Mercurial > octave
annotate scripts/optimization/fminsearch.m @ 15468:6437fa7263dd
use ' instead of ` in error messages, warnings and most comments
* qtinfo/parser.h, file-io.cc, graphics.in.h, lex.ll, version.in.h,
interp1.m, fminsearch.m, fix_depends.m, get_description.m:
Use ' instead of ` in error messages, warnings and most comments.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Mon, 01 Oct 2012 18:32:12 -0400 |
| parents | e0525ecf156e |
| children | bc924baa2c4e |
| rev | line source |
|---|---|
| 14895 | 1 ## Copyright (C) 2003,2012 Andy Adler |
| 2 ## Copyright (C) 2002 N.J.Higham | |
| 3 ## | |
| 4 ## This file is part of Octave. | |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 8 ## the Free Software Foundation; either version 3 of the License, or (at | |
| 9 ## your option) any later version. | |
| 10 ## | |
| 11 ## Octave is distributed in the hope that it will be useful, but | |
| 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 14 ## General Public License for more details. | |
| 15 ## | |
| 16 ## You should have received a copy of the GNU General Public License | |
| 17 ## along with Octave; see the file COPYING. If not, see | |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 19 | |
| 20 ## -*- texinfo -*- | |
| 21 ## @deftypefn {Function File} {@var{x} =} fminsearch (@var{fun}, @var{x0}) | |
| 22 ## @deftypefnx {Function File} {@var{x} =} fminsearch (@var{fun}, @var{x0}, @var{options}) | |
| 23 ## @deftypefnx {Function File} {[@var{x}, @var{fval}] =} fminsearch (@dots{}) | |
| 24 ## | |
| 25 ## Find a value of @var{x} which minimizes the function @var{fun}. | |
| 26 ## The search begins at the point @var{x0} and iterates using the | |
| 27 ## Nelder & Mead Simplex algorithm (a derivative-free method). This algorithm | |
| 28 ## is better-suited to functions which have discontinuities or for which | |
| 29 ## a gradient-based search such as @code{fminunc} fails. | |
| 30 ## | |
| 31 ## Options for the search are provided in the parameter @var{options} using | |
| 32 ## the function @code{optimset}. Currently, @code{fminsearch} accepts the | |
| 33 ## options: "TolX", "MaxFunEvals", "MaxIter", "Display". For a description of | |
| 34 ## these options, see @code{optimset}. | |
| 35 ## | |
| 36 ## On exit, the function returns @var{x}, the minimum point, | |
| 37 ## and @var{fval}, the function value thereof. | |
| 38 ## | |
| 39 ## Example usages: | |
| 40 ## | |
| 41 ## @example | |
| 42 ## @group | |
| 43 ## fminsearch (@@(x) (x(1)-5).^2+(x(2)-8).^4, [0;0]) | |
| 44 ## | |
| 45 ## fminsearch (inline ("(x(1)-5).^2+(x(2)-8).^4", "x"), [0;0]) | |
| 46 ## @end group | |
| 47 ## @end example | |
| 48 ## @seealso{fminbnd, fminunc, optimset} | |
| 49 ## @end deftypefn | |
| 50 | |
| 51 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. | |
| 52 ## PKG_ADD: [~] = __all_opts__ ("fminsearch"); | |
| 53 | |
| 54 ## FIXME: Add support for "exitflag" output variable | |
| 55 ## FIXME: Add support for "output" output variable | |
| 56 ## FIXME: For Display option, add 'final' and 'notify' options. Not too hard. | |
| 57 ## FIXME: Add support for OutputFcn. See fminunc for a template | |
| 58 ## FIXME: Add support for exiting based on TolFun. See fminunc for an idea. | |
| 59 | |
| 60 function [x, fval] = fminsearch (fun, x0, options = struct ()) | |
| 61 | |
| 62 ## Get default options if requested. | |
| 63 if (nargin == 1 && ischar (fun) && strcmp (fun, "defaults")) | |
| 64 x = optimset ("Display", "notify", "FunValCheck", "off", | |
| 65 "MaxFunEvals", 400, "MaxIter", 400, | |
| 66 "OutputFcn", [], | |
| 67 "TolFun", 1e-7, "TolX", 1e-4); | |
| 68 return; | |
| 69 endif | |
| 70 | |
| 71 if (nargin < 2 || nargin > 3) | |
| 72 print_usage (); | |
| 73 endif | |
| 74 | |
| 75 x = nmsmax (fun, x0, options); | |
| 76 | |
| 77 if (isargout (2)) | |
| 78 fval = feval (fun, x); | |
| 79 endif | |
| 80 | |
| 81 endfunction | |
| 82 | |
| 83 ##NMSMAX Nelder-Mead simplex method for direct search optimization. | |
| 84 ## [x, fmax, nf] = NMSMAX(FUN, x0, STOPIT, SAVIT) attempts to | |
| 85 ## maximize the function FUN, using the starting vector x0. | |
| 86 ## The Nelder-Mead direct search method is used. | |
| 87 ## Output arguments: | |
| 88 ## x = vector yielding largest function value found, | |
| 89 ## fmax = function value at x, | |
| 90 ## nf = number of function evaluations. | |
| 91 ## The iteration is terminated when either | |
| 92 ## - the relative size of the simplex is <= STOPIT(1) | |
| 93 ## (default 1e-3), | |
| 94 ## - STOPIT(2) function evaluations have been performed | |
| 95 ## (default inf, i.e., no limit), or | |
| 96 ## - a function value equals or exceeds STOPIT(3) | |
| 97 ## (default inf, i.e., no test on function values). | |
| 98 ## The form of the initial simplex is determined by STOPIT(4): | |
| 99 ## STOPIT(4) = 0: regular simplex (sides of equal length, the default) | |
| 100 ## STOPIT(4) = 1: right-angled simplex. | |
| 101 ## Progress of the iteration is not shown if STOPIT(5) = 0 (default 1). | |
| 102 ## STOPIT(6) indicates the direction (ie. minimization or | |
| 103 ## maximization.) Default is 1, maximization. | |
| 104 ## set STOPIT(6)=-1 for minimization | |
| 105 ## If a non-empty fourth parameter string SAVIT is present, then | |
|
15468
6437fa7263dd
use ' instead of ` in error messages, warnings and most comments
John W. Eaton <jwe@octave.org>
parents:
14895
diff
changeset
|
106 ## 'SAVE SAVIT x fmax nf' is executed after each inner iteration. |
| 14895 | 107 ## NB: x0 can be a matrix. In the output argument, in SAVIT saves, |
| 108 ## and in function calls, x has the same shape as x0. | |
| 109 ## NMSMAX(fun, x0, STOPIT, SAVIT, P1, P2,...) allows additional | |
| 110 ## arguments to be passed to fun, via feval(fun,x,P1,P2,...). | |
| 111 ## References: | |
| 112 ## N. J. Higham, Optimization by direct search in matrix computations, | |
| 113 ## SIAM J. Matrix Anal. Appl, 14(2): 317-333, 1993. | |
| 114 ## C. T. Kelley, Iterative Methods for Optimization, Society for Industrial | |
| 115 ## and Applied Mathematics, Philadelphia, PA, 1999. | |
| 116 | |
| 117 ## From Matrix Toolbox | |
| 118 ## Copyright (C) 2002 N.J.Higham | |
| 119 ## www.maths.man.ac.uk/~higham/mctoolbox | |
| 120 ## | |
| 121 ## Modifications for Octave by A.Adler 2003 | |
| 122 | |
| 123 function [stopit, savit, dirn, trace, tol, maxiter] = parse_options (options, x ); | |
| 124 | |
| 125 ## Tolerance for cgce test based on relative size of simplex. | |
| 126 stopit(1) = tol = optimget (options, "TolX", 1e-4); | |
| 127 | |
| 128 ## Max no. of f-evaluations. | |
| 129 stopit(2) = optimget (options, "MaxFunEvals", length (x) * 200); | |
| 130 | |
| 131 ## Max no. of iterations | |
| 132 maxiter = optimget (options, "MaxIter", length (x) * 200); | |
| 133 | |
| 134 ## Default target for f-values. | |
| 135 stopit(3) = Inf; # FIXME: expose this parameter to the outside | |
| 136 | |
| 137 ## Default initial simplex. | |
| 138 stopit(4) = 0; # FIXME: expose this parameter to the outside | |
| 139 | |
| 140 ## Default: show progress. | |
| 141 display = optimget (options, "Display", "notify"); | |
| 142 if (strcmp (display, "iter")) | |
| 143 stopit(5) = 1; | |
| 144 else | |
| 145 stopit(5) = 0; | |
| 146 endif | |
| 147 trace = stopit(5); | |
| 148 | |
| 149 ## Use function to minimize, not maximize | |
| 150 stopit(6) = dirn = -1; | |
| 151 | |
| 152 ## File name for snapshots. | |
| 153 savit = []; # FIXME: expose this parameter to the outside | |
| 154 | |
| 155 endfunction | |
| 156 | |
| 157 function [x, fmax, nf] = nmsmax (fun, x, options, savit, varargin) | |
| 158 | |
| 159 [stopit, savit, dirn, trace, tol, maxiter] = parse_options (options, x); | |
| 160 | |
| 161 if (strcmpi (optimget (options, "FunValCheck", "off"), "on")) | |
| 162 ## Replace fcn with a guarded version. | |
| 163 fun = @(x) guarded_eval (fun, x); | |
| 164 endif | |
| 165 | |
| 166 x0 = x(:); # Work with column vector internally. | |
| 167 n = length (x0); | |
| 168 | |
| 169 V = [zeros(n,1) eye(n)]; | |
| 170 f = zeros (n+1,1); | |
| 171 V(:,1) = x0; | |
| 172 f(1) = dirn * feval (fun,x,varargin{:}); | |
| 173 fmax_old = f(1); | |
| 174 | |
| 175 if (trace) | |
| 176 fprintf ("f(x0) = %9.4e\n", f(1)); | |
| 177 endif | |
| 178 | |
| 179 k = 0; m = 0; | |
| 180 | |
| 181 ## Set up initial simplex. | |
| 182 scale = max (norm (x0,Inf), 1); | |
| 183 if (stopit(4) == 0) | |
| 184 ## Regular simplex - all edges have same length. | |
| 185 ## Generated from construction given in reference [18, pp. 80-81] of [1]. | |
| 186 alpha = scale / (n*sqrt (2)) * [sqrt(n+1)-1+n, sqrt(n+1)-1]; | |
| 187 V(:,2:n+1) = (x0 + alpha(2)*ones (n,1)) * ones (1,n); | |
| 188 for j = 2:n+1 | |
| 189 V(j-1,j) = x0(j-1) + alpha(1); | |
| 190 x(:) = V(:,j); | |
| 191 f(j) = dirn * feval (fun,x,varargin{:}); | |
| 192 endfor | |
| 193 else | |
| 194 ## Right-angled simplex based on co-ordinate axes. | |
| 195 alpha = scale * ones(n+1,1); | |
| 196 for j=2:n+1 | |
| 197 V(:,j) = x0 + alpha(j)*V(:,j); | |
| 198 x(:) = V(:,j); | |
| 199 f(j) = dirn * feval (fun,x,varargin{:}); | |
| 200 endfor | |
| 201 endif | |
| 202 nf = n+1; | |
| 203 how = "initial "; | |
| 204 | |
| 205 [~,j] = sort (f); | |
| 206 j = j(n+1:-1:1); | |
| 207 f = f(j); | |
| 208 V = V(:,j); | |
| 209 | |
| 210 alpha = 1; beta = 1/2; gamma = 2; | |
| 211 | |
| 212 while (1) # Outer (and only) loop. | |
| 213 k++; | |
| 214 | |
| 215 if (k > maxiter) | |
| 216 msg = "Exceeded maximum iterations...quitting\n"; | |
| 217 break; | |
| 218 endif | |
| 219 | |
| 220 fmax = f(1); | |
| 221 if (fmax > fmax_old) | |
| 222 if (! isempty (savit)) | |
| 223 x(:) = V(:,1); | |
| 224 eval (["save " savit " x fmax nf"]); | |
| 225 endif | |
| 226 endif | |
| 227 if (trace) | |
| 228 fprintf ("Iter. %2.0f,", k); | |
| 229 fprintf ([" how = " how " "]); | |
| 230 fprintf ("nf = %3.0f, f = %9.4e (%2.1f%%)\n", nf, fmax, ... | |
| 231 100*(fmax-fmax_old)/(abs(fmax_old)+eps)); | |
| 232 endif | |
| 233 fmax_old = fmax; | |
| 234 | |
| 235 ## Three stopping tests from MDSMAX.M | |
| 236 | |
| 237 ## Stopping Test 1 - f reached target value? | |
| 238 if (fmax >= stopit(3)) | |
| 239 msg = "Exceeded target...quitting\n"; | |
| 240 break; | |
| 241 endif | |
| 242 | |
| 243 ## Stopping Test 2 - too many f-evals? | |
| 244 if (nf >= stopit(2)) | |
| 245 msg = "Max no. of function evaluations exceeded...quitting\n"; | |
| 246 break; | |
| 247 endif | |
| 248 | |
| 249 ## Stopping Test 3 - converged? This is test (4.3) in [1]. | |
| 250 v1 = V(:,1); | |
| 251 size_simplex = norm (V(:,2:n+1)-v1(:,ones (1,n)),1) / max (1, norm (v1,1)); | |
| 252 if (size_simplex <= tol) | |
| 253 msg = sprintf ("Simplex size %9.4e <= %9.4e...quitting\n", ... | |
| 254 size_simplex, tol); | |
| 255 break; | |
| 256 endif | |
| 257 | |
| 258 ## One step of the Nelder-Mead simplex algorithm | |
| 259 ## NJH: Altered function calls and changed CNT to NF. | |
|
15468
6437fa7263dd
use ' instead of ` in error messages, warnings and most comments
John W. Eaton <jwe@octave.org>
parents:
14895
diff
changeset
|
260 ## Changed each 'fr < f(1)' type test to '>' for maximization |
| 14895 | 261 ## and re-ordered function values after sort. |
| 262 | |
| 263 vbar = (sum (V(:,1:n)')/n)'; # Mean value | |
| 264 vr = (1 + alpha)*vbar - alpha*V(:,n+1); | |
| 265 x(:) = vr; | |
| 266 fr = dirn * feval (fun,x,varargin{:}); | |
| 267 nf = nf + 1; | |
| 268 vk = vr; fk = fr; how = "reflect, "; | |
| 269 if (fr > f(n)) | |
| 270 if (fr > f(1)) | |
| 271 ve = gamma*vr + (1-gamma)*vbar; | |
| 272 x(:) = ve; | |
| 273 fe = dirn * feval (fun,x,varargin{:}); | |
| 274 nf = nf + 1; | |
| 275 if (fe > f(1)) | |
| 276 vk = ve; | |
| 277 fk = fe; | |
| 278 how = "expand, "; | |
| 279 endif | |
| 280 endif | |
| 281 else | |
| 282 vt = V(:,n+1); | |
| 283 ft = f(n+1); | |
| 284 if (fr > ft) | |
| 285 vt = vr; | |
| 286 ft = fr; | |
| 287 endif | |
| 288 vc = beta*vt + (1-beta)*vbar; | |
| 289 x(:) = vc; | |
| 290 fc = dirn * feval (fun,x,varargin{:}); | |
| 291 nf = nf + 1; | |
| 292 if (fc > f(n)) | |
| 293 vk = vc; fk = fc; | |
| 294 how = "contract,"; | |
| 295 else | |
| 296 for j = 2:n | |
| 297 V(:,j) = (V(:,1) + V(:,j))/2; | |
| 298 x(:) = V(:,j); | |
| 299 f(j) = dirn * feval (fun,x,varargin{:}); | |
| 300 endfor | |
| 301 nf = nf + n-1; | |
| 302 vk = (V(:,1) + V(:,n+1))/2; | |
| 303 x(:) = vk; | |
| 304 fk = dirn * feval (fun,x,varargin{:}); | |
| 305 nf = nf + 1; | |
| 306 how = "shrink, "; | |
| 307 endif | |
| 308 endif | |
| 309 V(:,n+1) = vk; | |
| 310 f(n+1) = fk; | |
| 311 [~,j] = sort(f); | |
| 312 j = j(n+1:-1:1); | |
| 313 f = f(j); | |
| 314 V = V(:,j); | |
| 315 | |
| 316 endwhile # End of outer (and only) loop. | |
| 317 | |
| 318 ## Finished. | |
| 319 if (trace) | |
| 320 fprintf (msg); | |
| 321 endif | |
| 322 x(:) = V(:,1); | |
| 323 | |
| 324 endfunction | |
| 325 | |
| 326 ## A helper function that evaluates a function and checks for bad results. | |
| 327 function y = guarded_eval (fun, x) | |
| 328 | |
| 329 y = fun (x); | |
| 330 | |
| 331 if (! (isreal (f))) | |
| 332 error ("fminsearch:notreal", "fminsearch: non-real value encountered"); | |
| 333 elseif (any (isnan (f(:)))) | |
| 334 error ("fminsearch:isnan", "fminsearch: NaN value encountered"); | |
| 335 elseif (any (isinf (f(:)))) | |
| 336 error ("fminsearch:isinf", "fminsearch: Inf value encountered"); | |
| 337 endif | |
| 338 | |
| 339 endfunction | |
| 340 | |
| 341 | |
| 342 %!demo | |
| 343 %! fcn = @(x) (x(1)-5).^2 + (x(2)-8).^4 | |
| 344 %! x0 = [0;0]; | |
| 345 %! [xmin, fval] = fminsearch (fcn, x0) | |
| 346 | |
| 347 %!assert (fminsearch (@sin, 3, optimset ("MaxIter", 3)), 4.8750, 1e-4) | |
| 348 %!assert (fminsearch (@sin, 3, optimset ("MaxIter", 30)), 4.7124, 1e-4) | |
| 349 %!shared c | |
| 350 %! c = 1.5; | |
| 351 %!assert (fminsearch (@(x) x(1).^2+c*x(2).^2,[1;1]), [0;0], 1e-4) | |
| 352 |