# Floor planning

    % Section 8.8.1/2, Example 8.7, Boyd & Vandenberghe "Convex Optimization"
    % Original by Lieven Vandenberghe
    % Adapted for CVX by Joelle Skaf - 11/13/05
    % (a figure is generated)
    %
    % Rectangles aligned with the axies need to be place in the smallest
    % possible bounding box. No overlap is allowed. Each rectangle to be placed
    % can be reconfigured, within some limits. We are given relative
    % positioning contrainsts on those rectangles, and minimal required areas.
    % In the current problem, 5 rectangles are given

    cvx_quiet(1);
    % input data
    n = 5;
    Amin = [100 100 100 100 100; ...
             20  50  80 150 200; ...
            180  80  80  80  80; ...
             20 150  20 200 110];
    r = 1;          % minimum spacing constraints

    for iter = 1:4
        A = Amin(iter,:);
        cvx_begin
            variables x(n) y(n) w(n) h(n) W H
            minimize ( W + H )
            x >= r;
            y >= r;
            w >= 0;
            h >= 0;
            x(5) + w(5) + r <= W;    % No rectangles at the right of Rectangle 5
            x(1) + w(1) + r <= x(3); % Rectangle 1 is at the left of Rectangle 3
            x(2) + w(2) + r <= x(3); % Rectangle 2 is at the left of Rectangle 3
            x(3) + w(3) + r <= x(5); % Rectangle 3 is at the left of Rectangle 5
            x(4) + w(4) + r <= x(5); % Rectangle 4 is at the left of Rectangle 5
            y(4) + h(4) + r <= H;    % No rectangles on top of Rectangle 4
            y(5) + h(5) + r <= H;    % No rectangles on top of Rectangle 5
            y(2) + h(2) + r <= y(1); % Rectangle 2 is below Rectangle 1
            y(1) + h(1) + r <= y(4); % Rectangle 1 is below Rectangle 4
            y(3) + h(3) + r <= y(4); % Rectangle 3 is below Rectangle 4
            w <= 5*h;                % Aspect ratio constraints
            h <= 5*w;
            w' >= quad_over_lin([A.^.5;zeros(1,n)],h');
        cvx_end
        % Plotting
        subplot(2,2,iter)
        for i=1:n
            fill([x(i); x(i)+w(i); x(i)+w(i); x(i)],[y(i);y(i);y(i)+h(i);y(i)+h(i)],0.90*[1 1 1]);
            hold on;
            text(x(i)+w(i)/2, y(i)+h(i)/2,['B',int2str(i)]);
        end
        axis([0 W 0 H]);
        axis equal; axis off;
    end

    % print -deps floorplan-opt.eps