Mercurial > octave-nkf
view scripts/optimization/fminbnd.m @ 19631:db92e7e28e1f
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* NEWS, doc/interpreter/contributors.in, doc/interpreter/func.txi,
doc/interpreter/genpropdoc.m, doc/interpreter/octave_logo.eps,
doc/interpreter/plot.txi, doc/interpreter/stmt.txi,
examples/data/Makefile.am, libinterp/corefcn/data.cc,
libinterp/corefcn/debug.cc, libinterp/corefcn/error.cc,
libinterp/corefcn/file-io.cc, libinterp/corefcn/gl-render.cc,
libinterp/corefcn/graphics.cc, libinterp/corefcn/graphics.in.h,
libinterp/corefcn/load-path.cc, libinterp/corefcn/pr-output.cc,
libinterp/corefcn/pt-jit.cc, libinterp/corefcn/strfind.cc,
libinterp/corefcn/toplev.cc, libinterp/corefcn/toplev.h,
libinterp/corefcn/urlwrite.cc, libinterp/corefcn/variables.cc,
libinterp/octave-value/ov-classdef.cc,
libinterp/octave-value/ov-classdef.h, libinterp/octave.cc,
libinterp/parse-tree/lex.h, libinterp/parse-tree/oct-parse.in.yy,
libinterp/parse-tree/pt-classdef.h, liboctave/system/file-ops.cc,
liboctave/system/oct-env.cc, m4/acinclude.m4,
scripts/deprecated/finite.m, scripts/deprecated/fmod.m,
scripts/deprecated/fnmatch.m, scripts/deprecated/luinc.m,
scripts/deprecated/octave_tmp_file_name.m, scripts/deprecated/syl.m,
scripts/deprecated/usage.m, scripts/general/inputParser.m,
scripts/general/interp1.m, scripts/general/interp2.m,
scripts/general/interp3.m, scripts/general/isequal.m,
scripts/general/private/__isequal__.m, scripts/geometry/voronoi.m,
scripts/image/image.m, scripts/image/imshow.m,
scripts/image/ind2rgb.m, scripts/linear-algebra/bandwidth.m,
scripts/linear-algebra/isbanded.m, scripts/miscellaneous/bzip2.m,
scripts/miscellaneous/cast.m, scripts/miscellaneous/copyfile.m,
scripts/miscellaneous/delete.m, scripts/miscellaneous/fullfile.m,
scripts/miscellaneous/getappdata.m, scripts/miscellaneous/gunzip.m,
scripts/miscellaneous/isappdata.m, scripts/miscellaneous/ls.m,
scripts/miscellaneous/mex.m, scripts/miscellaneous/movefile.m,
scripts/miscellaneous/orderfields.m, scripts/miscellaneous/recycle.m,
scripts/miscellaneous/rmappdata.m, scripts/miscellaneous/setfield.m,
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scripts/miscellaneous/tmpnam.m, scripts/miscellaneous/unpack.m,
scripts/miscellaneous/ver.m, scripts/miscellaneous/what.m,
scripts/miscellaneous/xor.m, scripts/miscellaneous/zip.m,
scripts/optimization/fminbnd.m, scripts/optimization/sqp.m,
scripts/path/private/getsavepath.m, scripts/path/savepath.m,
scripts/pkg/pkg.m, scripts/pkg/private/installed_packages.m,
scripts/plot/draw/plotyy.m, scripts/plot/draw/polar.m,
scripts/plot/draw/private/__quiver__.m,
scripts/plot/draw/private/__scatter__.m,
scripts/plot/draw/private/__stem__.m, scripts/plot/draw/surface.m,
scripts/plot/draw/surfnorm.m, scripts/plot/util/copyobj.m,
scripts/plot/util/hgload.m, scripts/plot/util/hgsave.m,
scripts/plot/util/isprop.m, scripts/plot/util/linkprop.m,
scripts/plot/util/private/__go_draw_axes__.m, scripts/set/setdiff.m,
scripts/set/union.m, scripts/signal/periodogram.m,
scripts/sparse/eigs.m, scripts/sparse/ilu.m, scripts/sparse/qmr.m,
scripts/sparse/sprand.m, scripts/sparse/sprandn.m,
scripts/specfun/beta.m, scripts/specfun/ellipke.m,
scripts/specfun/isprime.m, scripts/statistics/base/lscov.m,
scripts/testfun/__run_test_suite__.m, scripts/testfun/test.m:
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author | John W. Eaton <jwe@octave.org> |
---|---|
date | Tue, 20 Jan 2015 10:29:54 -0500 |
parents | 0f79fa9b3a8c |
children | 4197fc428c7d |
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## Copyright (C) 2008-2013 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 (xmin > xmax) error ("Octave:invalid-input-arg", "fminbnd: the lower bound cannot be greater than the upper one"); 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)) %!assert (fminbnd (@(x) x > 0.3, 0, 1) < 0.3) %!assert (fminbnd (@(x) sin (x), 0, 0), 0, eps) %!error <lower bound cannot be greater> fminbnd (@(x) sin (x), 0, -pi)