% program to draw movie of the evolution.

% the first figure is more a small dock
close all
clear all
k_number = 500;k_max = pi*5;x_number =400;
L1 = 1;L2=1.25;h=1;theta =0;N=20;

k0 = 0:k_max/k_number:k_max;
x = -L1:L1/x_number:0;
x2 = -1-L2:L1/x_number:-L2;
phi = zeros(length(k0),length(x));
phi2 = zeros(length(k0),length(x2));
phi(1,:) = 2*ones(size(phi(1,:)));
phi2(1,:) = 2*ones(size(phi2(1,:)));

for count = 2:length(k0)
    count
    alpha = k0(count)*tanh(k0(count)*h);

    % if the depth is great than twice the wavelength set depth to twice
    % wavewavelength
    H = min(h,4*pi/k0(count));
    [a_s,b_s,c_s,d_s,a_a,b_a,c_a,d_a] = two_finite_docks_symmetry(alpha,h,L1,L2,theta,N);
    roots = dispersion_free_surface(alpha,N,h);
    for count2 = 1:N+1
        phi(count,:) = phi(count,:) + d_s(count2)*cosh(roots(count2)*x)/cosh(roots(count2)*L1);
        phi2(count,:) = phi2(count,:) + a_s(count2)*exp(roots(count2)*(x2+L2));
    end
    phi2(count,:) = phi2(count,:) + exp(-roots(1)*(x2+L2));
end


eta = exp(-4*(x).^2);
time = 0:0.5:10;time_display = time;
time(1) = 0.0001;
delta_h = L1/x_number;
weight = 2*delta_h/3*ones(size(x));weight(2:2:end-1) = 4*delta_h/3;weight(1) = delta_h/3;weight(end) = delta_h/3;
f= conj(phi(:,:))*(transpose(weight.*eta));
total_potential = zeros(length(k0),size(phi,2));
total_potential2 = zeros(length(k0),size(phi2,2));
for count = 1:length(k0)
    total_potential(count,:) = 1/(2*pi)*phi(count,:)*f(count);
    total_potential2(count,:) = 1/(2*pi)*phi2(count,:)*f(count);
end

delete small_dock_gem.gif

hf=figure('Position',[100,100,600,600]);
rect = get(hf,'Position');
rect(1:2) = [0 0]; % these commands ensure we capture the actual figure.

for count = 1:length(time)
    count

    out = k_integrate(time(count),k0,h,total_potential);
    out2 = k_integrate(time(count),k0,h,total_potential2);

    % now we plot the figure
    plot(x,out,x2,out2,'LineWidth',2);
    hold on
    plot(-fliplr(x),fliplr(out),'b',x2,out2,'b',-fliplr(x2),fliplr(out2),'b','LineWidth',2);
    plot([-L2,-L1],[0,0],'k','LineWidth',4);
    plot([L1,L2],[0,0],'k','LineWidth',4);
    text((1+L2)*0.5,0.8,['t = ',num2str(time_display(count),'%1.1f')],'Fontsize',14)
    axis([-1-L2,1+L2,-1,1])
    set(gca,'FontSize',14)
    xlabel('x','Fontsize',14)
    ylabel('\xi','Fontsize',16)
    hold off
    drawnow
    gif_add_frame(gcf,'small_dock_gem.gif',1);

end