DLAE2(3)                   MathKeisan LAPACK routine                  DLAE2(3)



NAME
       DLAE2 - 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  determi-
       nant  A*C-B*B; higher precision or correctly rounded or correctly trun-
       cated 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 auxiliary routine (versionNo3v.e1m)ber 2006                        DLAE2(3)