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function s = Urrextrapolation(X)
% s = Urrextrapolation(X)
% RRE vector extrapolation see
% Smith, Ford & Sidi SIREV 29 II 06/1987
% This file is part of
%
% SECS2D - A 2-D Drift--Diffusion Semiconductor Device Simulator
% -------------------------------------------------------------------
% Copyright (C) 2004-2006 Carlo de Falco
%
%
%
% SECS2D 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 2 of the License, or
% (at your option) any later version.
%
% SECS2D 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 SECS2D; If not, see <http://www.gnu.org/licenses/>.
if (Ucolumns(X)>Urows(X))
X=X';
end
% compute first and second variations
U = X(:,2:end) - X(:,1:end-1);
V = U(:,2:end) - U(:,1:end-1);
% eliminate unused u_k column
U(:,end) = [];
s = X(:,1) - U * pinv(V) * U(:,1);
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