Mercurial > octave
annotate scripts/optimization/pqpnonneg.m @ 17281:bc924baa2c4e
doc: Add new @qcode macro for code samples which are quoted.
Macro handles options ("on") or properties ("position") more elegantly
than @code{"text"}.
* doc/interpreter/macros.texi: Add new @qcode macro.
* doc/interpreter/tips.txi: Add documentation about @qcode macro.
* doc/interpreter/basics.txi, doc/interpreter/container.txi,
doc/interpreter/emacs.txi, doc/interpreter/errors.txi,
doc/interpreter/eval.txi, doc/interpreter/expr.txi,
doc/interpreter/external.txi, doc/interpreter/func.txi,
doc/interpreter/grammar.txi, doc/interpreter/image.txi,
doc/interpreter/install.txi, doc/interpreter/interp.txi,
doc/interpreter/io.txi, doc/interpreter/matrix.txi,
doc/interpreter/numbers.txi, doc/interpreter/oop.txi,
doc/interpreter/package.txi, doc/interpreter/plot.txi,
doc/interpreter/quad.txi, doc/interpreter/sparse.txi,
doc/interpreter/strings.txi, doc/interpreter/system.txi,
doc/interpreter/vectorize.txi, libinterp/corefcn/balance.cc,
libinterp/corefcn/bitfcns.cc, libinterp/corefcn/cellfun.cc,
libinterp/corefcn/conv2.cc, libinterp/corefcn/data.cc,
libinterp/corefcn/debug.cc, libinterp/corefcn/defaults.cc,
libinterp/corefcn/dirfns.cc, libinterp/corefcn/dlmread.cc,
libinterp/corefcn/error.cc, libinterp/corefcn/file-io.cc,
libinterp/corefcn/find.cc, libinterp/corefcn/gammainc.cc,
libinterp/corefcn/graphics.cc, libinterp/corefcn/help.cc,
libinterp/corefcn/hex2num.cc, libinterp/corefcn/input.cc,
libinterp/corefcn/load-path.cc, libinterp/corefcn/load-save.cc,
libinterp/corefcn/ls-oct-ascii.cc, libinterp/corefcn/lu.cc,
libinterp/corefcn/luinc.cc, libinterp/corefcn/matrix_type.cc,
libinterp/corefcn/oct-hist.cc, libinterp/corefcn/pager.cc,
libinterp/corefcn/pr-output.cc, libinterp/corefcn/pt-jit.cc,
libinterp/corefcn/qz.cc, libinterp/corefcn/rand.cc,
libinterp/corefcn/regexp.cc, libinterp/corefcn/schur.cc,
libinterp/corefcn/sighandlers.cc, libinterp/corefcn/sparse.cc,
libinterp/corefcn/spparms.cc, libinterp/corefcn/str2double.cc,
libinterp/corefcn/svd.cc, libinterp/corefcn/symtab.cc,
libinterp/corefcn/syscalls.cc, libinterp/corefcn/toplev.cc,
libinterp/corefcn/tril.cc, libinterp/corefcn/typecast.cc,
libinterp/corefcn/utils.cc, libinterp/corefcn/variables.cc,
libinterp/dldfcn/__init_fltk__.cc, libinterp/dldfcn/chol.cc,
libinterp/dldfcn/colamd.cc, libinterp/dldfcn/fftw.cc, libinterp/dldfcn/qr.cc,
libinterp/dldfcn/symbfact.cc, libinterp/octave-value/ov-base.cc,
libinterp/octave-value/ov-fcn-handle.cc,
libinterp/octave-value/ov-fcn-inline.cc, libinterp/octave-value/ov-java.cc,
libinterp/octave-value/ov-range.cc, libinterp/octave-value/ov-struct.cc,
libinterp/octave-value/ov-usr-fcn.cc, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/pt-binop.cc, libinterp/parse-tree/pt-eval.cc,
libinterp/parse-tree/pt-mat.cc, scripts/@ftp/ftp.m,
scripts/deprecated/java_convert_matrix.m, scripts/deprecated/java_debug.m,
scripts/deprecated/java_unsigned_conversion.m, scripts/deprecated/shell_cmd.m,
scripts/general/dblquad.m, scripts/general/display.m,
scripts/general/genvarname.m, scripts/general/idivide.m,
scripts/general/interp1.m, scripts/general/interp2.m,
scripts/general/interp3.m, scripts/general/interpn.m, scripts/general/isa.m,
scripts/general/profexplore.m, scripts/general/profile.m,
scripts/general/quadgk.m, scripts/general/randi.m, scripts/general/structfun.m,
scripts/general/subsindex.m, scripts/general/triplequad.m,
scripts/geometry/griddata.m, scripts/geometry/griddata3.m,
scripts/geometry/griddatan.m, scripts/geometry/voronoi.m, scripts/help/help.m,
scripts/help/lookfor.m, scripts/image/cmpermute.m, scripts/image/colormap.m,
scripts/image/image.m, scripts/image/imagesc.m, scripts/image/imfinfo.m,
scripts/image/imformats.m, scripts/image/imread.m, scripts/image/imshow.m,
scripts/image/imwrite.m, scripts/image/ind2gray.m, scripts/image/lines.m,
scripts/image/rgb2ind.m, scripts/image/spinmap.m, scripts/io/dlmwrite.m,
scripts/io/strread.m, scripts/io/textread.m, scripts/io/textscan.m,
scripts/java/javaclasspath.m, scripts/java/usejava.m,
scripts/miscellaneous/bzip2.m, scripts/miscellaneous/computer.m,
scripts/miscellaneous/copyfile.m, scripts/miscellaneous/debug.m,
scripts/miscellaneous/dos.m, scripts/miscellaneous/edit.m,
scripts/miscellaneous/gzip.m, scripts/miscellaneous/license.m,
scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/movefile.m,
scripts/miscellaneous/parseparams.m, scripts/miscellaneous/unix.m,
scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m,
scripts/optimization/fminunc.m, scripts/optimization/fsolve.m,
scripts/optimization/fzero.m, scripts/optimization/glpk.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/optimset.m,
scripts/optimization/pqpnonneg.m, scripts/pkg/pkg.m, scripts/plot/allchild.m,
scripts/plot/ancestor.m, scripts/plot/area.m, scripts/plot/axis.m,
scripts/plot/bar.m, scripts/plot/barh.m, scripts/plot/box.m,
scripts/plot/caxis.m, scripts/plot/cla.m, scripts/plot/clabel.m,
scripts/plot/clf.m, scripts/plot/close.m, scripts/plot/colorbar.m,
scripts/plot/daspect.m, scripts/plot/ezmesh.m, scripts/plot/ezmeshc.m,
scripts/plot/ezsurf.m, scripts/plot/ezsurfc.m, scripts/plot/findall.m,
scripts/plot/findobj.m, scripts/plot/gcbo.m, scripts/plot/gcf.m,
scripts/plot/gco.m, scripts/plot/grid.m, scripts/plot/guihandles.m,
scripts/plot/hdl2struct.m, scripts/plot/hidden.m, scripts/plot/hold.m,
scripts/plot/isonormals.m, scripts/plot/isosurface.m, scripts/plot/legend.m,
scripts/plot/mesh.m, scripts/plot/meshc.m, scripts/plot/meshz.m,
scripts/plot/newplot.m, scripts/plot/orient.m, scripts/plot/pareto.m,
scripts/plot/patch.m, scripts/plot/pbaspect.m, scripts/plot/pcolor.m,
scripts/plot/plot.m, scripts/plot/print.m,
scripts/plot/private/__add_default_menu__.m, scripts/plot/quiver.m,
scripts/plot/quiver3.m, scripts/plot/refreshdata.m, scripts/plot/saveas.m,
scripts/plot/scatter.m, scripts/plot/scatter3.m, scripts/plot/shading.m,
scripts/plot/shrinkfaces.m, scripts/plot/slice.m, scripts/plot/stem.m,
scripts/plot/stem3.m, scripts/plot/struct2hdl.m, scripts/plot/subplot.m,
scripts/plot/surf.m, scripts/plot/surfc.m, scripts/plot/surfl.m,
scripts/plot/tetramesh.m, scripts/plot/uigetfile.m, scripts/plot/uimenu.m,
scripts/plot/uiputfile.m, scripts/plot/waterfall.m, scripts/plot/whitebg.m,
scripts/plot/xlim.m, scripts/plot/ylim.m, scripts/plot/zlim.m,
scripts/polynomial/conv.m, scripts/polynomial/polyout.m,
scripts/polynomial/splinefit.m, scripts/set/ismember.m, scripts/set/powerset.m,
scripts/set/setdiff.m, scripts/set/union.m, scripts/set/unique.m,
scripts/signal/detrend.m, scripts/signal/filter2.m, scripts/signal/freqz.m,
scripts/signal/periodogram.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/sparse/eigs.m, scripts/sparse/svds.m,
scripts/specfun/legendre.m, scripts/special-matrix/gallery.m,
scripts/statistics/base/mean.m, scripts/statistics/base/moment.m,
scripts/statistics/tests/cor_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test_2.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/sign_test.m,
scripts/statistics/tests/t_test.m, scripts/statistics/tests/t_test_2.m,
scripts/statistics/tests/t_test_regression.m,
scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m,
scripts/statistics/tests/welch_test.m,
scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m,
scripts/statistics/tests/z_test_2.m, scripts/strings/base2dec.m,
scripts/strings/index.m, scripts/strings/isstrprop.m,
scripts/strings/mat2str.m, scripts/strings/regexptranslate.m,
scripts/strings/rindex.m, scripts/strings/str2num.m, scripts/strings/strcat.m,
scripts/strings/strjust.m, scripts/strings/strmatch.m,
scripts/strings/validatestring.m, scripts/testfun/demo.m,
scripts/testfun/example.m, scripts/testfun/test.m, scripts/time/addtodate.m,
scripts/time/asctime.m, scripts/time/datestr.m, scripts/time/datetick.m,
scripts/time/weekday.m, scripts/ui/errordlg.m, scripts/ui/helpdlg.m,
scripts/ui/inputdlg.m, scripts/ui/listdlg.m, scripts/ui/msgbox.m,
scripts/ui/questdlg.m, scripts/ui/warndlg.m: Use new @qcode macro.
| author | Rik <rik@octave.org> |
|---|---|
| date | Mon, 19 Aug 2013 20:46:38 -0700 |
| parents | b76f0740940e |
| children | 088d014a7fe2 |
| rev | line source |
|---|---|
|
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1 ## Copyright (C) 2008-2012 Bill Denney |
| 9635 | 2 ## Copyright (C) 2008 Jaroslav Hajek |
| 3 ## Copyright (C) 2009 VZLU Prague | |
| 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} =} pqpnonneg (@var{c}, @var{d}) |
| 9635 | 23 ## @deftypefnx {Function File} {@var{x} =} pqpnonneg (@var{c}, @var{d}, @var{x0}) |
| 24 ## @deftypefnx {Function File} {[@var{x}, @var{minval}] =} pqpnonneg (@dots{}) | |
| 25 ## @deftypefnx {Function File} {[@var{x}, @var{minval}, @var{exitflag}] =} pqpnonneg (@dots{}) | |
| 26 ## @deftypefnx {Function File} {[@var{x}, @var{minval}, @var{exitflag}, @var{output}] =} pqpnonneg (@dots{}) | |
| 27 ## @deftypefnx {Function File} {[@var{x}, @var{minval}, @var{exitflag}, @var{output}, @var{lambda}] =} pqpnonneg (@dots{}) | |
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28 ## Minimize @code{1/2*x'*c*x + d'*x} subject to @code{@var{x} >= 0}. @var{c} |
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29 ## and @var{d} must be real, and @var{c} must be symmetric and positive |
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30 ## definite. @var{x0} is an optional initial guess for @var{x}. |
| 9635 | 31 ## |
| 32 ## Outputs: | |
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33 ## |
| 9635 | 34 ## @itemize @bullet |
| 35 ## @item minval | |
| 36 ## | |
| 37 ## The minimum attained model value, 1/2*xmin'*c*xmin + d'*xmin | |
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38 ## |
| 9635 | 39 ## @item exitflag |
| 40 ## | |
| 41 ## An indicator of convergence. 0 indicates that the iteration count | |
| 42 ## was exceeded, and therefore convergence was not reached; >0 indicates | |
| 43 ## that the algorithm converged. (The algorithm is stable and will | |
| 44 ## converge given enough iterations.) | |
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45 ## |
| 9635 | 46 ## @item output |
| 47 ## | |
| 48 ## A structure with two fields: | |
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49 ## |
| 9635 | 50 ## @itemize @bullet |
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51 ## @item @qcode{"algorithm"}: The algorithm used (@qcode{"nnls"}) |
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52 ## |
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53 ## @item @qcode{"iterations"}: The number of iterations taken. |
| 9635 | 54 ## @end itemize |
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55 ## |
| 9635 | 56 ## @item lambda |
| 57 ## | |
| 58 ## Not implemented. | |
| 59 ## @end itemize | |
| 60 ## @seealso{optimset, lsqnonneg, qp} | |
| 61 ## @end deftypefn | |
| 62 | |
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63 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. |
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64 ## PKG_ADD: [~] = __all_opts__ ("pqpnonneg"); |
| 9635 | 65 |
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66 ## This is analogical to the lsqnonneg implementation, which is |
| 9635 | 67 ## implemented from Lawson and Hanson's 1973 algorithm on page |
| 68 ## 161 of Solving Least Squares Problems. | |
| 69 ## It shares the convergence guarantees. | |
| 70 | |
| 71 function [x, minval, exitflag, output, lambda] = pqpnonneg (c, d, x = [], options = struct ()) | |
| 72 | |
| 73 if (nargin == 1 && ischar (c) && strcmp (c, 'defaults')) | |
| 74 x = optimset ("MaxIter", 1e5); | |
| 75 return | |
| 76 endif | |
| 77 | |
| 78 if (! (nargin >= 2 && nargin <= 4 && ismatrix (c) && ismatrix (d) && isstruct (options))) | |
| 79 print_usage (); | |
| 80 endif | |
| 81 | |
| 82 ## Lawson-Hanson Step 1 (LH1): initialize the variables. | |
| 83 m = rows (c); | |
| 84 n = columns (c); | |
| 85 if (m != n) | |
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86 error ("pqpnonneg: matrix must be square"); |
| 9635 | 87 endif |
| 88 | |
| 89 if (isempty (x)) | |
| 90 ## Initial guess is 0s. | |
| 91 x = zeros (n, 1); | |
| 92 else | |
| 93 ## ensure nonnegative guess. | |
| 94 x = max (x, 0); | |
| 95 endif | |
| 96 | |
| 97 max_iter = optimget (options, "MaxIter", 1e5); | |
| 98 | |
| 99 ## Initialize P, according to zero pattern of x. | |
| 100 p = find (x > 0).'; | |
| 101 ## Initialize the Cholesky factorization. | |
| 102 r = chol (c(p, p)); | |
| 103 usechol = true; | |
| 104 | |
| 105 iter = 0; | |
| 106 | |
| 107 ## LH3: test for completion. | |
| 108 while (iter < max_iter) | |
| 109 while (iter < max_iter) | |
| 110 iter++; | |
| 111 | |
| 112 ## LH6: compute the positive matrix and find the min norm solution | |
| 113 ## of the positive problem. | |
| 114 if (usechol) | |
| 115 xtmp = -(r \ (r' \ d(p))); | |
| 116 else | |
| 117 xtmp = -(c(p,p) \ d(p)); | |
| 118 endif | |
| 119 idx = find (xtmp < 0); | |
| 120 | |
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121 if (isempty (idx)) |
| 9635 | 122 ## LH7: tmp solution found, iterate. |
| 123 x(:) = 0; | |
| 124 x(p) = xtmp; | |
| 125 break; | |
| 126 else | |
| 127 ## LH8, LH9: find the scaling factor. | |
| 128 pidx = p(idx); | |
| 129 sf = x(pidx)./(x(pidx) - xtmp(idx)); | |
| 130 alpha = min (sf); | |
| 131 ## LH10: adjust X. | |
| 132 xx = zeros (n, 1); | |
| 133 xx(p) = xtmp; | |
| 134 x += alpha*(xx - x); | |
| 135 ## LH11: move from P to Z all X == 0. | |
| 136 ## This corresponds to those indices where minimum of sf is attained. | |
| 137 idx = idx (sf == alpha); | |
| 138 p(idx) = []; | |
| 139 if (usechol) | |
| 140 ## update the Cholesky factorization. | |
| 141 r = choldelete (r, idx); | |
| 142 endif | |
| 143 endif | |
| 144 endwhile | |
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145 |
| 9635 | 146 ## compute the gradient. |
| 147 w = -(d + c*x); | |
| 148 w(p) = []; | |
| 149 if (! any (w > 0)) | |
| 150 if (usechol) | |
| 151 ## verify the solution achieved using qr updating. | |
| 152 ## in the best case, this should only take a single step. | |
| 153 usechol = false; | |
| 154 continue; | |
| 155 else | |
| 156 ## we're finished. | |
| 157 break; | |
| 158 endif | |
| 159 endif | |
| 160 | |
| 161 ## find the maximum gradient. | |
| 162 idx = find (w == max (w)); | |
| 163 if (numel (idx) > 1) | |
| 164 warning ("pqpnonneg:nonunique", | |
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165 "a non-unique solution may be returned due to equal gradients"); |
| 9635 | 166 idx = idx(1); |
| 167 endif | |
| 168 ## move the index from Z to P. Keep P sorted. | |
| 169 z = [1:n]; z(p) = []; | |
| 170 zidx = z(idx); | |
| 171 jdx = 1 + lookup (p, zidx); | |
| 172 p = [p(1:jdx-1), zidx, p(jdx:end)]; | |
| 173 if (usechol) | |
| 174 ## insert the column into the Cholesky factorization. | |
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175 [r, bad] = cholinsert (r, jdx, c(p,zidx)); |
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176 if (bad) |
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177 ## If the insertion failed, we switch off updates and go on. |
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178 usechol = false; |
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179 endif |
| 9635 | 180 endif |
| 181 | |
| 182 endwhile | |
| 183 ## LH12: complete. | |
| 184 | |
| 185 ## Generate the additional output arguments. | |
| 186 if (nargout > 1) | |
| 187 minval = 1/2*(x'*c*x) + d'*x; | |
| 188 endif | |
| 189 exitflag = iter; | |
| 190 if (nargout > 2 && iter >= max_iter) | |
| 191 exitflag = 0; | |
| 192 endif | |
| 193 if (nargout > 3) | |
| 194 output = struct ("algorithm", "nnls-pqp", "iterations", iter); | |
| 195 endif | |
| 196 if (nargout > 4) | |
| 197 lambda = zeros (size (x)); | |
| 198 lambda(p) = w; | |
| 199 endif | |
| 200 | |
| 201 endfunction | |
| 202 | |
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203 |
| 9635 | 204 %!test |
| 205 %! C = [5 2;2 2]; | |
| 206 %! d = [3; -1]; | |
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207 %! assert (pqpnonneg (C, d), [0;0.5], 100*eps); |
| 9635 | 208 |
| 209 ## Test equivalence of lsq and pqp | |
| 210 %!test | |
| 211 %! C = rand (20, 10); | |
| 212 %! d = rand (20, 1); | |
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213 %! assert (pqpnonneg (C'*C, -C'*d), lsqnonneg (C, d), 100*eps); |
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214 |