% MS-E2170 Simulation
% Exercise 1.1: Estimate area of a polygon using Monte Carlo simulation
% d) How does the sample size of your experiment affect your estimate 
%    and the confidence interval? Repeat the experiment using different 
%    sample sizes. Create a plot of the length of the confidence interval 
%    against sample size.
%
% Fill the '<your_code_here>' with your own input.
%
% Created: 2018-02-19 Heikki Puustinen


%% Initialization

% Sample sizes: (construct a vector holding sample sizes for experiments)
N = <your_code_here>;

% Define the x- and y-coordinate values of the polygon.
px = [0.2, 0.4, 0.8, 0.5];
py = [0, 0.25, 0, 1];

% Define the surrounding rectangle.
rx = [0, 0, 1, 1];
ry = [0, 1, 1, 0];

%% Simulation

% We now have to call the area estimation function multiple times (once for
% each sample size).

% It is good practice to initialize the variables in which we store the
% results.
V = zeros(length(N),1);
Ci = zeros(length(N),2);

% Loop trhough the sample size vector.
for ii = 1:length(N)
    % Call the area estimation function with the appropriate sample size
    % and store the output in appropriate indexes in the result variables.
    [<your_code_here>] = area_mc(<your_code_here>);
end



%% Plotting

% Create a window.
f1 = figure('Name','MS-E2170, Exercise 1 d), Monte Carlo Simulation');

% Create axes
ax1 = axes('Parent',f1);

% Hold axes.
hold(ax1,'on')

% Make title and labels
title(ax1,'Estimate of the area of polygon and CIs')
xlabel(ax1,'Sample size')
ylabel(ax1,'Area')

% Plot estimated areas.
% x-axis: sample size
% y-axis: estimated area
plot(ax1,N,V,'r')

% Plot confidence intervals.
% Lower
plot(ax1,N,Ci(:,1),'b')
% Upper
plot(ax1,N,Ci(:,2),'b')

% Calculate lengths of the confidence intervals.
Ci_lengths = Ci(:,2) - Ci(:,1);

% Create a window.
f2 = figure('Name','MS-E2170, Exercise 1 d), Monte Carlo Simulation');
% Move second window a bit to the right.
set(f2,'Position',get(f2,'Position') + [50 -50 0 0])

% Create axes
ax2 = axes('Parent',f2);

% Hold axes.
hold(ax2,'on')

% Make title and labels
title(ax2,'Lengths of CIs')
xlabel(ax2,'Sample size')
ylabel(ax2,'Length of CI')

% Plot the lengths of the interval against sample size.
plot(ax2,N,Ci_lengths,'k','LineWidth',2)