%% Generate an undecorated version of Figure 2(a)

function []=Figure2a()

%% Decide for which temperatures to plot autocorrelation functions;
% temperature_index=2 corresponds to T=1.000;
% temperature_index=3 corresponds to T=0.800;
% temperature_index=4 corresponds to T=0.600;
% temperature_index=5 corresponds to T=0.550;
% temperature_index=6 corresponds to T=0.510;
% temperature_index=7 corresponds to T=0.485;
% temperature_index=8 corresponds to T=0.465;
% temperature_index=9 corresponds to T=0.450;
temperature_indices=[2,3,4,6,9];

%% Plot data and a fit, one temperature by one temperature;
close all;
figure(1);
set(gca,'yscale','log')
hold on
for ii=1:size(temperature_indices,2)
    temperature_index=temperature_indices(ii);
    
    %% Read in the data
    % Dynamical correlation function
    data_name=sprintf('./Gdyn%d.dat',temperature_index); fid = fopen(data_name,'r'); numbers=fscanf(fid, '%f'); fclose('all');
    r=(0:0.1:8.0).'; Nr=size(r,1); % radii where dynamical correlation functions are measured
    Gd=numbers(2*(1:Nr)-1); % dynamical correlation functions
    Gd_error=numbers(2*(1:Nr)); % error bars
    
    %% Exponential fit
    % Throw away short-distance data points
    UVcut=1.5;
    Ikeep=logical(r>=UVcut);
    r=r(Ikeep); Gd=Gd(Ikeep); Gd_error=Gd_error(Ikeep); 

    % Exponential fit, B*exp(-(r/xi_DH))    
    x=r; y=Gd;
    Init=[y(1), 1]; weight=diag(ones(size(x))); Outliers=false(size(x));
    [fit_values,confidence_intervals]=exponential_decay_fit(x,y,weight,Init,Outliers);
    B=fit_values(1);
    xi_DH=fit_values(2);
    xi_DH_error=1.96*(confidence_intervals(2,2)-confidence_intervals(1,2))/2;  % 95-percent confidence interval
    r_fit=0:0.01:8;
    Gd_fit=B*exp(-(r_fit/xi_DH));
    
    %% Plot them
    plot(r_fit,Gd_fit)
    plot(r,Gd,'Linestyle','none','Marker','.')

end

%% Label axis and print it out
xlabel('$r$','Interpreter','latex')
ylabel('$G_{\rm dyn}$','Interpreter','latex')
xlim([0,8])
ylim([10^(-4),10^(-1)])
axis square
set(gcf, 'PaperPositionMode', 'auto');
print -depsc2 Figure2a.eps

end