dlae2()

subroutine dlae2	(	double precision	A,
		double precision	B,
		double precision	C,
		double precision	RT1,
		double precision	RT2
	)

DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

Download DLAE2 + dependencies [TGZ] [ZIP] [TXT]

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.

Parameters

[in]	A	A is DOUBLE PRECISION The (1,1) element of the 2-by-2 matrix.
[in]	B	B is DOUBLE PRECISION The (1,2) and (2,1) elements of the 2-by-2 matrix.
[in]	C	C is DOUBLE PRECISION The (2,2) element of the 2-by-2 matrix.
[out]	RT1	RT1 is DOUBLE PRECISION The eigenvalue of larger absolute value.
[out]	RT2	RT2 is DOUBLE PRECISION The eigenvalue of smaller absolute value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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.