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annotate scripts/optimization/fminunc.m @ 20695:6faaab833605

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fminunc.m: Clean up function to meet Octave coding standards. * fminunc.m: Rename xsiz variable to xsz. Use double quotes for strings. Use in-place accumulation operator +=1 instead of ++ for performance. Use '__' prefix and postfix for internal functions. Use two spaces between end of sentence period and start of next sentence. Only calculate third output argument if requested.
author Rik <rik@octave.org>
date Wed, 11 Nov 2015 16:58:18 -0800
parents a7dbc4fc3732
children 5b7643257978
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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} {} fminunc (@var{fcn}, @var{x0})
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23 ## @deftypefnx {Function File} {} fminunc (@var{fcn}, @var{x0}, @var{options})
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24 ## @deftypefnx {Function File} {[@var{x}, @var{fval}, @var{info}, @var{output}, @var{grad}, @var{hess}] =} fminunc (@var{fcn}, @dots{})
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25 ## Solve an unconstrained optimization problem defined by the function
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26 ## @var{fcn}.
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27 ##
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28 ## @var{fcn} should accept a vector (array) defining the unknown variables, and
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29 ## return the objective function value, optionally with gradient.
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30 ## @code{fminunc} attempts to determine a vector @var{x} such that
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31 ## @code{@var{fcn} (@var{x})} is a local minimum.
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32 ##
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33 ## @var{x0} determines a starting guess. The shape of @var{x0} is preserved in
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34 ## all calls to @var{fcn}, but otherwise is treated as a column vector.
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35 ##
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36 ## @var{options} is a structure specifying additional options. Currently,
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37 ## @code{fminunc} recognizes these options:
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38 ## @qcode{"FunValCheck"}, @qcode{"OutputFcn"}, @qcode{"TolX"},
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39 ## @qcode{"TolFun"}, @qcode{"MaxIter"}, @qcode{"MaxFunEvals"},
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40 ## @qcode{"GradObj"}, @qcode{"FinDiffType"}, @qcode{"TypicalX"},
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41 ## @qcode{"AutoScaling"}.
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42 ##
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43 ## If @qcode{"GradObj"} is @qcode{"on"}, it specifies that @var{fcn}, when
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44 ## called with two output arguments, also returns the Jacobian matrix of partial
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45 ## first derivatives at the requested point. @code{TolX} specifies the
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46 ## termination tolerance for the unknown variables @var{x}, while @code{TolFun}
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47 ## is a tolerance for the objective function value @var{fval}. The default is
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48 ## @code{1e-7} for both options.
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49 ##
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50 ## For a description of the other options, see @code{optimset}.
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51 ##
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52 ## On return, @var{x} is the location of the minimum and @var{fval} contains
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53 ## the value of the objective function at @var{x}.
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54 ##
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55 ## @var{info} may be one of the following values:
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56 ##
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57 ## @table @asis
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58 ## @item 1
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59 ## Converged to a solution point. Relative gradient error is less than
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60 ## specified by @code{TolFun}.
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61 ##
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62 ## @item 2
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63 ## Last relative step size was less than @code{TolX}.
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64 ##
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65 ## @item 3
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66 ## Last relative change in function value was less than @code{TolFun}.
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67 ##
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68 ## @item 0
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69 ## Iteration limit exceeded---either maximum number of algorithm iterations
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70 ## @code{MaxIter} or maximum number of function evaluations @code{MaxFunEvals}.
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71 ##
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72 ## @item -1
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73 ## Algorithm terminated by @code{OutputFcn}.
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74 ##
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75 ## @item -3
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76 ## The trust region radius became excessively small.
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77 ## @end table
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78 ##
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79 ## Optionally, @code{fminunc} can return a structure with convergence statistics
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80 ## (@var{output}), the output gradient (@var{grad}) at the solution @var{x},
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81 ## and approximate Hessian (@var{hess}) at the solution @var{x}.
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82 ##
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83 ## Application Notes: If the objective function is a single nonlinear equation
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84 ## of one variable then using @code{fminbnd} is usually a better choice.
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85 ##
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86 ## The algorithm used by @code{fminsearch} is a gradient search which depends
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87 ## on the objective function being differentiable. If the function has
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88 ## discontinuities it may be better to use a derivative-free algorithm such as
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89 ## @code{fminsearch}.
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90 ## @seealso{fminbnd, fminsearch, optimset}
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91 ## @end deftypefn
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92
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93 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup.
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94 ## PKG_ADD: [~] = __all_opts__ ("fminunc");
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95
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96 function [x, fval, info, output, grad, hess] = fminunc (fcn, x0, options = struct ())
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97
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98 ## Get default options if requested.
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99 if (nargin == 1 && strcmp (fcn, "defaults"))
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100 x = optimset ("MaxIter", 400, "MaxFunEvals", Inf,
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101 "GradObj", "off", "TolX", 1e-7, "TolFun", 1e-7,
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102 "OutputFcn", [], "FunValCheck", "off",
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103 "FinDiffType", "central",
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104 "TypicalX", [], "AutoScaling", "off");
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105 return;
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106 endif
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107
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108 if (nargin < 2 || nargin > 3 || ! ismatrix (x0))
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109 print_usage ();
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110 endif
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111
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112 if (ischar (fcn))
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113 fcn = str2func (fcn, "global");
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114 endif
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115
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116 xsz = size (x0);
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117 n = numel (x0);
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118
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119 has_grad = strcmpi (optimget (options, "GradObj", "off"), "on");
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120 cdif = strcmpi (optimget (options, "FinDiffType", "central"), "central");
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121 maxiter = optimget (options, "MaxIter", 400);
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122 maxfev = optimget (options, "MaxFunEvals", Inf);
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123 outfcn = optimget (options, "OutputFcn");
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124
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125 ## Get scaling matrix using the TypicalX option. If set to "auto", the
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126 ## scaling matrix is estimated using the Jacobian.
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127 typicalx = optimget (options, "TypicalX");
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128 if (isempty (typicalx))
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129 typicalx = ones (n, 1);
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130 endif
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131 autoscale = strcmpi (optimget (options, "AutoScaling", "off"), "on");
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132 if (! autoscale)
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133 dg = 1 ./ typicalx;
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134 endif
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135
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136 funvalchk = strcmpi (optimget (options, "FunValCheck", "off"), "on");
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137
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138 if (funvalchk)
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139 ## Replace fcn with a guarded version.
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140 fcn = @(x) guarded_eval (fcn, x);
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141 endif
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142
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143 ## These defaults are rather stringent. I think that normally, user
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144 ## prefers accuracy to performance.
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145
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146 macheps = eps (class (x0));
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147
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148 tolx = optimget (options, "TolX", 1e-7);
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149 tolf = optimget (options, "TolFun", 1e-7);
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150
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151 factor = 0.1;
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152 ## FIXME: TypicalX corresponds to user scaling (???)
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153 autodg = true;
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154
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155 niter = 1;
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156 nfev = 0;
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157
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158 x = x0(:);
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159 info = 0;
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160
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161 ## Initial evaluation.
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162 fval = fcn (reshape (x, xsz));
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163 n = length (x);
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164
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165 if (! isempty (outfcn))
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166 optimvalues.iter = niter;
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167 optimvalues.funccount = nfev;
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168 optimvalues.fval = fval;
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169 optimvalues.searchdirection = zeros (n, 1);
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170 state = "init";
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171 stop = outfcn (x, optimvalues, state);
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172 if (stop)
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173 info = -1;
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174 break;
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175 endif
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176 endif
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177
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178 nsuciter = 0;
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179 lastratio = 0;
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180
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181 grad = [];
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182
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183 ## Outer loop.
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184 while (niter < maxiter && nfev < maxfev && ! info)
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185
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186 grad0 = grad;
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187
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188 ## Calculate function value and gradient (possibly via FD).
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189 if (has_grad)
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190 [fval, grad] = fcn (reshape (x, xsz));
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191 grad = grad(:);
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192 nfev += 1;
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193 else
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194 grad = __fdjac__ (fcn, reshape (x, xsz), fval, typicalx, cdif)(:);
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195 nfev += (1 + cdif) * length (x);
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196 endif
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197
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198 if (niter == 1)
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199 ## Initialize by identity matrix.
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200 hesr = eye (n);
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201 else
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202 ## Use the damped BFGS formula.
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203 y = grad - grad0;
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204 sBs = sumsq (w);
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205 Bs = hesr' * w;
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206 sy = y' * s;
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207 theta = 0.8 / max (1 - sy / sBs, 0.8);
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208 r = theta * y + (1-theta) * Bs;
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209 hesr = cholupdate (hesr, r / sqrt (s' * r), "+");
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210 [hesr, info] = cholupdate (hesr, Bs / sqrt (sBs), "-");
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211 if (info)
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212 hesr = eye (n);
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213 endif
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214 endif
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215
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216 if (autoscale)
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217 ## Second derivatives approximate the Hessian.
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218 d2f = norm (hesr, "columns").';
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219 if (niter == 1)
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220 dg = d2f;
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221 else
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222 ## FIXME: maybe fixed lower and upper bounds?
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223 dg = max (0.1*dg, d2f);
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224 endif
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225 endif
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226
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227 if (niter == 1)
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228 xn = norm (dg .* x);
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229 ## FIXME: something better?
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230 delta = factor * max (xn, 1);
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231 endif
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232
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233 ## FIXME: why tolf*n*xn? If abs (e) ~ abs(x) * eps is a vector
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234 ## of perturbations of x, then norm (hesr*e) <= eps*xn, i.e. by
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235 ## tolf ~ eps we demand as much accuracy as we can expect.
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236 if (norm (grad) <= tolf*n*xn)
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237 info = 1;
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238 break;
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239 endif
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240
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241 suc = false;
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diff changeset
242 decfac = 0.5;
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243
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244 ## Inner loop.
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245 while (! suc && niter <= maxiter && nfev < maxfev && ! info)
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246
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247 s = - __doglegm__ (hesr, grad, dg, delta);
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248
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249 sn = norm (dg .* s);
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250 if (niter == 1)
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251 delta = min (delta, sn);
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252 endif
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253
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254 fval1 = fcn (reshape (x + s, xsz))(:);
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255 nfev += 1;
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256
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257 if (fval1 < fval)
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258 ## Scaled actual reduction.
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259 actred = (fval - fval1) / (abs (fval1) + abs (fval));
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260 else
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261 actred = -1;
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262 endif
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263
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264 w = hesr * s;
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265 ## Scaled predicted reduction, and ratio.
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266 t = 1/2 * sumsq (w) + grad'*s;
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267 if (t < 0)
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268 prered = -t/(abs (fval) + abs (fval + t));
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269 ratio = actred / prered;
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270 else
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271 prered = 0;
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272 ratio = 0;
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273 endif
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274
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275 ## Update delta.
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276 if (ratio < min (max (0.1, 0.8*lastratio), 0.9))
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277 delta *= decfac;
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278 decfac ^= 1.4142;
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279 if (delta <= 10*macheps*xn)
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280 ## Trust region became uselessly small.
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281 info = -3;
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282 break;
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283 endif
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284 else
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285 lastratio = ratio;
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286 decfac = 0.5;
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287 if (abs (1-ratio) <= 0.1)
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288 delta = 1.4142*sn;
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289 elseif (ratio >= 0.5)
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290 delta = max (delta, 1.4142*sn);
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291 endif
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292 endif
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293
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294 if (ratio >= 1e-4)
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295 ## Successful iteration.
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296 x += s;
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297 xn = norm (dg .* x);
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298 fval = fval1;
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299 nsuciter++;
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300 suc = true;
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301 endif
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302
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303 niter += 1;
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304
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305 ## FIXME: should outputfcn be called only after a successful iteration?
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306 if (! isempty (outfcn))
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307 optimvalues.iter = niter;
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308 optimvalues.funccount = nfev;
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309 optimvalues.fval = fval;
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310 optimvalues.searchdirection = s;
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311 state = "iter";
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312 stop = outfcn (x, optimvalues, state);
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313 if (stop)
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314 info = -1;
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315 break;
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316 endif
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317 endif
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318
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319 ## Tests for termination conditions. A mysterious place, anything
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320 ## can happen if you change something here...
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321
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322 ## The rule of thumb (which I'm not sure M*b is quite following)
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323 ## is that for a tolerance that depends on scaling, only 0 makes
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324 ## sense as a default value. But 0 usually means uselessly long
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325 ## iterations, so we need scaling-independent tolerances wherever
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326 ## possible.
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327
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328 ## The following tests done only after successful step.
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329 if (ratio >= 1e-4)
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330 ## This one is classic. Note that we use scaled variables again,
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331 ## but compare to scaled step, so nothing bad.
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332 if (sn <= tolx*xn)
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333 info = 2;
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334 ## Again a classic one.
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335 elseif (actred < tolf)
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336 info = 3;
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337 endif
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338 endif
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339
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340 endwhile
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341 endwhile
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342
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343 ## When info != 1, recalculate the gradient and Hessian using the final x.
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344 if (nargout > 4 && (info == -1 || info == 2 || info == 3))
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345 grad0 = grad;
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346 if (has_grad)
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347 [fval, grad] = fcn (reshape (x, xsz));
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diff changeset
348 grad = grad(:);
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349 else
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350 grad = __fdjac__ (fcn, reshape (x, xsz), fval, typicalx, cdif)(:);
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351 endif
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352
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diff changeset
353 if (nargout > 5)
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354 ## Use the damped BFGS formula.
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diff changeset
355 y = grad - grad0;
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José Vallet <jose.vallet@aalto.fi>
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diff changeset
356 sBs = sumsq (w);
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357 Bs = hesr' * w;
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358 sy = y' * s;
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diff changeset
359 theta = 0.8 / max (1 - sy / sBs, 0.8);
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José Vallet <jose.vallet@aalto.fi>
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diff changeset
360 r = theta * y + (1-theta) * Bs;
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diff changeset
361 hesr = cholupdate (hesr, r / sqrt (s' * r), "+");
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diff changeset
362 hesr = cholupdate (hesr, Bs / sqrt (sBs), "-");
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diff changeset
363 endif
a7dbc4fc3732 fminunc.m: Correctly calculate gradient and hessian even when fminunc fails (bug #40101)
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parents: 20165
diff changeset
364 ## Return the gradient in the same shape as x
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365 grad = reshape (grad, xsz);
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366 endif
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diff changeset
367
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368 ## Restore original shapes.
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369 x = reshape (x, xsz);
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370
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371 if (nargout > 3)
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diff changeset
372 output.iterations = niter;
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373 output.successful = nsuciter;
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374 output.funcCount = nfev;
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375 endif
9084
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376
9627
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parents: 9623
diff changeset
377 if (nargout > 5)
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diff changeset
378 hess = hesr'*hesr;
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379 endif
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parents: 9623
diff changeset
380
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381 endfunction
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382
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diff changeset
383 ## A helper function that evaluates a function and checks for bad results.
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diff changeset
384 function [fx, gx] = guarded_eval (fun, x)
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diff changeset
385 if (nargout > 1)
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diff changeset
386 [fx, gx] = fun (x);
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diff changeset
387 else
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diff changeset
388 fx = fun (x);
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diff changeset
389 gx = [];
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parents:
diff changeset
390 endif
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parents:
diff changeset
391
14383
07c55bceca23 Fix guarded_eval() subfunction in fminunc (bug #35534).
Olaf Till <olaf.till@uni-jena.de>
parents: 14138
diff changeset
392 if (! (isreal (fx) && isreal (gx)))
11587
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parents: 11523
diff changeset
393 error ("fminunc:notreal", "fminunc: non-real value encountered");
9084
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parents:
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394 elseif (any (isnan (fx(:))))
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parents: 11523
diff changeset
395 error ("fminunc:isnan", "fminunc: NaN value encountered");
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396 elseif (any (isinf (fx(:))))
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parents: 14383
diff changeset
397 error ("fminunc:isinf", "fminunc: Inf value encountered");
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parents:
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398 endif
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parents:
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399 endfunction
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parents:
diff changeset
400
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Rik <octave@nomad.inbox5.com>
parents: 14383
diff changeset
401
20695
6faaab833605 fminunc.m: Clean up function to meet Octave coding standards.
Rik <rik@octave.org>
parents: 20694
diff changeset
402 %!function f = __rosenb__ (x)
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parents:
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403 %! n = length (x);
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parents:
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404 %! f = sumsq (1 - x(1:n-1)) + 100 * sumsq (x(2:n) - x(1:n-1).^2);
13305
63463570d9fe Add %!endfunction block keyword to test.m
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parents: 13027
diff changeset
405 %!endfunction
19833
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Rik <rik@octave.org>
parents: 19697
diff changeset
406 %!
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parents:
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407 %!test
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parents: 20694
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408 %! [x, fval, info, out] = fminunc (@__rosenb__, [5, -5]);
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409 %! tol = 2e-5;
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parents:
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410 %! assert (info > 0);
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diff changeset
411 %! assert (x, ones (1, 2), tol);
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parents:
diff changeset
412 %! assert (fval, 0, tol);
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parents:
diff changeset
413 %!test
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414 %! [x, fval, info, out] = fminunc (@__rosenb__, zeros (1, 4));
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parents:
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415 %! tol = 2e-5;
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parents:
diff changeset
416 %! assert (info > 0);
b7210faa3ed0 implement fminunc using factored trust-region BFGS
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parents:
diff changeset
417 %! assert (x, ones (1, 4), tol);
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parents:
diff changeset
418 %! assert (fval, 0, tol);
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419
9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions.
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parents: 19697
diff changeset
420 ## Test FunValCheck works correctly
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diff changeset
421 %!assert (fminunc (@(x) x^2, 1, optimset ("FunValCheck", "on")), 0, eps)
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diff changeset
422 %!error <non-real value> fminunc (@(x) x + i, 1, optimset ("FunValCheck", "on"))
59aab666f2bf Extend "FunValCheck" option to optimization routines to detect Inf values.
Rik <octave@nomad.inbox5.com>
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diff changeset
423 %!error <NaN value> fminunc (@(x) x + NaN, 1, optimset ("FunValCheck", "on"))
59aab666f2bf Extend "FunValCheck" option to optimization routines to detect Inf values.
Rik <octave@nomad.inbox5.com>
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diff changeset
424 %!error <Inf value> fminunc (@(x) x + Inf, 1, optimset ("FunValCheck", "on"))
59aab666f2bf Extend "FunValCheck" option to optimization routines to detect Inf values.
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parents: 14383
diff changeset
425
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diff changeset
426
9899
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diff changeset
427 ## Solve the double dogleg trust-region minimization problem:
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diff changeset
428 ## Minimize 1/2*norm(r*x)^2 subject to the constraint norm(d.*x) <= delta,
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diff changeset
429 ## x being a convex combination of the gauss-newton and scaled gradient.
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diff changeset
430
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diff changeset
431 ## TODO: error checks
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diff changeset
432 ## TODO: handle singularity, or leave it up to mldivide?
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diff changeset
433
9f25290a35e8 more private function and subfunction changes
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diff changeset
434 function x = __doglegm__ (r, g, d, delta)
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diff changeset
435 ## Get Gauss-Newton direction.
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John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
436 b = r' \ g;
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diff changeset
437 x = r \ b;
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diff changeset
438 xn = norm (d .* x);
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diff changeset
439 if (xn > delta)
9f25290a35e8 more private function and subfunction changes
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diff changeset
440 ## GN is too big, get scaled gradient.
9f25290a35e8 more private function and subfunction changes
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diff changeset
441 s = g ./ d;
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diff changeset
442 sn = norm (s);
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diff changeset
443 if (sn > 0)
9f25290a35e8 more private function and subfunction changes
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diff changeset
444 ## Normalize and rescale.
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diff changeset
445 s = (s / sn) ./ d;
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diff changeset
446 ## Get the line minimizer in s direction.
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diff changeset
447 tn = norm (r*s);
9f25290a35e8 more private function and subfunction changes
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diff changeset
448 snm = (sn / tn) / tn;
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diff changeset
449 if (snm < delta)
10549
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parents: 10201
diff changeset
450 ## Get the dogleg path minimizer.
9899
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diff changeset
451 bn = norm (b);
9f25290a35e8 more private function and subfunction changes
John W. Eaton <jwe@octave.org>
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diff changeset
452 dxn = delta/xn; snmd = snm/delta;
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diff changeset
453 t = (bn/sn) * (bn/xn) * snmd;
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parents: 9758
diff changeset
454 t -= dxn * snmd^2 - sqrt ((t-dxn)^2 + (1-dxn^2)*(1-snmd^2));
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John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
455 alpha = dxn*(1-snmd^2) / t;
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diff changeset
456 else
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diff changeset
457 alpha = 0;
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diff changeset
458 endif
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diff changeset
459 else
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parents: 9758
diff changeset
460 alpha = delta / xn;
9f25290a35e8 more private function and subfunction changes
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
461 snm = 0;
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diff changeset
462 endif
9f25290a35e8 more private function and subfunction changes
John W. Eaton <jwe@octave.org>
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diff changeset
463 ## Form the appropriate convex combination.
9f25290a35e8 more private function and subfunction changes
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
464 x = alpha * x + ((1-alpha) * min (snm, delta)) * s;
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parents: 9758
diff changeset
465 endif
9f25290a35e8 more private function and subfunction changes
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
466 endfunction
17338
1c89599167a6 maint: End m-files with 1 blank line.
Rik <rik@octave.org>
parents: 17281
diff changeset
467