CXML
        	    
LAPACK version 3.0
dlae2(3)

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

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

      DOUBLE	    PRECISION A, B, C, RT1, RT2

DESCRIPTION
  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.