diff toolboxes/FullBNT-1.0.7/KPMtools/plotcov3.m @ 0:e9a9cd732c1e tip

first hg version after svn

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolboxes/FullBNT-1.0.7/KPMtools/plotcov3.m	Tue Feb 10 15:05:51 2015 +0000
@@ -0,0 +1,109 @@
+% PLOTCOV3 - Plots a covariance ellipsoid with axes for a trivariate
+%            Gaussian distribution.
+%
+% Usage:
+%   [h, s] = plotcov3(mu, Sigma[, OPTIONS]);
+% 
+% Inputs:
+%   mu    - a 3 x 1 vector giving the mean of the distribution.
+%   Sigma - a 3 x 3 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'   - if the value supplied is n, then (n + 1)^2 points
+%                 to be used to plot the ellipse; default is 20.
+%   'plot-opts' - a cell vector of arguments to be handed to PLOT3
+%                 to contol the appearance of the axes, e.g., 
+%                 {'Color', 'g', 'LineWidth', 1}; the default is {}
+%   'surf-opts' - a cell vector of arguments to be handed to SURF
+%                 to contol the appearance of the ellipsoid
+%                 surface; a nice possibility that yields
+%                 transparency is: {'EdgeAlpha', 0, 'FaceAlpha',
+%                 0.1, 'FaceColor', 'g'}; the default is {}
+% 
+% Outputs:
+%   h     - a vector of handles on the axis lines
+%   s     - a handle on the ellipsoid surface object
+%
+% See also: PLOTCOV2
+
+% 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, s] = plotcov3(mu, Sigma, varargin)
+
+if size(Sigma) ~= [3 3], error('Sigma must be a 3 by 3 matrix'); end
+if length(mu) ~= 3, error('mu must be a 3 by 1 vector'); end
+
+[p, ...
+ n, ...
+ plot_opts, ...
+ surf_opts] = process_options(varargin, 'conf', 0.9, ...
+					'num-pts', 20, ...
+			                'plot-opts', {}, ...
+			                'surf-opts', {});
+h = [];
+holding = ishold;
+if (Sigma == zeros(3, 3))
+  z = mu;
+else
+  % Compute the Mahalanobis radius of the ellipsoid that encloses
+  % the desired probability mass.
+  k = conf2mahal(p, 3);
+  % The 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
+  if (any(diag(D) < 0))
+    error('Invalid covariance matrix: not positive semi-definite.');
+  end
+  % Compute the points on the surface of the ellipsoid.
+  t = linspace(0, 2*pi, n);
+  [X, Y, Z] = sphere(n);
+  u = [X(:)'; Y(:)'; Z(:)'];
+  w = (k * V * sqrt(D)) * u;
+  z = repmat(mu(:), [1 (n + 1)^2]) + w;
+
+  % Plot the axes.
+  L = k * sqrt(diag(D));
+  h = plot3([mu(1); mu(1) + L(1) * V(1, 1)], ...
+	    [mu(2); mu(2) + L(1) * V(2, 1)], ...
+	    [mu(3); mu(3) + L(1) * V(3, 1)], plot_opts{:});
+  hold on;
+  h = [h; plot3([mu(1); mu(1) + L(2) * V(1, 2)], ...
+		[mu(2); mu(2) + L(2) * V(2, 2)], ...
+		[mu(3); mu(3) + L(2) * V(3, 2)], plot_opts{:})];
+  h = [h; plot3([mu(1); mu(1) + L(3) * V(1, 3)], ...
+		[mu(2); mu(2) + L(3) * V(2, 3)], ...
+		[mu(3); mu(3) + L(3) * V(3, 3)], plot_opts{:})];
+end
+
+s = surf(reshape(z(1, :), [(n + 1) (n + 1)]), ...
+	 reshape(z(2, :), [(n + 1) (n + 1)]), ...
+	 reshape(z(3, :), [(n + 1) (n + 1)]), ...
+	 surf_opts{:});
+
+if (~holding) hold off; end