Mercurial > octave-nkf
view scripts/optimization/lsqnonneg.m @ 20613:647db46ad754
eliminate more simple uses of error_state
* audioread.cc: Eliminate simple uses of error_state.
author | John W. Eaton <jwe@octave.org> |
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date | Thu, 08 Oct 2015 17:41:21 -0400 |
parents | 83792dd9bcc1 |
children |
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## Copyright (C) 2008-2015 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 ## <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} =} lsqnonneg (@var{c}, @var{d}, @var{x0}, @var{options}) ## @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}. ## ## Currently, @code{lsqnonneg} recognizes these options: @qcode{"MaxIter"}, ## @qcode{"TolX"}. For a description of these options, see ## @ref{XREFoptimset,,optimset}. ## ## 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 @qcode{"algorithm"}: The algorithm used (@qcode{"nnls"}) ## ## @item @qcode{"iterations"}: The number of iterations taken. ## @end itemize ## ## @item lambda ## ## Not implemented. ## @end itemize ## @seealso{optimset, pqpnonneg, lscov} ## @end deftypefn ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. ## PKG_ADD: [~] = __all_opts__ ("lsqnonneg"); ## This is implemented from Lawson and Hanson's 1973 algorithm on page ## 161 of Solving Least Squares Problems. function [x, resnorm, residual, exitflag, output, lambda] = lsqnonneg (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 (isempty (x)) ## Initial guess is 0s. x = zeros (n, 1); else ## ensure nonnegative guess. x = max (x, 0); endif useqr = m >= n; max_iter = optimget (options, "MaxIter", 1e5); ## Initialize P, according to zero pattern of x. p = find (x > 0).'; if (useqr) ## Initialize the QR factorization, economized form. [q, r] = qr (c(:,p), 0); endif 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 (useqr) xtmp = r \ q'*d; else xtmp = c(:,p) \ d; 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 (useqr) ## update the QR factorization. [q, r] = qrdelete (q, r, idx); endif endif endwhile ## compute the gradient. w = c'*(d - c*x); w(p) = []; tolx = optimget (options, "TolX", 10*eps*norm (c, 1)*length (c)); if (! any (w > tolx)) if (useqr) ## verify the solution achieved using qr updating. ## in the best case, this should only take a single step. useqr = false; continue; else ## we're finished. break; endif endif ## find the maximum gradient. 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 ## 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 (useqr) ## insert the column into the QR factorization. [q, r] = qrinsert (q, r, jdx, c(:,zidx)); endif endwhile ## LH12: complete. ## 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 >= max_iter) exitflag = 0; endif if (nargout > 4) output = struct ("algorithm", "nnls", "iterations", iter); endif if (nargout > 5) lambda = zeros (size (x)); lambda(p) = w; endif endfunction %!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);