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1 %DEMGAUSS Demonstrate sampling from Gaussian distributions.
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2 %
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3 % Description
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4 %
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5 % DEMGAUSS provides a simple illustration of the generation of data
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6 % from Gaussian distributions. It first samples from a one-dimensional
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7 % distribution using RANDN, and then plots a normalized histogram
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8 % estimate of the distribution using HISTP together with the true
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9 % density calculated using GAUSS.
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10 %
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11 % DEMGAUSS then demonstrates sampling from a Gaussian distribution in
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12 % two dimensions. It creates a mean vector and a covariance matrix, and
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13 % then plots contours of constant density using the function GAUSS. A
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14 % sample of points drawn from this distribution, obtained using the
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15 % function GSAMP, is then superimposed on the contours.
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16 %
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17 % See also
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18 % GAUSS, GSAMP, HISTP
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19 %
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20
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21 % Copyright (c) Ian T Nabney (1996-2001)
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22
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23 clc
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24 mean = 2; var = 5; nsamp = 3000;
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25 xmin = -10; xmax = 10; nbins = 30;
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26 disp('Demonstration of sampling from a uni-variate Gaussian with mean')
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27 dstring = [num2str(mean), ' and variance ', num2str(var), '. ', ...
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28 num2str(nsamp), ' samples are taken.'];
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29 disp(dstring);
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30 x = mean + sqrt(var)*randn(nsamp, 1);
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31 fh1 = figure;
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32 histp(x, xmin, xmax, nbins);
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33 hold on;
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34 axis([xmin xmax 0 0.2]);
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35 plotvals = linspace(xmin, xmax, 200)';
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36 probs = gauss(mean, var, plotvals);
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37 plot(plotvals, probs, '-r');
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38 xlabel('X')
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39 ylabel('Density')
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40
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41 disp(' ')
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42 disp('Press any key to continue')
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43 pause;
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44 mu = [3 2];
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45 lam1 = 0.5;
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46 lam2 = 5.0;
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47 Sigma = lam1*[1,1]'*[1,1] + lam2*[1,-1]'*[1,-1];
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48 disp(' ')
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49 disp('Demonstration of sampling from a bi-variate Gaussian. The mean is')
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50 dstring = ['[', num2str(mu(1)), ', ', num2str(mu(2)), ...
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51 '] and the covariance matrix is'];
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52 disp(dstring)
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53 disp(Sigma);
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54 ngrid = 40;
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55 cmin = -5; cmax = 10;
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56 cvals = linspace(cmin, cmax, ngrid);
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57 [X1, X2] = meshgrid(cvals, cvals);
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58 XX = [X1(:), X2(:)];
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59 probs = gauss(mu, Sigma, XX);
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60 probs = reshape(probs, ngrid, ngrid);
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61
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62 fh2 = figure;
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63 contour(X1, X2, probs, 'b');
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64 hold on
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65
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66 nsamp = 300;
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67 dstring = [num2str(nsamp), ' samples are generated.'];
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68 disp('The plot shows the sampled data points with a contour plot of their density.')
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69 samples = gsamp(mu, Sigma, nsamp);
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70 plot(samples(:,1), samples(:,2), 'or');
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71 xlabel('X1')
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72 ylabel('X2')
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73 grid off;
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74
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75 disp(' ')
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76 disp('Press any key to end')
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77 pause;
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78 close(fh1);
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79 close(fh2);
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80 clear all; |
