X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?a=blobdiff_plain;f=octave_packages%2Fm%2Foptimization%2Fpqpnonneg.m;fp=octave_packages%2Fm%2Foptimization%2Fpqpnonneg.m;h=3b6a8f21ddc4135ccaefc5c89c1fd1b5f11ea4c8;hb=1c0469ada9531828709108a4882a751d2816994a;hp=0000000000000000000000000000000000000000;hpb=63de9f36673d49121015e3695f2c336ea92bc278;p=CreaPhase.git diff --git a/octave_packages/m/optimization/pqpnonneg.m b/octave_packages/m/optimization/pqpnonneg.m new file mode 100644 index 0000000..3b6a8f2 --- /dev/null +++ b/octave_packages/m/optimization/pqpnonneg.m @@ -0,0 +1,211 @@ +## Copyright (C) 2008-2012 Bill Denney +## Copyright (C) 2008 Jaroslav Hajek +## Copyright (C) 2009 VZLU Prague +## +## This file is part of Octave. +## +## Octave 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. +## +## Octave 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 Octave; see the file COPYING. If not, see +## . + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{x} =} pqpnonneg (@var{c}, @var{d}) +## @deftypefnx {Function File} {@var{x} =} pqpnonneg (@var{c}, @var{d}, @var{x0}) +## @deftypefnx {Function File} {[@var{x}, @var{minval}] =} pqpnonneg (@dots{}) +## @deftypefnx {Function File} {[@var{x}, @var{minval}, @var{exitflag}] =} pqpnonneg (@dots{}) +## @deftypefnx {Function File} {[@var{x}, @var{minval}, @var{exitflag}, @var{output}] =} pqpnonneg (@dots{}) +## @deftypefnx {Function File} {[@var{x}, @var{minval}, @var{exitflag}, @var{output}, @var{lambda}] =} pqpnonneg (@dots{}) +## Minimize @code{1/2*x'*c*x + d'*x} subject to @code{@var{x} >= 0}. @var{c} +## and @var{d} must be real, and @var{c} must be symmetric and positive +## definite. @var{x0} is an optional initial guess for @var{x}. +## +## Outputs: +## @itemize @bullet +## @item minval +## +## The minimum attained model value, 1/2*xmin'*c*xmin + d'*xmin +## +## @item exitflag +## +## An indicator of convergence. 0 indicates that the iteration count +## was exceeded, and therefore convergence was not reached; >0 indicates +## that the algorithm converged. (The algorithm is stable and will +## converge given enough iterations.) +## +## @item output +## +## A structure with two fields: +## @itemize @bullet +## @item "algorithm": The algorithm used ("nnls") +## +## @item "iterations": The number of iterations taken. +## @end itemize +## +## @item lambda +## +## Not implemented. +## @end itemize +## @seealso{optimset, lsqnonneg, qp} +## @end deftypefn + +## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. +## PKG_ADD: [~] = __all_opts__ ("pqpnonneg"); + +## This is analogical to the lsqnonneg implementation, which is +## implemented from Lawson and Hanson's 1973 algorithm on page +## 161 of Solving Least Squares Problems. +## It shares the convergence guarantees. + +function [x, minval, exitflag, output, lambda] = pqpnonneg (c, d, x = [], options = struct ()) + + if (nargin == 1 && ischar (c) && strcmp (c, 'defaults')) + x = optimset ("MaxIter", 1e5); + return + endif + + if (! (nargin >= 2 && nargin <= 4 && ismatrix (c) && ismatrix (d) && isstruct (options))) + print_usage (); + endif + + ## Lawson-Hanson Step 1 (LH1): initialize the variables. + m = rows (c); + n = columns (c); + if (m != n) + error ("pqpnonneg: matrix must be square"); + endif + + if (isempty (x)) + ## Initial guess is 0s. + x = zeros (n, 1); + else + ## ensure nonnegative guess. + x = max (x, 0); + endif + + max_iter = optimget (options, "MaxIter", 1e5); + + ## Initialize P, according to zero pattern of x. + p = find (x > 0).'; + ## Initialize the Cholesky factorization. + r = chol (c(p, p)); + usechol = true; + + iter = 0; + + ## LH3: test for completion. + while (iter < max_iter) + while (iter < max_iter) + iter++; + + ## LH6: compute the positive matrix and find the min norm solution + ## of the positive problem. + if (usechol) + xtmp = -(r \ (r' \ d(p))); + else + xtmp = -(c(p,p) \ d(p)); + endif + idx = find (xtmp < 0); + + if (isempty (idx)) + ## LH7: tmp solution found, iterate. + x(:) = 0; + x(p) = xtmp; + break; + else + ## LH8, LH9: find the scaling factor. + pidx = p(idx); + sf = x(pidx)./(x(pidx) - xtmp(idx)); + alpha = min (sf); + ## LH10: adjust X. + xx = zeros (n, 1); + xx(p) = xtmp; + x += alpha*(xx - x); + ## LH11: move from P to Z all X == 0. + ## This corresponds to those indices where minimum of sf is attained. + idx = idx (sf == alpha); + p(idx) = []; + if (usechol) + ## update the Cholesky factorization. + r = choldelete (r, idx); + endif + endif + endwhile + + ## compute the gradient. + w = -(d + c*x); + w(p) = []; + if (! any (w > 0)) + if (usechol) + ## verify the solution achieved using qr updating. + ## in the best case, this should only take a single step. + usechol = false; + continue; + else + ## we're finished. + break; + endif + endif + + ## find the maximum gradient. + idx = find (w == max (w)); + if (numel (idx) > 1) + warning ("pqpnonneg:nonunique", + "a non-unique solution may be returned due to equal gradients"); + idx = idx(1); + endif + ## move the index from Z to P. Keep P sorted. + z = [1:n]; z(p) = []; + zidx = z(idx); + jdx = 1 + lookup (p, zidx); + p = [p(1:jdx-1), zidx, p(jdx:end)]; + if (usechol) + ## insert the column into the Cholesky factorization. + [r, bad] = cholinsert (r, jdx, c(p,zidx)); + if (bad) + ## If the insertion failed, we switch off updates and go on. + usechol = false; + endif + endif + + endwhile + ## LH12: complete. + + ## Generate the additional output arguments. + if (nargout > 1) + minval = 1/2*(x'*c*x) + d'*x; + endif + exitflag = iter; + if (nargout > 2 && iter >= max_iter) + exitflag = 0; + endif + if (nargout > 3) + output = struct ("algorithm", "nnls-pqp", "iterations", iter); + endif + if (nargout > 4) + lambda = zeros (size (x)); + lambda(p) = w; + endif + +endfunction + +## Tests +%!test +%! C = [5 2;2 2]; +%! d = [3; -1]; +%! assert (pqpnonneg (C, d), [0;0.5], 100*eps) + +## Test equivalence of lsq and pqp +%!test +%! C = rand (20, 10); +%! d = rand (20, 1); +%! assert (pqpnonneg (C'*C, -C'*d), lsqnonneg (C, d), 100*eps)