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# hrow_linear

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

### Function Synopsis

    Hi = hrow_linear(colp,PP,v,yset,yset_mag,geometry,nodes,cdvdiff,N,area2)

### Help Text

    HROW_LINEAR - Compute row in BEM geometry matrix for linear collocation
     function Hi = hrow_linear(colp,PP,v,yset,yset_mag,geometry,nodes,cdvdiff,N,area2)
     compute a row of the H matrix(1 by no_node) for linear BEM
     formula in:
     de Munck, IEEE Trans.BME, pp986-990,1992
     or schlitt et al, IEEE Trans, BME, pp52-58, 1995
     some global variables

### Cross-Reference Information

This function calls

    crossprod                          C:\BrainStorm_2001\Toolbox\crossprod.m
    dotprod                            C:\BrainStorm_2001\Toolbox\dotprod.m

This function is called by

    bem_xfer                           C:\BrainStorm_2001\Toolbox\bem_xfer.m
    kl_galerkin                        C:\BrainStorm_2001\Toolbox\kl_galerkin.m

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

    function Hi = hrow_linear(colp,PP,v,yset,yset_mag,geometry,nodes,cdvdiff,N,area2)
    %HROW_LINEAR - Compute row in BEM geometry matrix for linear collocation
    % function Hi = hrow_linear(colp,PP,v,yset,yset_mag,geometry,nodes,cdvdiff,N,area2)
    % compute a row of the H matrix(1 by no_node) for linear BEM
    % formula in:
    % de Munck, IEEE Trans.BME, pp986-990,1992
    % or schlitt et al, IEEE Trans, BME, pp52-58, 1995
    % some global variables
    %

    %<autobegin> ---------------------- 26-May-2004 11:30:41 -----------------------
    % --------- Automatically Generated Comments Block Using AUTO_COMMENTS ---------
    %
    % CATEGORY: Forward Modeling
    %
    % Alphabetical list of external functions (non-Matlab):
    %   toolbox\crossprod.m
    %   toolbox\dotprod.m
    %
    % At Check-in: $Author: Mosher $  $Revision: 14 $  $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 11:30:41 -----------------------

    % History -------------------------------
    % JCM 08-Sep-2003 Commenting
    % ---------------------------------------

    no_elt = size(geometry,1);
    no_node = size(nodes,1);
    Hi = zeros(1,no_node);
    Y = [nodes(:,1)-colp(1),nodes(:,2)-colp(2),nodes(:,3)-colp(3)];
    MAGY2  = (sum((Y.*Y)'))';
    MAGY = sqrt(MAGY2);
    y1 = Y(geometry(v,1),:);
    y2 = Y(geometry(v,2),:);
    y3 = Y(geometry(v,3),:);

    magy2 = [MAGY2(geometry(v,1)),MAGY2(geometry(v,2)),MAGY2(geometry(v,3))];
    magy2(magy2 == 0) = eps*min(abs(magy2(magy2 ~= 0))); % SB: Divide by or Log of Zeros issues
    magy = [MAGY(geometry(v,1)),MAGY(geometry(v,2)),MAGY(geometry(v,3))];
    magy(magy == 0) = eps*min(abs(magy(magy ~= 0))); % SB: Divide by or Log of Zeros issues

    %cp = [(cross(y2',y3'))',(cross(y3',y1'))',(cross(y1',y2'))'];  %je 4/20/00
    cp = [(crossprod(y2,y3)),(crossprod(y3,y1)),(crossprod(y1,y2))];

    %  solid angle
    %dp = [(dot(y2',y3'))',(dot(y3',y1'))',(dot(y1',y2'))'];  %je 4/20/00
    dp = [(dotprod(y2,y3)),(dotprod(y3,y1)),(dotprod(y1,y2))];

    sangle =  2*atan2(dotprod(y1,cp(:,1:3)) , ...
                      magy(:,1).*(magy(:,2).*magy(:,3)+dp(:,1)) +...
                      magy(:,2).*dp(:,2) +...
                      magy(:,3).*dp(:,3) );

    OMEGA = zeros(length(v),3);  % compute omegabar eq.(A.10) in Schlitt

    % Schlitt (A11)
    gammap =log( ( yset_mag(v,1).*magy(:,2)+magy2(:,2)-dp(:,3))./...
       ( yset_mag(v,1).* magy(:,1) + dp(:,3)-magy2(:,1) +eps*min(yset_mag(v,1)~=0)))./yset_mag(v,1);
    OMEGA = OMEGA -  yset(v,1:3).*[gammap,gammap,gammap];
    gammap =log( ( yset_mag(v,2).*magy(:,3)+magy2(:,3)-dp(:,1))./...
       ( yset_mag(v,2).* magy(:,2) + dp(:,1)-magy2(:,2) +eps*min(yset_mag(v,2)~=0)))./yset_mag(v,2);
    OMEGA = OMEGA -  yset(v,4:6).*[gammap,gammap,gammap];
    gammap =log( ( yset_mag(v,3).*magy(:,1)+magy2(:,1)-dp(:,2))./...
       ( yset_mag(v,3).* magy(:,3) + dp(:,2)-magy2(:,3) +eps*min(yset_mag(v,3)~=0)))./yset_mag(v,3); % eps*... here to avoid "divide by zero" messages
    OMEGA = OMEGA -  yset(v,7:9).*[gammap,gammap,gammap];

    beta = dotprod(N(v,:),y1);    %Schlitt (A1)

    % see schlitt (A8), 2*area is absorbed into P matrix
    h = zeros(no_elt,3);
    h(v,1)= dotprod(N(v,:), cp(:,1:3)).*sangle+ ...
                beta .*dotprod(-yset(v,4:6),OMEGA) ;
    h(v,2)= dotprod(N(v,:), cp(:,4:6)).*sangle+ ...
                beta .*dotprod(-yset(v,7:9),OMEGA) ;
    h(v,3)= dotprod(N(v,:), cp(:,7:9)).*sangle+ ...
                beta .*dotprod(-yset(v,1:3),OMEGA) ;

    Hi =  (PP*[h(:,1);h(:,2); h(:,3)])' .* cdvdiff';
    return

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