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version 1.7, 2010/12/21 13:53:29 version 1.8, 2011/11/21 20:42:55
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   *> \brief \b DLAEV2
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLAEV2 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaev2.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaev2.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaev2.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
   * 
   *       .. Scalar Arguments ..
   *       DOUBLE PRECISION   A, B, C, CS1, RT1, RT2, SN1
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
   *>    [  A   B  ]
   *>    [  B   C  ].
   *> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
   *> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
   *> eigenvector for RT1, giving the decomposition
   *>
   *>    [ CS1  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ]
   *>    [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ].
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] A
   *> \verbatim
   *>          A is DOUBLE PRECISION
   *>          The (1,1) element of the 2-by-2 matrix.
   *> \endverbatim
   *>
   *> \param[in] B
   *> \verbatim
   *>          B is DOUBLE PRECISION
   *>          The (1,2) element and the conjugate of the (2,1) element of
   *>          the 2-by-2 matrix.
   *> \endverbatim
   *>
   *> \param[in] C
   *> \verbatim
   *>          C is DOUBLE PRECISION
   *>          The (2,2) element of the 2-by-2 matrix.
   *> \endverbatim
   *>
   *> \param[out] RT1
   *> \verbatim
   *>          RT1 is DOUBLE PRECISION
   *>          The eigenvalue of larger absolute value.
   *> \endverbatim
   *>
   *> \param[out] RT2
   *> \verbatim
   *>          RT2 is DOUBLE PRECISION
   *>          The eigenvalue of smaller absolute value.
   *> \endverbatim
   *>
   *> \param[out] CS1
   *> \verbatim
   *>          CS1 is DOUBLE PRECISION
   *> \endverbatim
   *>
   *> \param[out] SN1
   *> \verbatim
   *>          SN1 is DOUBLE PRECISION
   *>          The vector (CS1, SN1) is a unit right eigenvector for RT1.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup auxOTHERauxiliary
   *
   *> \par Further Details:
   *  =====================
   *>
   *> \verbatim
   *>
   *>  RT1 is accurate to a few ulps barring over/underflow.
   *>
   *>  RT2 may be inaccurate if there is massive cancellation in the
   *>  determinant A*C-B*B; higher precision or correctly rounded or
   *>  correctly truncated arithmetic would be needed to compute RT2
   *>  accurately in all cases.
   *>
   *>  CS1 and SN1 are accurate to a few ulps barring over/underflow.
   *>
   *>  Overflow is possible only if RT1 is within a factor of 5 of overflow.
   *>  Underflow is harmless if the input data is 0 or exceeds
   *>     underflow_threshold / macheps.
   *> \endverbatim
   *>
   *  =====================================================================
       SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )        SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2) --  *  -- 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..--
 *     November 2006  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       DOUBLE PRECISION   A, B, C, CS1, RT1, RT2, SN1        DOUBLE PRECISION   A, B, C, CS1, RT1, RT2, SN1
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix  
 *     [  A   B  ]  
 *     [  B   C  ].  
 *  On return, RT1 is the eigenvalue of larger absolute value, RT2 is the  
 *  eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right  
 *  eigenvector for RT1, giving the decomposition  
 *  
 *     [ CS1  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ]  
 *     [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ].  
 *  
 *  Arguments  
 *  =========  
 *  
 *  A       (input) DOUBLE PRECISION  
 *          The (1,1) element of the 2-by-2 matrix.  
 *  
 *  B       (input) DOUBLE PRECISION  
 *          The (1,2) element and the conjugate of the (2,1) element of  
 *          the 2-by-2 matrix.  
 *  
 *  C       (input) DOUBLE PRECISION  
 *          The (2,2) element of the 2-by-2 matrix.  
 *  
 *  RT1     (output) DOUBLE PRECISION  
 *          The eigenvalue of larger absolute value.  
 *  
 *  RT2     (output) DOUBLE PRECISION  
 *          The eigenvalue of smaller absolute value.  
 *  
 *  CS1     (output) DOUBLE PRECISION  
 *  SN1     (output) DOUBLE PRECISION  
 *          The vector (CS1, SN1) is a unit right eigenvector for RT1.  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  RT1 is accurate to a few ulps barring over/underflow.  
 *  
 *  RT2 may be inaccurate if there is massive cancellation in the  
 *  determinant A*C-B*B; higher precision or correctly rounded or  
 *  correctly truncated arithmetic would be needed to compute RT2  
 *  accurately in all cases.  
 *  
 *  CS1 and SN1 are accurate to a few ulps barring over/underflow.  
 *  
 *  Overflow is possible only if RT1 is within a factor of 5 of overflow.  
 *  Underflow is harmless if the input data is 0 or exceeds  
 *     underflow_threshold / macheps.  
 *  
 * =====================================================================  * =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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