wolffd@0: % PLOTCOV2 - Plots a covariance ellipsoid with axes for a bivariate
wolffd@0: %            Gaussian distribution.
wolffd@0: %
wolffd@0: % Usage:
wolffd@0: %   [h, s] = plotcov2(mu, Sigma[, OPTIONS]);
wolffd@0: % 
wolffd@0: % Inputs:
wolffd@0: %   mu    - a 2 x 1 vector giving the mean of the distribution.
wolffd@0: %   Sigma - a 2 x 2 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: %   'label'     - if non-empty, a string that will label the
wolffd@0: %                 ellipsoid (default: [])
wolffd@0: %   'plot-axes' - a 0/1 flag indicating if the ellipsoid's axes
wolffd@0: %                 should be plotted (default: 1)
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: %   'fill-color' - a color specifier; is this is not [], the
wolffd@0: %                  covariance ellipse is filled with this color
wolffd@0: %                  (default: [])
wolffd@0: % 
wolffd@0: % Outputs:
wolffd@0: %   h     - a vector of handles on the axis lines
wolffd@0: %
wolffd@0: % See also: PLOTCOV3
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] = plotcov2New(mu, Sigma, varargin)
wolffd@0: 
wolffd@0: h = [];
wolffd@0: s = [];
wolffd@0: 
wolffd@0: if size(Sigma) ~= [2 2], error('Sigma must be a 2 by 2 matrix'); end
wolffd@0: if length(mu) ~= 2, error('mu must be a 2 by 1 vector'); end
wolffd@0: 
wolffd@0: Sigma = checkpsd(Sigma);
wolffd@0: 
wolffd@0: [p, ...
wolffd@0:  n, ...
wolffd@0:  label, ...
wolffd@0:  plot_axes, ...
wolffd@0:  plot_opts, ...
wolffd@0:  fill_color] = process_options(varargin, 'conf', 0.9, ...
wolffd@0: 			       'num-pts', 20, ...
wolffd@0: 			       'label', [], ...
wolffd@0: 			       'plot-axes', 1, ...
wolffd@0: 			       'plot-opts', {}, ...
wolffd@0: 			       'fill-color', []);
wolffd@0: holding = ishold;
wolffd@0: % Compute the Mahalanobis radius of the ellipsoid that encloses
wolffd@0: % the desired probability mass.
wolffd@0: k = conf2mahal(p, 2);
wolffd@0: % Scale the covariance matrix so the confidence region has unit
wolffd@0: % Mahalanobis distance.
wolffd@0: Sigma = Sigma * k;
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: [V, D] = eig(full(Sigma));
wolffd@0: V = real(V);
wolffd@0: D = real(D);
wolffd@0: D = abs(D);
wolffd@0: 
wolffd@0: % Compute the points on the boundary of the ellipsoid.
wolffd@0: t = linspace(0, 2*pi, n);
wolffd@0: u = [cos(t(:))'; sin(t(:))'];
wolffd@0: w = (V * sqrt(D)) * u;
wolffd@0: z = repmat(mu(:), [1 n]) + w;
wolffd@0: h = [h; plot(z(1, :), z(2, :), plot_opts{:})];
wolffd@0: if (~isempty(fill_color))
wolffd@0:   s = patch(z(1, :), z(2, :), fill_color);
wolffd@0: end
wolffd@0: 
wolffd@0: % Plot the axes.
wolffd@0: if (plot_axes)
wolffd@0:   hold on;
wolffd@0:   L = sqrt(diag(D));
wolffd@0:   h = plot([mu(1); mu(1) + L(1) * V(1, 1)], ...
wolffd@0: 	   [mu(2); mu(2) + L(1) * V(2, 1)], plot_opts{:});
wolffd@0:   h = [h; plot([mu(1); mu(1) + L(2) * V(1, 2)], ...
wolffd@0: 	       [mu(2); mu(2) + L(2) * V(2, 2)], plot_opts{:})];
wolffd@0: end
wolffd@0: 
wolffd@0: 
wolffd@0: if (~isempty(label))
wolffd@0:   th = text(mu(1), mu(2), label);
wolffd@0:   set(th, 'FontSize', 18);
wolffd@0:   set(th, 'FontName', 'Times');
wolffd@0:   set(th, 'FontWeight', 'bold');
wolffd@0:   set(th, 'FontAngle', 'italic');
wolffd@0:   set(th, 'HorizontalAlignment', 'center');
wolffd@0: end
wolffd@0: 
wolffd@0: if (~holding & plot_axes) hold off; end