CLAEV2 - compute the eigendecomposition of a 2-by-2 Hermi­
       tian matrix [ A B ] [ CONJG(B) C ]


SYNOPSIS

       SUBROUTINE CLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

           REAL           CS1, RT1, RT2

           COMPLEX        A, B, C, SN1


PURPOSE

       CLAEV2 computes the eigendecomposition of a 2-by-2  Hermi­
       tian  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
              The (1,1) element of the 2-by-2 matrix.

       B      (input) COMPLEX
              The (1,2) element and the conjugate  of  the  (2,1)
              element of the 2-by-2 matrix.

       C      (input) COMPLEX
              The (2,2) element of the 2-by-2 matrix.

       RT1    (output) REAL
              The eigenvalue of larger absolute value.

       RT2    (output) REAL
              The eigenvalue of smaller absolute value.

       CS1    (output) REAL
              SN1     (output) COMPLEX 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/under­
       flow.

       of overflow.  Underflow is harmless if the input data is 0
       or exceeds
          underflow_threshold / macheps.


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