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# regsubspace

## (Toolbox/regsubspace.m in BrainStorm 2.0 (Alpha))

### Function Synopsis

    SubSpace = regsubspace(GUI,U,S);

### Help Text

    REGSUBSPACE - Determine the subspace based on the regularization method
     function SubSpace = regsubspace(GUI,U,S);
     method is CASE Sensitive.
     See REGCHECK

### Cross-Reference Information

This function is called by

    least_squares_fit                  C:\BrainStorm_2001\Toolbox\least_squares_fit.m
    minnorm                            C:\BrainStorm_2001\Toolbox\minnorm.m
    rapmusic_gui                       C:\BrainStorm_2001\Toolbox\rapmusic_gui.m
    sourceimaging                      C:\BrainStorm_2001\Toolbox\sourceimaging.m
    subcorr_gui                        C:\BrainStorm_2001\Toolbox\subcorr_gui.m

### Listing of function C:\BrainStorm_2001\Toolbox\regsubspace.m

    function SubSpace = regsubspace(GUI,U,S);
    %REGSUBSPACE - Determine the subspace based on the regularization method
    % function SubSpace = regsubspace(GUI,U,S);
    % method is CASE Sensitive.
    % See REGCHECK

    %<autobegin> ---------------------- 26-May-2004 11:34:14 -----------------------
    % --------- Automatically Generated Comments Block Using AUTO_COMMENTS ---------
    %
    % CATEGORY: Inverse Modeling
    %
    % At Check-in: $Author: Mosher $  $Revision: 12 $  $Date: 5/26/04 10:02a $
    %
    % This software is part of BrainStorm Toolbox Version 2.0 (Alpha) 24-May-2004
    %
    % Principal Investigators and Developers:
    % ** Richard M. Leahy, PhD, Signal & Image Processing Institute,
    %    University of Southern California, Los Angeles, CA
    % ** John C. Mosher, PhD, Biophysics Group,
    %    Los Alamos National Laboratory, Los Alamos, NM
    % ** Sylvain Baillet, PhD, Cognitive Neuroscience & Brain Imaging Laboratory,
    %    CNRS, Hopital de la Salpetriere, Paris, France
    %
    % See BrainStorm website at http://neuroimage.usc.edu for further information.
    %
    % Copyright (c) 2004 BrainStorm by the University of Southern California
    % This software distributed  under the terms of the GNU General Public License
    % as published by the Free Software Foundation. Further details on the GPL
    % license can be found at http://www.gnu.org/copyleft/gpl.html .
    %
    % FOR RESEARCH PURPOSES ONLY. THE SOFTWARE IS PROVIDED "AS IS," AND THE
    % UNIVERSITY OF SOUTHERN CALIFORNIA AND ITS COLLABORATORS DO NOT MAKE ANY
    % WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO WARRANTIES OF
    % MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, NOR DO THEY ASSUME ANY
    % LIABILITY OR RESPONSIBILITY FOR THE USE OF THIS SOFTWARE.
    %<autoend> ------------------------ 26-May-2004 11:34:14 -----------------------

    % JCM 10/19/99 turned off lower and deblanking, since profiling showed
    %  to be expensive
    % $Date: 5/26/04 10:02a $ $Revision: 12 $

    % JCM 12/2/99 changed eps to eps = 1e-7, because gain matrices written in single precision

    eps = 1e-7;

    switch GUI.REG % regularization switch
    case 'Condition'

      S = diag(S);  % find only the non-zero values
      % and only those less than the condition value
      rnk = sum((S(1) ./ S(find(S))) <= GUI.Condition);

    case 'Energy'

      cS= cumsum(diag(S).^2); % cumulative energy
      rnk = sum((cS ./ cS(end)) <= GUI.Energy);

    case 'Tikhonov' % just keep all of the columns, to within tolerance
      % Tikhonov regularization, keeps non-null space
      %what's its rank? Assume more rows than columns
      tol = size(U,1) * S(1) * eps;
      rnk = sum(diag(S) > tol);

    case 'None'

      %what's its rank? Assume more rows than columns
      tol = size(U,1) * S(1) * eps;
      rnk = sum(diag(S) > tol);

    otherwise

      error(sprintf('Unknown regularization method: %s',GUI.REG))

    end % regularization switch

    SubSpace = U(:,1:rnk);

    return

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