ccl_learna_nhat

 [optimal, result] = ccl_learna_nhat (Un)

 Learn state independent null space projection P

 Input:

   Un                                      Observations of null space component

 Output:

   optimal                                 Returned optimal model
   result                                  Returned results

0001 function [optimal, result] = ccl_learna_nhat (Un)
0002 % [optimal, result] = ccl_learna_nhat (Un)
0003 %
0004 % Learn state independent null space projection P
0005 %
0006 % Input:
0007 %
0008 %   Un                                      Observations of null space component
0009 %
0010 % Output:
0011 %
0012 %   optimal                                 Returned optimal model
0013 %   result                                  Returned results
0014 
0015 
0016 
0017 
0018 % CCL: A MATLAB library for Constraint Consistent Learning
0019 % Copyright (C) 2007  Matthew Howard
0020 % Contact: matthew.j.howard@kcl.ac.uk
0021 %
0022 % This library is free software; you can redistribute it and/or
0023 % modify it under the terms of the GNU Lesser General Public
0024 % License as published by the Free Software Foundation; either
0025 % version 2.1 of the License, or (at your option) any later version.
0026 %
0027 % This library is distributed in the hope that it will be useful,
0028 % but WITHOUT ANY WARRANTY; without even the implied warranty of
0029 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0030 % Lesser General Public License for more details.
0031 %
0032 % You should have received a copy of the GNU Library General Public
0033 % License along with this library; if not, write to the Free
0034 % Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
0035 
0036 % setup parameters for search
0037 search.dim_u    = size(Un,1) ;          % dimensionality of the action space
0038 search.dim_n    = size(Un,2) ;          % number of data points
0039 search.num_theta= 20 ;                 % number of candidate constraints (from 0 to pi)
0040 search.dim_t    = search.dim_u - 1 ;    % number of parameters needed to represent an unit vector
0041 search.epsilon  = search.dim_u * 0.001 ;
0042 search          = ccl_math_ss (search) ;
0043 
0044 % vectorises the matrix
0045 Vn = zeros(search.dim_n, search.dim_u^2) ;
0046 for n = 1:search.dim_n
0047     UnUn    = Un(:,n)*Un(:,n)' ;
0048     Vn(n,:) = UnUn(:)' ;
0049 end
0050 
0051 % search the first constraint
0052 result.model{1} = ccl_learna_sfa (Vn, Un, [], search) ;
0053 optimal         = result.model{1} ;
0054 
0055 % search the next constraint until the new constraint does not fit
0056 for alpha_id = 2:search.dim_t
0057     result.model{alpha_id} = ccl_learna_sa_nhat (Vn, Un, result.model{alpha_id-1}, search) ;
0058     if result.model{alpha_id}.nmse_j < .1
0059         optimal = result.model{alpha_id} ;
0060     else
0061         return ;
0062     end
0063 end
0064 end