n = 1000;
ds = [0:5];
for k = 1:length(ds)
    d = ds(k);
    % generate data:
    x = randn(n, 1);
    y = randn(n, 1);
    z = randn(n, 1);
    y(1:n/2) = y(1:n/2) - d;
    y(1+n/2:end) = y(1+n/2:end) + d;
    z(1:n/2) = z(1:n/2) - d;
    z(1+n/2:end) = z(1+n/2:end) + d;
    % scatter plot of data:
    subplot(2, 2, 1)
    scatter3(x, y, z, 'filled', 'MarkerEdgeColor', 'white')
    title(sprintf('d=%g', d))
    xlabel('x')
    ylabel('y')
    zlabel('z')
    % histogram of data:
    subplot(2, 2, 3)
    hist(x, 20)
    xlabel('x')
    % pca:
    cv = cov([x y z]);
    [ev en] = eig(cv);
    [en inx] = sort(diag(en), 'descend');
    nc = [x y z]*ev(:,inx);
    % scatter in new coordinates:
    subplot(2, 2, 2)
    scatter3(nc(:, 1), nc(:, 2), nc(:, 3), 'filled', 'MarkerEdgeColor', 'white')
    title(sprintf('d=%g', d))
    xlabel('pca 1')
    ylabel('pca 2')
    zlabel('pca 3')
    % histogram of data:
    subplot(2, 2, 4)
    hist(nc(:, 1), 20)
    xlabel('pca 1')
    if d == 2
        savefigpdf(gcf, 'pca3d-2.pdf', 15, 15);
    end
    pause(1.0)
end