% trigfield6.m investigates the joint distribution of F(0,0) and F(x,y)

m    = 20;                                    % number of Fourier modes
Cmax = 1000;                                 % number of iid replications

x = 0.5;
y = 0.1;

F = [];

for C = 1:Cmax,
  A        = randn(1,m)*sqrt(2/m);                % amplitudes of Fourier modes
  phi      = 2 * pi * rand(m,1);                  % random phase
  norm     = sqrt(-2*log(rand(m,1)));             % magnitudes of wave numbers
  theta    = 2 * pi * rand(m,1);                  % arguments of wave numbers
  K        = [norm.*cos(theta) norm.*sin(theta)]; % isotropic wave numbers
  F(C,1)   = A * cos(phi);                        % field value at (0,0)
  F(C,2)   = A * cos(K*[x; y] + phi);             % field value at (x,y)
end

clf

plot(F(:,1), F(:,2),'*');
xlabel('Value at (0,0)');
ylabel('Value at (x,y)');