Mercurial > octave
annotate scripts/optimization/pqpnonneg.m @ 25579:07c2c42f457e stable
doc: Miscellaneous documentation fixes all over the manual (bug #54288).
* embedded.cc, defaults.cc, error.cc, hex2num.cc, load-save.cc, integral2.m,
integral3.m, quad2d.m, warning_ids.m, decic.m, lsqnonneg.m, pqpnonneg.m,
bicg.m, betaincinv.m: Removal of duplicate words and redundant ')' and ';'
characters. Added missing '"', ')' characters. Renamed variables to match
other occurrences in docstring. Use '*' instead of 'x' for multiply.
Surround variables with @var{}.
| author | Rik <rik@octave.org> |
|---|---|
| date | Wed, 11 Jul 2018 08:40:07 -0700 |
| parents | 6652d3823428 |
| children | 804e18e3e320 |
| rev | line source |
|---|---|
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1 ## Copyright (C) 2008-2018 Bill Denney |
| 9635 | 2 ## Copyright (C) 2008 Jaroslav Hajek |
| 3 ## Copyright (C) 2009 VZLU Prague | |
| 4 ## | |
| 5 ## This file is part of Octave. | |
| 6 ## | |
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7 ## Octave is free software: you can redistribute it and/or modify it |
| 9635 | 8 ## under the terms of the GNU General Public License as published by |
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9 ## the Free Software Foundation, either version 3 of the License, or |
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10 ## (at your option) any later version. |
| 9635 | 11 ## |
| 12 ## Octave is distributed in the hope that it will be useful, but | |
| 13 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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14 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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15 ## GNU General Public License for more details. |
| 9635 | 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 | |
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19 ## <https://www.gnu.org/licenses/>. |
| 9635 | 20 |
| 21 ## -*- texinfo -*- | |
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22 ## @deftypefn {} {@var{x} =} pqpnonneg (@var{c}, @var{d}) |
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23 ## @deftypefnx {} {@var{x} =} pqpnonneg (@var{c}, @var{d}, @var{x0}) |
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24 ## @deftypefnx {} {@var{x} =} pqpnonneg (@var{c}, @var{d}, @var{x0}, @var{options}) |
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25 ## @deftypefnx {} {[@var{x}, @var{minval}] =} pqpnonneg (@dots{}) |
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26 ## @deftypefnx {} {[@var{x}, @var{minval}, @var{exitflag}] =} pqpnonneg (@dots{}) |
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27 ## @deftypefnx {} {[@var{x}, @var{minval}, @var{exitflag}, @var{output}] =} pqpnonneg (@dots{}) |
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28 ## @deftypefnx {} {[@var{x}, @var{minval}, @var{exitflag}, @var{output}, @var{lambda}] =} pqpnonneg (@dots{}) |
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29 ## |
| 22764 | 30 ## Minimize @code{1/2*@var{x}'*@var{c}*@var{x} + @var{d}'*@var{x}} subject to |
| 31 ## @code{@var{x} >= 0}. | |
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32 ## |
| 22764 | 33 ## @var{c} and @var{d} must be real matrices, and @var{c} must be symmetric and |
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34 ## positive definite. |
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35 ## |
| 22764 | 36 ## @var{x0} is an optional initial guess for the solution @var{x}. |
| 9635 | 37 ## |
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38 ## @var{options} is an options structure to change the behavior of the |
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39 ## algorithm (@pxref{XREFoptimset,,optimset}). @code{pqpnonneg} recognizes |
| 22769 | 40 ## one option: @qcode{"MaxIter"}. |
| 9635 | 41 ## |
| 42 ## Outputs: | |
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43 ## |
| 22764 | 44 ## @table @var |
| 45 ## | |
| 46 ## @item x | |
| 47 ## The solution matrix | |
| 48 ## | |
| 9635 | 49 ## @item minval |
| 22764 | 50 ## The minimum attained model value, |
| 51 ## @code{1/2*@var{xmin}'*@var{c}*@var{xmin} + @var{d}'*@var{xmin}} | |
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52 ## |
| 9635 | 53 ## @item exitflag |
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54 ## An indicator of convergence. 0 indicates that the iteration count was |
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55 ## exceeded, and therefore convergence was not reached; >0 indicates that the |
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56 ## algorithm converged. (The algorithm is stable and will converge given |
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57 ## enough iterations.) |
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58 ## |
| 9635 | 59 ## @item output |
| 60 ## A structure with two fields: | |
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61 ## |
| 9635 | 62 ## @itemize @bullet |
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63 ## @item @qcode{"algorithm"}: The algorithm used (@nospell{@qcode{"nnls"}}) |
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64 ## |
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65 ## @item @qcode{"iterations"}: The number of iterations taken. |
| 9635 | 66 ## @end itemize |
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67 ## |
| 9635 | 68 ## @item lambda |
| 22764 | 69 ## @c FIXME: Something is output from the function, but what is it? |
| 70 ## Undocumented output | |
| 71 ## @end table | |
| 72 ## @seealso{lsqnonneg, qp, optimset} | |
| 9635 | 73 ## @end deftypefn |
| 74 | |
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75 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. |
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76 ## PKG_ADD: [~] = __all_opts__ ("pqpnonneg"); |
| 9635 | 77 |
| 22764 | 78 ## This is analogical to the lsqnonneg implementation, which is implemented |
| 79 ## from Lawson and Hanson's 1973 algorithm on page 161 of Solving Least Squares | |
| 80 ## Problems. It shares the convergence guarantees. | |
| 9635 | 81 |
| 22769 | 82 function [x, minval, exitflag, output, lambda] = pqpnonneg (c, d, x0 = [], |
| 83 options = struct ()) | |
| 9635 | 84 |
| 22764 | 85 ## Special case: called to find default optimization options |
| 86 if (nargin == 1 && ischar (c) && strcmp (c, "defaults")) | |
| 9635 | 87 x = optimset ("MaxIter", 1e5); |
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88 return; |
| 9635 | 89 endif |
| 90 | |
| 22764 | 91 if (nargin < 2 || nargin > 4) |
| 9635 | 92 print_usage (); |
| 93 endif | |
| 94 | |
| 22764 | 95 if (! (isnumeric (c) && ismatrix (c)) || ! (isnumeric (d) && ismatrix (d))) |
| 96 error ("pqpnonneg: C and D must be numeric matrices"); | |
| 97 endif | |
| 98 if (! issquare (c)) | |
| 99 error ("pqpnonneg: C must be a square matrix"); | |
| 100 endif | |
| 101 | |
| 102 if (! isstruct (options)) | |
| 103 error ("pqpnonneg: OPTIONS must be a struct"); | |
| 104 endif | |
| 105 | |
| 9635 | 106 ## Lawson-Hanson Step 1 (LH1): initialize the variables. |
| 107 n = columns (c); | |
| 22764 | 108 if (isempty (x0)) |
| 109 ## Initial guess is all zeros. | |
| 9635 | 110 x = zeros (n, 1); |
| 111 else | |
| 112 ## ensure nonnegative guess. | |
| 22764 | 113 x = max (x0, 0); |
| 9635 | 114 endif |
| 115 | |
| 116 max_iter = optimget (options, "MaxIter", 1e5); | |
| 117 | |
| 118 ## Initialize P, according to zero pattern of x. | |
| 119 p = find (x > 0).'; | |
| 120 ## Initialize the Cholesky factorization. | |
| 121 r = chol (c(p, p)); | |
| 122 usechol = true; | |
| 123 | |
| 124 iter = 0; | |
| 125 | |
| 126 ## LH3: test for completion. | |
| 127 while (iter < max_iter) | |
| 128 while (iter < max_iter) | |
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129 iter += 1; |
| 9635 | 130 |
| 131 ## LH6: compute the positive matrix and find the min norm solution | |
| 132 ## of the positive problem. | |
| 133 if (usechol) | |
| 134 xtmp = -(r \ (r' \ d(p))); | |
| 135 else | |
| 136 xtmp = -(c(p,p) \ d(p)); | |
| 137 endif | |
| 138 idx = find (xtmp < 0); | |
| 139 | |
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140 if (isempty (idx)) |
| 9635 | 141 ## LH7: tmp solution found, iterate. |
| 142 x(:) = 0; | |
| 143 x(p) = xtmp; | |
| 144 break; | |
| 145 else | |
| 146 ## LH8, LH9: find the scaling factor. | |
| 147 pidx = p(idx); | |
| 22764 | 148 sf = x(pidx) ./ (x(pidx) - xtmp(idx)); |
| 9635 | 149 alpha = min (sf); |
| 150 ## LH10: adjust X. | |
| 151 xx = zeros (n, 1); | |
| 152 xx(p) = xtmp; | |
| 153 x += alpha*(xx - x); | |
| 154 ## LH11: move from P to Z all X == 0. | |
| 155 ## This corresponds to those indices where minimum of sf is attained. | |
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156 idx = idx(sf == alpha); |
| 9635 | 157 p(idx) = []; |
| 158 if (usechol) | |
| 159 ## update the Cholesky factorization. | |
| 160 r = choldelete (r, idx); | |
| 161 endif | |
| 162 endif | |
| 163 endwhile | |
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164 |
| 9635 | 165 ## compute the gradient. |
| 166 w = -(d + c*x); | |
| 167 w(p) = []; | |
| 168 if (! any (w > 0)) | |
| 169 if (usechol) | |
| 170 ## verify the solution achieved using qr updating. | |
| 22764 | 171 ## In the best case, this should only take a single step. |
| 9635 | 172 usechol = false; |
| 173 continue; | |
| 174 else | |
| 175 ## we're finished. | |
| 176 break; | |
| 177 endif | |
| 178 endif | |
| 179 | |
| 180 ## find the maximum gradient. | |
| 181 idx = find (w == max (w)); | |
| 182 if (numel (idx) > 1) | |
| 183 warning ("pqpnonneg:nonunique", | |
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184 "a non-unique solution may be returned due to equal gradients"); |
| 9635 | 185 idx = idx(1); |
| 186 endif | |
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187 ## move the index from Z to P. Keep P sorted. |
| 9635 | 188 z = [1:n]; z(p) = []; |
| 189 zidx = z(idx); | |
| 190 jdx = 1 + lookup (p, zidx); | |
| 191 p = [p(1:jdx-1), zidx, p(jdx:end)]; | |
| 192 if (usechol) | |
| 193 ## insert the column into the Cholesky factorization. | |
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194 [r, bad] = cholinsert (r, jdx, c(p,zidx)); |
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195 if (bad) |
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196 ## If the insertion failed, we switch off updates and go on. |
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197 usechol = false; |
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198 endif |
| 9635 | 199 endif |
| 200 | |
| 201 endwhile | |
| 202 ## LH12: complete. | |
| 203 | |
| 204 ## Generate the additional output arguments. | |
| 22764 | 205 if (isargout (2)) |
| 9635 | 206 minval = 1/2*(x'*c*x) + d'*x; |
| 207 endif | |
| 22764 | 208 if (isargout (3)) |
| 209 if (iter >= max_iter) | |
| 210 exitflag = 0; | |
| 211 else | |
| 212 exitflag = iter; | |
| 213 endif | |
| 9635 | 214 endif |
| 22764 | 215 if (isargout (4)) |
| 9635 | 216 output = struct ("algorithm", "nnls-pqp", "iterations", iter); |
| 217 endif | |
| 22764 | 218 if (isargout (5)) |
| 9635 | 219 lambda = zeros (size (x)); |
| 220 lambda(p) = w; | |
| 221 endif | |
| 222 | |
| 223 endfunction | |
| 224 | |
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225 |
| 9635 | 226 %!test |
| 227 %! C = [5 2;2 2]; | |
| 228 %! d = [3; -1]; | |
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229 %! assert (pqpnonneg (C, d), [0;0.5], 100*eps); |
| 9635 | 230 |
| 231 ## Test equivalence of lsq and pqp | |
| 232 %!test | |
| 233 %! C = rand (20, 10); | |
| 234 %! d = rand (20, 1); | |
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235 %! assert (pqpnonneg (C'*C, -C'*d), lsqnonneg (C, d), 100*eps); |
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236 |
| 22764 | 237 # Test input validation |
| 238 %!error pqpnonneg () | |
| 239 %!error pqpnonneg (1) | |
| 240 %!error pqpnonneg (1,2,3,4,5) | |
| 241 %!error <C .* must be numeric matrices> pqpnonneg ({1},2) | |
| 242 %!error <C .* must be numeric matrices> pqpnonneg (ones (2,2,2),2) | |
| 243 %!error <D must be numeric matrices> pqpnonneg (1,{2}) | |
| 244 %!error <D must be numeric matrices> pqpnonneg (1, ones (2,2,2)) | |
| 245 %!error <C must be a square matrix> pqpnonneg ([1 2], 2) | |
| 246 %!error <OPTIONS must be a struct> pqpnonneg (1, 2, [], 3) |