matthiasm@8: % PLOTCOV3 - Plots a covariance ellipsoid with axes for a trivariate
matthiasm@8: %            Gaussian distribution.
matthiasm@8: %
matthiasm@8: % Usage:
matthiasm@8: %   [h, s] = plotcov3(mu, Sigma[, OPTIONS]);
matthiasm@8: % 
matthiasm@8: % Inputs:
matthiasm@8: %   mu    - a 3 x 1 vector giving the mean of the distribution.
matthiasm@8: %   Sigma - a 3 x 3 symmetric positive semi-definite matrix giving
matthiasm@8: %           the covariance of the distribution (or the zero matrix).
matthiasm@8: %
matthiasm@8: % Options:
matthiasm@8: %   'conf'      - a scalar between 0 and 1 giving the confidence
matthiasm@8: %                 interval (i.e., the fraction of probability mass to
matthiasm@8: %                 be enclosed by the ellipse); default is 0.9.
matthiasm@8: %   'num-pts'   - if the value supplied is n, then (n + 1)^2 points
matthiasm@8: %                 to be used to plot the ellipse; default is 20.
matthiasm@8: %   'plot-opts' - a cell vector of arguments to be handed to PLOT3
matthiasm@8: %                 to contol the appearance of the axes, e.g., 
matthiasm@8: %                 {'Color', 'g', 'LineWidth', 1}; the default is {}
matthiasm@8: %   'surf-opts' - a cell vector of arguments to be handed to SURF
matthiasm@8: %                 to contol the appearance of the ellipsoid
matthiasm@8: %                 surface; a nice possibility that yields
matthiasm@8: %                 transparency is: {'EdgeAlpha', 0, 'FaceAlpha',
matthiasm@8: %                 0.1, 'FaceColor', 'g'}; the default is {}
matthiasm@8: % 
matthiasm@8: % Outputs:
matthiasm@8: %   h     - a vector of handles on the axis lines
matthiasm@8: %   s     - a handle on the ellipsoid surface object
matthiasm@8: %
matthiasm@8: % See also: PLOTCOV2
matthiasm@8: 
matthiasm@8: % Copyright (C) 2002 Mark A. Paskin
matthiasm@8: %
matthiasm@8: % This program is free software; you can redistribute it and/or modify
matthiasm@8: % it under the terms of the GNU General Public License as published by
matthiasm@8: % the Free Software Foundation; either version 2 of the License, or
matthiasm@8: % (at your option) any later version.
matthiasm@8: %
matthiasm@8: % This program is distributed in the hope that it will be useful, but
matthiasm@8: % WITHOUT ANY WARRANTY; without even the implied warranty of
matthiasm@8: % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
matthiasm@8: % General Public License for more details.
matthiasm@8: %
matthiasm@8: % You should have received a copy of the GNU General Public License
matthiasm@8: % along with this program; if not, write to the Free Software
matthiasm@8: % Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
matthiasm@8: % USA.
matthiasm@8: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
matthiasm@8: 
matthiasm@8: function [h, s] = plotcov3(mu, Sigma, varargin)
matthiasm@8: 
matthiasm@8: if size(Sigma) ~= [3 3], error('Sigma must be a 3 by 3 matrix'); end
matthiasm@8: if length(mu) ~= 3, error('mu must be a 3 by 1 vector'); end
matthiasm@8: 
matthiasm@8: [p, ...
matthiasm@8:  n, ...
matthiasm@8:  plot_opts, ...
matthiasm@8:  surf_opts] = process_options(varargin, 'conf', 0.9, ...
matthiasm@8: 					'num-pts', 20, ...
matthiasm@8: 			                'plot-opts', {}, ...
matthiasm@8: 			                'surf-opts', {});
matthiasm@8: h = [];
matthiasm@8: holding = ishold;
matthiasm@8: if (Sigma == zeros(3, 3))
matthiasm@8:   z = mu;
matthiasm@8: else
matthiasm@8:   % Compute the Mahalanobis radius of the ellipsoid that encloses
matthiasm@8:   % the desired probability mass.
matthiasm@8:   k = conf2mahal(p, 3);
matthiasm@8:   % The axes of the covariance ellipse are given by the eigenvectors of
matthiasm@8:   % the covariance matrix.  Their lengths (for the ellipse with unit
matthiasm@8:   % Mahalanobis radius) are given by the square roots of the
matthiasm@8:   % corresponding eigenvalues.
matthiasm@8:   if (issparse(Sigma))
matthiasm@8:     [V, D] = eigs(Sigma);
matthiasm@8:   else
matthiasm@8:     [V, D] = eig(Sigma);
matthiasm@8:   end
matthiasm@8:   if (any(diag(D) < 0))
matthiasm@8:     error('Invalid covariance matrix: not positive semi-definite.');
matthiasm@8:   end
matthiasm@8:   % Compute the points on the surface of the ellipsoid.
matthiasm@8:   t = linspace(0, 2*pi, n);
matthiasm@8:   [X, Y, Z] = sphere(n);
matthiasm@8:   u = [X(:)'; Y(:)'; Z(:)'];
matthiasm@8:   w = (k * V * sqrt(D)) * u;
matthiasm@8:   z = repmat(mu(:), [1 (n + 1)^2]) + w;
matthiasm@8: 
matthiasm@8:   % Plot the axes.
matthiasm@8:   L = k * sqrt(diag(D));
matthiasm@8:   h = plot3([mu(1); mu(1) + L(1) * V(1, 1)], ...
matthiasm@8: 	    [mu(2); mu(2) + L(1) * V(2, 1)], ...
matthiasm@8: 	    [mu(3); mu(3) + L(1) * V(3, 1)], plot_opts{:});
matthiasm@8:   hold on;
matthiasm@8:   h = [h; plot3([mu(1); mu(1) + L(2) * V(1, 2)], ...
matthiasm@8: 		[mu(2); mu(2) + L(2) * V(2, 2)], ...
matthiasm@8: 		[mu(3); mu(3) + L(2) * V(3, 2)], plot_opts{:})];
matthiasm@8:   h = [h; plot3([mu(1); mu(1) + L(3) * V(1, 3)], ...
matthiasm@8: 		[mu(2); mu(2) + L(3) * V(2, 3)], ...
matthiasm@8: 		[mu(3); mu(3) + L(3) * V(3, 3)], plot_opts{:})];
matthiasm@8: end
matthiasm@8: 
matthiasm@8: s = surf(reshape(z(1, :), [(n + 1) (n + 1)]), ...
matthiasm@8: 	 reshape(z(2, :), [(n + 1) (n + 1)]), ...
matthiasm@8: 	 reshape(z(3, :), [(n + 1) (n + 1)]), ...
matthiasm@8: 	 surf_opts{:});
matthiasm@8: 
matthiasm@8: if (~holding) hold off; end