[BACK]Return to dlanv2.f CVS log [TXT] [DIR] Up to [local] / rpl / lapack / lapack

Diff for /rpl/lapack/lapack/dlanv2.f between versions 1.8 and 1.9

version 1.8, 2010/12/21 13:53:30 version 1.9, 2011/11/21 20:42:56
Line 1 Line 1
   *> \brief \b DLANV2
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLANV2 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlanv2.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlanv2.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlanv2.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
   * 
   *       .. Scalar Arguments ..
   *       DOUBLE PRECISION   A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
   *> matrix in standard form:
   *>
   *>      [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
   *>      [ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]
   *>
   *> where either
   *> 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
   *> 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
   *> conjugate eigenvalues.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in,out] A
   *> \verbatim
   *>          A is DOUBLE PRECISION
   *> \endverbatim
   *>
   *> \param[in,out] B
   *> \verbatim
   *>          B is DOUBLE PRECISION
   *> \endverbatim
   *>
   *> \param[in,out] C
   *> \verbatim
   *>          C is DOUBLE PRECISION
   *> \endverbatim
   *>
   *> \param[in,out] D
   *> \verbatim
   *>          D is DOUBLE PRECISION
   *>          On entry, the elements of the input matrix.
   *>          On exit, they are overwritten by the elements of the
   *>          standardised Schur form.
   *> \endverbatim
   *>
   *> \param[out] RT1R
   *> \verbatim
   *>          RT1R is DOUBLE PRECISION
   *> \endverbatim
   *>
   *> \param[out] RT1I
   *> \verbatim
   *>          RT1I is DOUBLE PRECISION
   *> \endverbatim
   *>
   *> \param[out] RT2R
   *> \verbatim
   *>          RT2R is DOUBLE PRECISION
   *> \endverbatim
   *>
   *> \param[out] RT2I
   *> \verbatim
   *>          RT2I is DOUBLE PRECISION
   *>          The real and imaginary parts of the eigenvalues. If the
   *>          eigenvalues are a complex conjugate pair, RT1I > 0.
   *> \endverbatim
   *>
   *> \param[out] CS
   *> \verbatim
   *>          CS is DOUBLE PRECISION
   *> \endverbatim
   *>
   *> \param[out] SN
   *> \verbatim
   *>          SN is DOUBLE PRECISION
   *>          Parameters of the rotation matrix.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleOTHERauxiliary
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  Modified by V. Sima, Research Institute for Informatics, Bucharest,
   *>  Romania, to reduce the risk of cancellation errors,
   *>  when computing real eigenvalues, and to ensure, if possible, that
   *>  abs(RT1R) >= abs(RT2R).
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )        SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2.2) --  *  -- 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..--
 *     June 2010  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       DOUBLE PRECISION   A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN        DOUBLE PRECISION   A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric  
 *  matrix in standard form:  
 *  
 *       [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]  
 *       [ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]  
 *  
 *  where either  
 *  1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or  
 *  2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex  
 *  conjugate eigenvalues.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  A       (input/output) DOUBLE PRECISION  
 *  B       (input/output) DOUBLE PRECISION  
 *  C       (input/output) DOUBLE PRECISION  
 *  D       (input/output) DOUBLE PRECISION  
 *          On entry, the elements of the input matrix.  
 *          On exit, they are overwritten by the elements of the  
 *          standardised Schur form.  
 *  
 *  RT1R    (output) DOUBLE PRECISION  
 *  RT1I    (output) DOUBLE PRECISION  
 *  RT2R    (output) DOUBLE PRECISION  
 *  RT2I    (output) DOUBLE PRECISION  
 *          The real and imaginary parts of the eigenvalues. If the  
 *          eigenvalues are a complex conjugate pair, RT1I > 0.  
 *  
 *  CS      (output) DOUBLE PRECISION  
 *  SN      (output) DOUBLE PRECISION  
 *          Parameters of the rotation matrix.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Modified by V. Sima, Research Institute for Informatics, Bucharest,  
 *  Romania, to reduce the risk of cancellation errors,  
 *  when computing real eigenvalues, and to ensure, if possible, that  
 *  abs(RT1R) >= abs(RT2R).  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.8  
changed lines
  Added in v.1.9

CVSweb interface <joel.bertrand@systella.fr>