Mercurial > octave-nkf
view scripts/optimization/lsqnonneg.m @ 7682:f7474c83c782
lsqnonneg: new function
author | bill@denney.ws |
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date | Tue, 01 Apr 2008 00:29:51 -0400 |
parents | |
children | 0bdfff62cc49 |
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## Copyright (C) 2008 Bill Denney ## ## 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 ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{x} =} lsqnonneg (@var{c}, @var{d}) ## @deftypefnx {Function File} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0}) ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}] =} lsqnonneg (@dots{}) ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}] =} lsqnonneg (@dots{}) ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}] =} lsqnonneg (@dots{}) ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}] =} lsqnonneg (@dots{}) ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}, @var{lambda}] =} lsqnonneg (@dots{}) ## Minimize @code{norm (@var{c}*@var{x}-d)} subject to @code{@var{x} >= ## 0}. @var{c} and @var{d} must be real. @var{x0} is an optional ## initial guess for @var{x}. ## ## Outputs: ## @itemize @bullet ## @item resnorm ## ## The squared 2-norm of the residual: norm(@var{c}*@var{x}-@var{d})^2 ## @item residual ## ## The residual: @var{d}-@var{c}*@var{x} ## @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} ## @end deftypefn ## This is implemented from Lawson and Hanson's 1973 algorithm on page function [x, resnorm, residual, exitflag, output, lambda] = lsqnonneg (c, d, x = [], options = []) if (isempty (x)) ## initial guess is 0s x = zeros (columns (c), 1); endif if (isempty (options)) ## FIXME: Optimset should be updated ## options = optimset (); options = struct ("maxiter", 1e5, "tolx", 1e-8); endif ## Initialize the values p = []; z = 1:numel (x); ## compute the gradient w = c'*(d - c*x); iter = 0; while (! isempty (z) && any (w(z) > 0) && iter < options.maxiter) idx = find (w == max (w)); if (numel (idx) > 1) warning ("lsqnonneg:nonunique", "A non-unique solution may be returned due to equal gradients."); idx = idx(1); endif p(end+1) = z(idx); z(idx) = []; newx = false; while (! newx && iter < options.maxiter) iter++; cpos = c; cpos(:,z) = 0; ## find min norm solution to the positive matrix [cpos_q, cpos_r] = qr (cpos, 0); xtmp = (cpos_r\cpos_q')*d; xtmp(z) = 0; if (all (xtmp >= 0)) ## complete the inner loop newx = true; x = xtmp; else mask = (xtmp < 0); alpha = min(x(mask)./(x(mask) - xtmp(mask))); x = x + alpha*(xtmp - x); idx = find (x == 0); p(ismember (p, x)) = []; z = [z idx]; endif endwhile w = c'*(d - c*x); endwhile ## generate the additional output arguments if (nargout > 1) resnorm = norm (C*x-d) ^ 2; endif if (nargout > 2) residual = d-C*x; endif exitflag = iter; if (nargout > 3 && iter >= options.maxiter) exitflag = 0; endif if (nargout > 4) output = struct ("algorithm", "nnls", "iterations", iter); endif if (nargout > 5) ## FIXME error ("lsqnonneg: lambda is not yet implemented"); endif endfunction ## Tests %!test %! C = [1 0;0 1;2 1]; %! d = [1;3;-2]; %! assert (lsqnonneg (C, d), [0;0.5], 100*eps) %!test %! C = [0.0372 0.2869;0.6861 0.7071;0.6233 0.6245;0.6344 0.6170]; %! d = [0.8587;0.1781;0.0747;0.8405]; %! xnew = [0;0.6929]; %! assert (lsqnonneg (C, d), xnew, 0.0001)