Mercurial > octave-nkf
view scripts/optimization/fminsearch.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 | 6437fa7263dd |
children | d63878346099 |
line wrap: on
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## Copyright (C) 2003,2012 Andy Adler ## Copyright (C) 2002 N.J.Higham ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{x} =} fminsearch (@var{fun}, @var{x0}) ## @deftypefnx {Function File} {@var{x} =} fminsearch (@var{fun}, @var{x0}, @var{options}) ## @deftypefnx {Function File} {[@var{x}, @var{fval}] =} fminsearch (@dots{}) ## ## Find a value of @var{x} which minimizes the function @var{fun}. ## The search begins at the point @var{x0} and iterates using the ## Nelder & Mead Simplex algorithm (a derivative-free method). This algorithm ## is better-suited to functions which have discontinuities or for which ## a gradient-based search such as @code{fminunc} fails. ## ## Options for the search are provided in the parameter @var{options} using ## the function @code{optimset}. Currently, @code{fminsearch} accepts the ## options: @qcode{"TolX"}, @qcode{"MaxFunEvals"}, @qcode{"MaxIter"}, ## @qcode{"Display"}. For a description of these options, see ## @code{optimset}. ## ## On exit, the function returns @var{x}, the minimum point, ## and @var{fval}, the function value thereof. ## ## Example usages: ## ## @example ## @group ## fminsearch (@@(x) (x(1)-5).^2+(x(2)-8).^4, [0;0]) ## ## fminsearch (inline ("(x(1)-5).^2+(x(2)-8).^4", "x"), [0;0]) ## @end group ## @end example ## @seealso{fminbnd, fminunc, optimset} ## @end deftypefn ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. ## PKG_ADD: [~] = __all_opts__ ("fminsearch"); ## FIXME: Add support for "exitflag" output variable ## FIXME: Add support for "output" output variable ## FIXME: For Display option, add 'final' and 'notify' options. Not too hard. ## FIXME: Add support for OutputFcn. See fminunc for a template ## FIXME: Add support for exiting based on TolFun. See fminunc for an idea. function [x, fval] = fminsearch (fun, x0, options = struct ()) ## Get default options if requested. if (nargin == 1 && ischar (fun) && strcmp (fun, "defaults")) x = optimset ("Display", "notify", "FunValCheck", "off", "MaxFunEvals", 400, "MaxIter", 400, "OutputFcn", [], "TolFun", 1e-7, "TolX", 1e-4); return; endif if (nargin < 2 || nargin > 3) print_usage (); endif x = nmsmax (fun, x0, options); if (isargout (2)) fval = feval (fun, x); endif endfunction ##NMSMAX Nelder-Mead simplex method for direct search optimization. ## [x, fmax, nf] = NMSMAX(FUN, x0, STOPIT, SAVIT) attempts to ## maximize the function FUN, using the starting vector x0. ## The Nelder-Mead direct search method is used. ## Output arguments: ## x = vector yielding largest function value found, ## fmax = function value at x, ## nf = number of function evaluations. ## The iteration is terminated when either ## - the relative size of the simplex is <= STOPIT(1) ## (default 1e-3), ## - STOPIT(2) function evaluations have been performed ## (default inf, i.e., no limit), or ## - a function value equals or exceeds STOPIT(3) ## (default inf, i.e., no test on function values). ## The form of the initial simplex is determined by STOPIT(4): ## STOPIT(4) = 0: regular simplex (sides of equal length, the default) ## STOPIT(4) = 1: right-angled simplex. ## Progress of the iteration is not shown if STOPIT(5) = 0 (default 1). ## STOPIT(6) indicates the direction (ie. minimization or ## maximization.) Default is 1, maximization. ## set STOPIT(6)=-1 for minimization ## If a non-empty fourth parameter string SAVIT is present, then ## 'SAVE SAVIT x fmax nf' is executed after each inner iteration. ## NB: x0 can be a matrix. In the output argument, in SAVIT saves, ## and in function calls, x has the same shape as x0. ## NMSMAX(fun, x0, STOPIT, SAVIT, P1, P2,...) allows additional ## arguments to be passed to fun, via feval(fun,x,P1,P2,...). ## References: ## N. J. Higham, Optimization by direct search in matrix computations, ## SIAM J. Matrix Anal. Appl, 14(2): 317-333, 1993. ## C. T. Kelley, Iterative Methods for Optimization, Society for Industrial ## and Applied Mathematics, Philadelphia, PA, 1999. ## From Matrix Toolbox ## Copyright (C) 2002 N.J.Higham ## www.maths.man.ac.uk/~higham/mctoolbox ## ## Modifications for Octave by A.Adler 2003 function [stopit, savit, dirn, trace, tol, maxiter] = parse_options (options, x ); ## Tolerance for cgce test based on relative size of simplex. stopit(1) = tol = optimget (options, "TolX", 1e-4); ## Max no. of f-evaluations. stopit(2) = optimget (options, "MaxFunEvals", length (x) * 200); ## Max no. of iterations maxiter = optimget (options, "MaxIter", length (x) * 200); ## Default target for f-values. stopit(3) = Inf; # FIXME: expose this parameter to the outside ## Default initial simplex. stopit(4) = 0; # FIXME: expose this parameter to the outside ## Default: show progress. display = optimget (options, "Display", "notify"); if (strcmp (display, "iter")) stopit(5) = 1; else stopit(5) = 0; endif trace = stopit(5); ## Use function to minimize, not maximize stopit(6) = dirn = -1; ## File name for snapshots. savit = []; # FIXME: expose this parameter to the outside endfunction function [x, fmax, nf] = nmsmax (fun, x, options, savit, varargin) [stopit, savit, dirn, trace, tol, maxiter] = parse_options (options, x); if (strcmpi (optimget (options, "FunValCheck", "off"), "on")) ## Replace fcn with a guarded version. fun = @(x) guarded_eval (fun, x); endif x0 = x(:); # Work with column vector internally. n = length (x0); V = [zeros(n,1) eye(n)]; f = zeros (n+1,1); V(:,1) = x0; f(1) = dirn * feval (fun,x,varargin{:}); fmax_old = f(1); if (trace) fprintf ("f(x0) = %9.4e\n", f(1)); endif k = 0; m = 0; ## Set up initial simplex. scale = max (norm (x0,Inf), 1); if (stopit(4) == 0) ## Regular simplex - all edges have same length. ## Generated from construction given in reference [18, pp. 80-81] of [1]. alpha = scale / (n*sqrt (2)) * [sqrt(n+1)-1+n, sqrt(n+1)-1]; V(:,2:n+1) = (x0 + alpha(2)*ones (n,1)) * ones (1,n); for j = 2:n+1 V(j-1,j) = x0(j-1) + alpha(1); x(:) = V(:,j); f(j) = dirn * feval (fun,x,varargin{:}); endfor else ## Right-angled simplex based on co-ordinate axes. alpha = scale * ones(n+1,1); for j=2:n+1 V(:,j) = x0 + alpha(j)*V(:,j); x(:) = V(:,j); f(j) = dirn * feval (fun,x,varargin{:}); endfor endif nf = n+1; how = "initial "; [~,j] = sort (f); j = j(n+1:-1:1); f = f(j); V = V(:,j); alpha = 1; beta = 1/2; gamma = 2; while (1) # Outer (and only) loop. k++; if (k > maxiter) msg = "Exceeded maximum iterations...quitting\n"; break; endif fmax = f(1); if (fmax > fmax_old) if (! isempty (savit)) x(:) = V(:,1); eval (["save " savit " x fmax nf"]); endif endif if (trace) fprintf ("Iter. %2.0f,", k); fprintf ([" how = " how " "]); fprintf ("nf = %3.0f, f = %9.4e (%2.1f%%)\n", nf, fmax, ... 100*(fmax-fmax_old)/(abs(fmax_old)+eps)); endif fmax_old = fmax; ## Three stopping tests from MDSMAX.M ## Stopping Test 1 - f reached target value? if (fmax >= stopit(3)) msg = "Exceeded target...quitting\n"; break; endif ## Stopping Test 2 - too many f-evals? if (nf >= stopit(2)) msg = "Max no. of function evaluations exceeded...quitting\n"; break; endif ## Stopping Test 3 - converged? This is test (4.3) in [1]. v1 = V(:,1); size_simplex = norm (V(:,2:n+1)-v1(:,ones (1,n)),1) / max (1, norm (v1,1)); if (size_simplex <= tol) msg = sprintf ("Simplex size %9.4e <= %9.4e...quitting\n", ... size_simplex, tol); break; endif ## One step of the Nelder-Mead simplex algorithm ## NJH: Altered function calls and changed CNT to NF. ## Changed each 'fr < f(1)' type test to '>' for maximization ## and re-ordered function values after sort. vbar = (sum (V(:,1:n)')/n)'; # Mean value vr = (1 + alpha)*vbar - alpha*V(:,n+1); x(:) = vr; fr = dirn * feval (fun,x,varargin{:}); nf = nf + 1; vk = vr; fk = fr; how = "reflect, "; if (fr > f(n)) if (fr > f(1)) ve = gamma*vr + (1-gamma)*vbar; x(:) = ve; fe = dirn * feval (fun,x,varargin{:}); nf = nf + 1; if (fe > f(1)) vk = ve; fk = fe; how = "expand, "; endif endif else vt = V(:,n+1); ft = f(n+1); if (fr > ft) vt = vr; ft = fr; endif vc = beta*vt + (1-beta)*vbar; x(:) = vc; fc = dirn * feval (fun,x,varargin{:}); nf = nf + 1; if (fc > f(n)) vk = vc; fk = fc; how = "contract,"; else for j = 2:n V(:,j) = (V(:,1) + V(:,j))/2; x(:) = V(:,j); f(j) = dirn * feval (fun,x,varargin{:}); endfor nf = nf + n-1; vk = (V(:,1) + V(:,n+1))/2; x(:) = vk; fk = dirn * feval (fun,x,varargin{:}); nf = nf + 1; how = "shrink, "; endif endif V(:,n+1) = vk; f(n+1) = fk; [~,j] = sort(f); j = j(n+1:-1:1); f = f(j); V = V(:,j); endwhile # End of outer (and only) loop. ## Finished. if (trace) fprintf (msg); endif x(:) = V(:,1); endfunction ## A helper function that evaluates a function and checks for bad results. function y = guarded_eval (fun, x) y = fun (x); if (! (isreal (f))) error ("fminsearch:notreal", "fminsearch: non-real value encountered"); elseif (any (isnan (f(:)))) error ("fminsearch:isnan", "fminsearch: NaN value encountered"); elseif (any (isinf (f(:)))) error ("fminsearch:isinf", "fminsearch: Inf value encountered"); endif endfunction %!demo %! fcn = @(x) (x(1)-5).^2 + (x(2)-8).^4 %! x0 = [0;0]; %! [xmin, fval] = fminsearch (fcn, x0) %!assert (fminsearch (@sin, 3, optimset ("MaxIter", 3)), 4.8750, 1e-4) %!assert (fminsearch (@sin, 3, optimset ("MaxIter", 30)), 4.7124, 1e-4) %!shared c %! c = 1.5; %!assert (fminsearch (@(x) x(1).^2+c*x(2).^2,[1;1]), [0;0], 1e-4)