Summary

Matlab script source

%Author: Bscan
%This script illustrates a multivariate Gaussian distribution and its
%marginal distributions

%This code is issued under the CC0 "license"

%Define limits of plotting
X=-5:0.1:5;
Y=-5:0.1:5;

%2-d Mean and covariance matrix
MeanVec=[00];
CovMatrix=[10.6;0.62];

%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 decomp
L=chol(CovMatrix,'lower');
t=linspace(0,2*pi,100);%Our ellipse will have 100 points on it
set(0,'DefaultAxesFontName','Times New Roman')
set(0,'DefaultAxesFontSize',36)
C=[cos(t);sin(t)];%A unit circle
E1=1*L*C;E2=2*L*C;E3=3*L*C;%Get the 1,2, and 3-sigma ellipses

figure;holdon;
%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 bars
n_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 points
plot3(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 histograms
plot3(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 nice
gridon;view(45,55);
axis([X(1)X(end)Y(1)Y(end)])
print-depscmultivariate_normal_sample.eps

Licensing