritten by the solution vector x.
   *> \endverbatim
   *>
   *> \param[in,out] TOL
   *> \verbatim
   *>          TOL is 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.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          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.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup auxOTHERauxiliary
   *
   *  =====================================================================
       SUBROUTINE DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO )        SUBROUTINE DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO )
 *  *
 *  -- LAPACK auxiliary routine (version 3.3.1) --  *  -- LAPACK auxiliary routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *  -- April 2011                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, JOB, N        INTEGER            INFO, JOB, N
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       DOUBLE PRECISION   A( * ), B( * ), C( * ), D( * ), Y( * )        DOUBLE PRECISION   A( * ), B( * ), C( * ), D( * ), Y( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLAGTS 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 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)**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       (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  
 *          .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.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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