gauss_surf

Contents

gauss_surf.m
The Multi-variate Gaussian pdf is given by:
Define the Gaussian
Define the grid for visualisation
Define the constant
Make the plots

gauss_surf.m

From A First Course in Machine Learning, Chapter 2. Simon Rogers, 01/11/11 [simon.rogers@glasgow.ac.uk] Surface and contour plots of a Gaussian

clear all;close all;

The Multi-variate Gaussian pdf is given by:

$p(\mathbf{x}|\mu,\Sigma) = \frac{1}{(2\pi)^{D/2}|\Sigma|^{1/2}}\exp\left\{-\frac{1}{2}(\mathbf{x}-\mu)^T\Sigma^{-1}(\mathbf{x}-\mu)\right\}$

Define the Gaussian

mu = [1;2];
sigma = [1 0.8;0.8 4];

Define the grid for visualisation

[X,Y] = meshgrid(-5:0.1:5,-5:0.1:5);

Define the constant

const = (1/sqrt(2*pi))^2;
const = const./sqrt(det(sigma));
temp = [X(:)-mu(1) Y(:)-mu(2)];
pdfv = const*exp(-0.5*diag(temp*inv(sigma)*temp'));
pdfv = reshape(pdfv,size(X));

Make the plots

figure(1);hold off
contour(X,Y,pdfv);
figure(2);hold off
surf(X,Y,pdfv);