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# cross_mat

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

### Function Synopsis

    CrossMat = cross_mat(A);

### Help Text

    CROSS_MAT - Sparse cross product matrix good for matrix equivalent operation
     function CrossMat = cross_mat(A);
     A comprises three dimensional vectors (row or column, preferably column).
     Result is sparse block diagonal matrix, suitable for cross products.

     Let B be the same size as A and both oriented as 3 x M.
      tmp = B(:);
      cross_product = reshape(full(CrossMat*tmp),3,M);
     Each column of cross_product corresponds to the cross product of the
     corresponding columns in A and B.

### Cross-Reference Information

This function calls

    blk_diag                           C:\BrainStorm_2001\Toolbox\blk_diag.m
    mby3check                          C:\BrainStorm_2001\Toolbox\mby3check.m

This function is called by

    os_meg                             C:\BrainStorm_2001\Toolbox\os_meg.m

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

    function CrossMat = cross_mat(A);
    %CROSS_MAT - Sparse cross product matrix good for matrix equivalent operation
    % function CrossMat = cross_mat(A);
    % A comprises three dimensional vectors (row or column, preferably column).
    % Result is sparse block diagonal matrix, suitable for cross products.
    %
    % Let B be the same size as A and both oriented as 3 x M.
    %  tmp = B(:);
    %  cross_product = reshape(full(CrossMat*tmp),3,M);
    % Each column of cross_product corresponds to the cross product of the
    % corresponding columns in A and B.

    %<autobegin> ---------------------- 26-May-2004 11:29:55 -----------------------
    % --------- Automatically Generated Comments Block Using AUTO_COMMENTS ---------
    %
    % CATEGORY: Utility - Numeric
    %
    % Alphabetical list of external functions (non-Matlab):
    %   toolbox\blk_diag.m
    %   toolbox\mby3check.m
    %
    % At Check-in: $Author: Mosher $  $Revision: 13 $  $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 11:29:55 -----------------------

    % ----------------------------- Script History ---------------------------------
    % September 6, 1995 author
    % JCM 19-May-2004  Comments cleaning
    % ----------------------------- Script History ---------------------------------

    A = mby3check(A);        % check and convert to 3 by M

    mA = size(A,2);         % how many vecs?

    CrossMat = zeros(3,mA*3);    % three by three per vector
    CrossMat(1,2:3:(mA*3)) = -A(3,:); % the z-component
    CrossMat(1,3:3:(mA*3)) = A(2,:); % the y-component
    CrossMat(2,3:3:(mA*3)) = -A(1,:); % the x-component
    CrossMat = blk_diag(CrossMat,3); % make block diagonal
    CrossMat = CrossMat - CrossMat'; % fill in anti-symmetric part

    return

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