Mercurial > hg > octave-lyh
annotate scripts/optimization/lsqnonneg.m @ 17525:1d0fa3c34ad7
Fully int16 type support
| author | LYH <lyh.kernel@gmail.com> |
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| date | Fri, 27 Sep 2013 04:14:51 +0800 |
| parents | 088d014a7fe2 |
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| rev | line source |
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1 ## Copyright (C) 2008-2012 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}. @var{c} and @var{d} must be real. @var{x0} is an |
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32 ## optional initial guess for @var{x}. |
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33 ## Currently, @code{lsqnonneg} |
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34 ## recognizes these options: @qcode{"MaxIter"}, @qcode{"TolX"}. |
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35 ## For a description of these options, see @ref{XREFoptimset,,optimset}. |
| 7682 | 36 ## |
| 37 ## Outputs: | |
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38 ## |
| 7682 | 39 ## @itemize @bullet |
| 40 ## @item resnorm | |
| 41 ## | |
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42 ## The squared 2-norm of the residual: norm (@var{c}*@var{x}-@var{d})^2 |
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43 ## |
| 7682 | 44 ## @item residual |
| 45 ## | |
| 46 ## The residual: @var{d}-@var{c}*@var{x} | |
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47 ## |
| 7682 | 48 ## @item exitflag |
| 49 ## | |
| 50 ## An indicator of convergence. 0 indicates that the iteration count | |
| 51 ## was exceeded, and therefore convergence was not reached; >0 indicates | |
| 52 ## that the algorithm converged. (The algorithm is stable and will | |
| 53 ## converge given enough iterations.) | |
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54 ## |
| 7682 | 55 ## @item output |
| 56 ## | |
| 57 ## A structure with two fields: | |
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58 ## |
| 7682 | 59 ## @itemize @bullet |
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60 ## @item @qcode{"algorithm"}: The algorithm used (@qcode{"nnls"}) |
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61 ## |
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62 ## @item @qcode{"iterations"}: The number of iterations taken. |
| 7682 | 63 ## @end itemize |
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64 ## |
| 7682 | 65 ## @item lambda |
| 66 ## | |
| 67 ## Not implemented. | |
| 68 ## @end itemize | |
| 9635 | 69 ## @seealso{optimset, pqpnonneg} |
| 7682 | 70 ## @end deftypefn |
| 71 | |
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72 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. |
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73 ## PKG_ADD: [~] = __all_opts__ ("lsqnonneg"); |
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74 |
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75 ## This is implemented from Lawson and Hanson's 1973 algorithm on page |
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76 ## 161 of Solving Least Squares Problems. |
| 7682 | 77 |
| 8600 | 78 function [x, resnorm, residual, exitflag, output, lambda] = lsqnonneg (c, d, x = [], options = struct ()) |
| 79 | |
| 80 if (nargin == 1 && ischar (c) && strcmp (c, 'defaults')) | |
| 81 x = optimset ("MaxIter", 1e5); | |
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82 return; |
| 8600 | 83 endif |
| 84 | |
| 85 if (! (nargin >= 2 && nargin <= 4 && ismatrix (c) && ismatrix (d) && isstruct (options))) | |
| 86 print_usage (); | |
| 87 endif | |
| 7682 | 88 |
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89 ## Lawson-Hanson Step 1 (LH1): initialize the variables. |
| 8600 | 90 m = rows (c); |
| 91 n = columns (c); | |
| 7682 | 92 if (isempty (x)) |
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93 ## Initial guess is 0s. |
| 8600 | 94 x = zeros (n, 1); |
| 95 else | |
| 96 ## ensure nonnegative guess. | |
| 97 x = max (x, 0); | |
| 7682 | 98 endif |
| 99 | |
| 8600 | 100 useqr = m >= n; |
| 8507 | 101 max_iter = optimget (options, "MaxIter", 1e5); |
| 7682 | 102 |
| 8600 | 103 ## Initialize P, according to zero pattern of x. |
| 104 p = find (x > 0).'; | |
| 105 if (useqr) | |
| 106 ## Initialize the QR factorization, economized form. | |
| 107 [q, r] = qr (c(:,p), 0); | |
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108 endif |
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109 |
| 7682 | 110 iter = 0; |
| 8600 | 111 |
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112 ## LH3: test for completion. |
| 8600 | 113 while (iter < max_iter) |
| 114 while (iter < max_iter) | |
| 115 iter++; | |
| 116 | |
| 117 ## LH6: compute the positive matrix and find the min norm solution | |
| 118 ## of the positive problem. | |
| 119 if (useqr) | |
| 120 xtmp = r \ q'*d; | |
| 121 else | |
| 122 xtmp = c(:,p) \ d; | |
| 123 endif | |
| 124 idx = find (xtmp < 0); | |
| 125 | |
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126 if (isempty (idx)) |
| 8600 | 127 ## LH7: tmp solution found, iterate. |
| 128 x(:) = 0; | |
| 129 x(p) = xtmp; | |
| 130 break; | |
| 131 else | |
| 132 ## LH8, LH9: find the scaling factor. | |
| 133 pidx = p(idx); | |
| 134 sf = x(pidx)./(x(pidx) - xtmp(idx)); | |
| 135 alpha = min (sf); | |
| 136 ## LH10: adjust X. | |
| 137 xx = zeros (n, 1); | |
| 138 xx(p) = xtmp; | |
| 139 x += alpha*(xx - x); | |
| 140 ## LH11: move from P to Z all X == 0. | |
| 141 ## This corresponds to those indices where minimum of sf is attained. | |
| 142 idx = idx (sf == alpha); | |
| 143 p(idx) = []; | |
| 144 if (useqr) | |
| 145 ## update the QR factorization. | |
| 146 [q, r] = qrdelete (q, r, idx); | |
| 147 endif | |
| 148 endif | |
| 149 endwhile | |
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150 |
| 8600 | 151 ## compute the gradient. |
| 152 w = c'*(d - c*x); | |
| 153 w(p) = []; | |
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154 tolx = optimget (options, "TolX", 10*eps*norm (c, 1)*length (c)); |
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155 if (! any (w > tolx)) |
| 8600 | 156 if (useqr) |
| 157 ## verify the solution achieved using qr updating. | |
| 158 ## in the best case, this should only take a single step. | |
| 159 useqr = false; | |
| 160 continue; | |
| 161 else | |
| 162 ## we're finished. | |
| 163 break; | |
| 164 endif | |
| 165 endif | |
| 166 | |
| 167 ## find the maximum gradient. | |
| 7682 | 168 idx = find (w == max (w)); |
| 169 if (numel (idx) > 1) | |
| 170 warning ("lsqnonneg:nonunique", | |
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171 "a non-unique solution may be returned due to equal gradients"); |
| 7682 | 172 idx = idx(1); |
| 173 endif | |
| 8600 | 174 ## move the index from Z to P. Keep P sorted. |
| 175 z = [1:n]; z(p) = []; | |
| 176 zidx = z(idx); | |
| 177 jdx = 1 + lookup (p, zidx); | |
| 178 p = [p(1:jdx-1), zidx, p(jdx:end)]; | |
| 179 if (useqr) | |
| 180 ## insert the column into the QR factorization. | |
| 181 [q, r] = qrinsert (q, r, jdx, c(:,zidx)); | |
| 182 endif | |
| 7682 | 183 |
| 184 endwhile | |
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185 ## LH12: complete. |
| 7682 | 186 |
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187 ## Generate the additional output arguments. |
| 7682 | 188 if (nargout > 1) |
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189 resnorm = norm (c*x - d) ^ 2; |
| 7682 | 190 endif |
| 191 if (nargout > 2) | |
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192 residual = d - c*x; |
| 7682 | 193 endif |
| 194 exitflag = iter; | |
| 8507 | 195 if (nargout > 3 && iter >= max_iter) |
| 7682 | 196 exitflag = 0; |
| 197 endif | |
| 198 if (nargout > 4) | |
| 199 output = struct ("algorithm", "nnls", "iterations", iter); | |
| 200 endif | |
| 201 if (nargout > 5) | |
| 8600 | 202 lambda = zeros (size (x)); |
| 203 lambda(p) = w; | |
| 7682 | 204 endif |
| 205 | |
| 206 endfunction | |
| 207 | |
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208 |
| 7682 | 209 %!test |
| 210 %! C = [1 0;0 1;2 1]; | |
| 211 %! d = [1;3;-2]; | |
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212 %! assert (lsqnonneg (C, d), [0;0.5], 100*eps); |
| 7682 | 213 |
| 214 %!test | |
| 215 %! C = [0.0372 0.2869;0.6861 0.7071;0.6233 0.6245;0.6344 0.6170]; | |
| 216 %! d = [0.8587;0.1781;0.0747;0.8405]; | |
| 217 %! xnew = [0;0.6929]; | |
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218 %! assert (lsqnonneg (C, d), xnew, 0.0001); |
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219 |