Mercurial > octave
annotate scripts/optimization/fminsearch.m @ 28912:0de38a6ef693
maint: Use Octave convention of space after function name in scripts dir.
* cplxpair.m, gradient.m, integral.m, integral3.m, interp2.m, interpft.m,
num2str.m, pol2cart.m, quad2d.m, quadgk.m, quadl.m, repelem.m, sph2cart.m,
convhull.m, delaunay.m, delaunayn.m, movegui.m, print_usage.m,
__strip_html_tags__.m, colormap.m, gray2ind.m, imformats.m, importdata.m,
javachk.m, condest.m, isbanded.m, krylov.m, lscov.m, rref.m, inputParser.m,
publish.m, symvar.m, validateattributes.m, ode15i.m, ode15s.m, ode23.m,
ode23s.m, ode45.m, fminbnd.m, fminsearch.m, glpk.m, qp.m, get_forge_pkg.m,
installed_packages.m, annotation.m, axis.m, camorbit.m, campos.m, camva.m,
camzoom.m, daspect.m, legend.m, pbaspect.m, __gnuplot_legend__.m, light.m,
patch.m, plotyy.m, __pie__.m, reducepatch.m, ribbon.m, streamline.m, trisurf.m,
figure.m, ndgrid.m, __gnuplot_draw_axes__.m, __opengl_print__.m, padecoef.m,
polygcd.m, ppval.m, spline.m, union.m, bicg.m, bicgstab.m, cgs.m, eigs.m,
gmres.m, pcg.m, pcr.m, __alltohandles__.m, __sprand__.m, qmr.m, tfqmr.m,
betaincinv.m, cosint.m, gammainc.m, discrete_cdf.m, discrete_inv.m,
discrete_rnd.m, base2dec.m, strtok.m, compare_plot_demos.m,
html_compare_plot_demos.m, speed.m, test.m, weboptions.m, webread.m, webwrite.m:
Use Octave convention of space after function name and before '(' in scripts
directory.
author | Rik <rik@octave.org> |
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date | Tue, 13 Oct 2020 18:17:29 -0700 |
parents | 90fea9cc9caa |
children | 6fd6ad758b10 |
rev | line source |
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 2003-2020 The Octave Project Developers |
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4 ## |
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5 ## See the file COPYRIGHT.md in the top-level directory of this |
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6 ## distribution or <https://octave.org/copyright/>. |
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8 ## This file is part of Octave. | |
9 ## | |
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10 ## Octave is free software: you can redistribute it and/or modify it |
14895 | 11 ## under the terms of the GNU General Public License as published by |
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12 ## the Free Software Foundation, either version 3 of the License, or |
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13 ## (at your option) any later version. |
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15 ## Octave is distributed in the hope that it will be useful, but | |
16 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 ## GNU General Public License for more details. |
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20 ## You should have received a copy of the GNU General Public License | |
21 ## along with Octave; see the file COPYING. If not, see | |
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22 ## <https://www.gnu.org/licenses/>. |
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23 ## |
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24 ######################################################################## |
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26 ## -*- texinfo -*- | |
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27 ## @deftypefn {} {@var{x} =} fminsearch (@var{fun}, @var{x0}) |
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28 ## @deftypefnx {} {@var{x} =} fminsearch (@var{fun}, @var{x0}, @var{options}) |
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29 ## @deftypefnx {} {@var{x} =} fminsearch (@var{problem}) |
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30 ## @deftypefnx {} {[@var{x}, @var{fval}, @var{exitflag}, @var{output}] =} fminsearch (@dots{}) |
14895 | 31 ## |
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32 ## Find a value of @var{x} which minimizes the multi-variable function |
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33 ## @var{fun}. |
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34 ## |
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35 ## @var{fun} is a function handle, inline function, or string containing the |
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36 ## name of the function to evaluate. |
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37 ## |
14895 | 38 ## The search begins at the point @var{x0} and iterates using the |
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39 ## @nospell{Nelder & Mead} Simplex algorithm (a derivative-free method). This |
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40 ## algorithm is better-suited to functions which have discontinuities or for |
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41 ## which a gradient-based search such as @code{fminunc} fails. |
14895 | 42 ## |
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43 ## Options for the search are provided in the parameter @var{options} using the |
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44 ## function @code{optimset}. Currently, @code{fminsearch} accepts the options: |
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45 ## @qcode{"Display"}, @qcode{"FunValCheck"},@qcode{"MaxFunEvals"}, |
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46 ## @qcode{"MaxIter"}, @qcode{"OutputFcn"}, @qcode{"TolFun"}, @qcode{"TolX"}. |
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47 ## |
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48 ## @qcode{"MaxFunEvals"} proscribes the maximum number of function evaluations |
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49 ## before optimization is halted. The default value is |
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50 ## @code{200 * number_of_variables}, i.e., @code{200 * length (@var{x0})}. |
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51 ## The value must be a positive integer. |
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52 ## |
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53 ## @qcode{"MaxIter"} proscribes the maximum number of algorithm iterations |
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54 ## before optimization is halted. The default value is |
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55 ## @code{200 * number_of_variables}, i.e., @code{200 * length (@var{x0})}. |
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56 ## The value must be a positive integer. |
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57 ## |
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58 ## For a description of the other options, see @code{optimset}. To initialize |
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59 ## an options structure with default values for @code{fminsearch} use |
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60 ## @code{options = optimset ("fminsearch")}. |
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62 ## @code{fminsearch} may also be called with a single structure argument |
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63 ## with the following fields: |
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64 ## |
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65 ## @table @code |
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66 ## @item objective |
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67 ## The objective function. |
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68 ## |
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69 ## @item x0 |
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70 ## The initial point. |
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71 ## |
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72 ## @item solver |
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73 ## Must be set to @qcode{"fminsearch"}. |
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74 ## |
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75 ## @item options |
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76 ## A structure returned from @code{optimset} or an empty matrix to |
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77 ## indicate that defaults should be used. |
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78 ## @end table |
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79 ## |
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80 ## @noindent |
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81 ## The field @code{options} is optional. All others are required. |
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82 ## |
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83 ## On exit, the function returns @var{x}, the minimum point, and @var{fval}, |
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84 ## the function value at the minimum. |
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86 ## The third output @var{exitflag} reports whether the algorithm succeeded and |
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87 ## may take one of the following values: |
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88 ## |
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89 ## @table @asis |
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90 ## @item 1 |
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91 ## if the algorithm converged |
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92 ## (size of the simplex is smaller than @code{TolX} @strong{AND} the step in |
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93 ## function value between iterations is smaller than @code{TolFun}). |
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95 ## @item 0 |
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96 ## if the maximum number of iterations or the maximum number of function |
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97 ## evaluations are exceeded. |
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98 ## |
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99 ## @item -1 |
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100 ## if the iteration is stopped by the @qcode{"OutputFcn"}. |
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101 ## @end table |
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102 ## |
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103 ## The fourth output is a structure @var{output} containing runtime |
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104 ## about the algorithm. Fields in the structure are @code{funcCount} |
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105 ## containing the number of function calls to @var{fun}, @code{iterations} |
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106 ## containing the number of iteration steps, @code{algorithm} with the name of |
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107 ## the search algorithm (always: |
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108 ## @nospell{@qcode{"Nelder-Mead simplex direct search"}}), and @code{message} |
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109 ## with the exit message. |
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110 ## |
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111 ## Example: |
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113 ## @example | |
114 ## fminsearch (@@(x) (x(1)-5).^2+(x(2)-8).^4, [0;0]) | |
115 ## @end example | |
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116 ## |
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117 ## Note: If you need to find the minimum of a single variable function it is |
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118 ## probably better to use @code{fminbnd}. |
14895 | 119 ## @seealso{fminbnd, fminunc, optimset} |
120 ## @end deftypefn | |
121 | |
122 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup. | |
123 ## PKG_ADD: [~] = __all_opts__ ("fminsearch"); | |
124 | |
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125 ## FIXME: Add support for output function with "state" set to "interrupt". |
14895 | 126 |
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127 function [x, fval, exitflag, output] = fminsearch (varargin) |
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128 |
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129 if (nargin < 1) |
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130 print_usage (); |
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131 endif |
14895 | 132 |
133 ## Get default options if requested. | |
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134 if (nargin == 1 && ischar (varargin{1}) && strcmp (varargin{1}, "defaults")) |
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135 x = struct ("Display", "notify", "FunValCheck", "off", |
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136 "MaxFunEvals", [], "MaxIter", [], |
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137 "OutputFcn", [], |
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138 "TolFun", 1e-4, "TolX", 1e-4); |
14895 | 139 return; |
140 endif | |
141 | |
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142 if (nargin == 1) |
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143 problem = varargin{1}; |
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144 varargin = {}; |
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145 if (! isstruct (problem)) |
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146 error ("fminsearch: PROBLEM must be a structure"); |
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147 endif |
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148 fun = problem.objective; |
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149 x0 = problem.x0; |
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150 if (! strcmp (problem.solver, "fminsearch")) |
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151 error ('fminsearch: problem.solver must be set to "fminsearch"'); |
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152 endif |
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153 if (isfield (problem, "options")) |
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154 options = problem.options; |
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155 else |
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156 options = []; |
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157 endif |
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158 elseif (nargin > 1) |
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159 fun = varargin{1}; |
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160 x0 = varargin{2}; |
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161 if (nargin > 2) |
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162 options = varargin{3}; |
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163 varargin(1:3) = []; |
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164 else |
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165 options = []; |
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166 varargin = {}; |
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167 endif |
14895 | 168 endif |
169 | |
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170 if (ischar (fun)) |
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171 fun = str2func (fun); |
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172 endif |
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173 |
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174 if (isempty (options)) |
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175 options = struct (); |
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176 endif |
14895 | 177 |
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178 [x, exitflag, output] = nmsmax (fun, x0, options, varargin{:}); |
14895 | 179 |
180 if (isargout (2)) | |
181 fval = feval (fun, x); | |
182 endif | |
183 | |
184 endfunction | |
185 | |
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186 ## NMSMAX Nelder-Mead simplex method for direct search optimization. |
14895 | 187 ## [x, fmax, nf] = NMSMAX(FUN, x0, STOPIT, SAVIT) attempts to |
188 ## maximize the function FUN, using the starting vector x0. | |
189 ## The Nelder-Mead direct search method is used. | |
190 ## Output arguments: | |
191 ## x = vector yielding largest function value found, | |
192 ## fmax = function value at x, | |
193 ## nf = number of function evaluations. | |
194 ## The iteration is terminated when either | |
195 ## - the relative size of the simplex is <= STOPIT(1) | |
196 ## (default 1e-3), | |
197 ## - STOPIT(2) function evaluations have been performed | |
198 ## (default inf, i.e., no limit), or | |
199 ## - a function value equals or exceeds STOPIT(3) | |
200 ## (default inf, i.e., no test on function values). | |
201 ## The form of the initial simplex is determined by STOPIT(4): | |
202 ## STOPIT(4) = 0: regular simplex (sides of equal length, the default) | |
203 ## STOPIT(4) = 1: right-angled simplex. | |
204 ## Progress of the iteration is not shown if STOPIT(5) = 0 (default 1). | |
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205 ## STOPIT(6) indicates the direction (i.e., minimization or |
14895 | 206 ## maximization.) Default is 1, maximization. |
207 ## set STOPIT(6)=-1 for minimization | |
208 ## If a non-empty fourth parameter string SAVIT is present, then | |
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209 ## 'SAVE SAVIT x fmax nf' is executed after each inner iteration. |
14895 | 210 ## NB: x0 can be a matrix. In the output argument, in SAVIT saves, |
211 ## and in function calls, x has the same shape as x0. | |
212 ## NMSMAX(fun, x0, STOPIT, SAVIT, P1, P2,...) allows additional | |
213 ## arguments to be passed to fun, via feval(fun,x,P1,P2,...). | |
214 ## References: | |
215 ## N. J. Higham, Optimization by direct search in matrix computations, | |
216 ## SIAM J. Matrix Anal. Appl, 14(2): 317-333, 1993. | |
217 ## C. T. Kelley, Iterative Methods for Optimization, Society for Industrial | |
218 ## and Applied Mathematics, Philadelphia, PA, 1999. | |
219 | |
220 ## From Matrix Toolbox | |
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221 ## Copyright (C) 2002, 2013 N.J.Higham |
14895 | 222 ## www.maths.man.ac.uk/~higham/mctoolbox |
223 ## | |
224 ## Modifications for Octave by A.Adler 2003 | |
225 | |
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226 function [stopit, savit, dirn, trace, tol, maxiter, tol_f, outfcn] = ... |
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227 parse_options (options, x) |
14895 | 228 |
229 ## Tolerance for cgce test based on relative size of simplex. | |
230 stopit(1) = tol = optimget (options, "TolX", 1e-4); | |
231 | |
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232 ## Tolerance for cgce test based on step in function value. |
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233 tol_f = optimget (options, "TolFun", 1e-4); |
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234 |
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235 ## Max number of function evaluations. |
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236 stopit(2) = optimget (options, "MaxFunEvals", 200 * length (x)); |
14895 | 237 |
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238 ## Max number of iterations |
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239 maxiter = optimget (options, "MaxIter", 200 * length (x)); |
14895 | 240 |
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241 ## Default target for function values. |
14895 | 242 stopit(3) = Inf; # FIXME: expose this parameter to the outside |
243 | |
244 ## Default initial simplex. | |
245 stopit(4) = 0; # FIXME: expose this parameter to the outside | |
246 | |
247 ## Default: show progress. | |
248 display = optimget (options, "Display", "notify"); | |
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249 switch (display) |
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250 case "iter" |
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251 stopit(5) = 1; |
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252 case "final" |
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253 stopit(5) = 2; |
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254 case "notify" |
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255 stopit(5) = 3; |
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256 otherwise # "none" |
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257 stopit(5) = 0; |
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258 endswitch |
14895 | 259 trace = stopit(5); |
260 | |
261 ## Use function to minimize, not maximize | |
262 stopit(6) = dirn = -1; | |
263 | |
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264 ## Filename for snapshots. |
14895 | 265 savit = []; # FIXME: expose this parameter to the outside |
266 | |
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267 ## OutputFcn |
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268 outfcn = optimget (options, "OutputFcn"); |
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269 |
14895 | 270 endfunction |
271 | |
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272 function [x, exitflag, output] = nmsmax (fun, x, options, varargin) |
14895 | 273 |
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274 [stopit, savit, dirn, trace, tol, maxiter, tol_f, outfcn] = ... |
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275 parse_options (options, x); |
14895 | 276 |
277 if (strcmpi (optimget (options, "FunValCheck", "off"), "on")) | |
278 ## Replace fcn with a guarded version. | |
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279 fun = @(x) guarded_eval (fun, x, varargin{:}); |
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280 else |
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281 fun = @(x) real (fun (x, varargin{:})); |
14895 | 282 endif |
283 | |
284 x0 = x(:); # Work with column vector internally. | |
285 n = length (x0); | |
286 | |
287 V = [zeros(n,1) eye(n)]; | |
288 f = zeros (n+1,1); | |
289 V(:,1) = x0; | |
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290 f(1) = dirn * fun (x); |
14895 | 291 fmax_old = f(1); |
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292 nf = 1; |
14895 | 293 |
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294 if (trace == 1) |
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295 printf ("f(x0) = %9.4e\n", dirn * f(1)); |
14895 | 296 endif |
297 | |
298 k = 0; m = 0; | |
299 | |
300 ## Set up initial simplex. | |
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301 scale = max (norm (x0, Inf), 1); |
14895 | 302 if (stopit(4) == 0) |
303 ## Regular simplex - all edges have same length. | |
304 ## Generated from construction given in reference [18, pp. 80-81] of [1]. | |
305 alpha = scale / (n*sqrt (2)) * [sqrt(n+1)-1+n, sqrt(n+1)-1]; | |
306 V(:,2:n+1) = (x0 + alpha(2)*ones (n,1)) * ones (1,n); | |
307 for j = 2:n+1 | |
308 V(j-1,j) = x0(j-1) + alpha(1); | |
309 x(:) = V(:,j); | |
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310 f(j) = dirn * fun (x); |
14895 | 311 endfor |
312 else | |
313 ## Right-angled simplex based on co-ordinate axes. | |
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314 alpha = scale * ones (n+1,1); |
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315 for j = 2:n+1 |
14895 | 316 V(:,j) = x0 + alpha(j)*V(:,j); |
317 x(:) = V(:,j); | |
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318 f(j) = dirn * fun (x); |
14895 | 319 endfor |
320 endif | |
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321 nf += n; |
14895 | 322 how = "initial "; |
323 | |
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324 [~, j] = sort (f); |
14895 | 325 j = j(n+1:-1:1); |
326 f = f(j); | |
327 V = V(:,j); | |
328 | |
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329 exitflag = 0; |
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330 |
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331 if (! isempty (outfcn)) |
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332 optimvalues.iteration = 0; |
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333 optimvalues.funccount = nf; |
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334 optimvalues.fval = dirn * f(1); |
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335 optimvalues.procedure = how; |
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336 state = "init"; |
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337 stop = outfcn (x, optimvalues, state); |
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338 if (stop) |
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339 msg = "Stopped by OutputFcn\n"; |
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340 exitflag = -1; |
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341 endif |
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342 endif |
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343 |
14895 | 344 alpha = 1; beta = 1/2; gamma = 2; |
345 | |
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346 while (exitflag != -1) # Outer (and only) loop. |
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347 k += 1; |
14895 | 348 |
349 if (k > maxiter) | |
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350 msg = "Exceeded maximum iterations\n"; |
14895 | 351 break; |
352 endif | |
353 | |
354 fmax = f(1); | |
355 if (fmax > fmax_old) | |
356 if (! isempty (savit)) | |
357 x(:) = V(:,1); | |
358 eval (["save " savit " x fmax nf"]); | |
359 endif | |
360 endif | |
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361 if (trace == 1) |
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362 printf ("Iter. %2.0f,", k); |
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363 printf (" how = %-11s", [how ","]); |
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364 printf ("nf = %3.0f, f = %9.4e (%2.1f%%)\n", nf, dirn * fmax, ... |
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365 100*(fmax-fmax_old)/(abs (fmax_old)+eps)); |
14895 | 366 endif |
367 fmax_old = fmax; | |
368 | |
369 ## Three stopping tests from MDSMAX.M | |
370 | |
371 ## Stopping Test 1 - f reached target value? | |
372 if (fmax >= stopit(3)) | |
373 msg = "Exceeded target...quitting\n"; | |
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374 ## FIXME: Add documentation when stopit(3) gets exposed to the outside |
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375 exitflag = -1; |
14895 | 376 break; |
377 endif | |
378 | |
379 ## Stopping Test 2 - too many f-evals? | |
380 if (nf >= stopit(2)) | |
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381 msg = "Exceeded maximum number of function evaluations\n"; |
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382 exitflag = 0; |
14895 | 383 break; |
384 endif | |
385 | |
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386 ## Stopping Test 3 - converged? The first part is test (4.3) in [1]. |
14895 | 387 v1 = V(:,1); |
388 size_simplex = norm (V(:,2:n+1)-v1(:,ones (1,n)),1) / max (1, norm (v1,1)); | |
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389 step_f = max (abs (f(1) - f(2:n+1))); |
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390 if (size_simplex <= tol && step_f <= tol_f ) |
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391 msg = sprintf (["Algorithm converged. Simplex size %9.4e <= %9.4e ", ... |
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392 "and step in function value %9.4e <= %9.4e\n"], ... |
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393 size_simplex, tol, step_f, tol_f); |
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394 exitflag = 1; |
14895 | 395 break; |
396 endif | |
397 | |
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398 ## Call OutputFcn |
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399 if (! isempty (outfcn)) |
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400 optimvalues.funccount = nf; |
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401 optimvalues.fval = dirn * f(1); |
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402 optimvalues.iteration = k; |
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403 optimvalues.procedure = how; |
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404 state = "iter"; |
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405 stop = outfcn (x, optimvalues, state); |
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406 if (stop) |
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407 msg = "Stopped by OutputFcn\n"; |
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408 exitflag = -1; |
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409 break; |
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410 endif |
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411 endif |
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412 |
14895 | 413 ## One step of the Nelder-Mead simplex algorithm |
414 ## NJH: Altered function calls and changed CNT to NF. | |
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415 ## Changed each 'fr < f(1)' type test to '>' for maximization |
14895 | 416 ## and re-ordered function values after sort. |
417 | |
418 vbar = (sum (V(:,1:n)')/n)'; # Mean value | |
419 vr = (1 + alpha)*vbar - alpha*V(:,n+1); | |
420 x(:) = vr; | |
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421 fr = dirn * fun (x); |
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422 nf += 1; |
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423 vk = vr; fk = fr; how = "reflect"; |
14895 | 424 if (fr > f(n)) |
425 if (fr > f(1)) | |
426 ve = gamma*vr + (1-gamma)*vbar; | |
427 x(:) = ve; | |
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428 fe = dirn * fun (x); |
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429 nf += 1; |
14895 | 430 if (fe > f(1)) |
431 vk = ve; | |
432 fk = fe; | |
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433 how = "expand"; |
14895 | 434 endif |
435 endif | |
436 else | |
437 vt = V(:,n+1); | |
438 ft = f(n+1); | |
439 if (fr > ft) | |
440 vt = vr; | |
441 ft = fr; | |
442 endif | |
443 vc = beta*vt + (1-beta)*vbar; | |
444 x(:) = vc; | |
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445 fc = dirn * fun (x); |
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446 nf += 1; |
14895 | 447 if (fc > f(n)) |
448 vk = vc; fk = fc; | |
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449 how = "contract"; |
14895 | 450 else |
451 for j = 2:n | |
452 V(:,j) = (V(:,1) + V(:,j))/2; | |
453 x(:) = V(:,j); | |
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454 f(j) = dirn * fun (x); |
14895 | 455 endfor |
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456 nf += n-1; |
14895 | 457 vk = (V(:,1) + V(:,n+1))/2; |
458 x(:) = vk; | |
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459 fk = dirn * fun (x); |
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460 nf += 1; |
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461 how = "shrink"; |
14895 | 462 endif |
463 endif | |
464 V(:,n+1) = vk; | |
465 f(n+1) = fk; | |
466 [~,j] = sort(f); | |
467 j = j(n+1:-1:1); | |
468 f = f(j); | |
469 V = V(:,j); | |
470 | |
471 endwhile # End of outer (and only) loop. | |
472 | |
473 ## Finished. | |
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474 if ( (trace == 1) || (trace == 2) || (trace == 3 && exitflag != 1) ) |
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475 printf (msg); |
14895 | 476 endif |
477 x(:) = V(:,1); | |
478 | |
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479 ## FIXME: Should outputfcn be called only if exitflag != 0, |
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480 ## i.e., only when we have successfully converged? |
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481 if (! isempty (outfcn)) |
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482 optimvalues.funccount = nf; |
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483 optimvalues.fval = dirn * f(1); |
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484 optimvalues.iteration = k; |
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485 optimvalues.procedure = how; |
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486 state = "done"; |
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487 outfcn (x, optimvalues, state); |
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488 endif |
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489 |
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490 ## output |
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491 output.iterations = k; |
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492 output.funcCount = nf; |
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493 output.algorithm = "Nelder-Mead simplex direct search"; |
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494 output.message = msg; |
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495 |
14895 | 496 endfunction |
497 | |
498 ## A helper function that evaluates a function and checks for bad results. | |
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499 function y = guarded_eval (fun, x, varargin) |
14895 | 500 |
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501 y = fun (x, varargin{:}); |
14895 | 502 |
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503 if (! (isreal (y))) |
14895 | 504 error ("fminsearch:notreal", "fminsearch: non-real value encountered"); |
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505 elseif (any (isnan (y(:)))) |
14895 | 506 error ("fminsearch:isnan", "fminsearch: NaN value encountered"); |
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507 elseif (any (isinf (y(:)))) |
14895 | 508 error ("fminsearch:isinf", "fminsearch: Inf value encountered"); |
509 endif | |
510 | |
511 endfunction | |
512 | |
513 | |
514 %!demo | |
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515 %! clf; |
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516 %! hold on; |
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517 %! draw_fcn = @(x) (plot (x(1), x(2)) && false); |
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518 %! fcn = @(x) (x(1)-5).^2 + (x(2)-8).^4; |
14895 | 519 %! x0 = [0;0]; |
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520 %! [xmin, fval] = fminsearch (fcn, x0, optimset ("OutputFcn", draw_fcn)) |
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521 %! hold off; |
14895 | 522 |
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523 %!assert (fminsearch (@sin, 3, optimset ("MaxIter", 30)), 3*pi/2, 1e-4) |
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524 |
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525 ## FIXME: The following test is for checking that fminsearch stops earlier |
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526 ## with these settings. If the optimizer algorithm is changed, it |
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527 ## may fail. Just adapt the values to make it pass again. |
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528 %!test |
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529 %! x = fminsearch (@sin, 3, optimset ("MaxIter", 3, "Display", "none")); |
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530 %! assert (x, 4.8750, 1e-4); |
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531 %! x = fminsearch (@sin, 3, optimset ("MaxFunEvals", 18, "Display", "none")); |
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532 %! assert (x, 4.7109, 1e-4); |
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533 |
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534 %!test |
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535 %! problem.objective = @sin; |
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536 %! problem.x0 = 3; |
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537 %! problem.solver = "fminsearch"; |
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538 %! problem.options = optimset ("MaxIter", 3, "Display", "none"); |
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539 %! x = fminsearch (problem); |
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540 %! assert (x, 4.8750, 1e-4); |
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541 %! problem.options = optimset ("MaxFunEvals", 18, "Display", "none"); |
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542 %! x = fminsearch (problem); |
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543 %! assert (x, 4.7109, 1e-4); |
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544 |
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545 %!test |
14895 | 546 %! c = 1.5; |
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547 %! assert (fminsearch (@(x) x(1).^2 + c*x(2).^2, [1;1]), [0;0], 1e-4); |
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548 |
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549 ## additional input argument |
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550 %!test |
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551 %! x1 = fminsearch (@(x, c) x(1).^2 + c*x(2).^2, [1;1], [], 1.5); |
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552 %! assert (x1, [0;0], 1e-4); |
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553 %! x1 = fminsearch (@(x, c) c(1)*x(1).^2 + c(2)*x(2).^2, [1;1], ... |
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554 %! optimset ("Display", "none"), [1 1.5]); |
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555 %! assert (x1, [0;0], 1e-4); |
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556 |
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557 ## all output arguments |
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558 %!test |
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559 %! options = optimset ("Display", "none", "TolX", 1e-4, "TolFun", 1e-7); |
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560 %! [x, fval, exitflag, output] = fminsearch (@sin, 3, options); |
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561 %! assert (x, 3*pi/2, options.TolX); |
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562 %! assert (fval, -1, options.TolFun); |
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563 %! assert (exitflag, 1); |
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564 %! assert (isstruct (output)); |
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565 %! assert (isfield (output, "iterations") && isnumeric (output.iterations) |
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566 %! && isscalar (output.iterations) && output.iterations > 0); |
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567 %! assert (isfield (output, "funcCount") && isnumeric (output.funcCount) |
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568 %! && isscalar (output.funcCount) && output.funcCount > 0); |
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569 %! assert (isfield (output, "algorithm") && ischar (output.algorithm)); |
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570 %! assert (isfield (output, "message") && ischar (output.message)); |
14895 | 571 |
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572 ## Tests for guarded_eval |
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573 %!error <non-real value encountered> |
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574 %! fminsearch (@(x) ([0 2i]), 0, optimset ("FunValCheck", "on")); |
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575 %!error <NaN value encountered> |
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576 %! fminsearch (@(x) (NaN), 0, optimset ("FunValCheck", "on")); |
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577 %!error <Inf value encountered> |
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578 %! fminsearch (@(x) (Inf), 0, optimset ("FunValCheck", "on")); |
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579 |
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580 ## Test input validation |
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581 %!error <Invalid call> fminsearch () |
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582 %!error fminsearch (1) |