claev2()

subroutine claev2	(	complex	a,
		complex	b,
		complex	c,
		real	rt1,
		real	rt2,
		real	cs1,
		complex	sn1 )

CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

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Purpose:

!>
!> CLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
!>    [  A         B  ]
!>    [  CONJG(B)  C  ].
!> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
!> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
!> eigenvector for RT1, giving the decomposition
!>
!> [ CS1  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
!> [-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].
!> 

Parameters

[in]	A	!> A is COMPLEX !> The (1,1) element of the 2-by-2 matrix. !>
[in]	B	!> B is COMPLEX !> The (1,2) element and the conjugate of the (2,1) element of !> the 2-by-2 matrix. !>
[in]	C	!> C is COMPLEX !> The (2,2) element of the 2-by-2 matrix. !>
[out]	RT1	!> RT1 is REAL !> The eigenvalue of larger absolute value. !>
[out]	RT2	!> RT2 is REAL !> The eigenvalue of smaller absolute value. !>
[out]	CS1	!> CS1 is REAL !>
[out]	SN1	!> SN1 is COMPLEX !> The vector (CS1, SN1) is a unit right eigenvector for RT1. !>

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.
!>
!>  CS1 and SN1 are accurate to a few ulps barring over/underflow.
!>
!>  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.
!>