% Create a grid. Set granularity to 100/1000, for low/high quality plots.
granularity = 1000;
a = -5;
b = 5;
domain = linspace (a, b, granularity);
[X,Y] = meshgrid (domain, domain);
x = X(:);
y = Y(:);
n = size(X,1);

% Generate 2D data from normal distributions.
mu = [-1 2.5;
      1 -2.5];
sig = [0.5 0; 0 0.5];
points_per_class = 20;
X_data = [mvnrnd(mu(1,:), sig, points_per_class);
          mvnrnd(mu(2,:), sig, points_per_class);];

% Prepare the training input.
X_train = [ones(1,size(X_data,1)); X_data'];
w = [zeros(points_per_class,1); ones(points_per_class,1)];
var_prior = 6;
X_test = [ones(1,granularity*granularity); x'; y'];

% Fit a logistic regression model.
initial_phi = [1; 1; 1];
[predictions, phi] = fit_logr (X_train, w, var_prior, X_test, initial_phi);

% Plot the results.
figure;
Z = reshape(predictions,n,n);
pcolor(X,Y,Z);
shading interp;
colormap(hot(4096));
set(gca,'YDir','normal');
axis([a,b,a,b]);
set(gca,'YTick',[a,0,b], 'XTick',[a,0,b], 'FontSize', 16);
xlabel('x', 'FontSize', 16);
ylabel('y', 'FontSize', 16);
title('(b)', 'FontSize', 16);

% Plot the data points on top.
hold on;
selector = 1:points_per_class;
scatter(X_data(selector,1), X_data(selector,2), 100, 'fill',...
       'MarkerEdgeColor','k','MarkerFaceColor','b','LineWidth',1);

hold on;
selector = points_per_class+1 : 2*points_per_class;
scatter(X_data(selector,1), X_data(selector,2), 100, 'fill',...
       'MarkerEdgeColor','k','MarkerFaceColor','g','LineWidth',1);

hold on;
decision_boundary = -(phi(1) + phi(2)*domain) / phi(3);
plot(domain,decision_boundary,'LineWidth',2,'LineSmoothing','on',...
    'Color','c');
hold off;