Mercurial > octave
view scripts/optimization/lsqnonneg.m @ 29358:0a5b15007766 stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Wed, 10 Feb 2021 09:52:15 -0500 |
parents | bd51beb6205e |
children | 7854d5752dd2 |
line wrap: on
line source
######################################################################## ## ## Copyright (C) 2008-2021 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## 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 ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {@var{x} =} lsqnonneg (@var{c}, @var{d}) ## @deftypefnx {} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0}) ## @deftypefnx {} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0}, @var{options}) ## @deftypefnx {} {[@var{x}, @var{resnorm}] =} lsqnonneg (@dots{}) ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}] =} lsqnonneg (@dots{}) ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}] =} lsqnonneg (@dots{}) ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}] =} lsqnonneg (@dots{}) ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}, @var{lambda}] =} lsqnonneg (@dots{}) ## ## Minimize @code{norm (@var{c}*@var{x} - @var{d})} subject to ## @code{@var{x} >= 0}. ## ## @var{c} and @var{d} must be real matrices. ## ## @var{x0} is an optional initial guess for the solution @var{x}. ## ## @var{options} is an options structure to change the behavior of the ## algorithm (@pxref{XREFoptimset,,optimset}). @code{lsqnonneg} recognizes ## these options: @qcode{"MaxIter"}, @qcode{"TolX"}. ## ## Outputs: ## ## @table @var ## @item resnorm ## The squared 2-norm of the residual: @code{norm (@var{c}*@var{x}-@var{d})^2} ## ## @item residual ## The residual: @code{@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 ## @c FIXME: Something is output from the function, but what is it? ## Undocumented output ## @end table ## @seealso{pqpnonneg, lscov, optimset} ## @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, x0 = [], options = struct ()) ## Special case: called to find default optimization options if (nargin == 1 && ischar (c) && strcmp (c, "defaults")) x = struct ("MaxIter", 1e5); return; endif if (nargin < 2 || nargin > 4) print_usage (); endif if (! (isnumeric (c) && ismatrix (c)) || ! (isnumeric (d) && ismatrix (d))) error ("lsqnonneg: C and D must be numeric matrices"); endif if (! isstruct (options)) error ("lsqnonneg: OPTIONS must be a struct"); endif ## Lawson-Hanson Step 1 (LH1): initialize the variables. m = rows (c); n = columns (c); if (isempty (x0)) ## Initial guess is all zeros. x = zeros (n, 1); else ## ensure nonnegative guess. x = max (x0, 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 += 1; ## 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 (isargout (2)) resnorm = norm (c*x - d) ^ 2; endif if (isargout (3)) residual = d - c*x; endif if (isargout (4)) if (iter >= max_iter) exitflag = 0; else exitflag = iter; endif endif if (isargout (5)) output = struct ("algorithm", "nnls", "iterations", iter); endif if (isargout (6)) 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); # Test input validation %!error lsqnonneg () %!error lsqnonneg (1) %!error lsqnonneg (1,2,3,4,5) %!error <C .* must be numeric matrices> lsqnonneg ({1},2) %!error <C .* must be numeric matrices> lsqnonneg (ones (2,2,2),2) %!error <D must be numeric matrices> lsqnonneg (1,{2}) %!error <D must be numeric matrices> lsqnonneg (1, ones (2,2,2)) %!error <OPTIONS must be a struct> lsqnonneg (1, 2, [], 3)