Mercurial > octave
annotate scripts/optimization/lsqnonneg.m @ 28942:fc4bb4bd1d5e
maint: Use '##' as lead-in for full-line comments.
* condeig.m, mustBeMember.m, runge_kutta_interpolate.m, lsqnonneg.m,
pqpnonneg.m, sqp.m, pkg.m, fplot.m, isosurface.m, __gnuplot_draw_axes__.m,
profexport.m, bicgstab.m, factorial.m, movmad.m, movmax.m, movmean.m,
movmedian.m, movmin.m, movprod.m, movstd.m, movsum.m, movvar.m, fA.m, fB.m,
fC.m, one.m, two.m, df_vr.m, u_vr.m, myclass2.m, foo_subsref_subsasgn.m,
Blork.m, CPrecedenceTester1.m, Cork.m, display.m, display.m, get.m, set.m,
display.m, Sneetch.m, Snork.m, Spork.m, jit.tst, line-continue.tst,
mk_bc_overloads_expected.m, arg_nest.m, no_closure.m, persistent_nest.m,
recursive_nest.m, recursive_nest2.m, scope0.m, scope1.m, scope2.m, scope3.m,
script_nest.m, script_nest_2.m, script_nest_script.m, script_nest_script_2.m,
pkg.tst:
Use '##' as lead-in for full-line comments.
| author | Rik <rik@octave.org> |
|---|---|
| date | Thu, 15 Oct 2020 14:30:01 -0700 |
| parents | 90fea9cc9caa |
| children | 5394d688d456 |
| 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/>. |
| 7682 | 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 |
| 7682 | 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. |
| 7682 | 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. |
| 7682 | 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 ######################################################################## |
| 7682 | 25 |
| 26 ## -*- texinfo -*- | |
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27 ## @deftypefn {} {@var{x} =} lsqnonneg (@var{c}, @var{d}) |
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28 ## @deftypefnx {} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0}) |
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29 ## @deftypefnx {} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0}, @var{options}) |
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30 ## @deftypefnx {} {[@var{x}, @var{resnorm}] =} lsqnonneg (@dots{}) |
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31 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}] =} lsqnonneg (@dots{}) |
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32 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}] =} lsqnonneg (@dots{}) |
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33 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}] =} lsqnonneg (@dots{}) |
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34 ## @deftypefnx {} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}, @var{lambda}] =} lsqnonneg (@dots{}) |
| 22769 | 35 ## |
| 36 ## Minimize @code{norm (@var{c}*@var{x} - @var{d})} subject to | |
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37 ## @code{@var{x} >= 0}. |
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38 ## |
| 22769 | 39 ## @var{c} and @var{d} must be real matrices. |
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40 ## |
| 22769 | 41 ## @var{x0} is an optional initial guess for the solution @var{x}. |
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42 ## |
| 22769 | 43 ## @var{options} is an options structure to change the behavior of the |
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44 ## algorithm (@pxref{XREFoptimset,,optimset}). @code{lsqnonneg} recognizes |
| 22769 | 45 ## these options: @qcode{"MaxIter"}, @qcode{"TolX"}. |
| 7682 | 46 ## |
| 47 ## Outputs: | |
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48 ## |
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49 ## @table @var |
| 7682 | 50 ## @item resnorm |
| 22769 | 51 ## The squared 2-norm of the residual: @code{norm (@var{c}*@var{x}-@var{d})^2} |
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52 ## |
| 7682 | 53 ## @item residual |
| 22769 | 54 ## The residual: @code{@var{d}-@var{c}*@var{x}} |
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55 ## |
| 7682 | 56 ## @item exitflag |
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57 ## An indicator of convergence. 0 indicates that the iteration count was |
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58 ## exceeded, and therefore convergence was not reached; >0 indicates that the |
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59 ## algorithm converged. (The algorithm is stable and will converge given |
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60 ## enough iterations.) |
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61 ## |
| 7682 | 62 ## @item output |
| 63 ## A structure with two fields: | |
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64 ## |
| 7682 | 65 ## @itemize @bullet |
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66 ## @item @qcode{"algorithm"}: The algorithm used (@qcode{"nnls"}) |
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67 ## |
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68 ## @item @qcode{"iterations"}: The number of iterations taken. |
| 7682 | 69 ## @end itemize |
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70 ## |
| 7682 | 71 ## @item lambda |
| 22769 | 72 ## @c FIXME: Something is output from the function, but what is it? |
| 73 ## Undocumented output | |
| 74 ## @end table | |
| 75 ## @seealso{pqpnonneg, lscov, optimset} | |
| 7682 | 76 ## @end deftypefn |
| 77 | |
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78 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. |
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79 ## PKG_ADD: [~] = __all_opts__ ("lsqnonneg"); |
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80 |
| 22769 | 81 ## This is implemented from Lawson and Hanson's 1973 algorithm on page 161 of |
| 82 ## Solving Least Squares Problems. | |
| 7682 | 83 |
| 22769 | 84 function [x, resnorm, residual, exitflag, output, lambda] = lsqnonneg (c, d, |
| 85 x0 = [], | |
| 86 options = struct ()) | |
| 8600 | 87 |
| 22769 | 88 ## Special case: called to find default optimization options |
| 89 if (nargin == 1 && ischar (c) && strcmp (c, "defaults")) | |
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90 x = struct ("MaxIter", 1e5); |
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91 return; |
| 8600 | 92 endif |
| 93 | |
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94 if (nargin < 2) |
| 8600 | 95 print_usage (); |
| 96 endif | |
| 7682 | 97 |
| 22769 | 98 if (! (isnumeric (c) && ismatrix (c)) || ! (isnumeric (d) && ismatrix (d))) |
| 99 error ("lsqnonneg: C and D must be numeric matrices"); | |
| 100 endif | |
| 101 | |
| 102 if (! isstruct (options)) | |
| 103 error ("lsqnonneg: OPTIONS must be a struct"); | |
| 104 endif | |
| 105 | |
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106 ## Lawson-Hanson Step 1 (LH1): initialize the variables. |
| 8600 | 107 m = rows (c); |
| 108 n = columns (c); | |
| 22769 | 109 if (isempty (x0)) |
| 110 ## Initial guess is all zeros. | |
| 8600 | 111 x = zeros (n, 1); |
| 112 else | |
| 113 ## ensure nonnegative guess. | |
| 22769 | 114 x = max (x0, 0); |
| 7682 | 115 endif |
| 116 | |
| 22769 | 117 useqr = (m >= n); |
| 8507 | 118 max_iter = optimget (options, "MaxIter", 1e5); |
| 7682 | 119 |
| 8600 | 120 ## Initialize P, according to zero pattern of x. |
| 121 p = find (x > 0).'; | |
| 122 if (useqr) | |
| 123 ## Initialize the QR factorization, economized form. | |
| 124 [q, r] = qr (c(:,p), 0); | |
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125 endif |
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126 |
| 7682 | 127 iter = 0; |
| 8600 | 128 |
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129 ## LH3: test for completion. |
| 8600 | 130 while (iter < max_iter) |
| 131 while (iter < max_iter) | |
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132 iter += 1; |
| 8600 | 133 |
| 134 ## LH6: compute the positive matrix and find the min norm solution | |
| 135 ## of the positive problem. | |
| 136 if (useqr) | |
| 137 xtmp = r \ q'*d; | |
| 138 else | |
| 139 xtmp = c(:,p) \ d; | |
| 140 endif | |
| 141 idx = find (xtmp < 0); | |
| 142 | |
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143 if (isempty (idx)) |
| 8600 | 144 ## LH7: tmp solution found, iterate. |
| 145 x(:) = 0; | |
| 146 x(p) = xtmp; | |
| 147 break; | |
| 148 else | |
| 149 ## LH8, LH9: find the scaling factor. | |
| 150 pidx = p(idx); | |
| 22769 | 151 sf = x(pidx) ./ (x(pidx) - xtmp(idx)); |
| 8600 | 152 alpha = min (sf); |
| 153 ## LH10: adjust X. | |
| 154 xx = zeros (n, 1); | |
| 155 xx(p) = xtmp; | |
| 156 x += alpha*(xx - x); | |
| 157 ## LH11: move from P to Z all X == 0. | |
| 158 ## This corresponds to those indices where minimum of sf is attained. | |
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159 idx = idx(sf == alpha); |
| 8600 | 160 p(idx) = []; |
| 161 if (useqr) | |
| 162 ## update the QR factorization. | |
| 163 [q, r] = qrdelete (q, r, idx); | |
| 164 endif | |
| 165 endif | |
| 166 endwhile | |
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167 |
| 8600 | 168 ## compute the gradient. |
| 169 w = c'*(d - c*x); | |
| 170 w(p) = []; | |
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171 tolx = optimget (options, "TolX", 10*eps*norm (c, 1)*length (c)); |
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172 if (! any (w > tolx)) |
| 8600 | 173 if (useqr) |
| 174 ## verify the solution achieved using qr updating. | |
| 175 ## in the best case, this should only take a single step. | |
| 176 useqr = false; | |
| 177 continue; | |
| 178 else | |
| 179 ## we're finished. | |
| 180 break; | |
| 181 endif | |
| 182 endif | |
| 183 | |
| 184 ## find the maximum gradient. | |
| 7682 | 185 idx = find (w == max (w)); |
| 186 if (numel (idx) > 1) | |
| 187 warning ("lsqnonneg:nonunique", | |
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188 "a non-unique solution may be returned due to equal gradients"); |
| 7682 | 189 idx = idx(1); |
| 190 endif | |
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191 ## move the index from Z to P. Keep P sorted. |
| 8600 | 192 z = [1:n]; z(p) = []; |
| 193 zidx = z(idx); | |
| 194 jdx = 1 + lookup (p, zidx); | |
| 195 p = [p(1:jdx-1), zidx, p(jdx:end)]; | |
| 196 if (useqr) | |
| 197 ## insert the column into the QR factorization. | |
| 198 [q, r] = qrinsert (q, r, jdx, c(:,zidx)); | |
| 199 endif | |
| 7682 | 200 |
| 201 endwhile | |
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202 ## LH12: complete. |
| 7682 | 203 |
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204 ## Generate the additional output arguments. |
| 22769 | 205 if (isargout (2)) |
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206 resnorm = norm (c*x - d) ^ 2; |
| 7682 | 207 endif |
| 22769 | 208 if (isargout (3)) |
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209 residual = d - c*x; |
| 7682 | 210 endif |
| 22769 | 211 if (isargout (4)) |
| 212 if (iter >= max_iter) | |
| 213 exitflag = 0; | |
| 214 else | |
| 215 exitflag = iter; | |
| 216 endif | |
| 7682 | 217 endif |
| 22769 | 218 if (isargout (5)) |
| 7682 | 219 output = struct ("algorithm", "nnls", "iterations", iter); |
| 220 endif | |
| 22769 | 221 if (isargout (6)) |
| 8600 | 222 lambda = zeros (size (x)); |
| 223 lambda(p) = w; | |
| 7682 | 224 endif |
| 225 | |
| 226 endfunction | |
| 227 | |
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228 |
| 7682 | 229 %!test |
| 230 %! C = [1 0;0 1;2 1]; | |
| 231 %! d = [1;3;-2]; | |
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232 %! assert (lsqnonneg (C, d), [0;0.5], 100*eps); |
| 7682 | 233 |
| 234 %!test | |
| 235 %! C = [0.0372 0.2869;0.6861 0.7071;0.6233 0.6245;0.6344 0.6170]; | |
| 236 %! d = [0.8587;0.1781;0.0747;0.8405]; | |
| 237 %! xnew = [0;0.6929]; | |
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238 %! assert (lsqnonneg (C, d), xnew, 0.0001); |
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239 |
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Rik <rik@octave.org>
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240 ## Test input validation |
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test: Add expected error message <Invalid call> to BIST tests for nargin.
Rik <rik@octave.org>
parents:
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241 %!error <Invalid call> lsqnonneg () |
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90fea9cc9caa
test: Add expected error message <Invalid call> to BIST tests for nargin.
Rik <rik@octave.org>
parents:
28789
diff
changeset
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242 %!error <Invalid call> lsqnonneg (1) |
| 22769 | 243 %!error <C .* must be numeric matrices> lsqnonneg ({1},2) |
| 244 %!error <C .* must be numeric matrices> lsqnonneg (ones (2,2,2),2) | |
| 245 %!error <D must be numeric matrices> lsqnonneg (1,{2}) | |
| 246 %!error <D must be numeric matrices> lsqnonneg (1, ones (2,2,2)) | |
| 247 %!error <OPTIONS must be a struct> lsqnonneg (1, 2, [], 3) |