%% Copyright (C) 2010 Olaf Till %% %% This program 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. %% %% 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, write to the Free Software %% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307USA function [lb, idx] = cpiv (v, m) %% [lb, idx] = cpiv (v, m) %% %% v: column vector; m: matrix. length (v) must equal rows (m). m must %% be positive definit, which is not be explicitely checked. Finds %% column vectors w and l with w == v + m * l, w >= 0, l >= 0, l.' * w %% == 0. lb: column vector of components of l for which the %% corresponding components of w are zero; idx: logical index of these %% components in l. This is called solving the 'complementary pivot %% problem' (Cottle, R. W. and Dantzig, G. B., 'Complementary pivot %% theory of mathematical programming', Linear Algebra and Appl. 1, %% 102--125. References for the current algorithm: Bard, Y.: Nonlinear %% Parameter Estimation, p. 147--149, Academic Press, New York and %% London 1974; Bard, Y., 'An eclectic approach to nonlinear %% programming', Proc. ANU Sem. Optimization, Canberra, Austral. Nat. %% Univ.). n = length (v); if (n > size (v, 1)) error ('first argument is no column vector'); % the most typical mistake end m = cat (2, m, v); id = ones (n, 1); nz = -eps; % This is arbitrary; components of w and -l are regarded as % non-negative if >= nz. nl = 100 * n; % maximum number of loop repeats, after that give up ready = false; while (~ ready && nl > 0) [vm, idm] = min (id .* m(:, end)); if (vm >= nz) ready = true; else id(idm) = -id(idm); m = gjp (m, idm); nl = nl - 1; end end if (~ ready) error ('not successful'); end idx = id < 0; lb = -m(idx, end);

Generated by Doxygen 1.6.0 Back to index