% x, y, slopes, and intercepts from exercise 8.3

slopes = -5:0.25:5;
intercepts = -30:1:30;
error_surface = zeros(length(slopes), length(intercepts));
for i = 1:length(slopes)
    for j = 1:length(intercepts)
	      error_surf(i,j) = meanSquaredError([slopes(i), intercepts(j)], x, y);
    end
end

error_surface = zeros(length(slopes), length(intercepts));
gradient_m = zeros(size(error_surface));
gradient_b = zeros(size(error_surface));

for i = 1:length(slopes)
    for j = 1:length(intercepts)
        error_surface(i,j) = meanSquaredError([slopes(i), intercepts(j)], x, y);
        grad = meanSquaredGradient([slopes(i), intercepts(j)], x, y);
        gradient_m(i,j) = grad(1);
        gradient_b(i,j) = grad(2);
    end
end

figure()
hold on
[N, M] = meshgrid(intercepts, slopes);
%surface(M, N, error_surface, 'FaceAlpha', 0.5);
contour(M, N, error_surface, 50);
quiver(M, N, gradient_m, gradient_b)
xlabel('Slope m')
ylabel('Intercept b')
zlabel('Mean squared error')
set(gcf, 'paperunits', 'centimeters', 'papersize', [15, 10.5], ... 
    'paperposition', [0., 0., 15, 10.5])
saveas(gcf, 'error_gradient', 'pdf')