Mercurial > octave
annotate scripts/optimization/pqpnonneg.m @ 20735:418ae0cb752f
Replace ++,-- with in-place operators for performance.
* inputParser.m, int2str.m, interp2.m, interp3.m, interpn.m, __isequal__.m,
voronoi.m, imshow.m, jet.m, __imread__.m, __imwrite__.m, imwrite_filename.m,
dlmwrite.m, importdata.m, strread.m, krylov.m, fact.m, genvarname.m, fminbnd.m,
fminsearch.m, fminunc.m, fsolve.m, fzero.m, lsqnonneg.m, pqpnonneg.m, qp.m,
sqp.m, annotation.m, legend.m, orient.m, __bar__.m, __contour__.m, __patch__.m,
__plt__.m, __scatter__.m, rectangle.m, surfc.m, figure.m, hdl2struct.m, pan.m,
__gnuplot_draw_axes__.m, __gnuplot_ginput__.m, rotate3d.m, struct2hdl.m,
zoom.m, freqz.m, periodogram.m, gmres.m, pcg.m, pcr.m, __sprand__.m,
sprandsym.m, treelayout.m, treeplot.m, hadamard.m, hilb.m, iqr.m, assert.m,
test.m: Replace ++,-- with in-place operators for performance.
| author | Rik <rik@octave.org> |
|---|---|
| date | Sun, 22 Nov 2015 20:25:17 -0800 |
| parents | f1d0f506ee78 |
| children | 516bb87ea72e |
| rev | line source |
|---|---|
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1 ## Copyright (C) 2008-2015 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}. |
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29 ## |
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30 ## @var{c} ## and @var{d} must be real, and @var{c} must be symmetric and |
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31 ## positive definite. |
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32 ## |
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33 ## @var{x0} is an optional initial guess for @var{x}. |
| 9635 | 34 ## |
| 35 ## Outputs: | |
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36 ## |
| 9635 | 37 ## @itemize @bullet |
| 38 ## @item minval | |
| 39 ## | |
| 40 ## The minimum attained model value, 1/2*xmin'*c*xmin + d'*xmin | |
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41 ## |
| 9635 | 42 ## @item exitflag |
| 43 ## | |
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44 ## An indicator of convergence. 0 indicates that the iteration count was |
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45 ## exceeded, and therefore convergence was not reached; >0 indicates that the |
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46 ## algorithm converged. (The algorithm is stable and will converge given |
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47 ## enough iterations.) |
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48 ## |
| 9635 | 49 ## @item output |
| 50 ## | |
| 51 ## A structure with two fields: | |
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52 ## |
| 9635 | 53 ## @itemize @bullet |
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54 ## @item @qcode{"algorithm"}: The algorithm used (@qcode{"nnls"}) |
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55 ## |
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56 ## @item @qcode{"iterations"}: The number of iterations taken. |
| 9635 | 57 ## @end itemize |
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58 ## |
| 9635 | 59 ## @item lambda |
| 60 ## | |
| 61 ## Not implemented. | |
| 62 ## @end itemize | |
| 63 ## @seealso{optimset, lsqnonneg, qp} | |
| 64 ## @end deftypefn | |
| 65 | |
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66 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. |
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67 ## PKG_ADD: [~] = __all_opts__ ("pqpnonneg"); |
| 9635 | 68 |
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69 ## This is analogical to the lsqnonneg implementation, which is |
| 9635 | 70 ## implemented from Lawson and Hanson's 1973 algorithm on page |
| 71 ## 161 of Solving Least Squares Problems. | |
| 72 ## It shares the convergence guarantees. | |
| 73 | |
| 74 function [x, minval, exitflag, output, lambda] = pqpnonneg (c, d, x = [], options = struct ()) | |
| 75 | |
| 76 if (nargin == 1 && ischar (c) && strcmp (c, 'defaults')) | |
| 77 x = optimset ("MaxIter", 1e5); | |
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78 return; |
| 9635 | 79 endif |
| 80 | |
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81 if (nargin < 2 || nargin > 4 |
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82 || ! (ismatrix (c) && ismatrix (d) && isstruct (options))) |
| 9635 | 83 print_usage (); |
| 84 endif | |
| 85 | |
| 86 ## Lawson-Hanson Step 1 (LH1): initialize the variables. | |
| 87 m = rows (c); | |
| 88 n = columns (c); | |
| 89 if (m != n) | |
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90 error ("pqpnonneg: matrix must be square"); |
| 9635 | 91 endif |
| 92 | |
| 93 if (isempty (x)) | |
| 94 ## Initial guess is 0s. | |
| 95 x = zeros (n, 1); | |
| 96 else | |
| 97 ## ensure nonnegative guess. | |
| 98 x = max (x, 0); | |
| 99 endif | |
| 100 | |
| 101 max_iter = optimget (options, "MaxIter", 1e5); | |
| 102 | |
| 103 ## Initialize P, according to zero pattern of x. | |
| 104 p = find (x > 0).'; | |
| 105 ## Initialize the Cholesky factorization. | |
| 106 r = chol (c(p, p)); | |
| 107 usechol = true; | |
| 108 | |
| 109 iter = 0; | |
| 110 | |
| 111 ## LH3: test for completion. | |
| 112 while (iter < max_iter) | |
| 113 while (iter < max_iter) | |
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114 iter += 1; |
| 9635 | 115 |
| 116 ## LH6: compute the positive matrix and find the min norm solution | |
| 117 ## of the positive problem. | |
| 118 if (usechol) | |
| 119 xtmp = -(r \ (r' \ d(p))); | |
| 120 else | |
| 121 xtmp = -(c(p,p) \ d(p)); | |
| 122 endif | |
| 123 idx = find (xtmp < 0); | |
| 124 | |
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125 if (isempty (idx)) |
| 9635 | 126 ## LH7: tmp solution found, iterate. |
| 127 x(:) = 0; | |
| 128 x(p) = xtmp; | |
| 129 break; | |
| 130 else | |
| 131 ## LH8, LH9: find the scaling factor. | |
| 132 pidx = p(idx); | |
| 133 sf = x(pidx)./(x(pidx) - xtmp(idx)); | |
| 134 alpha = min (sf); | |
| 135 ## LH10: adjust X. | |
| 136 xx = zeros (n, 1); | |
| 137 xx(p) = xtmp; | |
| 138 x += alpha*(xx - x); | |
| 139 ## LH11: move from P to Z all X == 0. | |
| 140 ## This corresponds to those indices where minimum of sf is attained. | |
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141 idx = idx(sf == alpha); |
| 9635 | 142 p(idx) = []; |
| 143 if (usechol) | |
| 144 ## update the Cholesky factorization. | |
| 145 r = choldelete (r, idx); | |
| 146 endif | |
| 147 endif | |
| 148 endwhile | |
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149 |
| 9635 | 150 ## compute the gradient. |
| 151 w = -(d + c*x); | |
| 152 w(p) = []; | |
| 153 if (! any (w > 0)) | |
| 154 if (usechol) | |
| 155 ## verify the solution achieved using qr updating. | |
| 156 ## in the best case, this should only take a single step. | |
| 157 usechol = false; | |
| 158 continue; | |
| 159 else | |
| 160 ## we're finished. | |
| 161 break; | |
| 162 endif | |
| 163 endif | |
| 164 | |
| 165 ## find the maximum gradient. | |
| 166 idx = find (w == max (w)); | |
| 167 if (numel (idx) > 1) | |
| 168 warning ("pqpnonneg:nonunique", | |
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169 "a non-unique solution may be returned due to equal gradients"); |
| 9635 | 170 idx = idx(1); |
| 171 endif | |
| 172 ## move the index from Z to P. Keep P sorted. | |
| 173 z = [1:n]; z(p) = []; | |
| 174 zidx = z(idx); | |
| 175 jdx = 1 + lookup (p, zidx); | |
| 176 p = [p(1:jdx-1), zidx, p(jdx:end)]; | |
| 177 if (usechol) | |
| 178 ## insert the column into the Cholesky factorization. | |
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179 [r, bad] = cholinsert (r, jdx, c(p,zidx)); |
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180 if (bad) |
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181 ## If the insertion failed, we switch off updates and go on. |
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182 usechol = false; |
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183 endif |
| 9635 | 184 endif |
| 185 | |
| 186 endwhile | |
| 187 ## LH12: complete. | |
| 188 | |
| 189 ## Generate the additional output arguments. | |
| 190 if (nargout > 1) | |
| 191 minval = 1/2*(x'*c*x) + d'*x; | |
| 192 endif | |
| 193 exitflag = iter; | |
| 194 if (nargout > 2 && iter >= max_iter) | |
| 195 exitflag = 0; | |
| 196 endif | |
| 197 if (nargout > 3) | |
| 198 output = struct ("algorithm", "nnls-pqp", "iterations", iter); | |
| 199 endif | |
| 200 if (nargout > 4) | |
| 201 lambda = zeros (size (x)); | |
| 202 lambda(p) = w; | |
| 203 endif | |
| 204 | |
| 205 endfunction | |
| 206 | |
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207 |
| 9635 | 208 %!test |
| 209 %! C = [5 2;2 2]; | |
| 210 %! d = [3; -1]; | |
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211 %! assert (pqpnonneg (C, d), [0;0.5], 100*eps); |
| 9635 | 212 |
| 213 ## Test equivalence of lsq and pqp | |
| 214 %!test | |
| 215 %! C = rand (20, 10); | |
| 216 %! d = rand (20, 1); | |
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217 %! assert (pqpnonneg (C'*C, -C'*d), lsqnonneg (C, d), 100*eps); |
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218 |