% letter plot for covariance

close all;
msize = 9;
psize = 20;
linewidth = 1.25;
dftcolors = colororder;

markers = {'s', '*', 'x', 'o'};
params = [1,0.99,1-1e-4 ];
opts = optimset('Display','off');

widthpix = 300;
heightpix = 200;
linewidth = 1.25;
leftmargin = 105;
bottommargin = 75;
topmargin = 70;
rightmargin = 75;
centermargin = 0;
widthtotal = widthpix*2.5+leftmargin+rightmargin;
heighttotal = heightpix*2+topmargin+bottommargin;
left = leftmargin/widthtotal;
bottom = bottommargin/heighttotal;
width = widthpix/widthtotal;
height = heightpix/heighttotal;


%% main plot
nowpanel = axes('Position', [left, bottom, width*1.5, height*2]);

phihat = 5;
dims = {'4D', '8D', '12D', '16D', '20D'};


n=length(dims);
rpp=(1:n)';
colors = [(rpp-1)/(n-1), zeros(n,1), 1 - (rpp-1)/(n-1)];

for rp=1:length(dims)
    dim = dims{rp};
    ndim = str2double(dim(1:end-1));
    ndimsqr = ndim*ndim*ndim;
    phistr = num2str(phihat*ndim);
    fname = strcat('../data/rlgdynamics/', dim, '/', phistr, '/msd.dat');
    data = dlmread(fname, '', 1, 0);
    xs = data(:,1)*sqrt(ndim);
    ys = ( ndim^2*data(:,5) ./  data(:,2).^2 - 1);
    plot(xs, ys, 'color', colors(rp,:) );
    if phihat < 5
        meanys = mean(ys(floor(end/2):end));
    else
        meanys = mean(ys(end-4:end));
    end
    fprintf('%g\t%g\t%g\n', phihat, ndim, meanys);
    if 1==rp, hold on, end
end

set(gca, 'xscale', 'log');
xlabel('$\hat{t}$', 'interpreter', 'latex');
ylabel('$ \mathrm{C}(\hat{t})$', 'interpreter', 'latex');
xlim([1e-1,1e5]);
ylim([-0.2, 1.08]);
xticks([1e0,1e2,1e4]);
yticks([-0.5, 0, 0.5, 1]);

set(gca, 'fontname', 'times new roman', 'fontsize', psize);

%% inset (b)

panelB = axes('Position', [left+width*1.5, bottom+height, width, height]);

alldata = dlmread('../data/rlgdynamics/rcovpfactor.dat');
phis = [3.5, 4, 5, 7, 10, 15, 20, 30, 40];
pltphis = [3.5, 5, 10, 20, nan];

n=length(pltphis)-1;
rpp=(1:n)';
colorsB = [1 - (rpp-1)/(n-1), (rpp-1)/(n-1), zeros(n,1)];

nowplt = 1;
allrst = [];
for rp=1:length(phis)
    phihat = phis(rp);
    takes = alldata(:,1)==phihat;
    xs = 1 ./ alldata(takes, 2);
    ys = alldata(takes, 3);
    xs = [xs, ones(numel(xs), 1)];
    [b, bint] = regress(ys(2:end), xs(2:end,:));
    allrst = [allrst; phihat, b(1), (bint(1,2)-bint(1,1))/2];
    if phihat == pltphis(nowplt)
        xreg = linspace(0, max(xs(:,1))*1.02);
        yreg = b(1)*xreg + b(2);
        plot(xreg, yreg, 'color', colorsB(nowplt,:) );
        if 1==nowplt
            hold on;
        end
        plot(xs(:,1), ys, 'x', 'markersize', msize, 'linewidth', 1.5, 'color',colorsB(nowplt,:) );
        nowplt = nowplt + 1;
    end
end

xlim([0, 0.26]);
xticks([0, 0.1 , 0.2]);
yticks([0, 1, 2]);
xx = gca;
xx.XRuler.TickLength = [0.02, 0];
xx.YRuler.TickLength = [0.03, 0];

xlabel('$1/d$', 'interpreter', 'latex');
ylabel('$\mathrm{C}(\hat{t} \rightarrow \infty)$', 'interpreter', 'latex');
set(panelB, 'XAxisLocation', 'top', 'YAxisLocation', 'right');
set(panelB, 'fontname', 'times new roman', 'fontsize', psize);

%% inset (c)
panelC = axes('Position', [left+width*1.5, bottom, width, height]);

plot( allrst(:,1), allrst(:,2), 'xk:', 'markersize', msize, 'linewidth', 1.5);
hold on;
plot([2.40339, 2.40339], [2, 7], '--k');
xlim([0, 40.1]);
ylim([2, 7]);
xticks([0, 20, 40]);
yticks([2, 4, 6]);
xx = gca;
xx.XRuler.TickLength = [0.02, 0];
xx.YRuler.TickLength = [0.03, 0];
xlabel('$\hat\varphi$', 'interpreter', 'latex');
ylabel('$\hat{\mathrm{C}}(\hat{t} \rightarrow \infty)$', 'interpreter', 'latex');
set(panelC, 'YAxisLocation', 'right');
set(panelC, 'fontname', 'times new roman', 'fontsize', psize);

annotation('textbox',[0.12, 0.78, 0.1, 0.1], 'String', '(a)', 'EdgeColor','none', 'Fontname', 'Times New Roman','fontsize',psize);
annotation('textbox',[0.84, 0.78, 0.1, 0.1], 'String', '(b)', 'EdgeColor','none', 'Fontname', 'Times New Roman','fontsize',psize);
annotation('textbox',[0.84, 0.41, 0.1, 0.1], 'String', '(c)', 'EdgeColor','none', 'Fontname', 'Times New Roman','fontsize',psize);

print('../figures/rlgmf_ncov.eps', '-depsc');