Plotting in 2D
- Plot the Equilateral Triangle (Simplex): You can plot an equilateral triangle by defining its vertices and using the plot function.
- Transform Probability Vectors: probability vectors (for 2D simplex, vectors of size 3 summing to 1) do not directly correspond to Cartesian coordinates, you'll need to transform them into the 2D space of the simplex.
- Plot Points: Use the transformed coordinates to plot points within the simplex.
% Define vertices of the equilateral triangle
vertices = [0, 0; 1, 0; 0.5, sqrt(3)/2];
vertices = [vertices; vertices(1,:)]; % Close the triangle
% Plot the simplex (equilateral triangle)
figure;
plot(vertices(:,1), vertices(:,2), '-');
hold on;
axis equal;
grid on;
% Example set of points (probability vectors)
P = [0.1, 0.6, 0.3; 0.3, 0.3, 0.4; 0.25, 0.25, 0.5];
% Transform and plot points
for i = 1:size(P,1)
% Transform points to Cartesian coordinates
x = P(i,1) + P(i,2)/2;
y = P(i,2)*sqrt(3)/2;
plot(x, y, 'ro');
end
title('2D Simplex with Points');
xlabel('X');
ylabel('Y');
Extending to 3D
% Define vertices of the tetrahedron
vertices = [0, 0, 0; 1, 0, 0; 0.5, sqrt(3)/2, 0; 0.5, sqrt(3)/6, sqrt(2/3)];
faces = [1, 2, 3; 1, 2, 4; 2, 3, 4; 1, 3, 4];
% Plot the simplex (tetrahedron)
figure;
hold on;
trisurf(faces, vertices(:,1), vertices(:,2), vertices(:,3), 'FaceColor', 'none', 'EdgeColor', 'b');
axis equal;
grid on;
% Example set of points (probability vectors for 3D simplex)
P = [0.1, 0.2, 0.3, 0.4; 0.25, 0.25, 0.25, 0.25];
% Transform and plot points
for i = 1:size(P,1)
% Transform points to Cartesian coordinates (specific to tetrahedron layout)
x = P(i,1) + P(i,2)/2 + P(i,4)/3;
y = P(i,2)*sqrt(3)/2 + P(i,4)*sqrt(3)/6;
z = P(i,4)*sqrt(2/3);
plot3(x, y, z, 'ro');
end
title('3D Simplex with Points');
xlabel('X');
ylabel('Y');
zlabel('Z');
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It's important to note that the advice and code are based on limited information and meant for educational purposes. Users should verify and adapt the code to their specific needs, ensuring compatibility and adherence to ethical standards.
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