Mercurial > octave
annotate scripts/optimization/pqpnonneg.m @ 28896:90fea9cc9caa
test: Add expected error message <Invalid call> to BIST tests for nargin.
* acosd.m, acot.m, acotd.m, acoth.m, acsc.m, acscd.m, acsch.m, asec.m,
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xor.m, convhull.m, delaunay.m, delaunayn.m, griddata.m, griddatan.m,
inpolygon.m, voronoi.m, voronoin.m, listdlg.m, msgbox.m, questdlg.m,
rmappdata.m, setappdata.m, __gripe_missing_component__.m,
get_first_help_sentence.m, type.m, which.m, cmpermute.m, cmunique.m,
gray2ind.m, imfinfo.m, imshow.m, imwrite.m, ind2rgb.m, movie.m, rgb2ind.m,
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copyfile.m, delete.m, dos.m, fileparts.m, getfield.m, menu.m, mkdir.m,
movefile.m, orderfields.m, publish.m, setfield.m, substruct.m, unix.m,
unpack.m, decic.m, ode23.m, ode23s.m, ode45.m, fminsearch.m, lsqnonneg.m,
pqpnonneg.m, sqp.m, annotation.m, lighting.m, shading.m, area.m, compass.m,
contourc.m, feather.m, fplot.m, hist.m, isocaps.m, isocolors.m, isonormals.m,
isosurface.m, ostreamtube.m, pie.m, pie3.m, reducepatch.m, reducevolume.m,
rose.m, smooth3.m, stairs.m, stem.m, stem3.m, stream2.m, stream3.m,
streamline.m, streamribbon.m, streamtube.m, surfnorm.m, trimesh.m, trisurf.m,
colstyle.m, hgload.m, linkprop.m, meshgrid.m, ndgrid.m, padecoef.m, polyfit.m,
polyval.m, unmkpp.m, profexport.m, ismember.m, unique.m, movfun.m, movslice.m,
periodogram.m, sinc.m, spdiags.m, sprandsym.m, betaincinv.m, ellipke.m,
factor.m, gammainc.m, gammaincinv.m, isprime.m, lcm.m, gallery.m, hadamard.m,
bounds.m, corrcoef.m, discrete_rnd.m, empirical_rnd.m, histc.m, mode.m,
movmad.m, movmax.m, movmean.m, movmedian.m, movmin.m, movprod.m, movstd.m,
movsum.m, movvar.m, ranks.m, runlength.m, zscore.m, str2num.m, strchr.m,
strsplit.m, strtok.m, untabify.m, assert.m, demo.m, example.m, speed.m, test.m,
datenum.m, datevec.m, webread.m, webwrite.m:
Add expected error message <Invalid call> to BIST tests for nargin.
Remove redundant tests for nargin greater than the number of declared inputs
which are now handled by interpreter.
| author | Rik <rik@octave.org> |
|---|---|
| date | Sun, 11 Oct 2020 21:59:35 -0700 |
| parents | 28de41192f3c |
| children | fc4bb4bd1d5e |
| 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,,optimset}). @code{pqpnonneg} recognizes |
| 22769 | 45 ## 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 |
| 22764 | 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) |