Mercurial > octave
annotate scripts/optimization/lsqnonneg.m @ 13027:b9a89ca0fb75
prevent optimization functions from setting ans in workspace at startup
* fminbnd.m, fminunc.m, fsolve.m, fzero.m, lsqnonneg.m, pqpnonneg.m,
qp.m: Discard result from call to __all_opt__ in PKG_ADD command.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Mon, 29 Aug 2011 13:07:22 -0400 |
| parents | d5bd2766c640 |
| children | 72c96de7a403 |
| rev | line source |
|---|---|
| 11523 | 1 ## Copyright (C) 2008-2011 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 | |
| 9 ## the Free Software Foundation; either version 3 of the License, or (at | |
| 10 ## your option) any later version. | |
| 11 ## | |
| 12 ## Octave is distributed in the hope that it will be useful, but | |
| 13 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 14 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 15 ## General Public License for more details. | |
| 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 {Function File} {@var{x} =} lsqnonneg (@var{c}, @var{d}) |
| 7682 | 23 ## @deftypefnx {Function File} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0}) |
| 24 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}] =} lsqnonneg (@dots{}) | |
| 25 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}] =} lsqnonneg (@dots{}) | |
| 26 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}] =} lsqnonneg (@dots{}) | |
| 27 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}] =} lsqnonneg (@dots{}) | |
| 28 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}, @var{lambda}] =} lsqnonneg (@dots{}) | |
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29 ## Minimize @code{norm (@var{c}*@var{x} - d)} subject to |
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30 ## @code{@var{x} >= 0}. @var{c} and @var{d} must be real. @var{x0} is an |
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31 ## optional initial guess for @var{x}. |
| 7682 | 32 ## |
| 33 ## Outputs: | |
| 34 ## @itemize @bullet | |
| 35 ## @item resnorm | |
| 36 ## | |
| 37 ## The squared 2-norm of the residual: norm(@var{c}*@var{x}-@var{d})^2 | |
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38 ## |
| 7682 | 39 ## @item residual |
| 40 ## | |
| 41 ## The residual: @var{d}-@var{c}*@var{x} | |
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42 ## |
| 7682 | 43 ## @item exitflag |
| 44 ## | |
| 45 ## An indicator of convergence. 0 indicates that the iteration count | |
| 46 ## was exceeded, and therefore convergence was not reached; >0 indicates | |
| 47 ## that the algorithm converged. (The algorithm is stable and will | |
| 48 ## converge given enough iterations.) | |
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49 ## |
| 7682 | 50 ## @item output |
| 51 ## | |
| 52 ## A structure with two fields: | |
| 53 ## @itemize @bullet | |
| 54 ## @item "algorithm": The algorithm used ("nnls") | |
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55 ## |
| 7682 | 56 ## @item "iterations": The number of iterations taken. |
| 57 ## @end itemize | |
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58 ## |
| 7682 | 59 ## @item lambda |
| 60 ## | |
| 61 ## Not implemented. | |
| 62 ## @end itemize | |
| 9635 | 63 ## @seealso{optimset, pqpnonneg} |
| 7682 | 64 ## @end deftypefn |
| 65 | |
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66 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. |
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67 ## PKG_ADD: [~] = __all_opts__ ("lsqnonneg"); |
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68 |
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69 ## This is implemented from Lawson and Hanson's 1973 algorithm on page |
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70 ## 161 of Solving Least Squares Problems. |
| 7682 | 71 |
| 8600 | 72 function [x, resnorm, residual, exitflag, output, lambda] = lsqnonneg (c, d, x = [], options = struct ()) |
| 73 | |
| 74 if (nargin == 1 && ischar (c) && strcmp (c, 'defaults')) | |
| 75 x = optimset ("MaxIter", 1e5); | |
| 76 return | |
| 77 endif | |
| 78 | |
| 79 if (! (nargin >= 2 && nargin <= 4 && ismatrix (c) && ismatrix (d) && isstruct (options))) | |
| 80 print_usage (); | |
| 81 endif | |
| 7682 | 82 |
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83 ## Lawson-Hanson Step 1 (LH1): initialize the variables. |
| 8600 | 84 m = rows (c); |
| 85 n = columns (c); | |
| 7682 | 86 if (isempty (x)) |
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87 ## Initial guess is 0s. |
| 8600 | 88 x = zeros (n, 1); |
| 89 else | |
| 90 ## ensure nonnegative guess. | |
| 91 x = max (x, 0); | |
| 7682 | 92 endif |
| 93 | |
| 8600 | 94 useqr = m >= n; |
| 8507 | 95 max_iter = optimget (options, "MaxIter", 1e5); |
| 7682 | 96 |
| 8600 | 97 ## Initialize P, according to zero pattern of x. |
| 98 p = find (x > 0).'; | |
| 99 if (useqr) | |
| 100 ## Initialize the QR factorization, economized form. | |
| 101 [q, r] = qr (c(:,p), 0); | |
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102 endif |
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103 |
| 7682 | 104 iter = 0; |
| 8600 | 105 |
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106 ## LH3: test for completion. |
| 8600 | 107 while (iter < max_iter) |
| 108 while (iter < max_iter) | |
| 109 iter++; | |
| 110 | |
| 111 ## LH6: compute the positive matrix and find the min norm solution | |
| 112 ## of the positive problem. | |
| 113 if (useqr) | |
| 114 xtmp = r \ q'*d; | |
| 115 else | |
| 116 xtmp = c(:,p) \ d; | |
| 117 endif | |
| 118 idx = find (xtmp < 0); | |
| 119 | |
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120 if (isempty (idx)) |
| 8600 | 121 ## LH7: tmp solution found, iterate. |
| 122 x(:) = 0; | |
| 123 x(p) = xtmp; | |
| 124 break; | |
| 125 else | |
| 126 ## LH8, LH9: find the scaling factor. | |
| 127 pidx = p(idx); | |
| 128 sf = x(pidx)./(x(pidx) - xtmp(idx)); | |
| 129 alpha = min (sf); | |
| 130 ## LH10: adjust X. | |
| 131 xx = zeros (n, 1); | |
| 132 xx(p) = xtmp; | |
| 133 x += alpha*(xx - x); | |
| 134 ## LH11: move from P to Z all X == 0. | |
| 135 ## This corresponds to those indices where minimum of sf is attained. | |
| 136 idx = idx (sf == alpha); | |
| 137 p(idx) = []; | |
| 138 if (useqr) | |
| 139 ## update the QR factorization. | |
| 140 [q, r] = qrdelete (q, r, idx); | |
| 141 endif | |
| 142 endif | |
| 143 endwhile | |
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144 |
| 8600 | 145 ## compute the gradient. |
| 146 w = c'*(d - c*x); | |
| 147 w(p) = []; | |
| 148 if (! any (w > 0)) | |
| 149 if (useqr) | |
| 150 ## verify the solution achieved using qr updating. | |
| 151 ## in the best case, this should only take a single step. | |
| 152 useqr = false; | |
| 153 continue; | |
| 154 else | |
| 155 ## we're finished. | |
| 156 break; | |
| 157 endif | |
| 158 endif | |
| 159 | |
| 160 ## find the maximum gradient. | |
| 7682 | 161 idx = find (w == max (w)); |
| 162 if (numel (idx) > 1) | |
| 163 warning ("lsqnonneg:nonunique", | |
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164 "a non-unique solution may be returned due to equal gradients"); |
| 7682 | 165 idx = idx(1); |
| 166 endif | |
| 8600 | 167 ## move the index from Z to P. Keep P sorted. |
| 168 z = [1:n]; z(p) = []; | |
| 169 zidx = z(idx); | |
| 170 jdx = 1 + lookup (p, zidx); | |
| 171 p = [p(1:jdx-1), zidx, p(jdx:end)]; | |
| 172 if (useqr) | |
| 173 ## insert the column into the QR factorization. | |
| 174 [q, r] = qrinsert (q, r, jdx, c(:,zidx)); | |
| 175 endif | |
| 7682 | 176 |
| 177 endwhile | |
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178 ## LH12: complete. |
| 7682 | 179 |
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180 ## Generate the additional output arguments. |
| 7682 | 181 if (nargout > 1) |
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182 resnorm = norm (c*x - d) ^ 2; |
| 7682 | 183 endif |
| 184 if (nargout > 2) | |
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185 residual = d - c*x; |
| 7682 | 186 endif |
| 187 exitflag = iter; | |
| 8507 | 188 if (nargout > 3 && iter >= max_iter) |
| 7682 | 189 exitflag = 0; |
| 190 endif | |
| 191 if (nargout > 4) | |
| 192 output = struct ("algorithm", "nnls", "iterations", iter); | |
| 193 endif | |
| 194 if (nargout > 5) | |
| 8600 | 195 lambda = zeros (size (x)); |
| 196 lambda(p) = w; | |
| 7682 | 197 endif |
| 198 | |
| 199 endfunction | |
| 200 | |
| 201 ## Tests | |
| 202 %!test | |
| 203 %! C = [1 0;0 1;2 1]; | |
| 204 %! d = [1;3;-2]; | |
| 205 %! assert (lsqnonneg (C, d), [0;0.5], 100*eps) | |
| 206 | |
| 207 %!test | |
| 208 %! C = [0.0372 0.2869;0.6861 0.7071;0.6233 0.6245;0.6344 0.6170]; | |
| 209 %! d = [0.8587;0.1781;0.0747;0.8405]; | |
| 210 %! xnew = [0;0.6929]; | |
| 211 %! assert (lsqnonneg (C, d), xnew, 0.0001) |