% Toy problem
clear;

marker2d_size = 50;
marker3d_size = 50;

%--------------------------------------------------------------------------
% Generate random 2D data
rand('state',0);
n = 2;
m = 2000;
width = 1;
rA = (rand(m,n)-0.5)*width*2;

%Decision function
%Coeff. for [x^2; y^2; sqrt(2)*x*y]
w = [1;2;1]*10;
gamma = 2.5;

% Classifier
fh = @(x,y) w(1)*x.^2 + w(3)*sqrt(2)*x.*y + w(2)*y.^2-gamma;

j = 1;
for i=1:m
    if(fh(rA(i,1),rA(i,2)) >= 1) % Accept as +
        A(j,:) = rA(i,:);
        d(j,1) = 1;
        j = j+1;
    elseif(fh(rA(i,1),rA(i,2)) <= -1) % Accept as -
        A(j,:) = rA(i,:);
        d(j,1) = -1;
        j = j+1;
    end % Discard otherwise
end

m = length(d);

idx_p = find(d == 1);
idx_m = find(d == -1);

% Map to a 3D feature space
mA(:,1) = A(:,1).^2;
mA(:,2) = A(:,2).^2;
mA(:,3) = sqrt(2)*A(:,1).*A(:,2);
%--------------------------------------------------------------------------

%--------------------------------------------------------------------------
% Run CRSVM function
opts.save_history = true;
opts.index_basis = 'omega';
machine = CRSVM(mA, d, opts);
%--------------------------------------------------------------------------

fprintf('# of SVs: %d\n', length(machine.support_vector_index));
fprintf('# of on boundary SVs: %d\n', length(machine.on_boundary_support_vector_index));

hf2d = figure;
set(hf2d,'nextplot','replacechildren');
for i=0:machine.iterations,
%     break;
    if( i == 0 ) 
        Q = 1:m;
    else
        Q = machine.history.Q{i};
    end
    w = machine.history.w{i+1};
    gamma = machine.history.bias(i+1);
        
    idx_p = Q(find(d(Q) == 1));
    idx_m = Q(find(d(Q) == -1));
        
    figure(hf2d);
    % plus
    scatter(A(idx_p,1), A(idx_p,2), marker2d_size+10, 'rs', 'filled', 'MarkerEdgeColor','k');
    axis([-width width -width width]);
    hold all;
    % minus
    scatter(A(idx_m,1), A(idx_m,2), marker2d_size, 'g^', 'filled', 'MarkerEdgeColor','k', 'MarkerFaceColor', 'w');
    
    fh = @(x,y) w(1)*x.^2 + w(3)*sqrt(2)*x.*y + w(2)*y.^2-gamma;
    h = ezplot(fh);
    linewidth = 2;
    set(h,'LineStyle','-', 'LineWidth', linewidth);
    hold all;
    fhp = @(x,y) fh(x,y)-1;
    h = ezplot(fhp);
    set(h,'Color', 'k','LineStyle','-.', 'LineWidth', linewidth);
    fhm = @(x,y) fh(x,y)+1;
    h = ezplot(fhm);
    set(h,'Color', 'k','LineStyle','--', 'LineWidth', linewidth);
    title(sprintf('Iteration: %2d, # of obs: %4d', i, length(Q)), 'FontSize', 28);

    axis off;
    set(hf2d,'PaperPositionMode','auto');
    Mv2d(i+1) = getframe(hf2d);
	hold off;
end
close(hf2d);

hf3d = figure;
az = -45;
el = 50;
hf3d = gcf;
ha3d = gca;
set(hf3d,'nextplot','replacechildren');
for i=0:machine.iterations,
    cla;
    hold all;
    if( i == 0 ) 
        Q = 1:m;
    else
        Q = machine.history.Q{i};
    end
    w = machine.history.w{i+1};
    gamma = machine.history.bias(i+1);
    
    idx_p = Q(find(d(Q) == 1));
    idx_m = Q(find(d(Q) == -1));

    f3h = @(x,y) (w(1)*x + w(2)*y - gamma)/-w(3);
    h = ezmesh(f3h,[0 width 0 width],6);
    colormap([0 0 1]);
    
    scatter3(mA(idx_p,1), mA(idx_p,2), mA(idx_p,3), marker3d_size+10, 'rs', 'filled', 'MarkerEdgeColor','k');
    scatter3(mA(idx_m,1), mA(idx_m,2), mA(idx_m,3), marker3d_size, 'g^', 'filled', 'MarkerEdgeColor','k', 'MarkerFaceColor', 'w');

    zlabel('sqrt(2)*x*y');
    axis([0 1 0 1 -1.414 1.414]);
    grid off;
    view(az, el);

    title(sprintf('Iteration: %2d, # of obs: %4d', i, length(Q)), 'FontSize', 28);

    set(hf2d,'PaperPositionMode','auto');
    Mv3d(i+1) = getframe(hf3d);
end
close(hf3d);

Mv = Mv2d;
for i = 1:length(Mv2d),
    Mv(i).cdata = [Mv2d(i).cdata Mv3d(i).cdata];
    Mv(i).colormap = [];
end
movie(Mv2d, 2, 2);