How to plot a covariance matrix on a 2D plot in MATLAB?

In MATLAB there is a function called cov. If I insert a matrix X into cov like this cov(X), then cov will return a square matrix of covariance.

My question is very simple: How can I, with MATLAB, plot that matrix cov(X) onto a 2D plot like this. I can see a lot of covariance matrix plots at Google. But how do they create them?

Solution 1:

My best guess is that you're trying to add the principal components to the plot. To do that, you could do something like this.

%% generate data points

S_tru = [2 1; 1 1];
N = 1000;
%% compute mean, covariance, principal components
X = mvnrnd([0,0],S_tru,N);
mu = mean(X);
S = cov(X);
[U,D] = eig(S);

%% specify base points/directions for arrows
base = [mu;mu];
vecs = sqrt(D)*U';
vecs = 2 * vecs;

%% plot
plot(X(:,1),X(:,2), 'r.')
axis equal
hold on
quiver(base(:,1),base(:,2),vecs(:,1),vecs(:,2),'blue','LineWidth',2)

Resulting graph: