% MS-E2170 Simulation
% Exercise 1.1: Estimate area of a polygon using Monte Carlo simulation
% f) Repeat the entire simulation experiment 1000 times using the 
%    worst-case sample size and define the proportion of cases where the 
%    absolute error is less than epsilon = 0.05.
% g) Construct 1000 confidence intervals for the estimate of the area and 
%    define their coverage, i.e. the proportion of CI's that contain the 
%    actual value of the area.
%
% Fill the '<your_code_here>' with your own input.
%
% Created: 2018-02-19 Heikki Puustinen


%% Initialization

% Sample size (worst-case):
N = <your_code_here>;

% Number of experiments:
M = <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).

% Initialize the variables in which we store the results.
V = zeros(M,1);
Ci = zeros(M,2);

% Loop through experiments.
for ii = 1:M
    % Call the area estimation function.
    [V(ii), Ci(ii,:)] = area_mc(px,py,rx,ry,N);
end

% Actual area of the polygon.
area = polyarea(px,py);

% Absolute errors
E = <your_code_here>;

% Proportion of cases where absolute error < 0.05.
P_error = <your_code_here>;

% Calculate which CI's include the actual area.
D = <your_code_here>;

% Calculate the proportion of the experiments where area is included in CI.
P_area = <your_code_here>;


%% Results

% Display results.
fprintf('Results f):\n')
fprintf('Proportion of cases where absolute error is less than epsilon: %.5f \n', P_error)

% Display results.
fprintf('Results g):\n')
fprintf('Proportion of Ci''s that contain actual area: %.4f \n',P_area)