annotate scripts/optimization/fminbnd.m @ 13027:b9a89ca0fb75

prevent optimization functions from setting ans in workspace at startup * fminbnd.m, fminunc.m, fsolve.m, fzero.m, lsqnonneg.m, pqpnonneg.m, qp.m: Discard result from call to __all_opt__ in PKG_ADD command.
author John W. Eaton <jwe@octave.org>
date Mon, 29 Aug 2011 13:07:22 -0400
parents c792872f8942
children 72c96de7a403
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1 ## Copyright (C) 2008-2011 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. @var{fun} should be a
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24 ## function
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25 ## handle or name. @var{a}, @var{b} specify a starting interval. @var{options}
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26 ## is a
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27 ## structure specifying additional options. Currently, @code{fminbnd}
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28 ## recognizes these options: @code{"FunValCheck"}, @code{"OutputFcn"},
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29 ## @code{"TolX"}, @code{"MaxIter"}, @code{"MaxFunEvals"}.
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30 ## For description of these options, see @ref{doc-optimset,,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 ## @seealso{optimset, fzero, fminunc}
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47 ## @end deftypefn
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48
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49 ## This is patterned after opt/fmin.f from Netlib, which in turn is taken from
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50 ## Richard Brent: Algorithms For Minimization Without Derivatives, Prentice-Hall (1973)
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51
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52 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup.
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53 ## PKG_ADD: [~] = __all_opts__ ("fminbnd");
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54
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55 function [x, fval, info, output] = fminbnd (fun, xmin, xmax, options = struct ())
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56
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57 ## Get default options if requested.
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58 if (nargin == 1 && ischar (fun) && strcmp (fun, 'defaults'))
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59 x = optimset ("MaxIter", Inf, "MaxFunEvals", Inf, "TolX", 1e-8, \
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60 "OutputFcn", [], "FunValCheck", "off");
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61 return;
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62 endif
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63
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64 if (nargin < 2 || nargin > 4)
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65 print_usage ();
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66 endif
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67
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68 if (ischar (fun))
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69 fun = str2func (fun, "global");
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70 endif
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71
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72 ## TODO
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73 ## displev = optimget (options, "Display", "notify");
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74 funvalchk = strcmpi (optimget (options, "FunValCheck", "off"), "on");
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75 outfcn = optimget (options, "OutputFcn");
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76 tolx = optimget (options, "TolX", 1e-8);
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77 maxiter = optimget (options, "MaxIter", Inf);
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78 maxfev = optimget (options, "MaxFunEvals", Inf);
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79
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80 if (funvalchk)
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81 ## Replace fun with a guarded version.
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82 fun = @(x) guarded_eval (fun, x);
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83 endif
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84
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85 ## The default exit flag if exceeded number of iterations.
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86 info = 0;
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87 niter = 0;
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88 nfev = 0;
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89 sqrteps = eps (class (xmin + xmax));
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90
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91 c = 0.5*(3-sqrt(5));
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92 a = xmin; b = xmax;
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93 v = a + c*(b-a);
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94 w = x = v;
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95 e = 0;
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96 fv = fw = fval = fun (x);
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97 nfev++;
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98
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99 while (niter < maxiter && nfev < maxfev)
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100 xm = 0.5*(a+b);
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101 ## FIXME: the golden section search can actually get closer than sqrt(eps)...
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102 ## sometimes. Sometimes not, it depends on the function. This is the strategy
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103 ## from the Netlib code. Something yet smarter would be good.
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104 tol = 2 * sqrteps * abs (x) + tolx / 3;
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105 if (abs (x - xm) <= (2*tol - 0.5*(b-a)))
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106 info = 1;
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107 break;
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108 endif
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109
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110 if (abs (e) > tol)
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111 dogs = false;
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112 ## Try inverse parabolic step.
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113 r = (x - w)*(fval - fv);
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114 q = (x - v)*(fval - fw);
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115 p = (x - v)*q - (x - w)*r;
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116 q = 2*(q - r);
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117 p *= -sign (q);
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118 q = abs (q);
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119 r = e;
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120 e = d;
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121
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122 if (abs (p) < abs (0.5*q*r) && p > q*(a-x) && p < q*(b-x))
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123 ## The parabolic step is acceptable.
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124 d = p / q;
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125 u = x + d;
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126
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127 ## f must not be evaluated too close to ax or bx.
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128 if (min (u-a, b-u) < 2*tol)
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129 d = tol * (sign (xm - x) + (xm == x));
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130 endif
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131 else
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132 dogs = true;
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133 endif
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134 else
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135 dogs = true;
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136 endif
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137 if (dogs)
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138 ## Default to golden section step.
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139 e = ifelse (x >= xm, a - x, b - x);
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140 d = c * e;
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141 endif
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142
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143 ## f must not be evaluated too close to x.
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144 u = x + max (abs (d), tol) * (sign (d) + (d == 0));
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145
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146 fu = fun (u);
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147 nfev++;
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148 niter++;
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149
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150 ## update a, b, v, w, and x
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151
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152 if (fu <= fval)
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153 if (u < x)
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154 b = x;
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155 else
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156 a = x;
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157 endif
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158 v = w; fv = fw;
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159 w = x; fw = fval;
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160 x = u; fval = fu;
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161 else
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162 ## The following if-statement was originally executed even if fu == fval.
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163 if (u < x)
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164 a = u;
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165 else
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166 b = u;
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167 endif
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168 if (fu <= fw || w == x)
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169 v = w; fv = fw;
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170 w = u; fw = fu;
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171 elseif (fu <= fv || v == x || v == w)
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172 v = u;
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173 fv = fu;
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174 endif
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175 endif
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176
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177 ## If there's an output function, use it now.
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178 if (outfcn)
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179 optv.funccount = nfev;
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180 optv.fval = fval;
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181 optv.iteration = niter;
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182 if (outfcn (x, optv, "iter"))
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183 info = -1;
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184 break;
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185 endif
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186 endif
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187 endwhile
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188
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189 output.iterations = niter;
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190 output.funcCount = nfev;
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191 output.bracket = [a, b];
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192 ## FIXME: bracketf possibly unavailable.
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193
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194 endfunction
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195
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196 ## An assistant function that evaluates a function handle and checks for
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197 ## bad results.
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198 function fx = guarded_eval (fun, x)
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199 fx = fun (x);
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200 fx = fx(1);
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201 if (! isreal (fx))
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202 error ("fminbnd:notreal", "fminbnd: non-real value encountered");
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203 elseif (isnan (fx))
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204 error ("fminbnd:isnan", "fminbnd: NaN value encountered");
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205 endif
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206 endfunction
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207
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208 %!shared opt0
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209 %! opt0 = optimset ("tolx", 0);
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210 %!assert (fminbnd (@cos, pi/2, 3*pi/2, opt0), pi, 10*sqrt(eps))
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211 %!assert (fminbnd (@(x) (x - 1e-3)^4, -1, 1, opt0), 1e-3, 10e-3*sqrt(eps))
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212 %!assert (fminbnd (@(x) abs(x-1e7), 0, 1e10, opt0), 1e7, 10e7*sqrt(eps))
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213 %!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))