Mercurial > octave
annotate scripts/optimization/lsqnonneg.m @ 23220:092078913d54
maint: Merge stable to default.
| author | John W. Eaton <jwe@octave.org> |
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| date | Wed, 22 Feb 2017 12:58:07 -0500 |
| parents | ef4d915df748 3ac9f9ecfae5 |
| children | 194eb4bd202b |
| rev | line source |
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1 ## Copyright (C) 2008-2017 Bill Denney |
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2 ## Copyright (C) 2008 Jaroslav Hajek |
| 8600 | 3 ## Copyright (C) 2009 VZLU Prague |
| 7682 | 4 ## |
| 5 ## This file is part of Octave. | |
| 6 ## | |
| 7 ## Octave is free software; you can redistribute it and/or modify it | |
| 8 ## under the terms of the GNU General Public License as published by | |
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9 ## the Free Software Foundation; either version 3 of the License, or |
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10 ## (at your option) any later version. |
| 7682 | 11 ## |
| 12 ## Octave is distributed in the hope that it will be useful, but | |
| 13 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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14 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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15 ## GNU General Public License for more details. |
| 7682 | 16 ## |
| 17 ## You should have received a copy of the GNU General Public License | |
| 18 ## along with Octave; see the file COPYING. If not, see | |
| 19 ## <http://www.gnu.org/licenses/>. | |
| 20 | |
| 21 ## -*- texinfo -*- | |
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22 ## @deftypefn {} {@var{x} =} lsqnonneg (@var{c}, @var{d}) |
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23 ## @deftypefnx {} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0}) |
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24 ## @deftypefnx {} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0}, @var{options}) |
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25 ## @deftypefnx {} {[@var{x}, @var{resnorm}] =} lsqnonneg (@dots{}) |
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26 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}] =} lsqnonneg (@dots{}) |
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27 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}] =} lsqnonneg (@dots{}) |
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28 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}] =} lsqnonneg (@dots{}) |
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29 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}, @var{lambda}] =} lsqnonneg (@dots{}) |
| 22769 | 30 ## |
| 31 ## Minimize @code{norm (@var{c}*@var{x} - @var{d})} subject to | |
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32 ## @code{@var{x} >= 0}. |
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33 ## |
| 22769 | 34 ## @var{c} and @var{d} must be real matrices. |
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35 ## |
| 22769 | 36 ## @var{x0} is an optional initial guess for the solution @var{x}. |
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37 ## |
| 22769 | 38 ## @var{options} is an options structure to change the behavior of the |
| 39 ## algorithm (@pxref{XREFoptimset,,optimset}. @code{lsqnonneg} recognizes | |
| 40 ## these options: @qcode{"MaxIter"}, @qcode{"TolX"}. | |
| 7682 | 41 ## |
| 42 ## Outputs: | |
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43 ## |
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44 ## @table @var |
| 7682 | 45 ## @item resnorm |
| 22769 | 46 ## The squared 2-norm of the residual: @code{norm (@var{c}*@var{x}-@var{d})^2} |
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47 ## |
| 7682 | 48 ## @item residual |
| 22769 | 49 ## The residual: @code{@var{d}-@var{c}*@var{x}} |
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50 ## |
| 7682 | 51 ## @item exitflag |
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52 ## An indicator of convergence. 0 indicates that the iteration count was |
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53 ## exceeded, and therefore convergence was not reached; >0 indicates that the |
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54 ## algorithm converged. (The algorithm is stable and will converge given |
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55 ## enough iterations.) |
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56 ## |
| 7682 | 57 ## @item output |
| 58 ## A structure with two fields: | |
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59 ## |
| 7682 | 60 ## @itemize @bullet |
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61 ## @item @qcode{"algorithm"}: The algorithm used (@qcode{"nnls"}) |
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62 ## |
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63 ## @item @qcode{"iterations"}: The number of iterations taken. |
| 7682 | 64 ## @end itemize |
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65 ## |
| 7682 | 66 ## @item lambda |
| 22769 | 67 ## @c FIXME: Something is output from the function, but what is it? |
| 68 ## Undocumented output | |
| 69 ## @end table | |
| 70 ## @seealso{pqpnonneg, lscov, optimset} | |
| 7682 | 71 ## @end deftypefn |
| 72 | |
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73 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. |
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74 ## PKG_ADD: [~] = __all_opts__ ("lsqnonneg"); |
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75 |
| 22769 | 76 ## This is implemented from Lawson and Hanson's 1973 algorithm on page 161 of |
| 77 ## Solving Least Squares Problems. | |
| 7682 | 78 |
| 22769 | 79 function [x, resnorm, residual, exitflag, output, lambda] = lsqnonneg (c, d, |
| 80 x0 = [], | |
| 81 options = struct ()) | |
| 8600 | 82 |
| 22769 | 83 ## Special case: called to find default optimization options |
| 84 if (nargin == 1 && ischar (c) && strcmp (c, "defaults")) | |
| 8600 | 85 x = optimset ("MaxIter", 1e5); |
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86 return; |
| 8600 | 87 endif |
| 88 | |
| 22769 | 89 if (nargin < 2 || nargin > 4) |
| 8600 | 90 print_usage (); |
| 91 endif | |
| 7682 | 92 |
| 22769 | 93 if (! (isnumeric (c) && ismatrix (c)) || ! (isnumeric (d) && ismatrix (d))) |
| 94 error ("lsqnonneg: C and D must be numeric matrices"); | |
| 95 endif | |
| 96 | |
| 97 if (! isstruct (options)) | |
| 98 error ("lsqnonneg: OPTIONS must be a struct"); | |
| 99 endif | |
| 100 | |
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101 ## Lawson-Hanson Step 1 (LH1): initialize the variables. |
| 8600 | 102 m = rows (c); |
| 103 n = columns (c); | |
| 22769 | 104 if (isempty (x0)) |
| 105 ## Initial guess is all zeros. | |
| 8600 | 106 x = zeros (n, 1); |
| 107 else | |
| 108 ## ensure nonnegative guess. | |
| 22769 | 109 x = max (x0, 0); |
| 7682 | 110 endif |
| 111 | |
| 22769 | 112 useqr = (m >= n); |
| 8507 | 113 max_iter = optimget (options, "MaxIter", 1e5); |
| 7682 | 114 |
| 8600 | 115 ## Initialize P, according to zero pattern of x. |
| 116 p = find (x > 0).'; | |
| 117 if (useqr) | |
| 118 ## Initialize the QR factorization, economized form. | |
| 119 [q, r] = qr (c(:,p), 0); | |
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120 endif |
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121 |
| 7682 | 122 iter = 0; |
| 8600 | 123 |
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124 ## LH3: test for completion. |
| 8600 | 125 while (iter < max_iter) |
| 126 while (iter < max_iter) | |
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127 iter += 1; |
| 8600 | 128 |
| 129 ## LH6: compute the positive matrix and find the min norm solution | |
| 130 ## of the positive problem. | |
| 131 if (useqr) | |
| 132 xtmp = r \ q'*d; | |
| 133 else | |
| 134 xtmp = c(:,p) \ d; | |
| 135 endif | |
| 136 idx = find (xtmp < 0); | |
| 137 | |
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138 if (isempty (idx)) |
| 8600 | 139 ## LH7: tmp solution found, iterate. |
| 140 x(:) = 0; | |
| 141 x(p) = xtmp; | |
| 142 break; | |
| 143 else | |
| 144 ## LH8, LH9: find the scaling factor. | |
| 145 pidx = p(idx); | |
| 22769 | 146 sf = x(pidx) ./ (x(pidx) - xtmp(idx)); |
| 8600 | 147 alpha = min (sf); |
| 148 ## LH10: adjust X. | |
| 149 xx = zeros (n, 1); | |
| 150 xx(p) = xtmp; | |
| 151 x += alpha*(xx - x); | |
| 152 ## LH11: move from P to Z all X == 0. | |
| 153 ## This corresponds to those indices where minimum of sf is attained. | |
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154 idx = idx(sf == alpha); |
| 8600 | 155 p(idx) = []; |
| 156 if (useqr) | |
| 157 ## update the QR factorization. | |
| 158 [q, r] = qrdelete (q, r, idx); | |
| 159 endif | |
| 160 endif | |
| 161 endwhile | |
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162 |
| 8600 | 163 ## compute the gradient. |
| 164 w = c'*(d - c*x); | |
| 165 w(p) = []; | |
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166 tolx = optimget (options, "TolX", 10*eps*norm (c, 1)*length (c)); |
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167 if (! any (w > tolx)) |
| 8600 | 168 if (useqr) |
| 169 ## verify the solution achieved using qr updating. | |
| 170 ## in the best case, this should only take a single step. | |
| 171 useqr = false; | |
| 172 continue; | |
| 173 else | |
| 174 ## we're finished. | |
| 175 break; | |
| 176 endif | |
| 177 endif | |
| 178 | |
| 179 ## find the maximum gradient. | |
| 7682 | 180 idx = find (w == max (w)); |
| 181 if (numel (idx) > 1) | |
| 182 warning ("lsqnonneg:nonunique", | |
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183 "a non-unique solution may be returned due to equal gradients"); |
| 7682 | 184 idx = idx(1); |
| 185 endif | |
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186 ## move the index from Z to P. Keep P sorted. |
| 8600 | 187 z = [1:n]; z(p) = []; |
| 188 zidx = z(idx); | |
| 189 jdx = 1 + lookup (p, zidx); | |
| 190 p = [p(1:jdx-1), zidx, p(jdx:end)]; | |
| 191 if (useqr) | |
| 192 ## insert the column into the QR factorization. | |
| 193 [q, r] = qrinsert (q, r, jdx, c(:,zidx)); | |
| 194 endif | |
| 7682 | 195 |
| 196 endwhile | |
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197 ## LH12: complete. |
| 7682 | 198 |
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199 ## Generate the additional output arguments. |
| 22769 | 200 if (isargout (2)) |
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201 resnorm = norm (c*x - d) ^ 2; |
| 7682 | 202 endif |
| 22769 | 203 if (isargout (3)) |
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204 residual = d - c*x; |
| 7682 | 205 endif |
| 22769 | 206 if (isargout (4)) |
| 207 if (iter >= max_iter) | |
| 208 exitflag = 0; | |
| 209 else | |
| 210 exitflag = iter; | |
| 211 endif | |
| 7682 | 212 endif |
| 22769 | 213 if (isargout (5)) |
| 7682 | 214 output = struct ("algorithm", "nnls", "iterations", iter); |
| 215 endif | |
| 22769 | 216 if (isargout (6)) |
| 8600 | 217 lambda = zeros (size (x)); |
| 218 lambda(p) = w; | |
| 7682 | 219 endif |
| 220 | |
| 221 endfunction | |
| 222 | |
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223 |
| 7682 | 224 %!test |
| 225 %! C = [1 0;0 1;2 1]; | |
| 226 %! d = [1;3;-2]; | |
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227 %! assert (lsqnonneg (C, d), [0;0.5], 100*eps); |
| 7682 | 228 |
| 229 %!test | |
| 230 %! C = [0.0372 0.2869;0.6861 0.7071;0.6233 0.6245;0.6344 0.6170]; | |
| 231 %! d = [0.8587;0.1781;0.0747;0.8405]; | |
| 232 %! xnew = [0;0.6929]; | |
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233 %! assert (lsqnonneg (C, d), xnew, 0.0001); |
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234 |
| 22769 | 235 # Test input validation |
| 236 %!error lsqnonneg () | |
| 237 %!error lsqnonneg (1) | |
| 238 %!error lsqnonneg (1,2,3,4,5) | |
| 239 %!error <C .* must be numeric matrices> lsqnonneg ({1},2) | |
| 240 %!error <C .* must be numeric matrices> lsqnonneg (ones (2,2,2),2) | |
| 241 %!error <D must be numeric matrices> lsqnonneg (1,{2}) | |
| 242 %!error <D must be numeric matrices> lsqnonneg (1, ones (2,2,2)) | |
| 243 %!error <OPTIONS must be a struct> lsqnonneg (1, 2, [], 3) |