/usr/share/octave/packages/optim-1.3.0/cpiv_bard.m is in octave-optim 1.3.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 | ## Copyright (C) 2010-2013 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
endif
if (nargin < 3)
incl = [];
elseif (islogical (incl))
incl = find (incl);
endif
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);
endfor
endif
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;
endif
endwhile
endif
if (~ready)
error ("not successful");
endif
idx = sgn < 0;
lb = -m(idx, end);
ridx = ~idx & abs (m(:, end)) <= nz;
endfunction
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