Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / optim-1.2.0 / cpiv_bard.m

diff --git a/octave_packages/optim-1.2.0/cpiv_bard.m b/octave_packages/optim-1.2.0/cpiv_bard.m
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+%% Copyright (C) 2010, 2011 Olaf Till <i7tiol@t-online.de>
+%%
+%% 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 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/>.
+
+%% [lb, idx, ridx, mv] = cpiv_bard (v, m[, incl])
+%%
+%% v: column vector; m: matrix; incl (optional): index. length (v)
+%% must equal rows (m). Finds column vectors w and l with w == v + m *
+%% l, w >= 0, l >= 0, l.' * w == 0. Chooses idx, w, and l so that
+%% l(~idx) == 0, l(idx) == -inv (m(idx, idx)) * v(idx), w(idx) roughly
+%% == 0, and w(~idx) == v(~idx) + m(idx, ~idx).' * l(idx). idx indexes
+%% at least everything indexed by incl, but l(incl) may be < 0. lb:
+%% l(idx) (column vector); idx: logical index, defined above; ridx:
+%% ~idx & w roughly == 0; mv: [m, v] after performing a Gauss-Jordan
+%% 'sweep' (with gjp.m) on each diagonal element indexed by idx.
+%% Except the handling of incl (which enables handling of equality
+%% constraints in the calling code), 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.).
+
+function [lb, idx, ridx, m] = cpiv_bard (v, m, incl)
+
+  n = length (v);
+  if (n > size (v, 1))
+    error ('first argument is no column vector'); % the most typical mistake
+  end
+  if (nargin < 3)
+    incl = [];
+  elseif (islogical (incl))
+    incl = find (incl);
+  end
+  nincl = 1:n;
+  nincl(incl) = [];
+  sgn = ones (n, 1);
+  if (length (incl) == n)
+    sgn = - sgn;
+    m = inv (m);
+    m = cat (2, m, m * v);
+  else
+    m = cat (2, m, v);
+    for id = incl(:).'
+      sgn(id) = -sgn(id);
+      m = gjp (m, id);
+    end
+  end
+  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
+  if (isempty (nincl))
+    ready = true;
+  else
+    ready = false;
+    while (~ready && nl > 0)
+      [vm, idm] = min (sgn(nincl) .* m(nincl, end));
+      if (vm >= -nz)
+       ready = true;
+      else
+       idm = nincl(idm);
+       sgn(idm) = -sgn(idm);
+       m = gjp (m, idm);
+       nl = nl - 1;
+      end
+    end
+  end
+  if (~ready)
+    error ('not successful');
+  end
+  idx = sgn < 0;
+  lb = -m(idx, end);
+  ridx = ~idx & abs (m(:, end)) <= nz;