% L5A quantile demo:
% Matlab and R style quantile functions from finite data

function L5Aquantiledemo(q, y)

if nargin<2,
    y = [1 2 4 8 10];
end
n = length(y);
y = sort(y);
ymin = min(y)-0.5;
ymax = max(y)+0.5;

qq = linspace(0,1,1000);
clf

% Matlab style quantile function
subplot(2,1,1)
myy = quantile(y, qq);
mqy = linspace(1/(2*n), 1-1/(2*n), n);
plot(mqy, y, 'bo', 'markerface', 'b', 'markersize', 10);
hold on
plot(qq, myy, 'b-', 'linewidth', 2);
set(gca, 'ylim', [ymin ymax]);
set(gca, 'xtick', 0:(1/(2*n)):1);
grid on
title('Matlab-style quantile function');
if nargin>=1
    my_example = quantile(y, q);
    plot([q q], [ymin ymax], 'k-', 'linewidth', 2);
    plot(q, my_example, 'k-o', 'markersize', 10);
    fprintf('M-style q(%.3f) = %.6f\n', q, my_example);
end

% R-style quantile function
subplot(2,1,2)
ryy = Rquantile(y, qq);
rqy = linspace(0, 1, n);
plot(rqy, y, 'ro', 'markerface', 'r', 'markersize', 10);
hold on
plot(qq, ryy, 'r-', 'linewidth', 2);
set(gca, 'ylim', [min(y)-0.5 max(y)+0.5]);
set(gca, 'xtick', rqy);
grid on
title('R-style quantile function');
if nargin>=1
    Rmy_example = Rquantile(y, q);
    plot([q q], [ymin ymax], 'k-', 'linewidth', 2);
    plot(q, Rmy_example, 'k-o', 'markersize', 10);
    fprintf('R-style q(%.3f) = %.6f\n', q, Rmy_example);
end

end