SLAEV2  -  compute the eigendecomposition of a 2-by-2 sym­
       metric matrix [ A B ] [ B C ]


SYNOPSIS

       SUBROUTINE SLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

           REAL           A, B, C, CS1, RT1, RT2, SN1


PURPOSE

       SLAEV2 computes the eigendecomposition of a 2-by-2 symmet­
       ric  matrix  [ A B ] [ B C ]. On return, RT1 is the eigen­
       value 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) REAL
               The (1,1) element of the 2-by-2 matrix.

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

       C       (input) REAL
               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) REAL 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.

       Overflow  is  possible only if RT1 is within a factor of 5
       of overflow.  Underflow is harmless if the input data is 0

          underflow_threshold / macheps.


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