Mercurial > octave
annotate scripts/optimization/lsqnonneg.m @ 8600:a6c1aa6f5915
improve lsqnonneg
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Tue, 27 Jan 2009 15:21:18 +0100 |
| parents | cadc73247d65 |
| children | ff61b53eb294 |
| rev | line source |
|---|---|
| 7682 | 1 ## Copyright (C) 2008 Bill Denney |
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2 ## Copyright (C) 2008 Jaroslav Hajek |
| 8600 | 3 ## Copyright (C) 2009 VZLU Prague |
| 7682 | 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 -*- | |
| 22 ## @deftypefn {Function File} {@var{x} =} lsqnonneg (@var{c}, @var{d}) | |
| 23 ## @deftypefnx {Function File} {@var{x} =} lsqnonneg (@var{c}, @var{d}, @var{x0}) | |
| 24 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}] =} lsqnonneg (@dots{}) | |
| 25 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}] =} lsqnonneg (@dots{}) | |
| 26 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}] =} lsqnonneg (@dots{}) | |
| 27 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}] =} lsqnonneg (@dots{}) | |
| 28 ## @deftypefnx {Function File} {[@var{x}, @var{resnorm}, @var{residual}, @var{exitflag}, @var{output}, @var{lambda}] =} lsqnonneg (@dots{}) | |
| 29 ## Minimize @code{norm (@var{c}*@var{x}-d)} subject to @code{@var{x} >= | |
| 30 ## 0}. @var{c} and @var{d} must be real. @var{x0} is an optional | |
| 31 ## initial guess for @var{x}. | |
| 32 ## | |
| 33 ## Outputs: | |
| 34 ## @itemize @bullet | |
| 35 ## @item resnorm | |
| 36 ## | |
| 37 ## The squared 2-norm of the residual: norm(@var{c}*@var{x}-@var{d})^2 | |
| 38 ## @item residual | |
| 39 ## | |
| 40 ## The residual: @var{d}-@var{c}*@var{x} | |
| 41 ## @item exitflag | |
| 42 ## | |
| 43 ## An indicator of convergence. 0 indicates that the iteration count | |
| 44 ## was exceeded, and therefore convergence was not reached; >0 indicates | |
| 45 ## that the algorithm converged. (The algorithm is stable and will | |
| 46 ## converge given enough iterations.) | |
| 47 ## @item output | |
| 48 ## | |
| 49 ## A structure with two fields: | |
| 50 ## @itemize @bullet | |
| 51 ## @item "algorithm": The algorithm used ("nnls") | |
| 52 ## @item "iterations": The number of iterations taken. | |
| 53 ## @end itemize | |
| 54 ## @item lambda | |
| 55 ## | |
| 56 ## Not implemented. | |
| 57 ## @end itemize | |
| 58 ## @seealso{optimset} | |
| 59 ## @end deftypefn | |
| 60 | |
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61 ## This is implemented from Lawson and Hanson's 1973 algorithm on page |
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62 ## 161 of Solving Least Squares Problems. |
| 7682 | 63 |
| 8600 | 64 function [x, resnorm, residual, exitflag, output, lambda] = lsqnonneg (c, d, x = [], options = struct ()) |
| 65 | |
| 66 if (nargin == 1 && ischar (c) && strcmp (c, 'defaults')) | |
| 67 x = optimset ("MaxIter", 1e5); | |
| 68 return | |
| 69 endif | |
| 70 | |
| 71 if (! (nargin >= 2 && nargin <= 4 && ismatrix (c) && ismatrix (d) && isstruct (options))) | |
| 72 print_usage (); | |
| 73 endif | |
| 7682 | 74 |
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75 ## Lawson-Hanson Step 1 (LH1): initialize the variables. |
| 8600 | 76 m = rows (c); |
| 77 n = columns (c); | |
| 7682 | 78 if (isempty (x)) |
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79 ## Initial guess is 0s. |
| 8600 | 80 x = zeros (n, 1); |
| 81 else | |
| 82 ## ensure nonnegative guess. | |
| 83 x = max (x, 0); | |
| 7682 | 84 endif |
| 85 | |
| 8600 | 86 useqr = m >= n; |
| 8507 | 87 max_iter = optimget (options, "MaxIter", 1e5); |
| 7682 | 88 |
| 8600 | 89 ## Initialize P, according to zero pattern of x. |
| 90 p = find (x > 0).'; | |
| 91 if (useqr) | |
| 92 ## Initialize the QR factorization, economized form. | |
| 93 [q, r] = qr (c(:,p), 0); | |
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fix & optimize lsqnonneg
Jaroslav Hajek <highegg@gmail.com>
parents:
8304
diff
changeset
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94 endif |
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0b7566aea627
fix & optimize lsqnonneg
Jaroslav Hajek <highegg@gmail.com>
parents:
8304
diff
changeset
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95 |
| 7682 | 96 iter = 0; |
| 8600 | 97 |
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7697
0bdfff62cc49
lsqnonneg: use optimset, correctly index Z and P in main loop
bill@denney.ws
parents:
7682
diff
changeset
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98 ## LH3: test for completion. |
| 8600 | 99 while (iter < max_iter) |
| 100 while (iter < max_iter) | |
| 101 iter++; | |
| 102 | |
| 103 ## LH6: compute the positive matrix and find the min norm solution | |
| 104 ## of the positive problem. | |
| 105 if (useqr) | |
| 106 xtmp = r \ q'*d; | |
| 107 else | |
| 108 xtmp = c(:,p) \ d; | |
| 109 endif | |
| 110 idx = find (xtmp < 0); | |
| 111 | |
| 112 if (isempty (idx)) | |
| 113 ## LH7: tmp solution found, iterate. | |
| 114 x(:) = 0; | |
| 115 x(p) = xtmp; | |
| 116 break; | |
| 117 else | |
| 118 ## LH8, LH9: find the scaling factor. | |
| 119 pidx = p(idx); | |
| 120 sf = x(pidx)./(x(pidx) - xtmp(idx)); | |
| 121 alpha = min (sf); | |
| 122 ## LH10: adjust X. | |
| 123 xx = zeros (n, 1); | |
| 124 xx(p) = xtmp; | |
| 125 x += alpha*(xx - x); | |
| 126 ## LH11: move from P to Z all X == 0. | |
| 127 ## This corresponds to those indices where minimum of sf is attained. | |
| 128 idx = idx (sf == alpha); | |
| 129 p(idx) = []; | |
| 130 if (useqr) | |
| 131 ## update the QR factorization. | |
| 132 [q, r] = qrdelete (q, r, idx); | |
| 133 endif | |
| 134 endif | |
| 135 endwhile | |
| 136 | |
| 137 ## compute the gradient. | |
| 138 w = c'*(d - c*x); | |
| 139 w(p) = []; | |
| 140 if (! any (w > 0)) | |
| 141 if (useqr) | |
| 142 ## verify the solution achieved using qr updating. | |
| 143 ## in the best case, this should only take a single step. | |
| 144 useqr = false; | |
| 145 continue; | |
| 146 else | |
| 147 ## we're finished. | |
| 148 break; | |
| 149 endif | |
| 150 endif | |
| 151 | |
| 152 ## find the maximum gradient. | |
| 7682 | 153 idx = find (w == max (w)); |
| 154 if (numel (idx) > 1) | |
| 155 warning ("lsqnonneg:nonunique", | |
| 156 "A non-unique solution may be returned due to equal gradients."); | |
| 157 idx = idx(1); | |
| 158 endif | |
| 8600 | 159 ## move the index from Z to P. Keep P sorted. |
| 160 z = [1:n]; z(p) = []; | |
| 161 zidx = z(idx); | |
| 162 jdx = 1 + lookup (p, zidx); | |
| 163 p = [p(1:jdx-1), zidx, p(jdx:end)]; | |
| 164 if (useqr) | |
| 165 ## insert the column into the QR factorization. | |
| 166 [q, r] = qrinsert (q, r, jdx, c(:,zidx)); | |
| 167 endif | |
| 7682 | 168 |
| 169 endwhile | |
|
7697
0bdfff62cc49
lsqnonneg: use optimset, correctly index Z and P in main loop
bill@denney.ws
parents:
7682
diff
changeset
|
170 ## LH12: complete. |
| 7682 | 171 |
|
7697
0bdfff62cc49
lsqnonneg: use optimset, correctly index Z and P in main loop
bill@denney.ws
parents:
7682
diff
changeset
|
172 ## Generate the additional output arguments. |
| 7682 | 173 if (nargout > 1) |
|
8406
0b7566aea627
fix & optimize lsqnonneg
Jaroslav Hajek <highegg@gmail.com>
parents:
8304
diff
changeset
|
174 resnorm = norm (c*x - d) ^ 2; |
| 7682 | 175 endif |
| 176 if (nargout > 2) | |
|
8406
0b7566aea627
fix & optimize lsqnonneg
Jaroslav Hajek <highegg@gmail.com>
parents:
8304
diff
changeset
|
177 residual = d - c*x; |
| 7682 | 178 endif |
| 179 exitflag = iter; | |
| 8507 | 180 if (nargout > 3 && iter >= max_iter) |
| 7682 | 181 exitflag = 0; |
| 182 endif | |
| 183 if (nargout > 4) | |
| 184 output = struct ("algorithm", "nnls", "iterations", iter); | |
| 185 endif | |
| 186 if (nargout > 5) | |
| 8600 | 187 lambda = zeros (size (x)); |
| 188 lambda(p) = w; | |
| 7682 | 189 endif |
| 190 | |
| 191 endfunction | |
| 192 | |
| 193 ## Tests | |
| 194 %!test | |
| 195 %! C = [1 0;0 1;2 1]; | |
| 196 %! d = [1;3;-2]; | |
| 197 %! assert (lsqnonneg (C, d), [0;0.5], 100*eps) | |
| 198 | |
| 199 %!test | |
| 200 %! C = [0.0372 0.2869;0.6861 0.7071;0.6233 0.6245;0.6344 0.6170]; | |
| 201 %! d = [0.8587;0.1781;0.0747;0.8405]; | |
| 202 %! xnew = [0;0.6929]; | |
| 203 %! assert (lsqnonneg (C, d), xnew, 0.0001) |