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version 1.1, 2010/01/26 15:22:46 version 1.19, 2023/08/07 08:38:57
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   *> \brief \b DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download DLARRK + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarrk.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarrk.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarrk.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLARRK( N, IW, GL, GU,
   *                           D, E2, PIVMIN, RELTOL, W, WERR, INFO)
   *
   *       .. Scalar Arguments ..
   *       INTEGER   INFO, IW, N
   *       DOUBLE PRECISION    PIVMIN, RELTOL, GL, GU, W, WERR
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   D( * ), E2( * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLARRK computes one eigenvalue of a symmetric tridiagonal
   *> matrix T to suitable accuracy. This is an auxiliary code to be
   *> called from DSTEMR.
   *>
   *> To avoid overflow, the matrix must be scaled so that its
   *> largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
   *> accuracy, it should not be much smaller than that.
   *>
   *> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
   *> Matrix", Report CS41, Computer Science Dept., Stanford
   *> University, July 21, 1966.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the tridiagonal matrix T.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] IW
   *> \verbatim
   *>          IW is INTEGER
   *>          The index of the eigenvalues to be returned.
   *> \endverbatim
   *>
   *> \param[in] GL
   *> \verbatim
   *>          GL is DOUBLE PRECISION
   *> \endverbatim
   *>
   *> \param[in] GU
   *> \verbatim
   *>          GU is DOUBLE PRECISION
   *>          An upper and a lower bound on the eigenvalue.
   *> \endverbatim
   *>
   *> \param[in] D
   *> \verbatim
   *>          D is DOUBLE PRECISION array, dimension (N)
   *>          The n diagonal elements of the tridiagonal matrix T.
   *> \endverbatim
   *>
   *> \param[in] E2
   *> \verbatim
   *>          E2 is DOUBLE PRECISION array, dimension (N-1)
   *>          The (n-1) squared off-diagonal elements of the tridiagonal matrix T.
   *> \endverbatim
   *>
   *> \param[in] PIVMIN
   *> \verbatim
   *>          PIVMIN is DOUBLE PRECISION
   *>          The minimum pivot allowed in the Sturm sequence for T.
   *> \endverbatim
   *>
   *> \param[in] RELTOL
   *> \verbatim
   *>          RELTOL is DOUBLE PRECISION
   *>          The minimum relative width of an interval.  When an interval
   *>          is narrower than RELTOL times the larger (in
   *>          magnitude) endpoint, then it is considered to be
   *>          sufficiently small, i.e., converged.  Note: this should
   *>          always be at least radix*machine epsilon.
   *> \endverbatim
   *>
   *> \param[out] W
   *> \verbatim
   *>          W is DOUBLE PRECISION
   *> \endverbatim
   *>
   *> \param[out] WERR
   *> \verbatim
   *>          WERR is DOUBLE PRECISION
   *>          The error bound on the corresponding eigenvalue approximation
   *>          in W.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:       Eigenvalue converged
   *>          = -1:      Eigenvalue did NOT converge
   *> \endverbatim
   *
   *> \par Internal Parameters:
   *  =========================
   *>
   *> \verbatim
   *>  FUDGE   DOUBLE PRECISION, default = 2
   *>          A "fudge factor" to widen the Gershgorin intervals.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \ingroup OTHERauxiliary
   *
   *  =====================================================================
       SUBROUTINE DLARRK( N, IW, GL, GU,        SUBROUTINE DLARRK( N, IW, GL, GU,
      $                    D, E2, PIVMIN, RELTOL, W, WERR, INFO)       $                    D, E2, PIVMIN, RELTOL, W, WERR, INFO)
       IMPLICIT NONE  
 *  *
 *  -- LAPACK auxiliary routine (version 3.2) --  *  -- LAPACK auxiliary routine --
 *  -- 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..--
 *     November 2006  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER   INFO, IW, N        INTEGER   INFO, IW, N
Line 15 Line 155
       DOUBLE PRECISION   D( * ), E2( * )        DOUBLE PRECISION   D( * ), E2( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLARRK computes one eigenvalue of a symmetric tridiagonal  
 *  matrix T to suitable accuracy. This is an auxiliary code to be  
 *  called from DSTEMR.  
 *  
 *  To avoid overflow, the matrix must be scaled so that its  
 *  largest element is no greater than overflow**(1/2) *  
 *  underflow**(1/4) in absolute value, and for greatest  
 *  accuracy, it should not be much smaller than that.  
 *  
 *  See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal  
 *  Matrix", Report CS41, Computer Science Dept., Stanford  
 *  University, July 21, 1966.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  N       (input) INTEGER  
 *          The order of the tridiagonal matrix T.  N >= 0.  
 *  
 *  IW      (input) INTEGER  
 *          The index of the eigenvalues to be returned.  
 *  
 *  GL      (input) DOUBLE PRECISION  
 *  GU      (input) DOUBLE PRECISION  
 *          An upper and a lower bound on the eigenvalue.  
 *  
 *  D       (input) DOUBLE PRECISION array, dimension (N)  
 *          The n diagonal elements of the tridiagonal matrix T.  
 *  
 *  E2      (input) DOUBLE PRECISION array, dimension (N-1)  
 *          The (n-1) squared off-diagonal elements of the tridiagonal matrix T.  
 *  
 *  PIVMIN  (input) DOUBLE PRECISION  
 *          The minimum pivot allowed in the Sturm sequence for T.  
 *  
 *  RELTOL  (input) DOUBLE PRECISION  
 *          The minimum relative width of an interval.  When an interval  
 *          is narrower than RELTOL times the larger (in  
 *          magnitude) endpoint, then it is considered to be  
 *          sufficiently small, i.e., converged.  Note: this should  
 *          always be at least radix*machine epsilon.  
 *  
 *  W       (output) DOUBLE PRECISION  
 *  
 *  WERR    (output) DOUBLE PRECISION  
 *          The error bound on the corresponding eigenvalue approximation  
 *          in W.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:       Eigenvalue converged  
 *          = -1:      Eigenvalue did NOT converge  
 *  
 *  Internal Parameters  
 *  ===================  
 *  
 *  FUDGE   DOUBLE PRECISION, default = 2  
 *          A "fudge factor" to widen the Gershgorin intervals.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
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 *     ..  *     ..
 *     .. Executable Statements ..  *     .. Executable Statements ..
 *  *
   *     Quick return if possible
   *
         IF( N.LE.0 ) THEN
            INFO = 0
            RETURN
         END IF
   *
 *     Get machine constants  *     Get machine constants
       EPS = DLAMCH( 'P' )        EPS = DLAMCH( 'P' )
   
Removed from v.1.1  
changed lines
  Added in v.1.19

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