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CLAESY(l)			       )			     CLAESY(l)

NAME
       CLAESY  - compute 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

SYNOPSIS
       SUBROUTINE CLAESY( A, B, C, RT1, RT2, EVSCAL, CS1, SN1 )

	   COMPLEX	  A, B, C, CS1, EVSCAL, RT1, RT2, SN1

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 ]

ARGUMENTS
       A       (input) COMPLEX
	       The ( 1, 1 ) element of input matrix.

       B       (input) 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.

       C       (input) COMPLEX
	       The ( 2, 2 ) element of input matrix.

       RT1     (output) COMPLEX
	       The eigenvalue of larger modulus.

       RT2     (output) COMPLEX
	       The eigenvalue of smaller modulus.

       EVSCAL  (output) 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 eigenā€
	       vectors before scaling was  larger  than	 the  threshold	 value
	       THRESH (set below).

       CS1     (output) COMPLEX
	       SN1     (output) COMPLEX If EVSCAL .NE. 0,  ( CS1, SN1 ) is the
	       unit right eigenvector for RT1.

LAPACK version 3.0		 15 June 2000			     CLAESY(l)
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