claesy()

subroutine claesy	(	complex	a,
		complex	b,
		complex	c,
		complex	rt1,
		complex	rt2,
		complex	evscal,
		complex	cs1,
		complex	sn1 )

CLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix.

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Purpose:

!>
!> CLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix
!>    ( ( A, B );( B, C ) )
!> provided the norm of the matrix of eigenvectors is larger than
!> some threshold value.
!>
!> RT1 is the eigenvalue of larger absolute value, and RT2 of
!> smaller absolute value.  If the eigenvectors are computed, then
!> on return ( CS1, SN1 ) is the unit eigenvector for RT1, hence
!>
!> [  CS1     SN1   ] . [ A  B ] . [ CS1    -SN1   ] = [ RT1  0  ]
!> [ -SN1     CS1   ]   [ B  C ]   [ SN1     CS1   ]   [  0  RT2 ]
!> 

Parameters

[in]	A	!> A is COMPLEX !> The ( 1, 1 ) element of input matrix. !>
[in]	B	!> B is COMPLEX !> The ( 1, 2 ) element of input matrix. The ( 2, 1 ) element !> is also given by B, since the 2-by-2 matrix is symmetric. !>
[in]	C	!> C is COMPLEX !> The ( 2, 2 ) element of input matrix. !>
[out]	RT1	!> RT1 is COMPLEX !> The eigenvalue of larger modulus. !>
[out]	RT2	!> RT2 is COMPLEX !> The eigenvalue of smaller modulus. !>
[out]	EVSCAL	!> EVSCAL is COMPLEX !> The complex value by which the eigenvector matrix was scaled !> to make it orthonormal. If EVSCAL is zero, the eigenvectors !> were not computed. This means one of two things: the 2-by-2 !> matrix could not be diagonalized, or the norm of the matrix !> of eigenvectors before scaling was larger than the threshold !> value THRESH (set below). !>
[out]	CS1	!> CS1 is COMPLEX !>
[out]	SN1	!> SN1 is COMPLEX !> If EVSCAL .NE. 0, ( CS1, SN1 ) is the unit right eigenvector !> for RT1. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.