%This script illustrates a multivariate Gaussian distribution and its%marginal distributions%This code is issued under the CC0 "license"%Define limits of plottingX = -5:0.1:5;Y = -5:0.1:5;%2-d Mean and covariance matrixMeanVec = [0 0];CovMatrix = [1 0.6; 0.6 2];%Get the 1-d PDFs for the "walls"Z_x = normpdf(X,MeanVec(1), sqrt(CovMatrix(1,1)));Z_y = normpdf(Y,MeanVec(2), sqrt(CovMatrix(2,2)));%Get the 2-d samples for the "floor"Samples = mvnrnd(MeanVec, CovMatrix, 10000);%Get the sigma ellipses by transform a circle by the cholesky decompL = chol(CovMatrix,'lower');t = linspace(0,2*pi,100); %Our ellipse will have 100 points on itC = [cos(t) ; sin(t)]; %A unit circleE1 = 1*L*C; E2 = 2*L*C; E3 = 3*L*C; %Get the 1,2, and 3-sigma ellipsesfigure; hold on; %Plot the samples on the "floor"plot3(Samples(:,1),Samples(:,2),zeros(size(Samples,1),1),'k.','MarkerSize',2)%Plot the 1,2, and 3-sigma ellipses slightly above the floor%plot3(E1(1,:), E1(2,:), 1e-3+zeros(1,size(E1,2)),'Color','g','LineWidth',2);%plot3(E2(1,:), E2(2,:), 1e-3+zeros(1,size(E2,2)),'Color','g','LineWidth',2);plot3(E3(1,:), E3(2,:), 1e-3+zeros(1,size(E3,2)),'Color','g','LineWidth',2);%Plot the histograms on the walls from the data in the middle[n_x, xout] = hist(Samples(:,1),20);%Creates 20 barsn_x = n_x ./ ( sum(n_x) *(xout(2)-xout(1)));%Normalizes to be a pdf[~,~,~,x_Pos,x_Height] = makebars(xout,n_x);%Creates the bar pointsplot3(x_Pos, Y(end)*ones(size(x_Pos)),x_Height,'-k')%Now plot the other histograms on the wall[n_y, yout] = hist(Samples(:,2),20);n_y = n_y ./ ( sum(n_y) *(yout(2)-yout(1)));[~,~,~,y_Pos,y_Height] = makebars(yout,n_y);plot3(X(1)*ones(size(y_Pos)),y_Pos, y_Height,'-k')%Now plot the 1-d pdfs over the histogramsplot3(X, ones(size(X))*Y(end), Z_x,'-b','LineWidth',2); plot3(ones(size(Y))*X(1), Y, Z_y,'-r','LineWidth',2);%Make the figure look nicegrid on; view(45,55);axis([X(1) X(end) Y(1) Y(end)])