Mercurial > octave-nkf
annotate scripts/optimization/lsqnonneg.m @ 20266:83792dd9bcc1
Use in-place operators in m-files where possible.
* scripts/audio/@audioplayer/set.m, scripts/audio/@audiorecorder/set.m,
scripts/audio/mu2lin.m, scripts/elfun/cosd.m, scripts/general/del2.m,
scripts/general/profexplore.m, scripts/general/quadl.m, scripts/general/rat.m,
scripts/general/rotdim.m, scripts/help/get_first_help_sentence.m,
scripts/help/private/__strip_html_tags__.m, scripts/image/cubehelix.m,
scripts/io/textread.m, scripts/linear-algebra/duplication_matrix.m,
scripts/linear-algebra/housh.m, scripts/linear-algebra/krylov.m,
scripts/linear-algebra/logm.m, scripts/linear-algebra/normest.m,
scripts/linear-algebra/onenormest.m, scripts/optimization/fminsearch.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/qp.m,
scripts/plot/appearance/annotation.m, scripts/plot/appearance/axis.m,
scripts/plot/appearance/legend.m, scripts/plot/appearance/specular.m,
scripts/plot/draw/colorbar.m, scripts/plot/draw/hist.m,
scripts/plot/draw/plotmatrix.m, scripts/plot/draw/private/__stem__.m,
scripts/plot/util/__actual_axis_position__.m,
scripts/plot/util/__gnuplot_drawnow__.m, scripts/plot/util/findobj.m,
scripts/plot/util/print.m, scripts/plot/util/private/__go_draw_axes__.m,
scripts/plot/util/private/__print_parse_opts__.m, scripts/plot/util/rotate.m,
scripts/polynomial/pchip.m, scripts/polynomial/polyaffine.m,
scripts/polynomial/polyder.m, scripts/polynomial/private/__splinefit__.m,
scripts/polynomial/residue.m, scripts/signal/arch_fit.m,
scripts/signal/arch_rnd.m, scripts/signal/bartlett.m,
scripts/signal/blackman.m, scripts/signal/freqz.m, scripts/signal/hamming.m,
scripts/signal/hanning.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/signal/stft.m,
scripts/sparse/bicgstab.m, scripts/sparse/cgs.m,
scripts/sparse/private/__sprand_impl__.m, scripts/sparse/qmr.m,
scripts/sparse/sprandsym.m, scripts/sparse/svds.m, scripts/specfun/legendre.m,
scripts/special-matrix/gallery.m, scripts/statistics/base/gls.m,
scripts/statistics/models/logistic_regression.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/manova.m, scripts/statistics/tests/wilcoxon_test.m,
scripts/time/datevec.m:
Use in-place operators in m-files where possible.
| author | Rik <rik@octave.org> |
|---|---|
| date | Tue, 26 May 2015 21:07:42 -0700 |
| parents | f1d0f506ee78 |
| children |
| rev | line source |
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1 ## Copyright (C) 2008-2015 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}) |
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24 ## @deftypefnx {Function File} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0}, @var{options}) |
| 7682 | 25 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}] =} lsqnonneg (@dots{}) |
| 26 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}] =} lsqnonneg (@dots{}) | |
| 27 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}] =} lsqnonneg (@dots{}) | |
| 28 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}] =} lsqnonneg (@dots{}) | |
| 29 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}, @var{lambda}] =} lsqnonneg (@dots{}) | |
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30 ## Minimize @code{norm (@var{c}*@var{x} - d)} subject to |
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31 ## @code{@var{x} >= 0}. |
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32 ## |
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33 ## @var{c} and @var{d} must be real. |
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34 ## |
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35 ## @var{x0} is an optional initial guess for @var{x}. |
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36 ## |
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37 ## Currently, @code{lsqnonneg} recognizes these options: @qcode{"MaxIter"}, |
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38 ## @qcode{"TolX"}. For a description of these options, see |
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39 ## @ref{XREFoptimset,,optimset}. |
| 7682 | 40 ## |
| 41 ## Outputs: | |
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42 ## |
| 7682 | 43 ## @itemize @bullet |
| 44 ## @item resnorm | |
| 45 ## | |
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46 ## The squared 2-norm of the residual: norm (@var{c}*@var{x}-@var{d})^2 |
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47 ## |
| 7682 | 48 ## @item residual |
| 49 ## | |
| 50 ## The residual: @var{d}-@var{c}*@var{x} | |
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51 ## |
| 7682 | 52 ## @item exitflag |
| 53 ## | |
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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 ## | |
| 61 ## A structure with two fields: | |
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62 ## |
| 7682 | 63 ## @itemize @bullet |
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64 ## @item @qcode{"algorithm"}: The algorithm used (@qcode{"nnls"}) |
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65 ## |
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66 ## @item @qcode{"iterations"}: The number of iterations taken. |
| 7682 | 67 ## @end itemize |
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68 ## |
| 7682 | 69 ## @item lambda |
| 70 ## | |
| 71 ## Not implemented. | |
| 72 ## @end itemize | |
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73 ## @seealso{optimset, pqpnonneg, lscov} |
| 7682 | 74 ## @end deftypefn |
| 75 | |
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76 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. |
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77 ## PKG_ADD: [~] = __all_opts__ ("lsqnonneg"); |
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78 |
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79 ## This is implemented from Lawson and Hanson's 1973 algorithm on page |
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80 ## 161 of Solving Least Squares Problems. |
| 7682 | 81 |
| 8600 | 82 function [x, resnorm, residual, exitflag, output, lambda] = lsqnonneg (c, d, x = [], options = struct ()) |
| 83 | |
| 84 if (nargin == 1 && ischar (c) && strcmp (c, 'defaults')) | |
| 85 x = optimset ("MaxIter", 1e5); | |
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86 return; |
| 8600 | 87 endif |
| 88 | |
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89 if (nargin < 2 || nargin > 4 |
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90 || ! (ismatrix (c) && ismatrix (d) && isstruct (options))) |
| 8600 | 91 print_usage (); |
| 92 endif | |
| 7682 | 93 |
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94 ## Lawson-Hanson Step 1 (LH1): initialize the variables. |
| 8600 | 95 m = rows (c); |
| 96 n = columns (c); | |
| 7682 | 97 if (isempty (x)) |
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98 ## Initial guess is 0s. |
| 8600 | 99 x = zeros (n, 1); |
| 100 else | |
| 101 ## ensure nonnegative guess. | |
| 102 x = max (x, 0); | |
| 7682 | 103 endif |
| 104 | |
| 8600 | 105 useqr = m >= n; |
| 8507 | 106 max_iter = optimget (options, "MaxIter", 1e5); |
| 7682 | 107 |
| 8600 | 108 ## Initialize P, according to zero pattern of x. |
| 109 p = find (x > 0).'; | |
| 110 if (useqr) | |
| 111 ## Initialize the QR factorization, economized form. | |
| 112 [q, r] = qr (c(:,p), 0); | |
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113 endif |
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114 |
| 7682 | 115 iter = 0; |
| 8600 | 116 |
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117 ## LH3: test for completion. |
| 8600 | 118 while (iter < max_iter) |
| 119 while (iter < max_iter) | |
| 120 iter++; | |
| 121 | |
| 122 ## LH6: compute the positive matrix and find the min norm solution | |
| 123 ## of the positive problem. | |
| 124 if (useqr) | |
| 125 xtmp = r \ q'*d; | |
| 126 else | |
| 127 xtmp = c(:,p) \ d; | |
| 128 endif | |
| 129 idx = find (xtmp < 0); | |
| 130 | |
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131 if (isempty (idx)) |
| 8600 | 132 ## LH7: tmp solution found, iterate. |
| 133 x(:) = 0; | |
| 134 x(p) = xtmp; | |
| 135 break; | |
| 136 else | |
| 137 ## LH8, LH9: find the scaling factor. | |
| 138 pidx = p(idx); | |
| 139 sf = x(pidx)./(x(pidx) - xtmp(idx)); | |
| 140 alpha = min (sf); | |
| 141 ## LH10: adjust X. | |
| 142 xx = zeros (n, 1); | |
| 143 xx(p) = xtmp; | |
| 144 x += alpha*(xx - x); | |
| 145 ## LH11: move from P to Z all X == 0. | |
| 146 ## This corresponds to those indices where minimum of sf is attained. | |
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147 idx = idx(sf == alpha); |
| 8600 | 148 p(idx) = []; |
| 149 if (useqr) | |
| 150 ## update the QR factorization. | |
| 151 [q, r] = qrdelete (q, r, idx); | |
| 152 endif | |
| 153 endif | |
| 154 endwhile | |
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155 |
| 8600 | 156 ## compute the gradient. |
| 157 w = c'*(d - c*x); | |
| 158 w(p) = []; | |
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159 tolx = optimget (options, "TolX", 10*eps*norm (c, 1)*length (c)); |
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160 if (! any (w > tolx)) |
| 8600 | 161 if (useqr) |
| 162 ## verify the solution achieved using qr updating. | |
| 163 ## in the best case, this should only take a single step. | |
| 164 useqr = false; | |
| 165 continue; | |
| 166 else | |
| 167 ## we're finished. | |
| 168 break; | |
| 169 endif | |
| 170 endif | |
| 171 | |
| 172 ## find the maximum gradient. | |
| 7682 | 173 idx = find (w == max (w)); |
| 174 if (numel (idx) > 1) | |
| 175 warning ("lsqnonneg:nonunique", | |
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176 "a non-unique solution may be returned due to equal gradients"); |
| 7682 | 177 idx = idx(1); |
| 178 endif | |
| 8600 | 179 ## move the index from Z to P. Keep P sorted. |
| 180 z = [1:n]; z(p) = []; | |
| 181 zidx = z(idx); | |
| 182 jdx = 1 + lookup (p, zidx); | |
| 183 p = [p(1:jdx-1), zidx, p(jdx:end)]; | |
| 184 if (useqr) | |
| 185 ## insert the column into the QR factorization. | |
| 186 [q, r] = qrinsert (q, r, jdx, c(:,zidx)); | |
| 187 endif | |
| 7682 | 188 |
| 189 endwhile | |
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190 ## LH12: complete. |
| 7682 | 191 |
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192 ## Generate the additional output arguments. |
| 7682 | 193 if (nargout > 1) |
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194 resnorm = norm (c*x - d) ^ 2; |
| 7682 | 195 endif |
| 196 if (nargout > 2) | |
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197 residual = d - c*x; |
| 7682 | 198 endif |
| 199 exitflag = iter; | |
| 8507 | 200 if (nargout > 3 && iter >= max_iter) |
| 7682 | 201 exitflag = 0; |
| 202 endif | |
| 203 if (nargout > 4) | |
| 204 output = struct ("algorithm", "nnls", "iterations", iter); | |
| 205 endif | |
| 206 if (nargout > 5) | |
| 8600 | 207 lambda = zeros (size (x)); |
| 208 lambda(p) = w; | |
| 7682 | 209 endif |
| 210 | |
| 211 endfunction | |
| 212 | |
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213 |
| 7682 | 214 %!test |
| 215 %! C = [1 0;0 1;2 1]; | |
| 216 %! d = [1;3;-2]; | |
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217 %! assert (lsqnonneg (C, d), [0;0.5], 100*eps); |
| 7682 | 218 |
| 219 %!test | |
| 220 %! C = [0.0372 0.2869;0.6861 0.7071;0.6233 0.6245;0.6344 0.6170]; | |
| 221 %! d = [0.8587;0.1781;0.0747;0.8405]; | |
| 222 %! xnew = [0;0.6929]; | |
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223 %! assert (lsqnonneg (C, d), xnew, 0.0001); |
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224 |