function [B,KeepVar] = RemoveRedundantColumns(A)
% RemoveRedundantColumns: Removes those columns of a matrix that are zero
%
% USAGE:
%
%       B = RemoveRedundantColumns(A)
%
% REQUIRED INPUT:  A (nxs) matrix with s<=n and with rank k. Here k<s if and only if A has some zero columns.
%
% REQUIRED OUTPUT: B (nxk) with only the columns of of A that are non-zero.
%
%                  KeepVar (1xk) vector with the column number of A the are used to create B.
%
%
%                       Written by: Anders Warne
%                                   New Area Wide Model Project
%                                   DG-R/EMO
%                                   European Central Bank (ECB)
%                                   Email: anders.warne@ecb.europa.eu
%                                   Copyright © 2006-2009 European Central Bank.
%
%                       First version: October 18, 2006.
%                        This version: January 21, 2009.
%
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%
% LICENSE INFORMATION:
%
%      YADA is free software: you can redistribute it and/or modify
%      it under the terms of the GNU General Public License as published by
%      the Free Software Foundation, either version 3 of the License, or
%      (at your option) any later version.
%
%      This program is distributed in the hope that it will be useful,
%      but WITHOUT ANY WARRANTY; without even the implied warranty of
%      MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%      GNU General Public License for more details.
%
%      You should have received a copy of the GNU General Public License
%      along with this program.  If not, see <http://www.gnu.org/licenses/>.
%
%      YADA is released under the GNU General Public License, Version 3,
%      29 June 2007 <http://www.gnu.org/licenses/>. The current release of
%      the program was last modified by the ECB on the "This version" date
%      above.
%
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%
% CHANGELOG:
%
% * 14-11-2006: Added the output variable KeepVar.
%
% * 13-11-2007: Updated the documentation.
%
% * 23-5-2008:  Updated the documentation.
%
% * 21-01-2009: Updated the documentation.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%

if rank(A)==min(size(A));
   B = A;
   KeepVar = (1:1:size(A,2));
   return;
end;
B = [];
KeepVar = [];
for i=1:size(A,2);
   if sum(abs(A(:,i)))>eps;
      B = [B A(:,i)];
      KeepVar = [KeepVar i];
   end;
end;

%
% end of RemoveRedundantColumns.m
%
