Diff for /rpl/lapack/lapack/dlartgs.f between versions 1.3 and 1.4

version 1.3, 2011/07/22 07:38:07 version 1.4, 2011/11/21 20:42:58
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       SUBROUTINE DLARTGS( X, Y, SIGMA, CS, SN )  *> \brief \b DLARTGS
       IMPLICIT NONE  
 *  
 *  -- LAPACK routine (version 3.3.0) --  
 *  
 *  -- Contributed by Brian Sutton of the Randolph-Macon College --  
 *  -- November 2010  
 *  
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--       
 *  
 *     .. Scalar Arguments ..  
       DOUBLE PRECISION        CS, SIGMA, SN, X, Y  
 *     ..  
 *  
 *  Purpose  
 *  =======  
 *  *
 *  DLARTGS generates a plane rotation designed to introduce a bulge in  *  =========== DOCUMENTATION ===========
 *  Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD  
 *  problem. X and Y are the top-row entries, and SIGMA is the shift.  
 *  The computed CS and SN define a plane rotation satisfying  
 *  *
 *     [  CS  SN  ]  .  [ X^2 - SIGMA ]  =  [ R ],  * Online html documentation available at 
 *     [ -SN  CS  ]     [    X * Y    ]     [ 0 ]  *            http://www.netlib.org/lapack/explore-html/ 
 *  *
 *  with R nonnegative.  If X^2 - SIGMA and X * Y are 0, then the  *> \htmlonly
 *  rotation is by PI/2.  *> Download DLARTGS + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlartgs.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlartgs.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlartgs.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLARTGS( X, Y, SIGMA, CS, SN )
   * 
   *       .. Scalar Arguments ..
   *       DOUBLE PRECISION        CS, SIGMA, SN, X, Y
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLARTGS generates a plane rotation designed to introduce a bulge in
   *> Golub-Reinsch-style implicit QR iteration for the bidiagonal SVD
   *> problem. X and Y are the top-row entries, and SIGMA is the shift.
   *> The computed CS and SN define a plane rotation satisfying
   *>
   *>    [  CS  SN  ]  .  [ X^2 - SIGMA ]  =  [ R ],
   *>    [ -SN  CS  ]     [    X * Y    ]     [ 0 ]
   *>
   *> with R nonnegative.  If X^2 - SIGMA and X * Y are 0, then the
   *> rotation is by PI/2.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] X
   *> \verbatim
   *>          X is DOUBLE PRECISION
   *>          The (1,1) entry of an upper bidiagonal matrix.
   *> \endverbatim
   *>
   *> \param[in] Y
   *> \verbatim
   *>          Y is DOUBLE PRECISION
   *>          The (1,2) entry of an upper bidiagonal matrix.
   *> \endverbatim
   *>
   *> \param[in] SIGMA
   *> \verbatim
   *>          SIGMA is DOUBLE PRECISION
   *>          The shift.
   *> \endverbatim
   *>
   *> \param[out] CS
   *> \verbatim
   *>          CS is DOUBLE PRECISION
   *>          The cosine of the rotation.
   *> \endverbatim
   *>
   *> \param[out] SN
   *> \verbatim
   *>          SN is DOUBLE PRECISION
   *>          The sine of the rotation.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
 *  *
 *  Arguments  *> \date November 2011
 *  =========  
 *  *
 *  X       (input) DOUBLE PRECISION  *> \ingroup auxOTHERcomputational
 *          The (1,1) entry of an upper bidiagonal matrix.  
 *  *
 *  Y       (input) DOUBLE PRECISION  *  =====================================================================
 *          The (1,2) entry of an upper bidiagonal matrix.        SUBROUTINE DLARTGS( X, Y, SIGMA, CS, SN )
 *  
 *  SIGMA   (input) DOUBLE PRECISION  
 *          The shift.  
 *  *
 *  CS      (output) DOUBLE PRECISION  *  -- LAPACK computational routine (version 3.4.0) --
 *          The cosine of the rotation.  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
   *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *     November 2011
 *  *
 *  SN      (output) DOUBLE PRECISION  *     .. Scalar Arguments ..
 *          The sine of the rotation.        DOUBLE PRECISION        CS, SIGMA, SN, X, Y
   *     ..
 *  *
 *  ===================================================================  *  ===================================================================
 *  *

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  Added in v.1.4


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