Mercurial > octave-nkf
annotate scripts/optimization/fminbnd.m @ 19631:db92e7e28e1f
strip trailing whitespace from most source files
* 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,
scripts/miscellaneous/symvar.m, scripts/miscellaneous/tar.m,
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:
Strip trailing whitespace.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Tue, 20 Jan 2015 10:29:54 -0500 |
| parents | 0f79fa9b3a8c |
| children | 4197fc428c7d |
| rev | line source |
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1 ## Copyright (C) 2008-2013 VZLU Prague, a.s. |
| 10296 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7 ## the Free Software Foundation; either version 3 of the License, or (at | |
| 8 ## your option) any later version. | |
| 9 ## | |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 16 ## along with Octave; see the file COPYING. If not, see | |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 18 ## | |
| 19 ## Author: Jaroslav Hajek <highegg@gmail.com> | |
| 20 | |
| 21 ## -*- texinfo -*- | |
| 22 ## @deftypefn {Function File} {[@var{x}, @var{fval}, @var{info}, @var{output}] =} fminbnd (@var{fun}, @var{a}, @var{b}, @var{options}) | |
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23 ## Find a minimum point of a univariate function. |
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24 ## |
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25 ## @var{fun} should be a function handle or name. @var{a}, @var{b} specify a |
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26 ## starting interval. @var{options} is a structure specifying additional |
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27 ## options. Currently, @code{fminbnd} recognizes these options: |
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28 ## @qcode{"FunValCheck"}, @qcode{"OutputFcn"}, @qcode{"TolX"}, |
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29 ## @qcode{"MaxIter"}, @qcode{"MaxFunEvals"}. For a description of these |
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30 ## options, see @ref{XREFoptimset,,optimset}. |
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31 ## |
| 10296 | 32 ## On exit, the function returns @var{x}, the approximate minimum point |
| 33 ## and @var{fval}, the function value thereof. | |
| 34 ## @var{info} is an exit flag that can have these values: | |
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35 ## |
| 10296 | 36 ## @itemize |
| 37 ## @item 1 | |
| 38 ## The algorithm converged to a solution. | |
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39 ## |
| 10296 | 40 ## @item 0 |
| 41 ## Maximum number of iterations or function evaluations has been exhausted. | |
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42 ## |
| 10296 | 43 ## @item -1 |
| 44 ## The algorithm has been terminated from user output function. | |
| 45 ## @end itemize | |
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46 ## |
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47 ## Notes: The search for a minimum is restricted to be in the interval |
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48 ## bound by @var{a} and @var{b}. If you only have an initial point |
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49 ## to begin searching from you will need to use an unconstrained |
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50 ## minimization algorithm such as @code{fminunc} or @code{fminsearch}. |
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51 ## @code{fminbnd} internally uses a Golden Section search strategy. |
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52 ## @seealso{fzero, fminunc, fminsearch, optimset} |
| 10296 | 53 ## @end deftypefn |
| 54 | |
| 55 ## This is patterned after opt/fmin.f from Netlib, which in turn is taken from | |
| 56 ## Richard Brent: Algorithms For Minimization Without Derivatives, Prentice-Hall (1973) | |
| 57 | |
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58 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. |
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59 ## PKG_ADD: [~] = __all_opts__ ("fminbnd"); |
| 10296 | 60 |
| 61 function [x, fval, info, output] = fminbnd (fun, xmin, xmax, options = struct ()) | |
| 62 | |
| 63 ## Get default options if requested. | |
| 64 if (nargin == 1 && ischar (fun) && strcmp (fun, 'defaults')) | |
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65 x = optimset ("MaxIter", Inf, "MaxFunEvals", Inf, "TolX", 1e-8, |
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66 "OutputFcn", [], "FunValCheck", "off"); |
| 10296 | 67 return; |
| 68 endif | |
| 69 | |
| 70 if (nargin < 2 || nargin > 4) | |
| 71 print_usage (); | |
| 72 endif | |
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73 |
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74 if (xmin > xmax) |
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75 error ("Octave:invalid-input-arg", |
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76 "fminbnd: the lower bound cannot be greater than the upper one"); |
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77 endif |
| 10296 | 78 |
| 79 if (ischar (fun)) | |
| 80 fun = str2func (fun, "global"); | |
| 81 endif | |
| 82 | |
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83 displ = optimget (options, "Display", "notify"); |
| 10296 | 84 funvalchk = strcmpi (optimget (options, "FunValCheck", "off"), "on"); |
| 85 outfcn = optimget (options, "OutputFcn"); | |
| 86 tolx = optimget (options, "TolX", 1e-8); | |
| 87 maxiter = optimget (options, "MaxIter", Inf); | |
| 88 maxfev = optimget (options, "MaxFunEvals", Inf); | |
| 89 | |
| 90 if (funvalchk) | |
| 91 ## Replace fun with a guarded version. | |
| 92 fun = @(x) guarded_eval (fun, x); | |
| 93 endif | |
| 94 | |
| 95 ## The default exit flag if exceeded number of iterations. | |
| 96 info = 0; | |
| 97 niter = 0; | |
| 98 nfev = 0; | |
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99 sqrteps = eps (class (xmin + xmax)); |
| 10296 | 100 |
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101 c = 0.5*(3 - sqrt (5)); |
| 10296 | 102 a = xmin; b = xmax; |
| 103 v = a + c*(b-a); | |
| 104 w = x = v; | |
| 105 e = 0; | |
| 106 fv = fw = fval = fun (x); | |
| 107 nfev++; | |
| 108 | |
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109 ## Only for display purposes. |
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110 iter(1).funccount = nfev; |
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111 iter(1).x = x; |
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112 iter(1).fx = fval; |
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113 |
| 10296 | 114 while (niter < maxiter && nfev < maxfev) |
| 115 xm = 0.5*(a+b); | |
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116 ## FIXME: the golden section search can actually get closer than sqrt(eps) |
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117 ## sometimes. Sometimes not, it depends on the function. This is the |
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118 ## strategy from the Netlib code. Something yet smarter would be good. |
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119 tol = 2 * sqrteps * abs (x) + tolx / 3; |
| 10296 | 120 if (abs (x - xm) <= (2*tol - 0.5*(b-a))) |
| 121 info = 1; | |
| 122 break; | |
| 123 endif | |
| 124 | |
| 125 if (abs (e) > tol) | |
| 126 dogs = false; | |
| 127 ## Try inverse parabolic step. | |
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128 iter(niter+1).procedure = "parabolic"; |
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129 |
| 10296 | 130 r = (x - w)*(fval - fv); |
| 131 q = (x - v)*(fval - fw); | |
| 132 p = (x - v)*q - (x - w)*r; | |
| 133 q = 2*(q - r); | |
| 134 p *= -sign (q); | |
| 135 q = abs (q); | |
| 136 r = e; | |
| 137 e = d; | |
| 138 | |
| 139 if (abs (p) < abs (0.5*q*r) && p > q*(a-x) && p < q*(b-x)) | |
| 140 ## The parabolic step is acceptable. | |
| 141 d = p / q; | |
| 142 u = x + d; | |
| 143 | |
| 144 ## f must not be evaluated too close to ax or bx. | |
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145 if (min (u-a, b-u) < 2*tol) |
| 10296 | 146 d = tol * (sign (xm - x) + (xm == x)); |
| 147 endif | |
| 148 else | |
| 149 dogs = true; | |
| 150 endif | |
| 151 else | |
| 152 dogs = true; | |
| 153 endif | |
| 154 if (dogs) | |
| 155 ## Default to golden section step. | |
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156 |
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157 ## WARNING: This is also the "initial" procedure following |
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158 ## MATLAB nomenclature. After the loop we'll fix the string |
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159 ## for the first step. |
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160 iter(niter+1).procedure = "golden"; |
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161 |
| 10296 | 162 e = ifelse (x >= xm, a - x, b - x); |
| 163 d = c * e; | |
| 164 endif | |
| 165 | |
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166 ## f must not be evaluated too close to x. |
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167 u = x + max (abs (d), tol) * (sign (d) + (d == 0)); |
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168 fu = fun (u); |
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169 |
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170 niter++; |
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171 |
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172 iter(niter).funccount = nfev++; |
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173 iter(niter).x = u; |
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174 iter(niter).fx = fu; |
| 10296 | 175 |
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176 ## update a, b, v, w, and x |
| 10296 | 177 |
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178 if (fu < fval) |
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179 if (u < x) |
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180 b = x; |
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181 else |
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182 a = x; |
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183 endif |
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184 v = w; fv = fw; |
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185 w = x; fw = fval; |
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186 x = u; fval = fu; |
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187 else |
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188 ## The following if-statement was originally executed even if fu == fval. |
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189 if (u < x) |
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190 a = u; |
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191 else |
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192 b = u; |
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193 endif |
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194 if (fu <= fw || w == x) |
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195 v = w; fv = fw; |
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196 w = u; fw = fu; |
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197 elseif (fu <= fv || v == x || v == w) |
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198 v = u; |
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199 fv = fu; |
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200 endif |
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201 endif |
| 10296 | 202 |
| 203 ## If there's an output function, use it now. | |
| 204 if (outfcn) | |
| 205 optv.funccount = nfev; | |
| 206 optv.fval = fval; | |
| 207 optv.iteration = niter; | |
| 208 if (outfcn (x, optv, "iter")) | |
| 209 info = -1; | |
| 210 break; | |
| 211 endif | |
| 212 endif | |
| 213 endwhile | |
| 214 | |
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215 ## Fix the first step procedure. |
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216 iter(1).procedure = "initial"; |
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217 |
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218 ## Handle the "Display" option |
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219 switch (displ) |
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220 case "iter" |
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221 print_formatted_table (iter); |
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222 print_exit_msg (info, struct("TolX", tolx, "fx", fval)); |
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223 case "notify" |
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224 if (info == 0) |
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225 print_exit_msg (info, struct("fx",fval)); |
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226 endif |
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227 case "final" |
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228 print_exit_msg (info, struct("TolX", tolx, "fx", fval)); |
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229 case "off" |
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230 "skip"; |
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231 otherwise |
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232 warning ("unknown option for Display: '%s'", displ); |
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233 endswitch |
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234 |
| 10296 | 235 output.iterations = niter; |
| 236 output.funcCount = nfev; | |
| 237 output.bracket = [a, b]; | |
| 238 ## FIXME: bracketf possibly unavailable. | |
| 239 | |
| 240 endfunction | |
| 241 | |
| 242 ## An assistant function that evaluates a function handle and checks for | |
| 243 ## bad results. | |
| 244 function fx = guarded_eval (fun, x) | |
| 245 fx = fun (x); | |
| 246 fx = fx(1); | |
| 247 if (! isreal (fx)) | |
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248 error ("fminbnd:notreal", "fminbnd: non-real value encountered"); |
| 10296 | 249 elseif (isnan (fx)) |
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250 error ("fminbnd:isnan", "fminbnd: NaN value encountered"); |
| 10296 | 251 endif |
| 252 endfunction | |
| 253 | |
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254 ## A hack for printing a formatted table |
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255 function print_formatted_table (table) |
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256 printf ("\n Func-count x f(x) Procedure\n"); |
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257 for row=table |
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258 printf("%5.5s %7.7s %8.8s\t%s\n", |
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259 int2str (row.funccount), num2str (row.x,"%.5f"), |
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260 num2str (row.fx,"%.6f"), row.procedure); |
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261 endfor |
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262 printf ("\n"); |
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263 endfunction |
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264 |
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265 ## Print either a success termination message or bad news |
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266 function print_exit_msg (info, opt=struct()) |
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267 printf (""); |
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268 switch (info) |
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269 case 1 |
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270 printf ("Optimization terminated:\n"); |
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271 printf (" the current x satisfies the termination criteria using OPTIONS.TolX of %e\n", opt.TolX); |
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272 case 0 |
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273 printf ("Exiting: Maximum number of iterations has been exceeded\n"); |
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274 printf (" - increase MaxIter option.\n"); |
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275 printf (" Current function value: %.6f\n", opt.fx); |
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276 case -1 |
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277 "FIXME"; # FIXME: what's the message MATLAB prints for this case? |
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278 otherwise |
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279 error ("internal error - fminbnd() is bug, sorry!"); |
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280 endswitch |
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281 printf ("\n"); |
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282 endfunction |
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283 |
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284 |
| 10296 | 285 %!shared opt0 |
| 286 %! opt0 = optimset ("tolx", 0); | |
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287 %!assert (fminbnd (@cos, pi/2, 3*pi/2, opt0), pi, 10*sqrt (eps)) |
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288 %!assert (fminbnd (@(x) (x - 1e-3)^4, -1, 1, opt0), 1e-3, 10e-3*sqrt (eps)) |
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289 %!assert (fminbnd (@(x) abs (x-1e7), 0, 1e10, opt0), 1e7, 10e7*sqrt (eps)) |
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290 %!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)) |
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291 %!assert (fminbnd (@(x) x > 0.3, 0, 1) < 0.3) |
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292 %!assert (fminbnd (@(x) sin (x), 0, 0), 0, eps) |
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293 |
|
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294 %!error <lower bound cannot be greater> fminbnd (@(x) sin (x), 0, -pi) |
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295 |