Mercurial > hg > octave-nkf
annotate scripts/optimization/fminbnd.m @ 14895:e0525ecf156e
Add new function fminsearch.m
* fminsearch.m: new function.
* optimization/module.mk: Add fminsearch to build system.
* NEWS: Add fminsearch to list of new functions in 3.8.0.
* nonlin.txi, fminbnd.m, fminunc.m: Add fminsearch to documentation.
Update other optimization functions to reference fminsearch.
| author | Andy Adler <andy@analyti.ca> |
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| date | Fri, 20 Jul 2012 09:25:37 -0700 |
| parents | 5d3a684236b0 |
| children | 242e9efd4315 |
| 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{doc-optimset,,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 | |
| 77 ## TODO | |
| 78 ## displev = optimget (options, "Display", "notify"); | |
| 79 funvalchk = strcmpi (optimget (options, "FunValCheck", "off"), "on"); | |
| 80 outfcn = optimget (options, "OutputFcn"); | |
| 81 tolx = optimget (options, "TolX", 1e-8); | |
| 82 maxiter = optimget (options, "MaxIter", Inf); | |
| 83 maxfev = optimget (options, "MaxFunEvals", Inf); | |
| 84 | |
| 85 if (funvalchk) | |
| 86 ## Replace fun with a guarded version. | |
| 87 fun = @(x) guarded_eval (fun, x); | |
| 88 endif | |
| 89 | |
| 90 ## The default exit flag if exceeded number of iterations. | |
| 91 info = 0; | |
| 92 niter = 0; | |
| 93 nfev = 0; | |
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94 sqrteps = eps (class (xmin + xmax)); |
| 10296 | 95 |
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96 c = 0.5*(3 - sqrt (5)); |
| 10296 | 97 a = xmin; b = xmax; |
| 98 v = a + c*(b-a); | |
| 99 w = x = v; | |
| 100 e = 0; | |
| 101 fv = fw = fval = fun (x); | |
| 102 nfev++; | |
| 103 | |
| 104 while (niter < maxiter && nfev < maxfev) | |
| 105 xm = 0.5*(a+b); | |
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106 ## FIXME: the golden section search can actually get closer than sqrt(eps) |
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107 ## sometimes. Sometimes not, it depends on the function. This is the |
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108 ## strategy from the Netlib code. Something yet smarter would be good. |
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109 tol = 2 * sqrteps * abs (x) + tolx / 3; |
| 10296 | 110 if (abs (x - xm) <= (2*tol - 0.5*(b-a))) |
| 111 info = 1; | |
| 112 break; | |
| 113 endif | |
| 114 | |
| 115 if (abs (e) > tol) | |
| 116 dogs = false; | |
| 117 ## Try inverse parabolic step. | |
| 118 r = (x - w)*(fval - fv); | |
| 119 q = (x - v)*(fval - fw); | |
| 120 p = (x - v)*q - (x - w)*r; | |
| 121 q = 2*(q - r); | |
| 122 p *= -sign (q); | |
| 123 q = abs (q); | |
| 124 r = e; | |
| 125 e = d; | |
| 126 | |
| 127 if (abs (p) < abs (0.5*q*r) && p > q*(a-x) && p < q*(b-x)) | |
| 128 ## The parabolic step is acceptable. | |
| 129 d = p / q; | |
| 130 u = x + d; | |
| 131 | |
| 132 ## f must not be evaluated too close to ax or bx. | |
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133 if (min (u-a, b-u) < 2*tol) |
| 10296 | 134 d = tol * (sign (xm - x) + (xm == x)); |
| 135 endif | |
| 136 else | |
| 137 dogs = true; | |
| 138 endif | |
| 139 else | |
| 140 dogs = true; | |
| 141 endif | |
| 142 if (dogs) | |
| 143 ## Default to golden section step. | |
| 144 e = ifelse (x >= xm, a - x, b - x); | |
| 145 d = c * e; | |
| 146 endif | |
| 147 | |
| 148 ## f must not be evaluated too close to x. | |
| 149 u = x + max (abs (d), tol) * (sign (d) + (d == 0)); | |
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150 |
| 10296 | 151 fu = fun (u); |
| 152 nfev++; | |
| 153 niter++; | |
| 154 | |
| 155 ## update a, b, v, w, and x | |
| 156 | |
| 157 if (fu <= fval) | |
| 158 if (u < x) | |
| 159 b = x; | |
| 160 else | |
| 161 a = x; | |
| 162 endif | |
| 163 v = w; fv = fw; | |
| 164 w = x; fw = fval; | |
| 165 x = u; fval = fu; | |
| 166 else | |
| 167 ## The following if-statement was originally executed even if fu == fval. | |
| 168 if (u < x) | |
| 169 a = u; | |
| 170 else | |
| 171 b = u; | |
| 172 endif | |
| 173 if (fu <= fw || w == x) | |
| 174 v = w; fv = fw; | |
| 175 w = u; fw = fu; | |
| 176 elseif (fu <= fv || v == x || v == w) | |
| 177 v = u; | |
| 178 fv = fu; | |
| 179 endif | |
| 180 endif | |
| 181 | |
| 182 ## If there's an output function, use it now. | |
| 183 if (outfcn) | |
| 184 optv.funccount = nfev; | |
| 185 optv.fval = fval; | |
| 186 optv.iteration = niter; | |
| 187 if (outfcn (x, optv, "iter")) | |
| 188 info = -1; | |
| 189 break; | |
| 190 endif | |
| 191 endif | |
| 192 endwhile | |
| 193 | |
| 194 output.iterations = niter; | |
| 195 output.funcCount = nfev; | |
| 196 output.bracket = [a, b]; | |
| 197 ## FIXME: bracketf possibly unavailable. | |
| 198 | |
| 199 endfunction | |
| 200 | |
| 201 ## An assistant function that evaluates a function handle and checks for | |
| 202 ## bad results. | |
| 203 function fx = guarded_eval (fun, x) | |
| 204 fx = fun (x); | |
| 205 fx = fx(1); | |
| 206 if (! isreal (fx)) | |
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207 error ("fminbnd:notreal", "fminbnd: non-real value encountered"); |
| 10296 | 208 elseif (isnan (fx)) |
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209 error ("fminbnd:isnan", "fminbnd: NaN value encountered"); |
| 10296 | 210 endif |
| 211 endfunction | |
| 212 | |
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213 |
| 10296 | 214 %!shared opt0 |
| 215 %! opt0 = optimset ("tolx", 0); | |
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216 %!assert (fminbnd (@cos, pi/2, 3*pi/2, opt0), pi, 10*sqrt (eps)) |
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217 %!assert (fminbnd (@(x) (x - 1e-3)^4, -1, 1, opt0), 1e-3, 10e-3*sqrt (eps)) |
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218 %!assert (fminbnd (@(x) abs (x-1e7), 0, 1e10, opt0), 1e7, 10e7*sqrt (eps)) |
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219 %!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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220 |