Mercurial > octave
annotate scripts/optimization/pqpnonneg.m @ 28959:5394d688d456
doc: Use @code{} within alternate text for @xref,@pxref macros for better Info display.
* accumarray.m, structfun.m, slash.m, csvread.m, csvwrite.m, edit.m,
setfield.m, lsqnonneg.m, pqpnonneg.m, camlookat.m, camorbit.m, camup.m, barh.m,
camlight.m, isocaps.m, isosurface.m, loglogerr.m, polar.m, reducepatch.m,
reducevolume.m, semilogxerr.m, semilogyerr.m, findall.m, findobj.m, beta.m,
movmad.m, movmax.m, movmean.m, movmedian.m, movmin.m, movprod.m, movstd.m,
movsum.m, movvar.m, test.m, datenum.m:
Place alternate text in @code{} macro so it displays better in plaintext Info.
author | Rik <rik@octave.org> |
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date | Mon, 19 Oct 2020 09:33:28 -0700 |
parents | fc4bb4bd1d5e |
children | 7854d5752dd2 |
rev | line source |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 2008-2020 The Octave Project Developers |
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4 ## |
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5 ## See the file COPYRIGHT.md in the top-level directory of this |
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6 ## distribution or <https://octave.org/copyright/>. |
9635 | 7 ## |
8 ## This file is part of Octave. | |
9 ## | |
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10 ## Octave is free software: you can redistribute it and/or modify it |
9635 | 11 ## under the terms of the GNU General Public License as published by |
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12 ## the Free Software Foundation, either version 3 of the License, or |
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13 ## (at your option) any later version. |
9635 | 14 ## |
15 ## Octave is distributed in the hope that it will be useful, but | |
16 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 ## GNU General Public License for more details. |
9635 | 19 ## |
20 ## You should have received a copy of the GNU General Public License | |
21 ## along with Octave; see the file COPYING. If not, see | |
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22 ## <https://www.gnu.org/licenses/>. |
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23 ## |
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24 ######################################################################## |
9635 | 25 |
26 ## -*- texinfo -*- | |
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27 ## @deftypefn {} {@var{x} =} pqpnonneg (@var{c}, @var{d}) |
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28 ## @deftypefnx {} {@var{x} =} pqpnonneg (@var{c}, @var{d}, @var{x0}) |
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29 ## @deftypefnx {} {@var{x} =} pqpnonneg (@var{c}, @var{d}, @var{x0}, @var{options}) |
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30 ## @deftypefnx {} {[@var{x}, @var{minval}] =} pqpnonneg (@dots{}) |
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31 ## @deftypefnx {} {[@var{x}, @var{minval}, @var{exitflag}] =} pqpnonneg (@dots{}) |
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32 ## @deftypefnx {} {[@var{x}, @var{minval}, @var{exitflag}, @var{output}] =} pqpnonneg (@dots{}) |
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33 ## @deftypefnx {} {[@var{x}, @var{minval}, @var{exitflag}, @var{output}, @var{lambda}] =} pqpnonneg (@dots{}) |
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34 ## |
22764 | 35 ## Minimize @code{1/2*@var{x}'*@var{c}*@var{x} + @var{d}'*@var{x}} subject to |
36 ## @code{@var{x} >= 0}. | |
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37 ## |
22764 | 38 ## @var{c} and @var{d} must be real matrices, and @var{c} must be symmetric and |
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39 ## positive definite. |
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40 ## |
22764 | 41 ## @var{x0} is an optional initial guess for the solution @var{x}. |
9635 | 42 ## |
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43 ## @var{options} is an options structure to change the behavior of the |
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44 ## algorithm (@pxref{XREFoptimset,,@code{optimset}}). @code{pqpnonneg} |
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45 ## recognizes one option: @qcode{"MaxIter"}. |
9635 | 46 ## |
47 ## Outputs: | |
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48 ## |
22764 | 49 ## @table @var |
50 ## | |
51 ## @item x | |
52 ## The solution matrix | |
53 ## | |
9635 | 54 ## @item minval |
22764 | 55 ## The minimum attained model value, |
56 ## @code{1/2*@var{xmin}'*@var{c}*@var{xmin} + @var{d}'*@var{xmin}} | |
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57 ## |
9635 | 58 ## @item exitflag |
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59 ## An indicator of convergence. 0 indicates that the iteration count was |
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60 ## exceeded, and therefore convergence was not reached; >0 indicates that the |
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61 ## algorithm converged. (The algorithm is stable and will converge given |
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62 ## enough iterations.) |
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63 ## |
9635 | 64 ## @item output |
65 ## A structure with two fields: | |
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66 ## |
9635 | 67 ## @itemize @bullet |
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68 ## @item @qcode{"algorithm"}: The algorithm used (@nospell{@qcode{"nnls"}}) |
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69 ## |
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70 ## @item @qcode{"iterations"}: The number of iterations taken. |
9635 | 71 ## @end itemize |
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72 ## |
9635 | 73 ## @item lambda |
22764 | 74 ## @c FIXME: Something is output from the function, but what is it? |
75 ## Undocumented output | |
76 ## @end table | |
77 ## @seealso{lsqnonneg, qp, optimset} | |
9635 | 78 ## @end deftypefn |
79 | |
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80 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. |
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81 ## PKG_ADD: [~] = __all_opts__ ("pqpnonneg"); |
9635 | 82 |
22764 | 83 ## This is analogical to the lsqnonneg implementation, which is implemented |
84 ## from Lawson and Hanson's 1973 algorithm on page 161 of Solving Least Squares | |
85 ## Problems. It shares the convergence guarantees. | |
9635 | 86 |
22769 | 87 function [x, minval, exitflag, output, lambda] = pqpnonneg (c, d, x0 = [], |
88 options = struct ()) | |
9635 | 89 |
22764 | 90 ## Special case: called to find default optimization options |
91 if (nargin == 1 && ischar (c) && strcmp (c, "defaults")) | |
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92 x = struct ("MaxIter", 1e5); |
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93 return; |
9635 | 94 endif |
95 | |
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96 if (nargin < 2) |
9635 | 97 print_usage (); |
98 endif | |
99 | |
22764 | 100 if (! (isnumeric (c) && ismatrix (c)) || ! (isnumeric (d) && ismatrix (d))) |
101 error ("pqpnonneg: C and D must be numeric matrices"); | |
102 endif | |
103 if (! issquare (c)) | |
104 error ("pqpnonneg: C must be a square matrix"); | |
105 endif | |
106 | |
107 if (! isstruct (options)) | |
108 error ("pqpnonneg: OPTIONS must be a struct"); | |
109 endif | |
110 | |
9635 | 111 ## Lawson-Hanson Step 1 (LH1): initialize the variables. |
112 n = columns (c); | |
22764 | 113 if (isempty (x0)) |
114 ## Initial guess is all zeros. | |
9635 | 115 x = zeros (n, 1); |
116 else | |
117 ## ensure nonnegative guess. | |
22764 | 118 x = max (x0, 0); |
9635 | 119 endif |
120 | |
121 max_iter = optimget (options, "MaxIter", 1e5); | |
122 | |
123 ## Initialize P, according to zero pattern of x. | |
124 p = find (x > 0).'; | |
125 ## Initialize the Cholesky factorization. | |
126 r = chol (c(p, p)); | |
127 usechol = true; | |
128 | |
129 iter = 0; | |
130 | |
131 ## LH3: test for completion. | |
132 while (iter < max_iter) | |
133 while (iter < max_iter) | |
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134 iter += 1; |
9635 | 135 |
136 ## LH6: compute the positive matrix and find the min norm solution | |
137 ## of the positive problem. | |
138 if (usechol) | |
139 xtmp = -(r \ (r' \ d(p))); | |
140 else | |
141 xtmp = -(c(p,p) \ d(p)); | |
142 endif | |
143 idx = find (xtmp < 0); | |
144 | |
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145 if (isempty (idx)) |
9635 | 146 ## LH7: tmp solution found, iterate. |
147 x(:) = 0; | |
148 x(p) = xtmp; | |
149 break; | |
150 else | |
151 ## LH8, LH9: find the scaling factor. | |
152 pidx = p(idx); | |
22764 | 153 sf = x(pidx) ./ (x(pidx) - xtmp(idx)); |
9635 | 154 alpha = min (sf); |
155 ## LH10: adjust X. | |
156 xx = zeros (n, 1); | |
157 xx(p) = xtmp; | |
158 x += alpha*(xx - x); | |
159 ## LH11: move from P to Z all X == 0. | |
160 ## This corresponds to those indices where minimum of sf is attained. | |
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161 idx = idx(sf == alpha); |
9635 | 162 p(idx) = []; |
163 if (usechol) | |
164 ## update the Cholesky factorization. | |
165 r = choldelete (r, idx); | |
166 endif | |
167 endif | |
168 endwhile | |
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169 |
9635 | 170 ## compute the gradient. |
171 w = -(d + c*x); | |
172 w(p) = []; | |
173 if (! any (w > 0)) | |
174 if (usechol) | |
175 ## verify the solution achieved using qr updating. | |
22764 | 176 ## In the best case, this should only take a single step. |
9635 | 177 usechol = false; |
178 continue; | |
179 else | |
180 ## we're finished. | |
181 break; | |
182 endif | |
183 endif | |
184 | |
185 ## find the maximum gradient. | |
186 idx = find (w == max (w)); | |
187 if (numel (idx) > 1) | |
188 warning ("pqpnonneg:nonunique", | |
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189 "a non-unique solution may be returned due to equal gradients"); |
9635 | 190 idx = idx(1); |
191 endif | |
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192 ## move the index from Z to P. Keep P sorted. |
9635 | 193 z = [1:n]; z(p) = []; |
194 zidx = z(idx); | |
195 jdx = 1 + lookup (p, zidx); | |
196 p = [p(1:jdx-1), zidx, p(jdx:end)]; | |
197 if (usechol) | |
198 ## insert the column into the Cholesky factorization. | |
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199 [r, bad] = cholinsert (r, jdx, c(p,zidx)); |
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200 if (bad) |
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201 ## If the insertion failed, we switch off updates and go on. |
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202 usechol = false; |
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203 endif |
9635 | 204 endif |
205 | |
206 endwhile | |
207 ## LH12: complete. | |
208 | |
209 ## Generate the additional output arguments. | |
22764 | 210 if (isargout (2)) |
9635 | 211 minval = 1/2*(x'*c*x) + d'*x; |
212 endif | |
22764 | 213 if (isargout (3)) |
214 if (iter >= max_iter) | |
215 exitflag = 0; | |
216 else | |
217 exitflag = iter; | |
218 endif | |
9635 | 219 endif |
22764 | 220 if (isargout (4)) |
9635 | 221 output = struct ("algorithm", "nnls-pqp", "iterations", iter); |
222 endif | |
22764 | 223 if (isargout (5)) |
9635 | 224 lambda = zeros (size (x)); |
225 lambda(p) = w; | |
226 endif | |
227 | |
228 endfunction | |
229 | |
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230 |
9635 | 231 %!test |
232 %! C = [5 2;2 2]; | |
233 %! d = [3; -1]; | |
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234 %! assert (pqpnonneg (C, d), [0;0.5], 100*eps); |
9635 | 235 |
236 ## Test equivalence of lsq and pqp | |
237 %!test | |
238 %! C = rand (20, 10); | |
239 %! d = rand (20, 1); | |
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240 %! assert (pqpnonneg (C'*C, -C'*d), lsqnonneg (C, d), 100*eps); |
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241 |
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242 ## Test input validation |
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243 %!error <Invalid call> pqpnonneg () |
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244 %!error <Invalid call> pqpnonneg (1) |
22764 | 245 %!error <C .* must be numeric matrices> pqpnonneg ({1},2) |
246 %!error <C .* must be numeric matrices> pqpnonneg (ones (2,2,2),2) | |
247 %!error <D must be numeric matrices> pqpnonneg (1,{2}) | |
248 %!error <D must be numeric matrices> pqpnonneg (1, ones (2,2,2)) | |
249 %!error <C must be a square matrix> pqpnonneg ([1 2], 2) | |
250 %!error <OPTIONS must be a struct> pqpnonneg (1, 2, [], 3) |