Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / geometry-1.5.0 / geom2d / ellipse2cov.m

diff --git a/octave_packages/geometry-1.5.0/geom2d/ellipse2cov.m b/octave_packages/geometry-1.5.0/geom2d/ellipse2cov.m
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+## Copyright (c) 2012 Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
+##
+## 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 3 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, see <http://www.gnu.org/licenses/>.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {@var{K} = } ellipse2cov (@var{elli})
+%% @deftypefnx {Function File} {@var{K} = } ellipse2cov (@var{ra}, @var{rb})
+%% @deftypefnx {Function File} {@var{K} = } ellipse2cov (@dots{}, @var{theta})
+%% Calculates covariance matrix from ellipse.
+%%
+%% If only one input is given, @var{elli} must define an ellipse as described in
+%% @command{ellipses2d}.
+%% If two inputs are given, @var{ra} and @var{rb} define the half-lenght of the
+%% axes.
+%% If a third input is given, @var{theta} must be the angle of rotation of the
+%% ellipse in radians, and in counter-clockwise direction.
+%%
+%% The output @var{K} contains the covariance matrix define by the ellipse.
+%%
+%% Run @code{demo ellipse2cov} to see an example.
+%%
+%% @seealso{ellipses2d, cov2ellipse, drawEllipse}
+%% @end deftypefn
+
+function K = ellipse2cov (elli, varargin);
+
+  ra    = 1;
+  rb    = 1;
+  theta = 0;
+  switch numel (varargin)
+    case 0
+    %% ellipse format
+      if numel (elli) != 5
+        print_usage ();
+      end
+      ra    = elli(1,3);
+      rb    = elli(1,4);
+      theta = elli(1,5)*pi/180;
+
+    case 2
+    %% ra,rb
+      if numel (elli) != 1
+        print_usage ();
+      end
+      ra = elli;
+      rb = varargin{1};
+
+    case 3
+    %% ra,rb, theta
+      if numel (elli) != 1
+        print_usage ();
+      end
+      ra    = elli;
+      rb    = varargin{1};
+      theta = varargin{2};
+
+    otherwise
+      print_usage ();
+  end
+
+  T = createRotation (theta)(1:2,1:2);
+  K = T*diag([ra rb])*T';
+
+endfunction
+
+%!demo
+%! elli = [0 0 1 3 -45];
+%!
+%! % Create 2D normal random variables with covarinace defined by elli.
+%! K = ellipse2cov (elli)
+%! L = chol(K,'lower');
+%! u = randn(1e3,2)*L';
+%!
+%! Kn = cov (u)
+%!
+%! figure(1)
+%! plot(u(:,1),u(:,2),'.r');
+%! hold on;
+%! drawEllipse(elli,'linewidth',2);
+%! hold off
+%! axis tight