computeProjectionFromConstraint

 compute projection to reduced space with given constraint matrix

 THIS FUNCTION IS NO USER FUNCTION.

• computeExtremePointsOfCone calculate the extreme points of degenerated cones

0001 function projectToReduced = computeProjectionFromConstraint(...
0002     constraintMatrix, zerotol)
0003 % compute projection to reduced space with given constraint matrix
0004 %
0005 % THIS FUNCTION IS NO USER FUNCTION.
0006 
0007 % The elk-library: convex geometry applied to crystallization modeling.
0008 %   Copyright (C) 2012 Alexander Reinhold
0009 %
0010 % This program is free software: you can redistribute it and/or modify it
0011 %   under the terms of the GNU General Public License as published by the
0012 %   Free Software Foundation, either version 3 of the License, or (at your
0013 %   option) any later version.
0014 %
0015 % This program is distributed in the hope that it will be useful, but
0016 %   WITHOUT ANY WARRANTY; without even the implied warranty of
0017 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0018 %   General Public License for more details.
0019 %
0020 % You should have received a copy of the GNU General Public License along
0021 %   with this program.  If not, see <http://www.gnu.org/licenses/>.
0022 
0023 [~, S, V] = svd(constraintMatrix);
0024 if size(S, 1) == 1
0025     reducedDimension = double(S(1) == 0);
0026 else
0027     S(isZero(S(:), zerotol)) = 0;
0028     reducedDimension = sum(diag(S) == 0);
0029 end
0030 projectToReduced = V(:, (end-reducedDimension+1):end);
0031 
0032 end