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view scripts/optimization/fminbnd.m @ 14363:f3d52523cde1
Use Octave coding conventions in all m-file %!test blocks
* wavread.m, acosd.m, acot.m, acotd.m, acoth.m, acsc.m, acscd.m, acsch.m,
asec.m, asecd.m, asech.m, asind.m, atand.m, cosd.m, cot.m, cotd.m, coth.m,
csc.m, cscd.m, csch.m, sec.m, secd.m, sech.m, sind.m, tand.m, accumarray.m,
accumdim.m, bitcmp.m, bitget.m, bitset.m, blkdiag.m, cart2pol.m, cart2sph.m,
celldisp.m, chop.m, circshift.m, colon.m, common_size.m, cplxpair.m,
cumtrapz.m, curl.m, dblquad.m, deal.m, divergence.m, flipdim.m, fliplr.m,
flipud.m, genvarname.m, gradient.m, idivide.m, int2str.m, interp1.m,
interp1q.m, interp2.m, interp3.m, interpft.m, interpn.m, isa.m, isdir.m,
isequal.m, isequalwithequalnans.m, issquare.m, logspace.m, nargchk.m,
narginchk.m, nargoutchk.m, nextpow2.m, nthargout.m, num2str.m, pol2cart.m,
polyarea.m, postpad.m, prepad.m, profile.m, profshow.m, quadgk.m, quadv.m,
randi.m, rat.m, repmat.m, rot90.m, rotdim.m, shift.m, shiftdim.m, sph2cart.m,
structfun.m, trapz.m, triplequad.m, convhull.m, dsearch.m, dsearchn.m,
griddata3.m, griddatan.m, rectint.m, tsearchn.m, __makeinfo__.m, doc.m,
get_first_help_sentence.m, help.m, type.m, unimplemented.m, which.m, imread.m,
imwrite.m, dlmwrite.m, fileread.m, is_valid_file_id.m, strread.m, textread.m,
textscan.m, commutation_matrix.m, cond.m, condest.m, cross.m,
duplication_matrix.m, expm.m, housh.m, isdefinite.m, ishermitian.m,
issymmetric.m, logm.m, normest.m, null.m, onenormest.m, orth.m, planerot.m,
qzhess.m, rank.m, rref.m, trace.m, vech.m, ans.m, bincoeff.m, bug_report.m,
bzip2.m, comma.m, compare_versions.m, computer.m, edit.m, fileparts.m,
fullfile.m, getfield.m, gzip.m, info.m, inputname.m, isappdata.m, isdeployed.m,
ismac.m, ispc.m, isunix.m, list_primes.m, ls.m, mexext.m, namelengthmax.m,
news.m, orderfields.m, paren.m, recycle.m, rmappdata.m, semicolon.m,
setappdata.m, setfield.m, substruct.m, symvar.m, ver.m, version.m,
warning_ids.m, xor.m, fminbnd.m, fsolve.m, fzero.m, lsqnonneg.m, optimset.m,
pqpnonneg.m, sqp.m, matlabroot.m, __gnuplot_drawnow__.m,
__plt_get_axis_arg__.m, ancestor.m, cla.m, clf.m, close.m, colorbar.m,
colstyle.m, comet3.m, contourc.m, figure.m, gca.m, gcbf.m, gcbo.m, gcf.m,
ginput.m, graphics_toolkit.m, gtext.m, hggroup.m, hist.m, hold.m, isfigure.m,
ishghandle.m, ishold.m, isocolors.m, isonormals.m, isosurface.m, isprop.m,
legend.m, line.m, loglog.m, loglogerr.m, meshgrid.m, ndgrid.m, newplot.m,
orient.m, patch.m, plot3.m, plotyy.m, __print_parse_opts__.m, quiver3.m,
refreshdata.m, ribbon.m, semilogx.m, semilogxerr.m, semilogy.m, stem.m,
stem3.m, subplot.m, title.m, uigetfile.m, view.m, whitebg.m, compan.m, conv.m,
deconv.m, mkpp.m, mpoles.m, pchip.m, poly.m, polyaffine.m, polyder.m,
polyfit.m, polygcd.m, polyint.m, polyout.m, polyval.m, polyvalm.m, ppder.m,
ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, intersect.m,
ismember.m, powerset.m, setdiff.m, setxor.m, union.m, unique.m,
autoreg_matrix.m, bartlett.m, blackman.m, detrend.m, fftconv.m, fftfilt.m,
fftshift.m, freqz.m, hamming.m, hanning.m, ifftshift.m, sinc.m, sinetone.m,
sinewave.m, unwrap.m, bicg.m, bicgstab.m, gmres.m, gplot.m, nonzeros.m, pcg.m,
pcr.m, spaugment.m, spconvert.m, spdiags.m, speye.m, spfun.m, spones.m,
sprand.m, sprandsym.m, spstats.m, spy.m, svds.m, treelayout.m, bessel.m,
beta.m, betaln.m, factor.m, factorial.m, isprime.m, lcm.m, legendre.m,
nchoosek.m, nthroot.m, perms.m, pow2.m, primes.m, reallog.m, realpow.m,
realsqrt.m, hadamard.m, hankel.m, hilb.m, invhilb.m, magic.m, rosser.m,
vander.m, __finish__.m, center.m, cloglog.m, corr.m, cov.m, gls.m, histc.m,
iqr.m, kendall.m, kurtosis.m, logit.m, mahalanobis.m, mean.m, meansq.m,
median.m, mode.m, moment.m, ols.m, ppplot.m, prctile.m, probit.m, quantile.m,
range.m, ranks.m, run_count.m, runlength.m, skewness.m, spearman.m,
statistics.m, std.m, table.m, var.m, zscore.m, betacdf.m, betainv.m, betapdf.m,
betarnd.m, binocdf.m, binoinv.m, binopdf.m, binornd.m, cauchy_cdf.m,
cauchy_inv.m, cauchy_pdf.m, cauchy_rnd.m, chi2cdf.m, chi2inv.m, chi2pdf.m,
chi2rnd.m, discrete_cdf.m, discrete_inv.m, discrete_pdf.m, discrete_rnd.m,
empirical_cdf.m, empirical_inv.m, empirical_pdf.m, empirical_rnd.m, expcdf.m,
expinv.m, exppdf.m, exprnd.m, fcdf.m, finv.m, fpdf.m, frnd.m, gamcdf.m,
gaminv.m, gampdf.m, gamrnd.m, geocdf.m, geoinv.m, geopdf.m, geornd.m,
hygecdf.m, hygeinv.m, hygepdf.m, hygernd.m, kolmogorov_smirnov_cdf.m,
laplace_cdf.m, laplace_inv.m, laplace_pdf.m, laplace_rnd.m, logistic_cdf.m,
logistic_inv.m, logistic_pdf.m, logistic_rnd.m, logncdf.m, logninv.m,
lognpdf.m, lognrnd.m, nbincdf.m, nbininv.m, nbinpdf.m, nbinrnd.m, normcdf.m,
norminv.m, normpdf.m, normrnd.m, poisscdf.m, poissinv.m, poisspdf.m,
poissrnd.m, stdnormal_cdf.m, stdnormal_inv.m, stdnormal_pdf.m, stdnormal_rnd.m,
tcdf.m, tinv.m, tpdf.m, trnd.m, unidcdf.m, unidinv.m, unidpdf.m, unidrnd.m,
unifcdf.m, unifinv.m, unifpdf.m, unifrnd.m, wblcdf.m, wblinv.m, wblpdf.m,
wblrnd.m, kolmogorov_smirnov_test.m, kruskal_wallis_test.m, base2dec.m,
bin2dec.m, blanks.m, cstrcat.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m,
findstr.m, hex2dec.m, index.m, isletter.m, mat2str.m, rindex.m, str2num.m,
strcat.m, strjust.m, strmatch.m, strsplit.m, strtok.m, strtrim.m, strtrunc.m,
substr.m, validatestring.m, demo.m, example.m, fail.m, speed.m, addtodate.m,
asctime.m, clock.m, ctime.m, date.m, datenum.m, datetick.m, datevec.m,
eomday.m, etime.m, is_leap_year.m, now.m:
Use Octave coding conventions in all m-file %!test blocks
author | Rik <octave@nomad.inbox5.com> |
---|---|
date | Mon, 13 Feb 2012 07:29:44 -0800 |
parents | 72c96de7a403 |
children | 86854d032a37 |
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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: @code{"FunValCheck"}, @code{"OutputFcn"}, ## @code{"TolX"}, @code{"MaxIter"}, @code{"MaxFunEvals"}. ## For description of these options, see @ref{doc-optimset,,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 ## @seealso{optimset, fzero, fminunc} ## @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 ## TODO ## displev = 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++; 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. 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. 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); nfev++; niter++; ## 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 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 %!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))