%% Generate an undecorated version of Figure 3(b)

function []=Figure3b()
%% Decide where to plot the probability distribution function (PDF)
temperature_index=6; % T=temperature=0.51
R_index=5; % R=cavity_size=2.6

%% Read in the data
% Static point-to-set overlaps
data_name=sprintf('./PTS%d_%d.dat',temperature_index,R_index); fid = fopen(data_name,'r'); numbers=fscanf(fid, '%f'); fclose('all');
qPTSs=numbers; Ncavity=size(numbers,1);

% Dynamical overlaps
data_name=sprintf('./Dynamical_overlap%d.dat',temperature_index); fid = fopen(data_name,'r'); numbers=fscanf(fid, '%f'); fclose('all');
qDs=numbers;

%% Histogram them into bins
q_bins=((-0.025):0.025:1)+0.5*(0.025); Ng=size(q_bins,2);
ys=(q_bins.')*ones(1,Ng); xs=ys.';
PDF=zeros(Ng,Ng);
% For a given data point, loacte to which bin it belongs
for i=1:Ncavity
    x=qPTSs(i);
    y=qDs(i);
    [~,kx]=min(abs(q_bins-x));
    [~,ky]=min(abs(q_bins-y));
    PDF(kx,ky)=PDF(kx,ky)+1;
end
PDF=PDF/(0.025*0.025*Ncavity);

%% Smoothen PDF
x_refine=(xs(1,1):0.001:xs(1,end)); y_refine=(ys(1,1):0.001:ys(end,1));
[X,Y]=meshgrid(x_refine,y_refine);
PDF=interp2(xs,ys,PDF,X,Y,'spline');

%% Plot the data
close all;
figure(1);
color_map=hot(1024);
colormap(color_map)
surf(X.',Y.',PDF,PDF,'EdgeColor','none','FaceColor','interp')       


%% Label axis and print it out
xlabel('$\bar{q}_{\rm PTS}$','Interpreter','latex')
ylabel('$\bar{q}_{\rm dyn}$','Interpreter','latex')
xlim([0,0.8])
ylim([0,0.8])
view([0,90])
axis square
set(gcf, 'PaperPositionMode', 'auto');
print -depsc2 Figure3b.eps

end