Mercurial > octave-nkf
view scripts/optimization/fminbnd.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 | e7a059a9a644 |
children | b81b9d079515 |
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## Copyright (C) 2008-2012 VZLU Prague, a.s. ## ## 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/>. ## ## Author: Jaroslav Hajek <highegg@gmail.com> ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{x}, @var{fval}, @var{info}, @var{output}] =} fminbnd (@var{fun}, @var{a}, @var{b}, @var{options}) ## Find a minimum point of a univariate function. ## ## @var{fun} should be a function handle or name. @var{a}, @var{b} specify a ## starting interval. @var{options} is a structure specifying additional ## options. Currently, @code{fminbnd} recognizes these options: ## @qcode{"FunValCheck"}, @qcode{"OutputFcn"}, @qcode{"TolX"}, ## @qcode{"MaxIter"}, @qcode{"MaxFunEvals"}. For a description of these ## options, see @ref{XREFoptimset,,optimset}. ## ## On exit, the function returns @var{x}, the approximate minimum point ## and @var{fval}, the function value thereof. ## @var{info} is an exit flag that can have these values: ## ## @itemize ## @item 1 ## The algorithm converged to a solution. ## ## @item 0 ## Maximum number of iterations or function evaluations has been exhausted. ## ## @item -1 ## The algorithm has been terminated from user output function. ## @end itemize ## ## Notes: The search for a minimum is restricted to be in the interval ## bound by @var{a} and @var{b}. If you only have an initial point ## to begin searching from you will need to use an unconstrained ## minimization algorithm such as @code{fminunc} or @code{fminsearch}. ## @code{fminbnd} internally uses a Golden Section search strategy. ## @seealso{fzero, fminunc, fminsearch, optimset} ## @end deftypefn ## This is patterned after opt/fmin.f from Netlib, which in turn is taken from ## Richard Brent: Algorithms For Minimization Without Derivatives, Prentice-Hall (1973) ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. ## PKG_ADD: [~] = __all_opts__ ("fminbnd"); function [x, fval, info, output] = fminbnd (fun, xmin, xmax, options = struct ()) ## Get default options if requested. if (nargin == 1 && ischar (fun) && strcmp (fun, 'defaults')) x = optimset ("MaxIter", Inf, "MaxFunEvals", Inf, "TolX", 1e-8, "OutputFcn", [], "FunValCheck", "off"); return; endif if (nargin < 2 || nargin > 4) print_usage (); endif if (ischar (fun)) fun = str2func (fun, "global"); endif displ = optimget (options, "Display", "notify"); funvalchk = strcmpi (optimget (options, "FunValCheck", "off"), "on"); outfcn = optimget (options, "OutputFcn"); tolx = optimget (options, "TolX", 1e-8); maxiter = optimget (options, "MaxIter", Inf); maxfev = optimget (options, "MaxFunEvals", Inf); if (funvalchk) ## Replace fun with a guarded version. fun = @(x) guarded_eval (fun, x); endif ## The default exit flag if exceeded number of iterations. info = 0; niter = 0; nfev = 0; sqrteps = eps (class (xmin + xmax)); c = 0.5*(3 - sqrt (5)); a = xmin; b = xmax; v = a + c*(b-a); w = x = v; e = 0; fv = fw = fval = fun (x); nfev++; ## Only for display purposes. iter(1).funccount = nfev; iter(1).x = x; iter(1).fx = fval; while (niter < maxiter && nfev < maxfev) xm = 0.5*(a+b); ## FIXME: the golden section search can actually get closer than sqrt(eps) ## sometimes. Sometimes not, it depends on the function. This is the ## strategy from the Netlib code. Something yet smarter would be good. tol = 2 * sqrteps * abs (x) + tolx / 3; if (abs (x - xm) <= (2*tol - 0.5*(b-a))) info = 1; break; endif if (abs (e) > tol) dogs = false; ## Try inverse parabolic step. iter(niter+1).procedure = "parabolic"; r = (x - w)*(fval - fv); q = (x - v)*(fval - fw); p = (x - v)*q - (x - w)*r; q = 2*(q - r); p *= -sign (q); q = abs (q); r = e; e = d; if (abs (p) < abs (0.5*q*r) && p > q*(a-x) && p < q*(b-x)) ## The parabolic step is acceptable. d = p / q; u = x + d; ## f must not be evaluated too close to ax or bx. if (min (u-a, b-u) < 2*tol) d = tol * (sign (xm - x) + (xm == x)); endif else dogs = true; endif else dogs = true; endif if (dogs) ## Default to golden section step. ## WARNING: This is also the "initial" procedure following ## MATLAB nomenclature. After the loop we'll fix the string ## for the first step. iter(niter+1).procedure = "golden"; e = ifelse (x >= xm, a - x, b - x); d = c * e; endif ## f must not be evaluated too close to x. u = x + max (abs (d), tol) * (sign (d) + (d == 0)); fu = fun (u); niter++; iter(niter).funccount = nfev++; iter(niter).x = u; iter(niter).fx = fu; ## update a, b, v, w, and x if (fu <= fval) if (u < x) b = x; else a = x; endif v = w; fv = fw; w = x; fw = fval; x = u; fval = fu; else ## The following if-statement was originally executed even if fu == fval. if (u < x) a = u; else b = u; endif if (fu <= fw || w == x) v = w; fv = fw; w = u; fw = fu; elseif (fu <= fv || v == x || v == w) v = u; fv = fu; endif endif ## If there's an output function, use it now. if (outfcn) optv.funccount = nfev; optv.fval = fval; optv.iteration = niter; if (outfcn (x, optv, "iter")) info = -1; break; endif endif endwhile ## Fix the first step procedure. iter(1).procedure = "initial"; ## Handle the "Display" option switch (displ) case "iter" print_formatted_table (iter); print_exit_msg (info, struct("TolX", tolx, "fx", fval)); case "notify" if (info == 0) print_exit_msg (info, struct("fx",fval)); endif case "final" print_exit_msg (info, struct("TolX", tolx, "fx", fval)); case "off" "skip"; otherwise warning ("unknown option for Display: '%s'", displ); endswitch output.iterations = niter; output.funcCount = nfev; output.bracket = [a, b]; ## FIXME: bracketf possibly unavailable. endfunction ## An assistant function that evaluates a function handle and checks for ## bad results. function fx = guarded_eval (fun, x) fx = fun (x); fx = fx(1); if (! isreal (fx)) error ("fminbnd:notreal", "fminbnd: non-real value encountered"); elseif (isnan (fx)) error ("fminbnd:isnan", "fminbnd: NaN value encountered"); endif endfunction ## A hack for printing a formatted table function print_formatted_table (table) printf ("\n Func-count x f(x) Procedure\n"); for row=table printf("%5.5s %7.7s %8.8s\t%s\n", int2str (row.funccount), num2str (row.x,"%.5f"), num2str (row.fx,"%.6f"), row.procedure); endfor printf ("\n"); endfunction ## Print either a success termination message or bad news function print_exit_msg (info, opt=struct()) printf (""); switch (info) case 1 printf ("Optimization terminated:\n"); printf (" the current x satisfies the termination criteria using OPTIONS.TolX of %e\n", opt.TolX); case 0 printf ("Exiting: Maximum number of iterations has been exceeded\n"); printf (" - increase MaxIter option.\n"); printf (" Current function value: %.6f\n", opt.fx); case -1 "FIXME"; ## FIXME: what's the message MATLAB prints for this case? otherwise error ("internal error - fminbnd() is bug, sorry!"); endswitch printf ("\n"); endfunction %!shared opt0 %! opt0 = optimset ("tolx", 0); %!assert (fminbnd (@cos, pi/2, 3*pi/2, opt0), pi, 10*sqrt (eps)) %!assert (fminbnd (@(x) (x - 1e-3)^4, -1, 1, opt0), 1e-3, 10e-3*sqrt (eps)) %!assert (fminbnd (@(x) abs (x-1e7), 0, 1e10, opt0), 1e7, 10e7*sqrt (eps)) %!assert (fminbnd (@(x) x^2 + sin (2*pi*x), 0.4, 1, opt0), fzero (@(x) 2*x + 2*pi*cos (2*pi*x), [0.4, 1], opt0), sqrt (eps))