% charge densities on a line gives size of monic polynomial with roots as nodes
% Barnett 10/9/08, after Trefethen
n = 20;                                    % # nodes - 1
x = -2:.01:2; y = -1.5:0.01:1.5;
[xx yy] = meshgrid(x, y); zz = xx + 1i*yy; % zz is rect array of complex #s
for d='uc'   % loop over 'u' uniform then 'c' Chebychev density
  if d=='u'
    xj = linspace(-1,1,n+1); t = 'uniform';
  else
    xj = cos(pi*(0:n)/n); t = 'Chebychev';
  end
  a = poly(xj);                            % coeffs of monic poly with roots xj
  phi = log(polyval(a,zz))/(n+1);
  figure; contour(x,y,phi,[-1:.1:1]);
  hold on; plot(xj, 0, 'k.', 'markersize', 20);
  xlabel('Re z');ylabel('Im z');title(sprintf('phi(z) contours, %s density',t))
end
 
