How do you plot an ellipse on a poincare graph using standard deviation 1 and 2 as the radii?

How would I go about plotting an ellipse on a poincare graph using standard deviation 1 and 2 as the radii and the mean as the middle?

Answer 1

[Suraj Kumar]

Hi @Louise Kennedy,

To plot an ellipse on a poincare graph using MATLAB, where the ellipse is centered at the mean and has standard deviations as its radii, you can follow these steps:

1. Compute the mean of your data and the standard deviations along the principal axes.

data = randn(100, 2);
meanData = mean(data);
stdDev1 = std(data(:,1));
stdDev2 = std(data(:,2));

2. Generate points for the ellipse and use parametric equations for the ellipse.

% Parametric angle
theta = linspace(0, 2*pi, 100);
% Ellipse parameters
xEllipse = meanData(1) + stdDev1 * cos(theta);
yEllipse = meanData(2) + stdDev2 * sin(theta);

3. Use the "plot" function to draw the ellipse on the poincare graph.

figure;
scatter(data(:,1), data(:,2), 'b.');
hold on;
plot(xEllipse, yEllipse, 'r-', 'LineWidth', 2);
xlabel('x');
ylabel('y');
title('Poincaré Plot with Ellipse');
grid on;
axis equal;
hold off;

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Hope this works for you!