matthiasm@8: % PLOTCOV2 - Plots a covariance ellipsoid with axes for a bivariate
matthiasm@8: %            Gaussian distribution.
matthiasm@8: %
matthiasm@8: % Usage:
matthiasm@8: %   [h, s] = plotcov2(mu, Sigma[, OPTIONS]);
matthiasm@8: % 
matthiasm@8: % Inputs:
matthiasm@8: %   mu    - a 2 x 1 vector giving the mean of the distribution.
matthiasm@8: %   Sigma - a 2 x 2 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: %   'label'     - if non-empty, a string that will label the
matthiasm@8: %                 ellipsoid (default: [])
matthiasm@8: %   'plot-axes' - a 0/1 flag indicating if the ellipsoid's axes
matthiasm@8: %                 should be plotted (default: 1)
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: %   'fill-color' - a color specifier; is this is not [], the
matthiasm@8: %                  covariance ellipse is filled with this color
matthiasm@8: %                  (default: [])
matthiasm@8: % 
matthiasm@8: % Outputs:
matthiasm@8: %   h     - a vector of handles on the axis lines
matthiasm@8: %
matthiasm@8: % See also: PLOTCOV3
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] = plotcov2New(mu, Sigma, varargin)
matthiasm@8: 
matthiasm@8: h = [];
matthiasm@8: s = [];
matthiasm@8: 
matthiasm@8: if size(Sigma) ~= [2 2], error('Sigma must be a 2 by 2 matrix'); end
matthiasm@8: if length(mu) ~= 2, error('mu must be a 2 by 1 vector'); end
matthiasm@8: 
matthiasm@8: Sigma = checkpsd(Sigma);
matthiasm@8: 
matthiasm@8: [p, ...
matthiasm@8:  n, ...
matthiasm@8:  label, ...
matthiasm@8:  plot_axes, ...
matthiasm@8:  plot_opts, ...
matthiasm@8:  fill_color] = process_options(varargin, 'conf', 0.9, ...
matthiasm@8: 			       'num-pts', 20, ...
matthiasm@8: 			       'label', [], ...
matthiasm@8: 			       'plot-axes', 1, ...
matthiasm@8: 			       'plot-opts', {}, ...
matthiasm@8: 			       'fill-color', []);
matthiasm@8: holding = ishold;
matthiasm@8: % Compute the Mahalanobis radius of the ellipsoid that encloses
matthiasm@8: % the desired probability mass.
matthiasm@8: k = conf2mahal(p, 2);
matthiasm@8: % Scale the covariance matrix so the confidence region has unit
matthiasm@8: % Mahalanobis distance.
matthiasm@8: Sigma = Sigma * k;
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: [V, D] = eig(full(Sigma));
matthiasm@8: V = real(V);
matthiasm@8: D = real(D);
matthiasm@8: D = abs(D);
matthiasm@8: 
matthiasm@8: % Compute the points on the boundary of the ellipsoid.
matthiasm@8: t = linspace(0, 2*pi, n);
matthiasm@8: u = [cos(t(:))'; sin(t(:))'];
matthiasm@8: w = (V * sqrt(D)) * u;
matthiasm@8: z = repmat(mu(:), [1 n]) + w;
matthiasm@8: h = [h; plot(z(1, :), z(2, :), plot_opts{:})];
matthiasm@8: if (~isempty(fill_color))
matthiasm@8:   s = patch(z(1, :), z(2, :), fill_color);
matthiasm@8: end
matthiasm@8: 
matthiasm@8: % Plot the axes.
matthiasm@8: if (plot_axes)
matthiasm@8:   hold on;
matthiasm@8:   L = sqrt(diag(D));
matthiasm@8:   h = plot([mu(1); mu(1) + L(1) * V(1, 1)], ...
matthiasm@8: 	   [mu(2); mu(2) + L(1) * V(2, 1)], plot_opts{:});
matthiasm@8:   h = [h; plot([mu(1); mu(1) + L(2) * V(1, 2)], ...
matthiasm@8: 	       [mu(2); mu(2) + L(2) * V(2, 2)], plot_opts{:})];
matthiasm@8: end
matthiasm@8: 
matthiasm@8: 
matthiasm@8: if (~isempty(label))
matthiasm@8:   th = text(mu(1), mu(2), label);
matthiasm@8:   set(th, 'FontSize', 18);
matthiasm@8:   set(th, 'FontName', 'Times');
matthiasm@8:   set(th, 'FontWeight', 'bold');
matthiasm@8:   set(th, 'FontAngle', 'italic');
matthiasm@8:   set(th, 'HorizontalAlignment', 'center');
matthiasm@8: end
matthiasm@8: 
matthiasm@8: if (~holding & plot_axes) hold off; end