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version 1.7, 2010/12/21 13:53:49 version 1.8, 2011/11/21 20:43:15
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   *> \brief \b ZLAEV2
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZLAEV2 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaev2.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaev2.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaev2.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
   * 
   *       .. Scalar Arguments ..
   *       DOUBLE PRECISION   CS1, RT1, RT2
   *       COMPLEX*16         A, B, C, SN1
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
   *>    [  A         B  ]
   *>    [  CONJG(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  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
   *> [-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] A
   *> \verbatim
   *>          A is COMPLEX*16
   *>         The (1,1) element of the 2-by-2 matrix.
   *> \endverbatim
   *>
   *> \param[in] B
   *> \verbatim
   *>          B is COMPLEX*16
   *>         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 COMPLEX*16
   *>         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 COMPLEX*16
   *>         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 complex16OTHERauxiliary
   *
   *> \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 ZLAEV2( A, B, C, RT1, RT2, CS1, SN1 )        SUBROUTINE ZLAEV2( 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   CS1, RT1, RT2        DOUBLE PRECISION   CS1, RT1, RT2
       COMPLEX*16         A, B, C, SN1        COMPLEX*16         A, B, C, SN1
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix  
 *     [  A         B  ]  
 *     [  CONJG(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  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]  
 *  [-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].  
 *  
 *  Arguments  
 *  =========  
 *  
 *  A      (input) COMPLEX*16  
 *         The (1,1) element of the 2-by-2 matrix.  
 *  
 *  B      (input) COMPLEX*16  
 *         The (1,2) element and the conjugate of the (2,1) element of  
 *         the 2-by-2 matrix.  
 *  
 *  C      (input) COMPLEX*16  
 *         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) COMPLEX*16  
 *         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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