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 ]

A

          A is COMPLEX


          The ( 1, 1 ) element of input matrix.

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.

C

          C is COMPLEX


          The ( 2, 2 ) element of input matrix.

RT1

          RT1 is COMPLEX


          The eigenvalue of larger modulus.

RT2

          RT2 is COMPLEX


          The eigenvalue of smaller modulus.

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).

CS1

          CS1 is COMPLEX

SN1

          SN1 is COMPLEX


          If EVSCAL .NE. 0,  ( CS1, SN1 ) is the unit right eigenvector


          for RT1.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012