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1 % PLOTCOV2 - Plots a covariance ellipse with major and minor axes
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2 % for a bivariate Gaussian distribution.
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3 %
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4 % Usage:
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5 % h = plotcov2(mu, Sigma[, OPTIONS]);
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6 %
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7 % Inputs:
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8 % mu - a 2 x 1 vector giving the mean of the distribution.
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9 % Sigma - a 2 x 2 symmetric positive semi-definite matrix giving
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10 % the covariance of the distribution (or the zero matrix).
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11 %
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12 % Options:
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13 % 'conf' - a scalar between 0 and 1 giving the confidence
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14 % interval (i.e., the fraction of probability mass to
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15 % be enclosed by the ellipse); default is 0.9.
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16 % 'num-pts' - the number of points to be used to plot the
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17 % ellipse; default is 100.
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18 %
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19 % This function also accepts options for PLOT.
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20 %
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21 % Outputs:
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22 % h - a vector of figure handles to the ellipse boundary and
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23 % its major and minor axes
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24 %
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25 % See also: PLOTCOV3
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26
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27 % Copyright (C) 2002 Mark A. Paskin
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28 %
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29 % This program is free software; you can redistribute it and/or modify
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30 % it under the terms of the GNU General Public License as published by
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31 % the Free Software Foundation; either version 2 of the License, or
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32 % (at your option) any later version.
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33 %
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34 % This program is distributed in the hope that it will be useful, but
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35 % WITHOUT ANY WARRANTY; without even the implied warranty of
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36 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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37 % General Public License for more details.
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38 %
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39 % You should have received a copy of the GNU General Public License
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40 % along with this program; if not, write to the Free Software
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41 % Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
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42 % USA.
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43 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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44
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45 function h = plotcov2(mu, Sigma, varargin)
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46
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47 if size(Sigma) ~= [2 2], error('Sigma must be a 2 by 2 matrix'); end
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48 if length(mu) ~= 2, error('mu must be a 2 by 1 vector'); end
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49
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50 [p, ...
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51 n, ...
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52 plot_opts] = process_options(varargin, 'conf', 0.9, ...
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53 'num-pts', 100);
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54 h = [];
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55 holding = ishold;
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56 if (Sigma == zeros(2, 2))
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57 z = mu;
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58 else
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59 % Compute the Mahalanobis radius of the ellipsoid that encloses
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60 % the desired probability mass.
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61 k = conf2mahal(p, 2);
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62 % The major and minor axes of the covariance ellipse are given by
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63 % the eigenvectors of the covariance matrix. Their lengths (for
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64 % the ellipse with unit Mahalanobis radius) are given by the
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65 % square roots of the corresponding eigenvalues.
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66 if (issparse(Sigma))
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67 [V, D] = eigs(Sigma);
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68 else
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69 [V, D] = eig(Sigma);
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70 end
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71 % Compute the points on the surface of the ellipse.
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72 t = linspace(0, 2*pi, n);
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73 u = [cos(t); sin(t)];
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74 w = (k * V * sqrt(D)) * u;
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75 z = repmat(mu, [1 n]) + w;
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76 % Plot the major and minor axes.
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77 L = k * sqrt(diag(D));
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78 h = plot([mu(1); mu(1) + L(1) * V(1, 1)], ...
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79 [mu(2); mu(2) + L(1) * V(2, 1)], plot_opts{:});
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80 hold on;
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81 h = [h; plot([mu(1); mu(1) + L(2) * V(1, 2)], ...
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82 [mu(2); mu(2) + L(2) * V(2, 2)], plot_opts{:})];
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83 end
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84
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85 h = [h; plot(z(1, :), z(2, :), plot_opts{:})];
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86 if (~holding) hold off; end
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