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.

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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.
!>