%Create 3D cloud of data points, then do pca on it
clc;
disp('3D PCA analysis');
CorXY = input('Correlation between X & Y values: ');
CorXZ = input('Correlation between X & Z values: ');
for K = 1:100;
    X = 10*randn; Y = CorXY*X + (1 - CorXY)*7*randn; Z = CorXZ*X + (1 - CorXZ)*5*randn;
    Dta(K, :) = [X, Y, Z];
end;
CVAR = cov(Dta)
CCF = corrcoef(Dta);
[V, Ev] = eig(CVAR)
Variance = flipud(diag(Ev)/sum(diag(Ev)))
CumulativeVariance = cumsum(Variance)
PC1 = V(:, 3)*[44, -30];
PC2 = V(:, 2)*[44, -30];
figure(1); P1 = plot(Dta(:, 1), Dta(:, 2), 'or'); axis equal;
figure(2); P2 = plot(Dta(:, 1), Dta(:, 2), 'or', PC1(1, :), PC1(2, :), 'k-', PC2(1, :), PC2(2, :), 'k--'); axis equal;
title('Solid line = PC1, Dashed line = PC2');
set(P1, 'linewidth', 2);
set(P2, 'linewidth', 2);
figure(3); P3D = scatter3(Dta(:, 1), Dta(:, 2), Dta(:, 3), 'or', 'fill');
line(PC1(1, :), PC1(2, :), PC1(3, :), 'linewidth', 3, 'color', 'k');
line(PC2(1, :), PC2(2, :), PC2(3, :), 'linewidth', 3, 'color', 'b', 'linestyle', '--');
rotate3d on;