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# gain_interp

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

### Function Synopsis

    [Ginterp] = gain_interp(Rq,bem_gaingrid_mfname)

### Help Text

    GAIN_INTERP - Gain matrix interpolation from a set of pre-computed forward fields defined over grid points in 3D space
     function [Ginterp] = gain_interp(Rq,bem_gaingrid_mfname)
      FORWARD MODEL CALCULATION USING 3-D INTERPOLATION ON A PRE-COMPUTED GRID
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

      FORWARD MODEL CALCULATION USING 3-D INTERPOLATION ON A PRE-COMPUTED GRID

     This program computes the (voltage potential)/(radial magnetic field component)
     forward gain matrix for an array of (EEG electrodes)/(MEG magnetometers)
     interpolating between pre-computed forward model solution points on a densely sampled grid.
     The grid sampling and associated BEM solution are pre-computed using external programs.

     INPUTS: (Required)

      Rq: dipole locations in subjectsc coordinate system (meters)                 (P x 3)

      bem_gaingrid_mfname: ".mat" filename which contains the set of
                           3-D grid points, variables indicating sampling
                           density and the associated pre-computed forward
                           model solution.                                    (char string)

     OUTPUTS:
                  Ginterp: Forward Gain Solution determined via 3-D
                           interpolation between 8 adjacent grid points    (M x 3P)

       John Ermer 03/18/00 (Initial Version)
       John Ermer 03/21/00 (Optimization of code)
       John Ermer 03/22/00 (Addition of Persistent Variables)
       John Ermer 05/21/00 (Added output of Sensor Positions)
       SB 04/04/2001 (Management of unused entries of the gaingrid matrix )
       SB 07-03-2003 Major update and code and creation of gain_interp from John Ermer's bem_gain_interp2
                     Implementation of inverse-distance weighted interpolation using Shepards method
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

### Cross-Reference Information

This function calls

    dip                                C:\BrainStorm_2001\Toolbox\dip.m
    norlig                             C:\BrainStorm_2001\Toolbox\norlig.m

This function is called by

    eeg_bem                            C:\BrainStorm_2001\Toolbox\eeg_bem.m
    meg_bem                            C:\BrainStorm_2001\Toolbox\meg_bem.m

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

    function [Ginterp] = gain_interp(Rq,bem_gaingrid_mfname)
    %GAIN_INTERP - Gain matrix interpolation from a set of pre-computed forward fields defined over grid points in 3D space
    % function [Ginterp] = gain_interp(Rq,bem_gaingrid_mfname)
    %  FORWARD MODEL CALCULATION USING 3-D INTERPOLATION ON A PRE-COMPUTED GRID
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %
    %  FORWARD MODEL CALCULATION USING 3-D INTERPOLATION ON A PRE-COMPUTED GRID
    %
    % This program computes the (voltage potential)/(radial magnetic field component)
    % forward gain matrix for an array of (EEG electrodes)/(MEG magnetometers)
    % interpolating between pre-computed forward model solution points on a densely sampled grid.
    % The grid sampling and associated BEM solution are pre-computed using external programs.
    %
    % INPUTS: (Required)
    %
    %  Rq: dipole locations in subjectsc coordinate system (meters)                 (P x 3)
    %
    %
    %  bem_gaingrid_mfname: ".mat" filename which contains the set of
    %                       3-D grid points, variables indicating sampling
    %                       density and the associated pre-computed forward
    %                       model solution.                                    (char string)
    %
    % OUTPUTS:
    %              Ginterp: Forward Gain Solution determined via 3-D
    %                       interpolation between 8 adjacent grid points    (M x 3P)
    %
    %   John Ermer 03/18/00 (Initial Version)
    %   John Ermer 03/21/00 (Optimization of code)
    %   John Ermer 03/22/00 (Addition of Persistent Variables)
    %   John Ermer 05/21/00 (Added output of Sensor Positions)
    %   SB 04/04/2001 (Management of unused entries of the gaingrid matrix )
    %   SB 07-03-2003 Major update and code and creation of gain_interp from John Ermer's bem_gain_interp2
    %                 Implementation of inverse-distance weighted interpolation using Shepards method
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    %<autobegin> ---------------------- 26-May-2004 11:30:18 -----------------------
    % --------- Automatically Generated Comments Block Using AUTO_COMMENTS ---------
    %
    % CATEGORY: Forward Modeling
    %
    % Alphabetical list of external functions (non-Matlab):
    %   toolbox\norlig.m
    %
    % At Check-in: $Author: Mosher $  $Revision: 10 $  $Date: 5/26/04 9:59a $
    %
    % 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 11:30:18 -----------------------

    load(bem_gaingrid_mfname);  % Load Pre-computed Fwd Gain Matrix
    load(bem_grid_mfname); % load associated grid point locations

    GBEM_grid( find(isnan(GBEM_grid(:,1))) ,: ) = [];  % Remove unused entries (for MEG reference channels and EEG reference)

    M = size(GBEM_grid,1);             % Number of sensors
    P = size(Rq,1);                    % Number of dipole locations

    if size(Rq,1) > 100
        hw = waitbar(0,'Forward field interpolation in progress. . .');
    end

    Ginterp = zeros(size(GBEM_grid,1),3*size(Rq,1));

    for dip = 1:size(Rq,1)
        if ~rem(dip,200) & exist('hw','var')
            waitbar(dip/size(Rq,1),hw)
        end

        % For each dipole - compute trilinear interpolation
        dist2grid = norlig(Rq_bemgrid - repmat(Rq(dip,:), size(Rq_bemgrid,1),1));
        [dist2grid isort] = sort(dist2grid);
        icube = isort(1:8); % Take 8 closest neightbors
        dist2cube = dist2grid(1:8);
        clear dist2grid isort
        %     cube = [Rq_bemgrid(icube,:) - repmat(Rq_bemgrid(icube(1),:),8,1)];
        %     dippos = Rq(dip,:) - Rq_bemgrid(icube(1),:);
        %     dist2cube = norlig(cube - repmat(dippos, 8,1))+eps;

        R = max(dist2cube);
        W = power((R - dist2cube)./ (R*dist2cube),2); % Interpolation weights from Shepards method
        W = W/sum(W);

        for k = 1:length(W)-1 % length(W)-1 because W(end) = 0 by construction.
            Ginterp(:,3*(dip-1)+1) = Ginterp(:,3*(dip-1)+1) + W(k) * GBEM_grid(:,3*(icube(k)-1)+1) ;
            Ginterp(:,3*(dip-1)+2) = Ginterp(:,3*(dip-1)+2) + W(k) * GBEM_grid(:,3*(icube(k)-1)+2) ;
            Ginterp(:,3*(dip-1)+3) = Ginterp(:,3*(dip-1)+3) + W(k) * GBEM_grid(:,3*(icube(k)-1)+3) ;
        end

    end

    if exist('hw','var')
        close(hw)
    end

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