SLAE2(3)       LAPACK routine of NEC Numeric Library Collection       SLAE2(3)



NAME
       SLAE2

SYNOPSIS
       SUBROUTINE SLAE2 (A, B, C, RT1, RT2)



PURPOSE
            SLAE2  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)
                     A is REAL
                     The (1,1) element of the 2-by-2 matrix.

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

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

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

           RT2       (output)
                     RT2 is REAL
                     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.



LAPACK routine                  31 October 2017                       SLAE2(3)