NAME

       slae2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slae2 (A, B, C, RT1, RT2)
           SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

Function/Subroutine Documentation

   subroutine slae2 (realA, realB, realC, realRT1, realRT2)
       SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

       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.

       Parameters:
           A

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

           B

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

           C

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

           RT1

                     RT1 is REAL
                     The eigenvalue of larger absolute value.

           RT2

                     RT2 is REAL
                     The eigenvalue of smaller absolute value.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       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.

       Definition at line 103 of file slae2.f.

Author

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