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claesy

 NAME
      CLAESY - compute the eigendecomposition of a 2x2 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 2x2 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 ) entry of input matrix.

      B       (input) COMPLEX
              The ( 1, 2 ) entry of input matrix.  The ( 2, 1 )
              entry is also given by B, since the 2 x 2 matrix is
              symmetric.

      C       (input) COMPLEX
              The ( 2, 2 ) entry 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 x 2 matrix could not
              be diagonalized, or the norm of the matrix of eigen-
              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.