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# overlapping_sphere_fmins

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

### Function Synopsis

    [err,SphereSc,Radius] = overlapping_sphere_fmins(X,TrueSc,Loc,Orient,Weight,Vertices);

### Help Text

    OVERLAPPING_SPHERE_FMINS - for use with OVERLAPPING_SPHERE
     function [err,SphereSc,Radius] = overlapping_sphere_fmins(X,TrueSc,Loc,Orient,Weight,Vertices);
     calculate the error between true and estimated weighting scalars

### Cross-Reference Information

This function calls

    colnorm                            C:\BrainStorm_2001\Toolbox\colnorm.m
    weighting_scalar                   C:\BrainStorm_2001\Toolbox\weighting_scalar.m

This function is called by

    overlapping_sphere                 C:\BrainStorm_2001\Toolbox\overlapping_sphere.m

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

    function [err,SphereSc,Radius] = overlapping_sphere_fmins(X,TrueSc,Loc,Orient,Weight,Vertices);
    %OVERLAPPING_SPHERE_FMINS - for use with OVERLAPPING_SPHERE
    % function [err,SphereSc,Radius] = overlapping_sphere_fmins(X,TrueSc,Loc,Orient,Weight,Vertices);
    % calculate the error between true and estimated weighting scalars

    %<autobegin> ---------------------- 26-May-2004 11:34:04 -----------------------
    % --------- Automatically Generated Comments Block Using AUTO_COMMENTS ---------
    %
    % CATEGORY: Forward Modeling
    %
    % Alphabetical list of external functions (non-Matlab):
    %   toolbox\colnorm.m
    %   toolbox\weighting_scalar.m
    %
    % 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 11:34:04 -----------------------

    % John C. Mosher, Ph.D. See Copyright.m file for information
    %
    % $Date: 5/26/04 10:02a $ $Revision: 12 $

    Center = X(1:3);
    Radius = X(4);
    N = size(Vertices,2); % number of vertices
    OneN = ones(1,N); % convenient vector of ones

    % two cases here. 'Scalar' attempts to fit the weighting scalar function between
    %  the true surface and the spherical surface. The problem is a strong dependency
    %  on surface normals that appears to skew the spheres. Theoretical assumption flaw
    %  may be that the fictitious currents are not that similar.
    %  'Weights' instead simply fits a sphere to the vertices, but uses the Scalar function
    %  to weight the least-squares fit.
    %  Need to test more formally

    % leave one uncommented:
    %switch 'Scalar'
    switch 'Weights'

    case 'Scalar'

      % First synthesize the normals as vectors passing from the center through the vertices
      [ignore,Normals] = colnorm(Vertices - Center(:,OneN));

      % then synthesize vertices as points on the sphere
      Vertices = Radius * Normals + Center(:,OneN);

      % now calculate the weighting scalar to the sphere points
      SphereSc = weighting_scalar(Loc,Orient,Weight,Vertices,Normals);

      % now calculate the least-squares error between the two scalar sets
      err = sum((TrueSc - SphereSc).^2);

    case 'Weights'

      % Scale the true scalar to be a weighting function
      Weights = abs(TrueSc)/sum(abs(TrueSc)); % don't care about sign.

      % extracted from sphererr.m
      b = Vertices - Center(:,OneN);  % data - estimated center

      % form distances to center estimate
      b = sqrt(sum(b.^2))'; % col vector of distances
      r = sum(b.*Weights); % average distance weighted by Scalar

      % squared error, weighted by scalars
      err = ((b-r).*Weights).^2; % squared error between distances and sphere
      % map for informative purposes
      SphereSc = err;
      err = sum(err); % sum squared error

      Radius = r; % overrides what the user sent

    end

    return

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