Mercurial > octave-nkf
annotate scripts/optimization/fminbnd.m @ 16772:7eff3032d144
Fix seealso HTML links when using Texinfo 4.X (bug #38862).
Use the prefix 'docX' instead of 'doc-' for Texinfo references.
* doc/interpreter/arith.txi, doc/interpreter/basics.txi,
doc/interpreter/container.txi, doc/interpreter/func.txi,
doc/interpreter/java.txi, doc/interpreter/matrix.txi,
doc/interpreter/munge-texi.pl, doc/interpreter/package.txi,
doc/interpreter/plot.txi, doc/interpreter/stats.txi,
doc/interpreter/strings.txi, doc/interpreter/system.txi,
doc/interpreter/var.txi, doc/interpreter/vectorize.txi,
libinterp/corefcn/qz.cc, libinterp/corefcn/regexp.cc,
libinterp/interpfcn/error.cc, scripts/general/accumarray.m,
scripts/general/structfun.m, scripts/miscellaneous/setfield.m,
scripts/optimization/fminbnd.m, scripts/optimization/fzero.m,
scripts/optimization/lsqnonneg.m:
Use the prefix 'docX' instead of 'doc-' for Texinfo references.
| author | Rik <rik@octave.org> |
|---|---|
| date | Tue, 18 Jun 2013 20:35:12 -0700 |
| parents | 242e9efd4315 |
| children | e39f00a32dc7 |
| rev | line source |
|---|---|
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1 ## Copyright (C) 2008-2012 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 ## "FunValCheck", "OutputFcn", "TolX", "MaxIter", "MaxFunEvals". For a |
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29 ## description of these options, see @ref{docXoptimset,,optimset}. |
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30 ## |
| 10296 | 31 ## On exit, the function returns @var{x}, the approximate minimum point |
| 32 ## and @var{fval}, the function value thereof. | |
| 33 ## @var{info} is an exit flag that can have these values: | |
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34 ## |
| 10296 | 35 ## @itemize |
| 36 ## @item 1 | |
| 37 ## The algorithm converged to a solution. | |
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38 ## |
| 10296 | 39 ## @item 0 |
| 40 ## Maximum number of iterations or function evaluations has been exhausted. | |
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41 ## |
| 10296 | 42 ## @item -1 |
| 43 ## The algorithm has been terminated from user output function. | |
| 44 ## @end itemize | |
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45 ## |
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46 ## Notes: The search for a minimum is restricted to be in the interval |
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47 ## bound by @var{a} and @var{b}. If you only have an initial point |
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48 ## to begin searching from you will need to use an unconstrained |
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49 ## minimization algorithm such as @code{fminunc} or @code{fminsearch}. |
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50 ## @code{fminbnd} internally uses a Golden Section search strategy. |
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51 ## @seealso{fzero, fminunc, fminsearch, optimset} |
| 10296 | 52 ## @end deftypefn |
| 53 | |
| 54 ## This is patterned after opt/fmin.f from Netlib, which in turn is taken from | |
| 55 ## Richard Brent: Algorithms For Minimization Without Derivatives, Prentice-Hall (1973) | |
| 56 | |
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57 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. |
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58 ## PKG_ADD: [~] = __all_opts__ ("fminbnd"); |
| 10296 | 59 |
| 60 function [x, fval, info, output] = fminbnd (fun, xmin, xmax, options = struct ()) | |
| 61 | |
| 62 ## Get default options if requested. | |
| 63 if (nargin == 1 && ischar (fun) && strcmp (fun, 'defaults')) | |
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64 x = optimset ("MaxIter", Inf, "MaxFunEvals", Inf, "TolX", 1e-8, |
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65 "OutputFcn", [], "FunValCheck", "off"); |
| 10296 | 66 return; |
| 67 endif | |
| 68 | |
| 69 if (nargin < 2 || nargin > 4) | |
| 70 print_usage (); | |
| 71 endif | |
| 72 | |
| 73 if (ischar (fun)) | |
| 74 fun = str2func (fun, "global"); | |
| 75 endif | |
| 76 | |
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77 displ = optimget (options, "Display", "notify"); |
| 10296 | 78 funvalchk = strcmpi (optimget (options, "FunValCheck", "off"), "on"); |
| 79 outfcn = optimget (options, "OutputFcn"); | |
| 80 tolx = optimget (options, "TolX", 1e-8); | |
| 81 maxiter = optimget (options, "MaxIter", Inf); | |
| 82 maxfev = optimget (options, "MaxFunEvals", Inf); | |
| 83 | |
| 84 if (funvalchk) | |
| 85 ## Replace fun with a guarded version. | |
| 86 fun = @(x) guarded_eval (fun, x); | |
| 87 endif | |
| 88 | |
| 89 ## The default exit flag if exceeded number of iterations. | |
| 90 info = 0; | |
| 91 niter = 0; | |
| 92 nfev = 0; | |
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93 sqrteps = eps (class (xmin + xmax)); |
| 10296 | 94 |
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95 c = 0.5*(3 - sqrt (5)); |
| 10296 | 96 a = xmin; b = xmax; |
| 97 v = a + c*(b-a); | |
| 98 w = x = v; | |
| 99 e = 0; | |
| 100 fv = fw = fval = fun (x); | |
| 101 nfev++; | |
| 102 | |
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103 ## Only for display purposes. |
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104 iter(1).funccount = nfev; |
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105 iter(1).x = x; |
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106 iter(1).fx = fval; |
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107 |
| 10296 | 108 while (niter < maxiter && nfev < maxfev) |
| 109 xm = 0.5*(a+b); | |
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110 ## FIXME: the golden section search can actually get closer than sqrt(eps) |
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111 ## sometimes. Sometimes not, it depends on the function. This is the |
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112 ## strategy from the Netlib code. Something yet smarter would be good. |
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113 tol = 2 * sqrteps * abs (x) + tolx / 3; |
| 10296 | 114 if (abs (x - xm) <= (2*tol - 0.5*(b-a))) |
| 115 info = 1; | |
| 116 break; | |
| 117 endif | |
| 118 | |
| 119 if (abs (e) > tol) | |
| 120 dogs = false; | |
| 121 ## Try inverse parabolic step. | |
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122 iter(niter+1).procedure = "parabolic"; |
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123 |
| 10296 | 124 r = (x - w)*(fval - fv); |
| 125 q = (x - v)*(fval - fw); | |
| 126 p = (x - v)*q - (x - w)*r; | |
| 127 q = 2*(q - r); | |
| 128 p *= -sign (q); | |
| 129 q = abs (q); | |
| 130 r = e; | |
| 131 e = d; | |
| 132 | |
| 133 if (abs (p) < abs (0.5*q*r) && p > q*(a-x) && p < q*(b-x)) | |
| 134 ## The parabolic step is acceptable. | |
| 135 d = p / q; | |
| 136 u = x + d; | |
| 137 | |
| 138 ## f must not be evaluated too close to ax or bx. | |
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139 if (min (u-a, b-u) < 2*tol) |
| 10296 | 140 d = tol * (sign (xm - x) + (xm == x)); |
| 141 endif | |
| 142 else | |
| 143 dogs = true; | |
| 144 endif | |
| 145 else | |
| 146 dogs = true; | |
| 147 endif | |
| 148 if (dogs) | |
| 149 ## Default to golden section step. | |
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150 |
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151 ## WARNING: This is also the "initial" procedure following |
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152 ## MATLAB nomenclature. After the loop we'll fix the string |
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153 ## for the first step. |
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154 iter(niter+1).procedure = "golden"; |
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155 |
| 10296 | 156 e = ifelse (x >= xm, a - x, b - x); |
| 157 d = c * e; | |
| 158 endif | |
| 159 | |
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160 ## f must not be evaluated too close to x. |
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161 u = x + max (abs (d), tol) * (sign (d) + (d == 0)); |
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162 fu = fun (u); |
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163 |
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164 niter++; |
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165 |
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166 iter(niter).funccount = nfev++; |
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167 iter(niter).x = u; |
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168 iter(niter).fx = fu; |
| 10296 | 169 |
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170 ## update a, b, v, w, and x |
| 10296 | 171 |
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172 if (fu <= fval) |
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173 if (u < x) |
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174 b = x; |
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175 else |
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176 a = x; |
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177 endif |
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178 v = w; fv = fw; |
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179 w = x; fw = fval; |
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180 x = u; fval = fu; |
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181 else |
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182 ## The following if-statement was originally executed even if fu == fval. |
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183 if (u < x) |
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184 a = u; |
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185 else |
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186 b = u; |
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187 endif |
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188 if (fu <= fw || w == x) |
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189 v = w; fv = fw; |
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190 w = u; fw = fu; |
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191 elseif (fu <= fv || v == x || v == w) |
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192 v = u; |
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193 fv = fu; |
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194 endif |
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195 endif |
| 10296 | 196 |
| 197 ## If there's an output function, use it now. | |
| 198 if (outfcn) | |
| 199 optv.funccount = nfev; | |
| 200 optv.fval = fval; | |
| 201 optv.iteration = niter; | |
| 202 if (outfcn (x, optv, "iter")) | |
| 203 info = -1; | |
| 204 break; | |
| 205 endif | |
| 206 endif | |
| 207 endwhile | |
| 208 | |
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209 ## Fix the first step procedure. |
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210 iter(1).procedure = "initial"; |
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211 |
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212 ## Handle the "Display" option |
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213 switch displ |
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214 case "iter" |
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215 print_formatted_table (iter); |
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216 print_exit_msg (info, struct("TolX", tolx, "fx", fval)); |
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217 case "notify" |
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218 if (info == 0) |
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219 print_exit_msg (info, struct("fx",fval)); |
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220 endif |
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221 case "final" |
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222 print_exit_msg (info, struct("TolX", tolx, "fx", fval)); |
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223 case "off" |
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224 "skip"; |
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225 otherwise |
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226 warning ("unknown option for Display: '%s'", displ); |
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227 endswitch |
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228 |
| 10296 | 229 output.iterations = niter; |
| 230 output.funcCount = nfev; | |
| 231 output.bracket = [a, b]; | |
| 232 ## FIXME: bracketf possibly unavailable. | |
| 233 | |
| 234 endfunction | |
| 235 | |
| 236 ## An assistant function that evaluates a function handle and checks for | |
| 237 ## bad results. | |
| 238 function fx = guarded_eval (fun, x) | |
| 239 fx = fun (x); | |
| 240 fx = fx(1); | |
| 241 if (! isreal (fx)) | |
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242 error ("fminbnd:notreal", "fminbnd: non-real value encountered"); |
| 10296 | 243 elseif (isnan (fx)) |
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244 error ("fminbnd:isnan", "fminbnd: NaN value encountered"); |
| 10296 | 245 endif |
| 246 endfunction | |
| 247 | |
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248 ## A hack for printing a formatted table |
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249 function print_formatted_table (table) |
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250 printf ("\n Func-count x f(x) Procedure\n"); |
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251 for row=table |
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252 printf("%5.5s %7.7s %8.8s\t%s\n", |
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253 int2str (row.funccount), num2str (row.x,"%.5f"), |
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254 num2str (row.fx,"%.6f"), row.procedure); |
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255 endfor |
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256 printf ("\n"); |
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257 endfunction |
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258 |
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259 ## Print either a success termination message or bad news |
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260 function print_exit_msg (info, opt=struct()) |
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261 printf (""); |
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262 switch info |
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263 case 1 |
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264 printf ("Optimization terminated:\n"); |
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265 printf (" the current x satisfies the termination criteria using OPTIONS.TolX of %e\n", opt.TolX); |
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266 case 0 |
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267 printf ("Exiting: Maximum number of iterations has been exceeded\n"); |
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268 printf (" - increase MaxIter option.\n"); |
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269 printf (" Current function value: %.6f\n", opt.fx); |
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270 case -1 |
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271 "FIXME"; ## FIXME: what's the message MATLAB prints for this case? |
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272 otherwise |
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273 error ("internal error - fminbnd() is bug, sorry!"); |
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274 endswitch |
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275 printf ("\n"); |
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276 endfunction |
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277 |
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278 |
| 10296 | 279 %!shared opt0 |
| 280 %! opt0 = optimset ("tolx", 0); | |
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281 %!assert (fminbnd (@cos, pi/2, 3*pi/2, opt0), pi, 10*sqrt (eps)) |
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282 %!assert (fminbnd (@(x) (x - 1e-3)^4, -1, 1, opt0), 1e-3, 10e-3*sqrt (eps)) |
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283 %!assert (fminbnd (@(x) abs (x-1e7), 0, 1e10, opt0), 1e7, 10e7*sqrt (eps)) |
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284 %!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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285 |