%define sample size
sampleSize = 20;

% define window widths
h = [5]';

% define discrete values of x
xs = [-sampleSize:1:sampleSize]';

% define mu and sigma
mu = 0;
sigma = 5;


% calculate actual pdf values
targetValues1 = zeros(size(xs,1),1);
for i=1:size(xs,1)
targetValues1(i) = normpdf(xs(i),mu,sigma);
end


% start finding p-hat(x) values for each bandwidth
probValues = zeros(size(xs,1),size(h,1));
% UNIFORM KERNEL 
for i = 1:size(xs,1)
    myX = xs(i);
    myProbability = 0;
    if (abs(myX)/h) > 1
        myProbability = 0;
    else
        for j = 1:sampleSize
            u = (myX - allPoints(j))/h;
            myProbability = myProbability + (0.5);
        end
        myProbability = myProbability / (size(xs,1) * h);
        % below line is matlab version of the above 5 lines
        %             probValue = ksdensity(trainEffort, effToEstimate,'width',h,'kernel','box');
    end
    probValues(i) = myProbability;
end

% uniform weights
uniformWeighingProbs = ones(size(xs,1),size(h,1)) * (1/(2*sampleSize));

% now draw the figure
figure;
hold on;
axis([-sampleSize sampleSize 0 (max(probValues)+0.05)]);
set(gca,'FontSize', 22,'FontName','Times New Roman');

h1 = semilogy(xs,probValues(:,1));
h2 = semilogy(xs,uniformWeighingProbs);
h3 = semilogy(xs,targetValues1);

markerSize = 6;

set(h1, 'LineStyle', '--', 'LineWidth', 1.0, 'Color', 'Black');
set(h1, 'Marker', 'o', 'MarkerFaceColor', [0.5 0.5 0.5], 'MarkerEdgeColor', [0 0 0], 'MarkerSize', markerSize);
set(h2, 'LineStyle', '-', 'LineWidth', 1.0, 'Color',' Black');
set(h2, 'Marker', 's', 'MarkerFaceColor', [1 1 1], 'MarkerEdgeColor', [0 0 0], 'MarkerSize', markerSize);
set(h3, 'LineStyle', '-', 'LineWidth', 1.0, 'Color',' Black');
set(h3,'LineWidth', 1.5, 'MarkerFaceColor', [1 1 1], 'MarkerEdgeColor', [0 0 0], 'MarkerSize', markerSize);

% title('Uniform vs. Non-Uniform Weighting');
xlabel('Instances IDs');
ylabel('Actual Probability Values in Log Scale');
legend('Uniform Kernel','ABE0','Actual Probability Values');