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gjp.m

%% 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 m = gjp (m, k, l)

  %% 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.

  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;

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