Mercurial > hg > octave-nkf
annotate scripts/optimization/fminbnd.m @ 20393:4e7f12a763cd stable
doc: Remove typo of same word twice in a row.
* data.cc (nzmax), mappers.cc (isinf), contourc.m, cylinder.m, ellipsoid.m:
Remove typo of same word twice in a row.
| author | Rik <rik@octave.org> |
|---|---|
| date | Tue, 12 May 2015 10:05:02 -0700 |
| parents | f1d0f506ee78 |
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| rev | line source |
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1 ## Copyright (C) 2008-2015 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 ## |
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32 ## On exit, the function returns @var{x}, the approximate minimum point and |
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33 ## @var{fval}, the function value thereof. |
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34 ## |
| 10296 | 35 ## @var{info} is an exit flag that can have these values: |
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36 ## |
| 10296 | 37 ## @itemize |
| 38 ## @item 1 | |
| 39 ## The algorithm converged to a solution. | |
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40 ## |
| 10296 | 41 ## @item 0 |
| 42 ## Maximum number of iterations or function evaluations has been exhausted. | |
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43 ## |
| 10296 | 44 ## @item -1 |
| 45 ## The algorithm has been terminated from user output function. | |
| 46 ## @end itemize | |
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47 ## |
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48 ## Notes: The search for a minimum is restricted to be in the interval bound by |
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49 ## @var{a} and @var{b}. If you only have an initial point to begin searching |
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50 ## from you will need to use an unconstrained minimization algorithm such as |
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51 ## @code{fminunc} or @code{fminsearch}. @code{fminbnd} internally uses a |
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52 ## Golden Section search strategy. |
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53 ## @seealso{fzero, fminunc, fminsearch, optimset} |
| 10296 | 54 ## @end deftypefn |
| 55 | |
| 56 ## This is patterned after opt/fmin.f from Netlib, which in turn is taken from | |
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57 ## Richard Brent: Algorithms For Minimization Without Derivatives, |
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58 ## Prentice-Hall (1973) |
| 10296 | 59 |
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60 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. |
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61 ## PKG_ADD: [~] = __all_opts__ ("fminbnd"); |
| 10296 | 62 |
| 63 function [x, fval, info, output] = fminbnd (fun, xmin, xmax, options = struct ()) | |
| 64 | |
| 65 ## Get default options if requested. | |
| 66 if (nargin == 1 && ischar (fun) && strcmp (fun, 'defaults')) | |
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67 x = optimset ("MaxIter", Inf, "MaxFunEvals", Inf, "TolX", 1e-8, |
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68 "OutputFcn", [], "FunValCheck", "off"); |
| 10296 | 69 return; |
| 70 endif | |
| 71 | |
| 72 if (nargin < 2 || nargin > 4) | |
| 73 print_usage (); | |
| 74 endif | |
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75 |
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76 if (xmin > xmax) |
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77 error ("Octave:invalid-input-arg", |
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78 "fminbnd: the lower bound cannot be greater than the upper one"); |
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79 endif |
| 10296 | 80 |
| 81 if (ischar (fun)) | |
| 82 fun = str2func (fun, "global"); | |
| 83 endif | |
| 84 | |
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85 displ = optimget (options, "Display", "notify"); |
| 10296 | 86 funvalchk = strcmpi (optimget (options, "FunValCheck", "off"), "on"); |
| 87 outfcn = optimget (options, "OutputFcn"); | |
| 88 tolx = optimget (options, "TolX", 1e-8); | |
| 89 maxiter = optimget (options, "MaxIter", Inf); | |
| 90 maxfev = optimget (options, "MaxFunEvals", Inf); | |
| 91 | |
| 92 if (funvalchk) | |
| 93 ## Replace fun with a guarded version. | |
| 94 fun = @(x) guarded_eval (fun, x); | |
| 95 endif | |
| 96 | |
| 97 ## The default exit flag if exceeded number of iterations. | |
| 98 info = 0; | |
| 99 niter = 0; | |
| 100 nfev = 0; | |
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101 sqrteps = eps (class (xmin + xmax)); |
| 10296 | 102 |
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103 c = 0.5*(3 - sqrt (5)); |
| 10296 | 104 a = xmin; b = xmax; |
| 105 v = a + c*(b-a); | |
| 106 w = x = v; | |
| 107 e = 0; | |
| 108 fv = fw = fval = fun (x); | |
| 109 nfev++; | |
| 110 | |
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111 ## Only for display purposes. |
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112 iter(1).funccount = nfev; |
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113 iter(1).x = x; |
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114 iter(1).fx = fval; |
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115 |
| 10296 | 116 while (niter < maxiter && nfev < maxfev) |
| 117 xm = 0.5*(a+b); | |
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118 ## FIXME: the golden section search can actually get closer than sqrt(eps) |
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119 ## sometimes. Sometimes not, it depends on the function. This is the |
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120 ## strategy from the Netlib code. Something yet smarter would be good. |
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121 tol = 2 * sqrteps * abs (x) + tolx / 3; |
| 10296 | 122 if (abs (x - xm) <= (2*tol - 0.5*(b-a))) |
| 123 info = 1; | |
| 124 break; | |
| 125 endif | |
| 126 | |
| 127 if (abs (e) > tol) | |
| 128 dogs = false; | |
| 129 ## Try inverse parabolic step. | |
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130 iter(niter+1).procedure = "parabolic"; |
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131 |
| 10296 | 132 r = (x - w)*(fval - fv); |
| 133 q = (x - v)*(fval - fw); | |
| 134 p = (x - v)*q - (x - w)*r; | |
| 135 q = 2*(q - r); | |
| 136 p *= -sign (q); | |
| 137 q = abs (q); | |
| 138 r = e; | |
| 139 e = d; | |
| 140 | |
| 141 if (abs (p) < abs (0.5*q*r) && p > q*(a-x) && p < q*(b-x)) | |
| 142 ## The parabolic step is acceptable. | |
| 143 d = p / q; | |
| 144 u = x + d; | |
| 145 | |
| 146 ## f must not be evaluated too close to ax or bx. | |
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147 if (min (u-a, b-u) < 2*tol) |
| 10296 | 148 d = tol * (sign (xm - x) + (xm == x)); |
| 149 endif | |
| 150 else | |
| 151 dogs = true; | |
| 152 endif | |
| 153 else | |
| 154 dogs = true; | |
| 155 endif | |
| 156 if (dogs) | |
| 157 ## Default to golden section step. | |
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158 |
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159 ## WARNING: This is also the "initial" procedure following |
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160 ## MATLAB nomenclature. After the loop we'll fix the string |
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161 ## for the first step. |
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162 iter(niter+1).procedure = "golden"; |
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163 |
| 10296 | 164 e = ifelse (x >= xm, a - x, b - x); |
| 165 d = c * e; | |
| 166 endif | |
| 167 | |
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168 ## f must not be evaluated too close to x. |
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169 u = x + max (abs (d), tol) * (sign (d) + (d == 0)); |
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170 fu = fun (u); |
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171 |
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172 niter++; |
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173 |
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174 iter(niter).funccount = nfev++; |
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175 iter(niter).x = u; |
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176 iter(niter).fx = fu; |
| 10296 | 177 |
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178 ## update a, b, v, w, and x |
| 10296 | 179 |
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180 if (fu < fval) |
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181 if (u < x) |
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182 b = x; |
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183 else |
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184 a = x; |
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185 endif |
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186 v = w; fv = fw; |
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187 w = x; fw = fval; |
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188 x = u; fval = fu; |
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189 else |
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190 ## The following if-statement was originally executed even if fu == fval. |
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191 if (u < x) |
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192 a = u; |
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193 else |
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194 b = u; |
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195 endif |
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196 if (fu <= fw || w == x) |
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197 v = w; fv = fw; |
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198 w = u; fw = fu; |
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199 elseif (fu <= fv || v == x || v == w) |
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200 v = u; |
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201 fv = fu; |
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202 endif |
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203 endif |
| 10296 | 204 |
| 205 ## If there's an output function, use it now. | |
| 206 if (outfcn) | |
| 207 optv.funccount = nfev; | |
| 208 optv.fval = fval; | |
| 209 optv.iteration = niter; | |
| 210 if (outfcn (x, optv, "iter")) | |
| 211 info = -1; | |
| 212 break; | |
| 213 endif | |
| 214 endif | |
| 215 endwhile | |
| 216 | |
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217 ## Fix the first step procedure. |
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218 iter(1).procedure = "initial"; |
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219 |
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220 ## Handle the "Display" option |
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221 switch (displ) |
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222 case "iter" |
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223 print_formatted_table (iter); |
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224 print_exit_msg (info, struct("TolX", tolx, "fx", fval)); |
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225 case "notify" |
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226 if (info == 0) |
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227 print_exit_msg (info, struct("fx",fval)); |
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228 endif |
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229 case "final" |
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230 print_exit_msg (info, struct("TolX", tolx, "fx", fval)); |
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231 case "off" |
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232 "skip"; |
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233 otherwise |
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234 warning ("unknown option for Display: '%s'", displ); |
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235 endswitch |
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236 |
| 10296 | 237 output.iterations = niter; |
| 238 output.funcCount = nfev; | |
| 239 output.bracket = [a, b]; | |
| 240 ## FIXME: bracketf possibly unavailable. | |
| 241 | |
| 242 endfunction | |
| 243 | |
| 244 ## An assistant function that evaluates a function handle and checks for | |
| 245 ## bad results. | |
| 246 function fx = guarded_eval (fun, x) | |
| 247 fx = fun (x); | |
| 248 fx = fx(1); | |
| 249 if (! isreal (fx)) | |
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250 error ("fminbnd:notreal", "fminbnd: non-real value encountered"); |
| 10296 | 251 elseif (isnan (fx)) |
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252 error ("fminbnd:isnan", "fminbnd: NaN value encountered"); |
| 10296 | 253 endif |
| 254 endfunction | |
| 255 | |
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256 ## A hack for printing a formatted table |
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257 function print_formatted_table (table) |
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258 printf ("\n Func-count x f(x) Procedure\n"); |
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259 for row=table |
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260 printf("%5.5s %7.7s %8.8s\t%s\n", |
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261 int2str (row.funccount), num2str (row.x,"%.5f"), |
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262 num2str (row.fx,"%.6f"), row.procedure); |
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263 endfor |
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264 printf ("\n"); |
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265 endfunction |
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266 |
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267 ## Print either a success termination message or bad news |
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268 function print_exit_msg (info, opt=struct()) |
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269 printf (""); |
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270 switch (info) |
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271 case 1 |
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272 printf ("Optimization terminated:\n"); |
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273 printf (" the current x satisfies the termination criteria using OPTIONS.TolX of %e\n", opt.TolX); |
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274 case 0 |
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275 printf ("Exiting: Maximum number of iterations has been exceeded\n"); |
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276 printf (" - increase MaxIter option.\n"); |
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277 printf (" Current function value: %.6f\n", opt.fx); |
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278 case -1 |
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279 "FIXME"; # FIXME: what's the message MATLAB prints for this case? |
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280 otherwise |
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281 error ("internal error - fminbnd() is bug, sorry!"); |
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282 endswitch |
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283 printf ("\n"); |
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284 endfunction |
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285 |
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286 |
| 10296 | 287 %!shared opt0 |
| 288 %! opt0 = optimset ("tolx", 0); | |
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289 %!assert (fminbnd (@cos, pi/2, 3*pi/2, opt0), pi, 10*sqrt (eps)) |
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290 %!assert (fminbnd (@(x) (x - 1e-3)^4, -1, 1, opt0), 1e-3, 10e-3*sqrt (eps)) |
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291 %!assert (fminbnd (@(x) abs (x-1e7), 0, 1e10, opt0), 1e7, 10e7*sqrt (eps)) |
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292 %!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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293 %!assert (fminbnd (@(x) x > 0.3, 0, 1) < 0.3) |
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294 %!assert (fminbnd (@(x) sin (x), 0, 0), 0, eps) |
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295 |
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296 %!error <lower bound cannot be greater> fminbnd (@(x) sin (x), 0, -pi) |
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297 |