Mercurial > hg > octave-nkf

annotate scripts/optimization/fminbnd.m @ 20076:781adfc2958c draft obsolete nkf

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Build qt graphics toolkit menus with uimenu * libgui/graphics/Figure.cc, libgui/graphics/Figure.h: Revert cset 7335cc071ab0 and remove all menu items. * scripts/gui/private/__get_funcname__.m: Fix typo * scripts/plot/util/private/__add_default_menu__.m: Enable uimenu for qt graphics toolkit and fix setting pan/rotate/zoom for qt and fltk
author Stefan Mahr <dac922@gmx.de>
date Fri, 27 Feb 2015 18:36:05 +0100
parents 9fc020886ae9
children f1d0f506ee78
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rev   line source
19898
4197fc428c7d maint: Update copyright notices for 2015.
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1 ## Copyright (C) 2008-2015 VZLU Prague, a.s.
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18 ##
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19 ## Author: Jaroslav Hajek <highegg@gmail.com>
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20
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21 ## -*- texinfo -*-
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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
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33 ## and @var{fval}, the function value thereof.
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34 ## @var{info} is an exit flag that can have these values:
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35 ##
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36 ## @itemize
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37 ## @item 1
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38 ## The algorithm converged to a solution.
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39 ##
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40 ## @item 0
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41 ## Maximum number of iterations or function evaluations has been exhausted.
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42 ##
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43 ## @item -1
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44 ## The algorithm has been terminated from user output function.
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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}
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53 ## @end deftypefn
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54
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55 ## This is patterned after opt/fmin.f from Netlib, which in turn is taken from
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56 ## Richard Brent: Algorithms For Minimization Without Derivatives,
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57 ## Prentice-Hall (1973)
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58
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59 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup.
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60 ## PKG_ADD: [~] = __all_opts__ ("fminbnd");
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61
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62 function [x, fval, info, output] = fminbnd (fun, xmin, xmax, options = struct ())
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63
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64 ## Get default options if requested.
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65 if (nargin == 1 && ischar (fun) && strcmp (fun, 'defaults'))
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66 x = optimset ("MaxIter", Inf, "MaxFunEvals", Inf, "TolX", 1e-8,
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67 "OutputFcn", [], "FunValCheck", "off");
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68 return;
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69 endif
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70
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71 if (nargin < 2 || nargin > 4)
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72 print_usage ();
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73 endif
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74
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75 if (xmin > xmax)
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76 error ("Octave:invalid-input-arg",
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77 "fminbnd: the lower bound cannot be greater than the upper one");
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78 endif
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79
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80 if (ischar (fun))
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81 fun = str2func (fun, "global");
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82 endif
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83
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84 displ = optimget (options, "Display", "notify");
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85 funvalchk = strcmpi (optimget (options, "FunValCheck", "off"), "on");
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86 outfcn = optimget (options, "OutputFcn");
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87 tolx = optimget (options, "TolX", 1e-8);
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88 maxiter = optimget (options, "MaxIter", Inf);
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89 maxfev = optimget (options, "MaxFunEvals", Inf);
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90
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91 if (funvalchk)
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92 ## Replace fun with a guarded version.
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93 fun = @(x) guarded_eval (fun, x);
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94 endif
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95
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96 ## The default exit flag if exceeded number of iterations.
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97 info = 0;
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98 niter = 0;
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99 nfev = 0;
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100 sqrteps = eps (class (xmin + xmax));
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101
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102 c = 0.5*(3 - sqrt (5));
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103 a = xmin; b = xmax;
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104 v = a + c*(b-a);
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105 w = x = v;
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106 e = 0;
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107 fv = fw = fval = fun (x);
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108 nfev++;
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109
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110 ## Only for display purposes.
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111 iter(1).funccount = nfev;
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112 iter(1).x = x;
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113 iter(1).fx = fval;
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114
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115 while (niter < maxiter && nfev < maxfev)
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116 xm = 0.5*(a+b);
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117 ## FIXME: the golden section search can actually get closer than sqrt(eps)
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118 ## sometimes. Sometimes not, it depends on the function. This is the
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119 ## strategy from the Netlib code. Something yet smarter would be good.
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120 tol = 2 * sqrteps * abs (x) + tolx / 3;
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121 if (abs (x - xm) <= (2*tol - 0.5*(b-a)))
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122 info = 1;
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123 break;
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124 endif
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125
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126 if (abs (e) > tol)
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127 dogs = false;
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128 ## Try inverse parabolic step.
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129 iter(niter+1).procedure = "parabolic";
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130
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131 r = (x - w)*(fval - fv);
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132 q = (x - v)*(fval - fw);
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133 p = (x - v)*q - (x - w)*r;
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134 q = 2*(q - r);
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135 p *= -sign (q);
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136 q = abs (q);
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137 r = e;
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138 e = d;
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139
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140 if (abs (p) < abs (0.5*q*r) && p > q*(a-x) && p < q*(b-x))
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141 ## The parabolic step is acceptable.
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142 d = p / q;
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143 u = x + d;
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144
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145 ## f must not be evaluated too close to ax or bx.
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146 if (min (u-a, b-u) < 2*tol)
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147 d = tol * (sign (xm - x) + (xm == x));
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148 endif
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149 else
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150 dogs = true;
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151 endif
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152 else
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153 dogs = true;
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154 endif
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155 if (dogs)
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156 ## Default to golden section step.
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157
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158 ## WARNING: This is also the "initial" procedure following
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159 ## MATLAB nomenclature. After the loop we'll fix the string
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160 ## for the first step.
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161 iter(niter+1).procedure = "golden";
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162
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163 e = ifelse (x >= xm, a - x, b - x);
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164 d = c * e;
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165 endif
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166
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167 ## f must not be evaluated too close to x.
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168 u = x + max (abs (d), tol) * (sign (d) + (d == 0));
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169 fu = fun (u);
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170
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171 niter++;
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172
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173 iter(niter).funccount = nfev++;
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174 iter(niter).x = u;
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175 iter(niter).fx = fu;
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176
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177 ## update a, b, v, w, and x
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178
18315
61dab64aa5a6 fminbnd.m: Correctly handle certain functions with odd discontinuities (bug #36923)
Rik <rik@octave.org>
parents: 17744
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179 if (fu < fval)
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180 if (u < x)
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181 b = x;
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182 else
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183 a = x;
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184 endif
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185 v = w; fv = fw;
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186 w = x; fw = fval;
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187 x = u; fval = fu;
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188 else
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189 ## The following if-statement was originally executed even if fu == fval.
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190 if (u < x)
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191 a = u;
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192 else
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193 b = u;
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194 endif
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195 if (fu <= fw || w == x)
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196 v = w; fv = fw;
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197 w = u; fw = fu;
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198 elseif (fu <= fv || v == x || v == w)
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199 v = u;
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200 fv = fu;
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201 endif
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202 endif
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203
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204 ## If there's an output function, use it now.
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205 if (outfcn)
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206 optv.funccount = nfev;
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207 optv.fval = fval;
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208 optv.iteration = niter;
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209 if (outfcn (x, optv, "iter"))
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210 info = -1;
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211 break;
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212 endif
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213 endif
035ac548a67e implement fminbnd
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214 endwhile
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215
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216 ## Fix the first step procedure.
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217 iter(1).procedure = "initial";
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218
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219 ## Handle the "Display" option
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Rik <rik@octave.org>
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diff changeset
220 switch (displ)
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221 case "iter"
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222 print_formatted_table (iter);
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223 print_exit_msg (info, struct("TolX", tolx, "fx", fval));
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224 case "notify"
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225 if (info == 0)
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226 print_exit_msg (info, struct("fx",fval));
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227 endif
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228 case "final"
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229 print_exit_msg (info, struct("TolX", tolx, "fx", fval));
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230 case "off"
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231 "skip";
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232 otherwise
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233 warning ("unknown option for Display: '%s'", displ);
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234 endswitch
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235
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diff changeset
236 output.iterations = niter;
035ac548a67e implement fminbnd
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diff changeset
237 output.funcCount = nfev;
035ac548a67e implement fminbnd
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diff changeset
238 output.bracket = [a, b];
035ac548a67e implement fminbnd
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parents:
diff changeset
239 ## FIXME: bracketf possibly unavailable.
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parents:
diff changeset
240
035ac548a67e implement fminbnd
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parents:
diff changeset
241 endfunction
035ac548a67e implement fminbnd
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parents:
diff changeset
242
035ac548a67e implement fminbnd
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parents:
diff changeset
243 ## An assistant function that evaluates a function handle and checks for
035ac548a67e implement fminbnd
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diff changeset
244 ## bad results.
035ac548a67e implement fminbnd
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diff changeset
245 function fx = guarded_eval (fun, x)
035ac548a67e implement fminbnd
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diff changeset
246 fx = fun (x);
035ac548a67e implement fminbnd
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parents:
diff changeset
247 fx = fx(1);
035ac548a67e implement fminbnd
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diff changeset
248 if (! isreal (fx))
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diff changeset
249 error ("fminbnd:notreal", "fminbnd: non-real value encountered");
10296
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diff changeset
250 elseif (isnan (fx))
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diff changeset
251 error ("fminbnd:isnan", "fminbnd: NaN value encountered");
10296
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252 endif
035ac548a67e implement fminbnd
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253 endfunction
035ac548a67e implement fminbnd
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254
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255 ## A hack for printing a formatted table
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diff changeset
256 function print_formatted_table (table)
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257 printf ("\n Func-count x f(x) Procedure\n");
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258 for row=table
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diff changeset
259 printf("%5.5s %7.7s %8.8s\t%s\n",
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diff changeset
260 int2str (row.funccount), num2str (row.x,"%.5f"),
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diff changeset
261 num2str (row.fx,"%.6f"), row.procedure);
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diff changeset
262 endfor
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diff changeset
263 printf ("\n");
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264 endfunction
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diff changeset
265
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266 ## Print either a success termination message or bad news
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diff changeset
267 function print_exit_msg (info, opt=struct())
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diff changeset
268 printf ("");
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parents: 16772
diff changeset
269 switch (info)
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270 case 1
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271 printf ("Optimization terminated:\n");
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diff changeset
272 printf (" the current x satisfies the termination criteria using OPTIONS.TolX of %e\n", opt.TolX);
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diff changeset
273 case 0
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diff changeset
274 printf ("Exiting: Maximum number of iterations has been exceeded\n");
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diff changeset
275 printf (" - increase MaxIter option.\n");
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diff changeset
276 printf (" Current function value: %.6f\n", opt.fx);
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diff changeset
277 case -1
17336
b81b9d079515 Use '##' for comments which stand alone on a line.
Rik <rik@octave.org>
parents: 17281
diff changeset
278 "FIXME"; # FIXME: what's the message MATLAB prints for this case?
15706
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diff changeset
279 otherwise
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diff changeset
280 error ("internal error - fminbnd() is bug, sorry!");
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diff changeset
281 endswitch
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diff changeset
282 printf ("\n");
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diff changeset
283 endfunction
242e9efd4315 Added Display option for fminbnd()
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diff changeset
284
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
diff changeset
285
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Jaroslav Hajek <highegg@gmail.com>
parents:
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286 %!shared opt0
035ac548a67e implement fminbnd
Jaroslav Hajek <highegg@gmail.com>
parents:
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287 %! opt0 = optimset ("tolx", 0);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
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288 %!assert (fminbnd (@cos, pi/2, 3*pi/2, opt0), pi, 10*sqrt (eps))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
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289 %!assert (fminbnd (@(x) (x - 1e-3)^4, -1, 1, opt0), 1e-3, 10e-3*sqrt (eps))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
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290 %!assert (fminbnd (@(x) abs (x-1e7), 0, 1e10, opt0), 1e7, 10e7*sqrt (eps))
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14138
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291 %!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))
19794
db92e7e28e1f strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 19640
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292 %!assert (fminbnd (@(x) x > 0.3, 0, 1) < 0.3)
db92e7e28e1f strip trailing whitespace from most source files
John W. Eaton <jwe@octave.org>
parents: 19640
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293 %!assert (fminbnd (@(x) sin (x), 0, 0), 0, eps)
14363
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Rik <octave@nomad.inbox5.com>
parents: 14138
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294
19640
0f79fa9b3a8c fmindbnd.m: Check input range is low to high (bug #43219).
Massimiliano Fasi <massimiliano.fasi@gmail.com>
parents: 18315
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295 %!error <lower bound cannot be greater> fminbnd (@(x) sin (x), 0, -pi)
0f79fa9b3a8c fmindbnd.m: Check input range is low to high (bug #43219).
Massimiliano Fasi <massimiliano.fasi@gmail.com>
parents: 18315
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296