Mercurial > octave
annotate scripts/optimization/lsqnonneg.m @ 27919:1891570abac8
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2020.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Mon, 06 Jan 2020 22:29:51 -0500 |
| parents | b442ec6dda5c |
| children | bd51beb6205e |
| rev | line source |
|---|---|
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1 ## Copyright (C) 2008-2020 The Octave Project Developers |
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2 ## |
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3 ## See the file COPYRIGHT.md in the top-level directory of this distribution |
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4 ## or <https://octave.org/COPYRIGHT.html/>. |
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5 ## |
| 7682 | 6 ## |
| 7 ## This file is part of Octave. | |
| 8 ## | |
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9 ## Octave is free software: you can redistribute it and/or modify it |
| 7682 | 10 ## under the terms of the GNU General Public License as published by |
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11 ## the Free Software Foundation, either version 3 of the License, or |
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12 ## (at your option) any later version. |
| 7682 | 13 ## |
| 14 ## Octave is distributed in the hope that it will be useful, but | |
| 15 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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16 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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17 ## GNU General Public License for more details. |
| 7682 | 18 ## |
| 19 ## You should have received a copy of the GNU General Public License | |
| 20 ## along with Octave; see the file COPYING. If not, see | |
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21 ## <https://www.gnu.org/licenses/>. |
| 7682 | 22 |
| 23 ## -*- texinfo -*- | |
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24 ## @deftypefn {} {@var{x} =} lsqnonneg (@var{c}, @var{d}) |
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25 ## @deftypefnx {} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0}) |
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26 ## @deftypefnx {} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0}, @var{options}) |
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27 ## @deftypefnx {} {[@var{x}, @var{resnorm}] =} lsqnonneg (@dots{}) |
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28 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}] =} lsqnonneg (@dots{}) |
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29 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}] =} lsqnonneg (@dots{}) |
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30 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}] =} lsqnonneg (@dots{}) |
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31 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}, @var{lambda}] =} lsqnonneg (@dots{}) |
| 22769 | 32 ## |
| 33 ## Minimize @code{norm (@var{c}*@var{x} - @var{d})} subject to | |
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34 ## @code{@var{x} >= 0}. |
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35 ## |
| 22769 | 36 ## @var{c} and @var{d} must be real matrices. |
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37 ## |
| 22769 | 38 ## @var{x0} is an optional initial guess for the solution @var{x}. |
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39 ## |
| 22769 | 40 ## @var{options} is an options structure to change the behavior of the |
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41 ## algorithm (@pxref{XREFoptimset,,optimset}). @code{lsqnonneg} recognizes |
| 22769 | 42 ## these options: @qcode{"MaxIter"}, @qcode{"TolX"}. |
| 7682 | 43 ## |
| 44 ## Outputs: | |
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45 ## |
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46 ## @table @var |
| 7682 | 47 ## @item resnorm |
| 22769 | 48 ## The squared 2-norm of the residual: @code{norm (@var{c}*@var{x}-@var{d})^2} |
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49 ## |
| 7682 | 50 ## @item residual |
| 22769 | 51 ## The residual: @code{@var{d}-@var{c}*@var{x}} |
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52 ## |
| 7682 | 53 ## @item exitflag |
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54 ## An indicator of convergence. 0 indicates that the iteration count was |
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55 ## exceeded, and therefore convergence was not reached; >0 indicates that the |
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56 ## algorithm converged. (The algorithm is stable and will converge given |
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57 ## enough iterations.) |
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58 ## |
| 7682 | 59 ## @item output |
| 60 ## A structure with two fields: | |
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61 ## |
| 7682 | 62 ## @itemize @bullet |
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63 ## @item @qcode{"algorithm"}: The algorithm used (@qcode{"nnls"}) |
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64 ## |
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65 ## @item @qcode{"iterations"}: The number of iterations taken. |
| 7682 | 66 ## @end itemize |
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67 ## |
| 7682 | 68 ## @item lambda |
| 22769 | 69 ## @c FIXME: Something is output from the function, but what is it? |
| 70 ## Undocumented output | |
| 71 ## @end table | |
| 72 ## @seealso{pqpnonneg, lscov, optimset} | |
| 7682 | 73 ## @end deftypefn |
| 74 | |
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75 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. |
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76 ## PKG_ADD: [~] = __all_opts__ ("lsqnonneg"); |
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77 |
| 22769 | 78 ## This is implemented from Lawson and Hanson's 1973 algorithm on page 161 of |
| 79 ## Solving Least Squares Problems. | |
| 7682 | 80 |
| 22769 | 81 function [x, resnorm, residual, exitflag, output, lambda] = lsqnonneg (c, d, |
| 82 x0 = [], | |
| 83 options = struct ()) | |
| 8600 | 84 |
| 22769 | 85 ## Special case: called to find default optimization options |
| 86 if (nargin == 1 && ischar (c) && strcmp (c, "defaults")) | |
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87 x = struct ("MaxIter", 1e5); |
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88 return; |
| 8600 | 89 endif |
| 90 | |
| 22769 | 91 if (nargin < 2 || nargin > 4) |
| 8600 | 92 print_usage (); |
| 93 endif | |
| 7682 | 94 |
| 22769 | 95 if (! (isnumeric (c) && ismatrix (c)) || ! (isnumeric (d) && ismatrix (d))) |
| 96 error ("lsqnonneg: C and D must be numeric matrices"); | |
| 97 endif | |
| 98 | |
| 99 if (! isstruct (options)) | |
| 100 error ("lsqnonneg: OPTIONS must be a struct"); | |
| 101 endif | |
| 102 | |
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103 ## Lawson-Hanson Step 1 (LH1): initialize the variables. |
| 8600 | 104 m = rows (c); |
| 105 n = columns (c); | |
| 22769 | 106 if (isempty (x0)) |
| 107 ## Initial guess is all zeros. | |
| 8600 | 108 x = zeros (n, 1); |
| 109 else | |
| 110 ## ensure nonnegative guess. | |
| 22769 | 111 x = max (x0, 0); |
| 7682 | 112 endif |
| 113 | |
| 22769 | 114 useqr = (m >= n); |
| 8507 | 115 max_iter = optimget (options, "MaxIter", 1e5); |
| 7682 | 116 |
| 8600 | 117 ## Initialize P, according to zero pattern of x. |
| 118 p = find (x > 0).'; | |
| 119 if (useqr) | |
| 120 ## Initialize the QR factorization, economized form. | |
| 121 [q, r] = qr (c(:,p), 0); | |
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122 endif |
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123 |
| 7682 | 124 iter = 0; |
| 8600 | 125 |
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126 ## LH3: test for completion. |
| 8600 | 127 while (iter < max_iter) |
| 128 while (iter < max_iter) | |
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129 iter += 1; |
| 8600 | 130 |
| 131 ## LH6: compute the positive matrix and find the min norm solution | |
| 132 ## of the positive problem. | |
| 133 if (useqr) | |
| 134 xtmp = r \ q'*d; | |
| 135 else | |
| 136 xtmp = c(:,p) \ d; | |
| 137 endif | |
| 138 idx = find (xtmp < 0); | |
| 139 | |
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140 if (isempty (idx)) |
| 8600 | 141 ## LH7: tmp solution found, iterate. |
| 142 x(:) = 0; | |
| 143 x(p) = xtmp; | |
| 144 break; | |
| 145 else | |
| 146 ## LH8, LH9: find the scaling factor. | |
| 147 pidx = p(idx); | |
| 22769 | 148 sf = x(pidx) ./ (x(pidx) - xtmp(idx)); |
| 8600 | 149 alpha = min (sf); |
| 150 ## LH10: adjust X. | |
| 151 xx = zeros (n, 1); | |
| 152 xx(p) = xtmp; | |
| 153 x += alpha*(xx - x); | |
| 154 ## LH11: move from P to Z all X == 0. | |
| 155 ## This corresponds to those indices where minimum of sf is attained. | |
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156 idx = idx(sf == alpha); |
| 8600 | 157 p(idx) = []; |
| 158 if (useqr) | |
| 159 ## update the QR factorization. | |
| 160 [q, r] = qrdelete (q, r, idx); | |
| 161 endif | |
| 162 endif | |
| 163 endwhile | |
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164 |
| 8600 | 165 ## compute the gradient. |
| 166 w = c'*(d - c*x); | |
| 167 w(p) = []; | |
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168 tolx = optimget (options, "TolX", 10*eps*norm (c, 1)*length (c)); |
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169 if (! any (w > tolx)) |
| 8600 | 170 if (useqr) |
| 171 ## verify the solution achieved using qr updating. | |
| 172 ## in the best case, this should only take a single step. | |
| 173 useqr = false; | |
| 174 continue; | |
| 175 else | |
| 176 ## we're finished. | |
| 177 break; | |
| 178 endif | |
| 179 endif | |
| 180 | |
| 181 ## find the maximum gradient. | |
| 7682 | 182 idx = find (w == max (w)); |
| 183 if (numel (idx) > 1) | |
| 184 warning ("lsqnonneg:nonunique", | |
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185 "a non-unique solution may be returned due to equal gradients"); |
| 7682 | 186 idx = idx(1); |
| 187 endif | |
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188 ## move the index from Z to P. Keep P sorted. |
| 8600 | 189 z = [1:n]; z(p) = []; |
| 190 zidx = z(idx); | |
| 191 jdx = 1 + lookup (p, zidx); | |
| 192 p = [p(1:jdx-1), zidx, p(jdx:end)]; | |
| 193 if (useqr) | |
| 194 ## insert the column into the QR factorization. | |
| 195 [q, r] = qrinsert (q, r, jdx, c(:,zidx)); | |
| 196 endif | |
| 7682 | 197 |
| 198 endwhile | |
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199 ## LH12: complete. |
| 7682 | 200 |
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201 ## Generate the additional output arguments. |
| 22769 | 202 if (isargout (2)) |
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203 resnorm = norm (c*x - d) ^ 2; |
| 7682 | 204 endif |
| 22769 | 205 if (isargout (3)) |
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206 residual = d - c*x; |
| 7682 | 207 endif |
| 22769 | 208 if (isargout (4)) |
| 209 if (iter >= max_iter) | |
| 210 exitflag = 0; | |
| 211 else | |
| 212 exitflag = iter; | |
| 213 endif | |
| 7682 | 214 endif |
| 22769 | 215 if (isargout (5)) |
| 7682 | 216 output = struct ("algorithm", "nnls", "iterations", iter); |
| 217 endif | |
| 22769 | 218 if (isargout (6)) |
| 8600 | 219 lambda = zeros (size (x)); |
| 220 lambda(p) = w; | |
| 7682 | 221 endif |
| 222 | |
| 223 endfunction | |
| 224 | |
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225 |
| 7682 | 226 %!test |
| 227 %! C = [1 0;0 1;2 1]; | |
| 228 %! d = [1;3;-2]; | |
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229 %! assert (lsqnonneg (C, d), [0;0.5], 100*eps); |
| 7682 | 230 |
| 231 %!test | |
| 232 %! C = [0.0372 0.2869;0.6861 0.7071;0.6233 0.6245;0.6344 0.6170]; | |
| 233 %! d = [0.8587;0.1781;0.0747;0.8405]; | |
| 234 %! xnew = [0;0.6929]; | |
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235 %! assert (lsqnonneg (C, d), xnew, 0.0001); |
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236 |
| 22769 | 237 # Test input validation |
| 238 %!error lsqnonneg () | |
| 239 %!error lsqnonneg (1) | |
| 240 %!error lsqnonneg (1,2,3,4,5) | |
| 241 %!error <C .* must be numeric matrices> lsqnonneg ({1},2) | |
| 242 %!error <C .* must be numeric matrices> lsqnonneg (ones (2,2,2),2) | |
| 243 %!error <D must be numeric matrices> lsqnonneg (1,{2}) | |
| 244 %!error <D must be numeric matrices> lsqnonneg (1, ones (2,2,2)) | |
| 245 %!error <OPTIONS must be a struct> lsqnonneg (1, 2, [], 3) |