comparison toolboxes/FullBNT-1.0.7/netlab3.3/demgauss.m @ 0:e9a9cd732c1e tip

first hg version after svn

+%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)
+
+clc
+mean = 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 on
+
+nsamp = 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;