DLAEV2  -  compute the eigendecomposition of a 2-by-2 sym­
       metric matrix [ A B ] [ B C ]


SYNOPSIS

       SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 )

           DOUBLE         PRECISION A, B, C, CS1, RT1, RT2, SN1


PURPOSE

       DLAEV2 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) 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/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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