wolffd@0: % PLOTCOV3 - Plots a covariance ellipsoid with axes for a trivariate
wolffd@0: %            Gaussian distribution.
wolffd@0: %
wolffd@0: % Usage:
wolffd@0: %   [h, s] = plotcov3(mu, Sigma[, OPTIONS]);
wolffd@0: % 
wolffd@0: % Inputs:
wolffd@0: %   mu    - a 3 x 1 vector giving the mean of the distribution.
wolffd@0: %   Sigma - a 3 x 3 symmetric positive semi-definite matrix giving
wolffd@0: %           the covariance of the distribution (or the zero matrix).
wolffd@0: %
wolffd@0: % Options:
wolffd@0: %   'conf'      - a scalar between 0 and 1 giving the confidence
wolffd@0: %                 interval (i.e., the fraction of probability mass to
wolffd@0: %                 be enclosed by the ellipse); default is 0.9.
wolffd@0: %   'num-pts'   - if the value supplied is n, then (n + 1)^2 points
wolffd@0: %                 to be used to plot the ellipse; default is 20.
wolffd@0: %   'plot-opts' - a cell vector of arguments to be handed to PLOT3
wolffd@0: %                 to contol the appearance of the axes, e.g., 
wolffd@0: %                 {'Color', 'g', 'LineWidth', 1}; the default is {}
wolffd@0: %   'surf-opts' - a cell vector of arguments to be handed to SURF
wolffd@0: %                 to contol the appearance of the ellipsoid
wolffd@0: %                 surface; a nice possibility that yields
wolffd@0: %                 transparency is: {'EdgeAlpha', 0, 'FaceAlpha',
wolffd@0: %                 0.1, 'FaceColor', 'g'}; the default is {}
wolffd@0: % 
wolffd@0: % Outputs:
wolffd@0: %   h     - a vector of handles on the axis lines
wolffd@0: %   s     - a handle on the ellipsoid surface object
wolffd@0: %
wolffd@0: % See also: PLOTCOV2
wolffd@0: 
wolffd@0: % Copyright (C) 2002 Mark A. Paskin
wolffd@0: %
wolffd@0: % This program is free software; you can redistribute it and/or modify
wolffd@0: % it under the terms of the GNU General Public License as published by
wolffd@0: % the Free Software Foundation; either version 2 of the License, or
wolffd@0: % (at your option) any later version.
wolffd@0: %
wolffd@0: % This program is distributed in the hope that it will be useful, but
wolffd@0: % WITHOUT ANY WARRANTY; without even the implied warranty of
wolffd@0: % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
wolffd@0: % General Public License for more details.
wolffd@0: %
wolffd@0: % You should have received a copy of the GNU General Public License
wolffd@0: % along with this program; if not, write to the Free Software
wolffd@0: % Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
wolffd@0: % USA.
wolffd@0: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
wolffd@0: 
wolffd@0: function [h, s] = plotcov3(mu, Sigma, varargin)
wolffd@0: 
wolffd@0: if size(Sigma) ~= [3 3], error('Sigma must be a 3 by 3 matrix'); end
wolffd@0: if length(mu) ~= 3, error('mu must be a 3 by 1 vector'); end
wolffd@0: 
wolffd@0: [p, ...
wolffd@0:  n, ...
wolffd@0:  plot_opts, ...
wolffd@0:  surf_opts] = process_options(varargin, 'conf', 0.9, ...
wolffd@0: 					'num-pts', 20, ...
wolffd@0: 			                'plot-opts', {}, ...
wolffd@0: 			                'surf-opts', {});
wolffd@0: h = [];
wolffd@0: holding = ishold;
wolffd@0: if (Sigma == zeros(3, 3))
wolffd@0:   z = mu;
wolffd@0: else
wolffd@0:   % Compute the Mahalanobis radius of the ellipsoid that encloses
wolffd@0:   % the desired probability mass.
wolffd@0:   k = conf2mahal(p, 3);
wolffd@0:   % The axes of the covariance ellipse are given by the eigenvectors of
wolffd@0:   % the covariance matrix.  Their lengths (for the ellipse with unit
wolffd@0:   % Mahalanobis radius) are given by the square roots of the
wolffd@0:   % corresponding eigenvalues.
wolffd@0:   if (issparse(Sigma))
wolffd@0:     [V, D] = eigs(Sigma);
wolffd@0:   else
wolffd@0:     [V, D] = eig(Sigma);
wolffd@0:   end
wolffd@0:   if (any(diag(D) < 0))
wolffd@0:     error('Invalid covariance matrix: not positive semi-definite.');
wolffd@0:   end
wolffd@0:   % Compute the points on the surface of the ellipsoid.
wolffd@0:   t = linspace(0, 2*pi, n);
wolffd@0:   [X, Y, Z] = sphere(n);
wolffd@0:   u = [X(:)'; Y(:)'; Z(:)'];
wolffd@0:   w = (k * V * sqrt(D)) * u;
wolffd@0:   z = repmat(mu(:), [1 (n + 1)^2]) + w;
wolffd@0: 
wolffd@0:   % Plot the axes.
wolffd@0:   L = k * sqrt(diag(D));
wolffd@0:   h = plot3([mu(1); mu(1) + L(1) * V(1, 1)], ...
wolffd@0: 	    [mu(2); mu(2) + L(1) * V(2, 1)], ...
wolffd@0: 	    [mu(3); mu(3) + L(1) * V(3, 1)], plot_opts{:});
wolffd@0:   hold on;
wolffd@0:   h = [h; plot3([mu(1); mu(1) + L(2) * V(1, 2)], ...
wolffd@0: 		[mu(2); mu(2) + L(2) * V(2, 2)], ...
wolffd@0: 		[mu(3); mu(3) + L(2) * V(3, 2)], plot_opts{:})];
wolffd@0:   h = [h; plot3([mu(1); mu(1) + L(3) * V(1, 3)], ...
wolffd@0: 		[mu(2); mu(2) + L(3) * V(2, 3)], ...
wolffd@0: 		[mu(3); mu(3) + L(3) * V(3, 3)], plot_opts{:})];
wolffd@0: end
wolffd@0: 
wolffd@0: s = surf(reshape(z(1, :), [(n + 1) (n + 1)]), ...
wolffd@0: 	 reshape(z(2, :), [(n + 1) (n + 1)]), ...
wolffd@0: 	 reshape(z(3, :), [(n + 1) (n + 1)]), ...
wolffd@0: 	 surf_opts{:});
wolffd@0: 
wolffd@0: if (~holding) hold off; end