Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/optim-1.2.0/gjp.m b/octave_packages/optim-1.2.0/gjp.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/>.
+
+%% m = gjp (m, k[, l])
+%%
+%% m: matrix; k, l: row- and column-index of pivot, l defaults to k.
+%%
+%% Gauss-Jordon pivot as defined in Bard, Y.: Nonlinear Parameter
+%% Estimation, p. 296, Academic Press, New York and London 1974. In
+%% the pivot column, this seems not quite the same as the usual
+%% Gauss-Jordan(-Clasen) pivot. Bard gives Beaton, A. E., 'The use of
+%% special matrix operators in statistical calculus' Research Bulletin
+%% RB-64-51 (1964), Educational Testing Service, Princeton, New Jersey
+%% as a reference, but this article is not easily accessible. Another
+%% reference, whose definition of gjp differs from Bards by some
+%% signs, is Clarke, R. B., 'Algorithm AS 178: The Gauss-Jordan sweep
+%% operator with detection of collinearity', Journal of the Royal
+%% Statistical Society, Series C (Applied Statistics) (1982), 31(2),
+%% 166--168.
+
+function m = gjp (m, k, l)
+
+  if (nargin < 3)
+    l = k;
+  end
+
+  p = m(k, l);
+
+  if (p == 0)
+    error ('pivot is zero');
+  end
+
+  %% This is a case where I really hate to remain Matlab compatible,
+  %% giving so many indices twice.
+  m(k, [1:l-1, l+1:end]) = m(k, [1:l-1, l+1:end]) / p; % pivot row
+  m([1:k-1, k+1:end], [1:l-1, l+1:end]) = ... % except pivot row and col
+      m([1:k-1, k+1:end], [1:l-1, l+1:end]) - ...
+      m([1:k-1, k+1:end], l) * m(k, [1:l-1, l+1:end]);
+  m([1:k-1, k+1:end], l) = - m([1:k-1, k+1:end], l) / p; % pivot column
+  m(k, l) = 1 / p;