DLAE2  -  compute  the  eigenvalues  of a 2-by-2 symmetric
       matrix [ A B ] [ B C ]


SYNOPSIS

       SUBROUTINE DLAE2( A, B, C, RT1, RT2 )

           DOUBLE        PRECISION A, B, C, RT1, RT2


PURPOSE

       DLAE2 computes  the  eigenvalues  of  a  2-by-2  symmetric
       matrix  [  A B ] [ B C ]. On return, RT1 is the eigenvalue
       of larger absolute value, and RT2  is  the  eigenvalue  of
       smaller absolute value.


ARGUMENTS

       A       (input) DOUBLE PRECISION
               The (1,1) element of the 2-by-2 matrix.

       B       (input) DOUBLE PRECISION
               The (1,2) and (2,1) elements 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.


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.

       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.


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