covalpha.m.svn-base

Bayesian Surprise Toolkit for Matlab T. Nathan Mundhenk, Laurent Itti

%COVALPHA find J as a solution to E(alpha) = J*alpha 
%   J = COVALPHA(ALPHA,E_ALPHA,MODE) Will return the simple solution to the
%   linear problem A = MX. There are two modes of operation. The first mode 
%   computes the basic inverse of X (alpha). In this case the matrix alpha 
%   MUST be a sqaure NxN matrix. Additionally, we can compute the 
%   overdetermined solution where samples > dimensions. In this case we use 
%   QR decomposition. However, the psuedo-inverse would also work.  
%
%   ALPHA - This is the value of the alpha hyperparameters. It must be NxN
%   and independant in order to use mode 0. If it is overdetermined with a
%   large set of samples, use mode 1 and compute the estimated inverse by
%   method of least sqaures. 
%
%   E_ALPHA - This is a matrix of estimates for ALPHA. It need not be
%   square. However, it will have more power if it is the same size as
%   ALPHA. Notice that J will be the same size as E_ALPHA. 
%
%   MODE - Can be set to either 0 or 1. If it is 0, then we assume that
%   ALPHA is strictly invertable. Otherwise, if we use mode 1, then we
%   will find the least sqaures solution to the inverse of ALPHA. 
%
%   See also: digamma, gamma, psi, eulermasch, klgamma, betavalues
%
%   T. Nathan Mundhenk
%   [e-mail]
%

% //////////////////////////////////////////////////////////////////// %
% The Baysian Surprise Matlab Toolkit - Copyright (C) 2004-2007        %
% by the University of Southern California (USC) and the iLab at USC.  %
% See http://iLab.usc.edu for information about this project.          %
% //////////////////////////////////////////////////////////////////// %
% This file is part of the Baysian Surprise Matlab Toolkit             %
%                                                                      %
% The Baysian Surprise Matlab Toolkit 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.     %
%                                                                      %
% The Baysian Surprise Matlab Toolkit 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 the iBaysian Surprise Matlab Toolkit; if not, write       %
% to the Free Software Foundation, Inc., 59 Temple Place, Suite 330,   %
% Boston, MA 02111-1307 USA.                                           %
% //////////////////////////////////////////////////////////////////// %
%
% Primary maintainer for this file: T. Nathan Mundhenk <[e-mail]>


function J = covalpha(alpha,e_alpha,mode)

if mode == 0
    J = e_alpha * inv(alpha);
elseif mode == 1
    [Q,R] = qr(alpha,0);    
    J = R\(Q' * e_alpha); % Least Sqaures Approximation. 
    %NOTE: We can also use J = inv(R)*Q' * e_alpha which is slower but more
    %accurate
else
    error('Unknown mode given for computing J passed as an option. Only 0 and 1 supported');
end