## Plot 3D ellipsoid

Plot 3D Gaussian distribution? The harder part is to plot the 3D ellipsoid which can be done by calculating the axes (radii) of the ellipsoid from its eigenvalues. Simultaneously, We will get its corresponding eigenvectors which tells how to rotate the ellipsoid. The function ellipsoid(.) can plot canonical ellipsoid, and hence we need to rotate the canonical ellipsoid using the eigenvectors. That is it. Here are some codes adapted from Rajiv Singh’s version.

% plot 3D ellipsoid % developed from the original demo by Rajiv Singh % http://www.mathworks.com/matlabcentral/newsreader/view_thread/42966 % 5 Dec, 2002 13:44:34 % Example data (Cov=covariance,mu=mean) is included. Cov = [1 0.5 0.3 0.5 2 0 0.3 0 3]; mu = [1 2 3]'; [U,L] = eig(Cov); % L: eigenvalue diagonal matrix % U: eigen vector matrix, each column is an eigenvector % For N standard deviations spread of data, the radii of the eliipsoid will % be given by N*SQRT(eigenvalues). N = 1; % choose your own N radii = N*sqrt(diag(L)); % generate data for "unrotated" ellipsoid [xc,yc,zc] = ellipsoid(0,0,0,radii(1),radii(2),radii(3)); % rotate data with orientation matrix U and center mu a = kron(U(:,1),xc); b = kron(U(:,2),yc); c = kron(U(:,3),zc); data = a+b+c; n = size(data,2); x = data(1:n,:)+mu(1); y = data(n+1:2*n,:)+mu(2); z = data(2*n+1:end,:)+mu(3); % now plot the rotated ellipse % sc = surf(x,y,z); shading interp; colormap copper h = surfl(x, y, z); colormap copper title('actual ellipsoid represented by mu and Cov') axis equal alpha(0.7)

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% Your algorithm does not work correct. In my verivication:

n=1;% or any index number

% (x-mu)’*inv(Cov)*(x-mu)

([x(n);yy(n);zz(n)]-mu)’*inv(Cov)*([xx(n);yy(n);zz(n)]-mu)

% should be =1 for all n