comparison toolboxes/FullBNT-1.0.7/KPMtools/plotcov2.m @ 0:e9a9cd732c1e tip

first hg version after svn

+% PLOTCOV2 - Plots a covariance ellipse with major and minor axes
+%            for a bivariate Gaussian distribution.
+%
+% Usage:
+%   h = plotcov2(mu, Sigma[, OPTIONS]);
+% 
+% Inputs:
+%   mu    - a 2 x 1 vector giving the mean of the distribution.
+%   Sigma - a 2 x 2 symmetric positive semi-definite matrix giving
+%           the covariance of the distribution (or the zero matrix).
+%
+% Options:
+%   'conf'    - a scalar between 0 and 1 giving the confidence
+%               interval (i.e., the fraction of probability mass to
+%               be enclosed by the ellipse); default is 0.9.
+%   'num-pts' - the number of points to be used to plot the
+%               ellipse; default is 100.
+%
+% This function also accepts options for PLOT.
+%
+% Outputs:
+%   h     - a vector of figure handles to the ellipse boundary and
+%           its major and minor axes
+%
+% See also: PLOTCOV3
+
+% Copyright (C) 2002 Mark A. Paskin
+%
+% This program is free software; you can redistribute it and/or modify
+% it under the terms of the GNU General Public License as published by
+% the Free Software Foundation; either version 2 of the License, or
+% (at your option) any later version.
+%
+% This program is distributed in the hope that it will be useful, but
+% WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+% General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this program; if not, write to the Free Software
+% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
+% USA.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+function h = plotcov2(mu, Sigma, varargin)
+
+if size(Sigma) ~= [2 2], error('Sigma must be a 2 by 2 matrix'); end
+if length(mu) ~= 2, error('mu must be a 2 by 1 vector'); end
+
+[p, ...
+ n, ...
+ plot_opts] = process_options(varargin, 'conf', 0.9, ...
+					'num-pts', 100);
+h = [];
+holding = ishold;
+if (Sigma == zeros(2, 2))
+  z = mu;
+else
+  % Compute the Mahalanobis radius of the ellipsoid that encloses
+  % the desired probability mass.
+  k = conf2mahal(p, 2);
+  % The major and minor axes of the covariance ellipse are given by
+  % the eigenvectors of the covariance matrix.  Their lengths (for
+  % the ellipse with unit Mahalanobis radius) are given by the
+  % square roots of the corresponding eigenvalues.
+  if (issparse(Sigma))
+    [V, D] = eigs(Sigma);
+  else
+    [V, D] = eig(Sigma);
+  end
+  % Compute the points on the surface of the ellipse.
+  t = linspace(0, 2*pi, n);
+  u = [cos(t); sin(t)];
+  w = (k * V * sqrt(D)) * u;
+  z = repmat(mu, [1 n]) + w;
+  % Plot the major and minor axes.
+  L = k * sqrt(diag(D));
+  h = plot([mu(1); mu(1) + L(1) * V(1, 1)], ...
+	   [mu(2); mu(2) + L(1) * V(2, 1)], plot_opts{:});
+  hold on;
+  h = [h; plot([mu(1); mu(1) + L(2) * V(1, 2)], ...
+	       [mu(2); mu(2) + L(2) * V(2, 2)], plot_opts{:})];
+end
+
+h = [h; plot(z(1, :), z(2, :), plot_opts{:})];
+if (~holding) hold off; end