%DEMGAUSS Demonstrate sampling from Gaussian distributions.%%	Description%%	DEMGAUSS provides a simple illustration of the generation of data%	from Gaussian distributions. It first samples from a one-dimensional%	distribution using RANDN, and then plots a normalized histogram%	estimate of the distribution using HISTP together with the true%	density calculated using GAUSS.%%	DEMGAUSS then demonstrates sampling from a Gaussian distribution in%	two dimensions. It creates a mean vector and a covariance matrix, and%	then plots contours of constant density using the function GAUSS. A%	sample of points drawn from this distribution, obtained using the%	function GSAMP, is then superimposed on the contours.%%	See also%	GAUSS, GSAMP, HISTP%%	Copyright (c) Ian T Nabney (1996-2001)clcmean = 2; var = 5; nsamp = 3000;xmin = -10; xmax = 10; nbins = 30;disp('Demonstration of sampling from a uni-variate Gaussian with mean')dstring = [num2str(mean), ' and variance ', num2str(var), '.  ', ...    num2str(nsamp), ' samples are taken.'];disp(dstring);x = mean + sqrt(var)*randn(nsamp, 1);fh1 = figure;histp(x, xmin, xmax, nbins);hold on;axis([xmin xmax 0 0.2]);plotvals = linspace(xmin, xmax, 200)';probs = gauss(mean, var, plotvals);plot(plotvals, probs, '-r');xlabel('X')ylabel('Density')disp(' ')disp('Press any key to continue')pause; mu = [3 2];lam1 = 0.5;lam2 = 5.0;Sigma = lam1*[1,1]'*[1,1] + lam2*[1,-1]'*[1,-1];disp(' ')disp('Demonstration of sampling from a bi-variate Gaussian.  The mean is')dstring = ['[', num2str(mu(1)), ', ', num2str(mu(2)), ...      '] and the covariance matrix is'];disp(dstring)disp(Sigma);ngrid = 40;cmin = -5; cmax = 10; cvals = linspace(cmin, cmax, ngrid);[X1, X2] = meshgrid(cvals, cvals);XX = [X1(:), X2(:)];probs = gauss(mu, Sigma, XX);probs = reshape(probs, ngrid, ngrid);fh2 = figure;contour(X1, X2, probs, 'b');hold onnsamp = 300;dstring = [num2str(nsamp), ' samples are generated.'];disp('The plot shows the sampled data points with a contour plot of their density.')samples = gsamp(mu, Sigma, nsamp);plot(samples(:,1), samples(:,2), 'or');xlabel('X1')ylabel('X2')grid off;disp(' ')disp('Press any key to end')pause; close(fh1);close(fh2);clear all;