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remove unused variable from libgui/module.mk * libgui/module.mk: remove empty variable OCTAVE_GUI_EDITOR_MOC
author Torsten Lilge <ttl-octave@mailbox.org>
date Mon, 27 May 2024 19:42:05 +0200
parents 2e484f9f1f18
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2008-2024 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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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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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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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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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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19 ##
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20 ## You should have received a copy of the GNU General Public License
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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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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {@var{x} =} fsolve (@var{fcn}, @var{x0})
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28 ## @deftypefnx {} {@var{x} =} fsolve (@var{fcn}, @var{x0}, @var{options})
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29 ## @deftypefnx {} {[@var{x}, @var{fval}] =} fsolve (@dots{})
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30 ## @deftypefnx {} {[@var{x}, @var{fval}, @var{info}] =} fsolve (@dots{})
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31 ## @deftypefnx {} {[@var{x}, @var{fval}, @var{info}, @var{output}] =} fsolve (@dots{})
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32 ## @deftypefnx {} {[@var{x}, @var{fval}, @var{info}, @var{output}, @var{fjac}] =} fsolve (@dots{})
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33 ## Solve a system of nonlinear equations defined by the function @var{fcn}.
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34 ##
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35 ## @var{fcn} is a function handle, inline function, or string containing the
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36 ## name of the function to evaluate. @var{fcn} should accept a vector (array)
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37 ## defining the unknown variables, and return a vector of left-hand sides of
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38 ## the equations. Right-hand sides are defined to be zeros. In other words,
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39 ## this function attempts to determine a vector @var{x} such that
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40 ## @code{@var{fcn} (@var{x})} gives (approximately) all zeros.
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41 ##
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42 ## @var{x0} is an initial guess for the solution. The shape of @var{x0} is
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43 ## preserved in all calls to @var{fcn}, but otherwise is treated as a column
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44 ## vector.
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45 ##
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46 ## @var{options} is a structure specifying additional parameters which
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47 ## control the algorithm. Currently, @code{fsolve} recognizes these options:
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48 ## @qcode{"AutoScaling"}, @qcode{"ComplexEqn"}, @qcode{"FinDiffType"},
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49 ## @qcode{"FunValCheck"}, @qcode{"Jacobian"}, @qcode{"MaxFunEvals"},
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50 ## @qcode{"MaxIter"}, @qcode{"OutputFcn"}, @qcode{"TolFun"}, @qcode{"TolX"},
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51 ## @qcode{"TypicalX"}, and @qcode{"Updating"}.
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52 ##
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53 ## If @qcode{"AutoScaling"} is @qcode{"on"}, the variables will be
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54 ## automatically scaled according to the column norms of the (estimated)
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55 ## Jacobian. As a result, @qcode{"TolFun"} becomes scaling-independent. By
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56 ## default, this option is @qcode{"off"} because it may sometimes deliver
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57 ## unexpected (though mathematically correct) results.
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58 ##
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59 ## If @qcode{"ComplexEqn"} is @qcode{"on"}, @code{fsolve} will attempt to solve
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60 ## complex equations in complex variables, assuming that the equations possess
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61 ## a complex derivative (i.e., are holomorphic). If this is not what you want,
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62 ## you should unpack the real and imaginary parts of the system to get a real
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63 ## system.
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64 ##
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65 ## If @qcode{"Jacobian"} is @qcode{"on"}, it specifies that @var{fcn}---when
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66 ## called with 2 output arguments---also returns the Jacobian matrix of
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67 ## right-hand sides at the requested point.
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68 ##
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69 ## @qcode{"MaxFunEvals"} proscribes the maximum number of function evaluations
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70 ## before optimization is halted. The default value is
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71 ## @code{100 * number_of_variables}, i.e., @code{100 * length (@var{x0})}.
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72 ## The value must be a positive integer.
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73 ##
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74 ## If @qcode{"Updating"} is @qcode{"on"}, the function will attempt to use
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75 ## @nospell{Broyden} updates to update the Jacobian, in order to reduce the
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76 ## number of Jacobian calculations. If your user function always calculates
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77 ## the Jacobian (regardless of number of output arguments) then this option
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78 ## provides no advantage and should be disabled.
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79 ##
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80 ## @qcode{"TolX"} specifies the termination tolerance in the unknown variables,
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81 ## while @qcode{"TolFun"} is a tolerance for equations. Default is @code{1e-6}
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82 ## for both @qcode{"TolX"} and @qcode{"TolFun"}.
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83 ##
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84 ## For a description of the other options,
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85 ## @pxref{XREFoptimset,,@code{optimset}}. To initialize an options structure
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86 ## with default values for @code{fsolve} use
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87 ## @code{options = optimset ("fsolve")}.
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88 ##
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89 ## The first output @var{x} is the solution while the second output @var{fval}
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90 ## contains the value of the function @var{fcn} evaluated at @var{x} (ideally
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91 ## a vector of all zeros).
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92 ##
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93 ## The third output @var{info} reports whether the algorithm succeeded and may
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94 ## take one of the following values:
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95 ##
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96 ## @table @asis
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97 ## @item 1
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98 ## Converged to a solution point. Relative residual error is less than
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99 ## specified by @code{TolFun}.
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100 ##
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101 ## @item 2
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102 ## Last relative step size was less than @code{TolX}.
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103 ##
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104 ## @item 3
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105 ## Last relative decrease in residual was less than @code{TolFun}.
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106 ##
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107 ## @item 0
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108 ## Iteration limit (either @code{MaxIter} or @code{MaxFunEvals}) exceeded.
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109 ##
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110 ## @item -1
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111 ## Stopped by @code{OutputFcn}.
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112 ##
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113 ## @item -2
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114 ## The Jacobian became excessively small and the search stalled.
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115 ##
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116 ## @item -3
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117 ## The trust region radius became excessively small.
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118 ## @end table
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119 ##
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120 ## @var{output} is a structure containing runtime information about the
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121 ## @code{fsolve} algorithm. Fields in the structure are:
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122 ##
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123 ## @table @code
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124 ## @item iterations
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125 ## Number of iterations through loop.
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126 ##
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127 ## @item successful
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128 ## Number of successful iterations.
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129 ##
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130 ## @item @nospell{funcCount}
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131 ## Number of function evaluations.
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132 ##
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133 ## @end table
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134 ##
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135 ## The final output @var{fjac} contains the value of the Jacobian evaluated
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136 ## at @var{x}.
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137 ##
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138 ## Note: If you only have a single nonlinear equation of one variable, using
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139 ## @code{fzero} is usually a much better idea.
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140 ##
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141 ## Note about user-supplied Jacobians:
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142 ## As an inherent property of the algorithm, a Jacobian is always requested for
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143 ## a solution vector whose residual vector is already known, and it is the last
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144 ## accepted successful step. Often this will be one of the last two calls, but
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145 ## not always. If the savings by reusing intermediate results from residual
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146 ## calculation in Jacobian calculation are significant, the best strategy is to
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147 ## employ @code{OutputFcn}: After a vector is evaluated for residuals, if
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148 ## @code{OutputFcn} is called with that vector, then the intermediate results
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149 ## should be saved for future Jacobian evaluation, and should be kept until a
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150 ## Jacobian evaluation is requested or until @code{OutputFcn} is called with a
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151 ## different vector, in which case they should be dropped in favor of this most
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152 ## recent vector. A short example how this can be achieved follows:
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153 ##
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154 ## @example
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155 ## function [fval, fjac] = user_fcn (x, optimvalues, state)
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156 ## persistent sav = [], sav0 = [];
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157 ## if (nargin == 1)
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158 ## ## evaluation call
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159 ## if (nargout == 1)
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160 ## sav0.x = x; # mark saved vector
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161 ## ## calculate fval, save results to sav0.
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162 ## elseif (nargout == 2)
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163 ## ## calculate fjac using sav.
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164 ## endif
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165 ## else
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166 ## ## outputfcn call.
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167 ## if (all (x == sav0.x))
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168 ## sav = sav0;
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169 ## endif
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170 ## ## maybe output iteration status, etc.
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171 ## endif
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172 ## endfunction
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173 ##
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174 ## ## @dots{}
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175 ##
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176 ## fsolve (@@user_fcn, x0, optimset ("OutputFcn", @@user_fcn, @dots{}))
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177 ## @end example
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178 ## @seealso{fzero, optimset}
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179 ## @end deftypefn
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180
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181 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup.
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182 ## PKG_ADD: [~] = __all_opts__ ("fsolve");
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183
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184 function [x, fval, info, output, fjac] = fsolve (fcn, x0, options = struct ())
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185
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186 ## Get default options if requested.
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187 if (nargin == 1 && ischar (fcn) && strcmp (fcn, "defaults"))
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188 x = struct ("AutoScaling", "off", "ComplexEqn", "off",
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189 "FunValCheck", "off", "FinDiffType", "forward",
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190 "Jacobian", "off", "MaxFunEvals", [], "MaxIter", 400,
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191 "OutputFcn", [], "Updating", "off", "TolFun", 1e-6,
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192 "TolX", 1e-6, "TypicalX", []);
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193 return;
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194 endif
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195
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196 if (nargin < 2 || ! isnumeric (x0))
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197 print_usage ();
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198 endif
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199
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200 if (ischar (fcn))
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201 fcn = str2func (fcn);
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202 elseif (iscell (fcn))
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203 fcn = @(x) make_fcn_jac (x, fcn{1}, fcn{2});
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204 endif
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205
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206 xsiz = size (x0);
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207 n = numel (x0);
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208
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209 has_jac = strcmpi (optimget (options, "Jacobian", "off"), "on");
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210 cdif = strcmpi (optimget (options, "FinDiffType", "forward"), "central");
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211 maxiter = optimget (options, "MaxIter", 400);
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212 maxfev = optimget (options, "MaxFunEvals", 100*n);
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213 outfcn = optimget (options, "OutputFcn");
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214 updating = strcmpi (optimget (options, "Updating", "off"), "on");
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215 complexeqn = strcmpi (optimget (options, "ComplexEqn", "off"), "on");
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216
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217 ## Get scaling matrix using the TypicalX option. If set to "auto", the
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218 ## scaling matrix is estimated using the Jacobian.
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219 typicalx = optimget (options, "TypicalX", ones (n, 1));
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220
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221 autoscale = strcmpi (optimget (options, "AutoScaling", "off"), "on");
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222 if (! autoscale)
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223 dg = 1 ./ typicalx;
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224 endif
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225
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226 funvalchk = strcmpi (optimget (options, "FunValCheck", "off"), "on");
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227
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228 if (funvalchk)
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229 ## Replace fcn with a guarded version.
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230 fcn = @(x) guarded_eval (fcn, x, complexeqn);
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231 endif
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232
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233 ## These defaults are rather stringent.
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234 ## Normally user prefers accuracy to performance.
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235
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236 tolx = optimget (options, "TolX", 1e-6);
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237 tolf = optimget (options, "TolFun", 1e-6);
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238
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239 factor = 1;
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240
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241 niter = 1;
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242 nfev = 1;
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243
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244 x = x0(:);
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245 info = 0;
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246
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247 ## Initial evaluation.
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248 ## Handle arbitrary shapes of x and f and remember them.
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249 fval = fcn (reshape (x, xsiz));
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250 fsiz = size (fval);
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251 fval = fval(:);
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252 fn = norm (fval);
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253 m = length (fval);
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254 n = length (x);
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255
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256 if (! isempty (outfcn))
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257 optimvalues.iter = niter;
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258 optimvalues.funccount = nfev;
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diff changeset
259 optimvalues.fval = fn;
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diff changeset
260 optimvalues.searchdirection = zeros (n, 1);
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261 state = "init";
8986
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262 stop = outfcn (x, optimvalues, state);
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diff changeset
263 if (stop)
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diff changeset
264 info = -1;
29397
ce425b657693 fsolve.m: Fix undefined output error when using Output function (bug #60144).
Jim Van Zandt <jim.vanzandt@gmail.com>
parents: 29358
diff changeset
265 output.iterations = niter;
ce425b657693 fsolve.m: Fix undefined output error when using Output function (bug #60144).
Jim Van Zandt <jim.vanzandt@gmail.com>
parents: 29358
diff changeset
266 output.successful = 0;
ce425b657693 fsolve.m: Fix undefined output error when using Output function (bug #60144).
Jim Van Zandt <jim.vanzandt@gmail.com>
parents: 29358
diff changeset
267 output.funcCount = nfev;
ce425b657693 fsolve.m: Fix undefined output error when using Output function (bug #60144).
Jim Van Zandt <jim.vanzandt@gmail.com>
parents: 29358
diff changeset
268 fjac = NaN;
22785
9c6661004167 error if break statement is in script file separate from loop (bug #39168)
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parents: 22755
diff changeset
269 return;
8986
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diff changeset
270 endif
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diff changeset
271 endif
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diff changeset
272
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273 if (isa (x0, "single") || isa (fval, "single"))
21099
52af4092f863 For optimization scripts, correctly choose tolerance (eps) based on class of fun and X0.
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274 macheps = eps ("single");
52af4092f863 For optimization scripts, correctly choose tolerance (eps) based on class of fun and X0.
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275 else
52af4092f863 For optimization scripts, correctly choose tolerance (eps) based on class of fun and X0.
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276 macheps = eps ("double");
52af4092f863 For optimization scripts, correctly choose tolerance (eps) based on class of fun and X0.
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diff changeset
277 endif
52af4092f863 For optimization scripts, correctly choose tolerance (eps) based on class of fun and X0.
Rik <rik@octave.org>
parents: 20852
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278
8986
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279 nsuciter = 0;
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280
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281 ## Outer loop.
8306
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282 while (niter < maxiter && nfev < maxfev && ! info)
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283
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284 ## Calculate function value and Jacobian (possibly via FD).
8306
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285 if (has_jac)
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diff changeset
286 [fval, fjac] = fcn (reshape (x, xsiz));
23563
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parents: 23474
diff changeset
287 if (! all (size (fjac) == [m, n]))
23474
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Rik <rik@octave.org>
parents: 23220
diff changeset
288 error ("fsolve: Jacobian size should be (%d,%d), not (%d,%d)",
70edb5512c6e fsolve.m: Issue an error for incorrectly sized user Jacobian (bug #50454).
Rik <rik@octave.org>
parents: 23220
diff changeset
289 m, n, rows (fjac), columns (fjac));
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parents: 23220
diff changeset
290 endif
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diff changeset
291 ## If the Jacobian is sparse, disable Broyden updating.
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292 if (issparse (fjac))
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293 updating = false;
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294 endif
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diff changeset
295 fval = fval(:);
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296 nfev += 1;
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297 else
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diff changeset
298 fjac = __fdjac__ (fcn, reshape (x, xsiz), fval, typicalx, cdif);
9212
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299 nfev += (1 + cdif) * length (x);
8306
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300 endif
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diff changeset
301
25730
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diff changeset
302 ## For square and overdetermined systems, we update a QR factorization of
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
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diff changeset
303 ## the Jacobian to avoid solving a full system in each step. In this case,
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
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diff changeset
304 ## we pass a triangular matrix to __dogleg__.
8590
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diff changeset
305 useqr = updating && m >= n && n > 10;
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diff changeset
306
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diff changeset
307 if (useqr)
8616
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diff changeset
308 ## FIXME: Currently, pivoting is mostly useless because the \ operator
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diff changeset
309 ## cannot exploit the resulting props of the triangular factor.
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diff changeset
310 ## Unpivoted QR is significantly faster so it doesn't seem right to pivot
21937
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parents: 21759
diff changeset
311 ## just to get invariance. Original MINPACK didn't pivot either,
21751
b571fc85953f maint: Use two spaces after period to indicate sentence break.
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diff changeset
312 ## at least when qr updating was used.
8616
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diff changeset
313 [q, r] = qr (fjac, 0);
8383
a762d9daa700 allow overdetermined systems in fsolve
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diff changeset
314 endif
8306
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315
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diff changeset
316 if (autoscale)
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parents: 10050
diff changeset
317 ## Get column norms, use them as scaling factors.
25730
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diff changeset
318 jcn = norm (fjac, "columns").';
10201
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diff changeset
319 if (niter == 1)
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diff changeset
320 dg = jcn;
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diff changeset
321 dg(dg == 0) = 1;
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diff changeset
322 else
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diff changeset
323 ## Rescale adaptively.
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parents: 10050
diff changeset
324 ## FIXME: the original minpack used the following rescaling strategy:
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diff changeset
325 ## dg = max (dg, jcn);
10821
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diff changeset
326 ## but it seems not good if we start with a bad guess yielding Jacobian
19833
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Rik <rik@octave.org>
parents: 19697
diff changeset
327 ## columns with large norms that later decrease, because the
21751
b571fc85953f maint: Use two spaces after period to indicate sentence break.
Rik <rik@octave.org>
parents: 21578
diff changeset
328 ## corresponding variable will still be overscaled. Instead, we only
19833
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Rik <rik@octave.org>
parents: 19697
diff changeset
329 ## give the old scaling a small momentum, but do not honor it.
10201
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Jaroslav Hajek <highegg@gmail.com>
parents: 10050
diff changeset
330
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default
Jaroslav Hajek <highegg@gmail.com>
parents: 10050
diff changeset
331 dg = max (0.1*dg, jcn);
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default
Jaroslav Hajek <highegg@gmail.com>
parents: 10050
diff changeset
332 endif
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default
Jaroslav Hajek <highegg@gmail.com>
parents: 10050
diff changeset
333 endif
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default
Jaroslav Hajek <highegg@gmail.com>
parents: 10050
diff changeset
334
8306
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diff changeset
335 if (niter == 1)
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
336 xn = norm (dg .* x);
8590
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diff changeset
337 ## FIXME: something better?
9628
73e6ad869f08 further correct initial TR step strategy
Jaroslav Hajek <highegg@gmail.com>
parents: 9623
diff changeset
338 delta = factor * max (xn, 1);
8306
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
339 endif
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
340
8990
349d75161672 more cosmetic adjustments to fsolve
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parents: 8988
diff changeset
341 ## It also seems that in the case of fast (and inhomogeneously) changing
10821
693e22af08ae Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents: 10793
diff changeset
342 ## Jacobian, the Broyden updates are of little use, so maybe we could
21751
b571fc85953f maint: Use two spaces after period to indicate sentence break.
Rik <rik@octave.org>
parents: 21578
diff changeset
343 ## skip them if a big disproportional change is expected. The question is,
8990
349d75161672 more cosmetic adjustments to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8988
diff changeset
344 ## of course, how to define the above terms :)
8306
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parents:
diff changeset
345
8986
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diff changeset
346 lastratio = 0;
8306
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parents:
diff changeset
347 nfail = 0;
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
348 nsuc = 0;
9207
25f50d2d76b3 improve TR updating strategy for fminunc and fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 9153
diff changeset
349 decfac = 0.5;
25f50d2d76b3 improve TR updating strategy for fminunc and fsolve
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parents: 9153
diff changeset
350
8507
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parents: 8468
diff changeset
351 ## Inner loop.
8306
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parents:
diff changeset
352 while (niter <= maxiter && nfev < maxfev && ! info)
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
353
8590
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diff changeset
354 ## Get trust-region model (dogleg) minimizer.
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
355 if (useqr)
25486
dffd9f6ee85c fsolve.m: exit with info=-2 when singularity reached (bug #53991).
Rik <rik@octave.org>
parents: 25054
diff changeset
356 if (norm (r, 1) < macheps * rows (r))
dffd9f6ee85c fsolve.m: exit with info=-2 when singularity reached (bug #53991).
Rik <rik@octave.org>
parents: 25054
diff changeset
357 info = -2;
dffd9f6ee85c fsolve.m: exit with info=-2 when singularity reached (bug #53991).
Rik <rik@octave.org>
parents: 25054
diff changeset
358 break;
dffd9f6ee85c fsolve.m: exit with info=-2 when singularity reached (bug #53991).
Rik <rik@octave.org>
parents: 25054
diff changeset
359 endif
26075
5d28fc32a7c7 doc: Consistent use of "fval" for optimization functions.
Kai T. Ohlhus <k.ohlhus@gmail.com>
parents: 25828
diff changeset
360 qtf = q'*fval;
8590
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diff changeset
361 s = - __dogleg__ (r, qtf, dg, delta);
c136d313206a improvements to fsolve
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parents: 8562
diff changeset
362 w = qtf + r * s;
c136d313206a improvements to fsolve
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parents: 8562
diff changeset
363 else
25486
dffd9f6ee85c fsolve.m: exit with info=-2 when singularity reached (bug #53991).
Rik <rik@octave.org>
parents: 25054
diff changeset
364 if (norm (fjac, 1) < macheps * rows (fjac))
dffd9f6ee85c fsolve.m: exit with info=-2 when singularity reached (bug #53991).
Rik <rik@octave.org>
parents: 25054
diff changeset
365 info = -2;
dffd9f6ee85c fsolve.m: exit with info=-2 when singularity reached (bug #53991).
Rik <rik@octave.org>
parents: 25054
diff changeset
366 break;
dffd9f6ee85c fsolve.m: exit with info=-2 when singularity reached (bug #53991).
Rik <rik@octave.org>
parents: 25054
diff changeset
367 endif
26075
5d28fc32a7c7 doc: Consistent use of "fval" for optimization functions.
Kai T. Ohlhus <k.ohlhus@gmail.com>
parents: 25828
diff changeset
368 s = - __dogleg__ (fjac, fval, dg, delta);
5d28fc32a7c7 doc: Consistent use of "fval" for optimization functions.
Kai T. Ohlhus <k.ohlhus@gmail.com>
parents: 25828
diff changeset
369 w = fval + fjac * s;
8395
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
370 endif
8590
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
371
8395
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
372 sn = norm (dg .* s);
8306
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
373 if (niter == 1)
8395
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
374 delta = min (delta, sn);
8306
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
375 endif
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
376
26075
5d28fc32a7c7 doc: Consistent use of "fval" for optimization functions.
Kai T. Ohlhus <k.ohlhus@gmail.com>
parents: 25828
diff changeset
377 fval1 = fcn (reshape (x + s, xsiz)) (:);
5d28fc32a7c7 doc: Consistent use of "fval" for optimization functions.
Kai T. Ohlhus <k.ohlhus@gmail.com>
parents: 25828
diff changeset
378 fn1 = norm (fval1);
20735
418ae0cb752f Replace ++,-- with in-place operators for performance.
Rik <rik@octave.org>
parents: 20714
diff changeset
379 nfev += 1;
8306
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parents:
diff changeset
380
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
381 if (fn1 < fn)
8507
cadc73247d65 style fixes
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parents: 8468
diff changeset
382 ## Scaled actual reduction.
8306
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parents:
diff changeset
383 actred = 1 - (fn1/fn)^2;
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
384 else
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
385 actred = -1;
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
386 endif
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
387
8507
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John W. Eaton <jwe@octave.org>
parents: 8468
diff changeset
388 ## Scaled predicted reduction, and ratio.
8306
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parents:
diff changeset
389 t = norm (w);
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
390 if (t < fn)
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
391 prered = 1 - (t/fn)^2;
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
392 ratio = actred / prered;
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
393 else
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
394 prered = 0;
43795cf108d0 initial implementation of fsolve
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parents:
diff changeset
395 ratio = 0;
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
396 endif
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
397
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8468
diff changeset
398 ## Update delta.
14868
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory
Rik <octave@nomad.inbox5.com>
parents: 14386
diff changeset
399 if (ratio < min (max (0.1, 0.8*lastratio), 0.9))
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
400 nsuc = 0;
20735
418ae0cb752f Replace ++,-- with in-place operators for performance.
Rik <rik@octave.org>
parents: 20714
diff changeset
401 nfail += 1;
9207
25f50d2d76b3 improve TR updating strategy for fminunc and fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 9153
diff changeset
402 delta *= decfac;
25f50d2d76b3 improve TR updating strategy for fminunc and fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 9153
diff changeset
403 decfac ^= 1.4142;
25500
b3c35a130f94 fsolve.m: Return info=1 when initial guess (x0) is correct (bug #53991).
Rik <rik@octave.org>
parents: 25499
diff changeset
404 if (fn <= tolf*n*xn)
b3c35a130f94 fsolve.m: Return info=1 when initial guess (x0) is correct (bug #53991).
Rik <rik@octave.org>
parents: 25499
diff changeset
405 info = 1;
b3c35a130f94 fsolve.m: Return info=1 when initial guess (x0) is correct (bug #53991).
Rik <rik@octave.org>
parents: 25499
diff changeset
406 elseif (delta <= 1e1*macheps*xn)
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8468
diff changeset
407 ## Trust region became uselessly small.
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
408 info = -3;
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
409 break;
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
410 endif
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
411 else
8986
22c8272af34b improvements to fsolve & family
Jaroslav Hajek <highegg@gmail.com>
parents: 8857
diff changeset
412 lastratio = ratio;
9207
25f50d2d76b3 improve TR updating strategy for fminunc and fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 9153
diff changeset
413 decfac = 0.5;
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
414 nfail = 0;
20735
418ae0cb752f Replace ++,-- with in-place operators for performance.
Rik <rik@octave.org>
parents: 20714
diff changeset
415 nsuc += 1;
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
416 if (abs (1-ratio) <= 0.1)
9207
25f50d2d76b3 improve TR updating strategy for fminunc and fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 9153
diff changeset
417 delta = 1.4142*sn;
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
418 elseif (ratio >= 0.5 || nsuc > 1)
9207
25f50d2d76b3 improve TR updating strategy for fminunc and fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 9153
diff changeset
419 delta = max (delta, 1.4142*sn);
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
420 endif
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
421 endif
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
422
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
423 if (ratio >= 1e-4)
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8468
diff changeset
424 ## Successful iteration.
8395
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
425 x += s;
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
426 xn = norm (dg .* x);
26075
5d28fc32a7c7 doc: Consistent use of "fval" for optimization functions.
Kai T. Ohlhus <k.ohlhus@gmail.com>
parents: 25828
diff changeset
427 fval = fval1;
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
428 fn = fn1;
20735
418ae0cb752f Replace ++,-- with in-place operators for performance.
Rik <rik@octave.org>
parents: 20714
diff changeset
429 nsuciter += 1;
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
430 endif
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
431
20735
418ae0cb752f Replace ++,-- with in-place operators for performance.
Rik <rik@octave.org>
parents: 20714
diff changeset
432 niter += 1;
8857
20589a8f1a33 fix fsolve bug
Jaroslav Hajek <highegg@gmail.com>
parents: 8763
diff changeset
433
8590
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
434 ## FIXME: should outputfcn be only called after a successful iteration?
8615
7baacb6a8a65 fix typo in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8613
diff changeset
435 if (! isempty (outfcn))
8590
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
436 optimvalues.iter = niter;
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
437 optimvalues.funccount = nfev;
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
438 optimvalues.fval = fn;
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
439 optimvalues.searchdirection = s;
25730
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
440 state = "iter";
8590
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
441 stop = outfcn (x, optimvalues, state);
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
442 if (stop)
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
443 info = -1;
29397
ce425b657693 fsolve.m: Fix undefined output error when using Output function (bug #60144).
Jim Van Zandt <jim.vanzandt@gmail.com>
parents: 29358
diff changeset
444 output.iterations = niter;
ce425b657693 fsolve.m: Fix undefined output error when using Output function (bug #60144).
Jim Van Zandt <jim.vanzandt@gmail.com>
parents: 29358
diff changeset
445 output.successful = nsuciter;
ce425b657693 fsolve.m: Fix undefined output error when using Output function (bug #60144).
Jim Van Zandt <jim.vanzandt@gmail.com>
parents: 29358
diff changeset
446 output.funcCount = nfev;
8590
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
447 break;
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
448 endif
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
449 endif
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
450
21751
b571fc85953f maint: Use two spaces after period to indicate sentence break.
Rik <rik@octave.org>
parents: 21578
diff changeset
451 ## Tests for termination conditions. A mysterious place, anything
8466
4d008d9f0ccf fsolve.m: style fixes
John W. Eaton <jwe@octave.org>
parents: 8395
diff changeset
452 ## can happen if you change something here...
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
453
8466
4d008d9f0ccf fsolve.m: style fixes
John W. Eaton <jwe@octave.org>
parents: 8395
diff changeset
454 ## The rule of thumb (which I'm not sure M*b is quite following)
4d008d9f0ccf fsolve.m: style fixes
John W. Eaton <jwe@octave.org>
parents: 8395
diff changeset
455 ## is that for a tolerance that depends on scaling, only 0 makes
21751
b571fc85953f maint: Use two spaces after period to indicate sentence break.
Rik <rik@octave.org>
parents: 21578
diff changeset
456 ## sense as a default value. But 0 usually means uselessly long
8466
4d008d9f0ccf fsolve.m: style fixes
John W. Eaton <jwe@octave.org>
parents: 8395
diff changeset
457 ## iterations, so we need scaling-independent tolerances wherever
4d008d9f0ccf fsolve.m: style fixes
John W. Eaton <jwe@octave.org>
parents: 8395
diff changeset
458 ## possible.
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
459
18857
7bbe3658c5ef maint: Use "FIXME:" coding convention in m-files.
Rik <rik@octave.org>
parents: 17744
diff changeset
460 ## FIXME: Why tolf*n*xn? If abs (e) ~ abs(x) * eps is a vector
21751
b571fc85953f maint: Use two spaces after period to indicate sentence break.
Rik <rik@octave.org>
parents: 21578
diff changeset
461 ## of perturbations of x, then norm (fjac*e) <= eps*n*xn, i.e., by
8466
4d008d9f0ccf fsolve.m: style fixes
John W. Eaton <jwe@octave.org>
parents: 8395
diff changeset
462 ## tolf ~ eps we demand as much accuracy as we can expect.
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
463 if (fn <= tolf*n*xn)
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
464 info = 1;
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10201
diff changeset
465 ## The following tests done only after successful step.
9075
7b35d3b21c1c fix test in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 9065
diff changeset
466 elseif (ratio >= 1e-4)
21751
b571fc85953f maint: Use two spaces after period to indicate sentence break.
Rik <rik@octave.org>
parents: 21578
diff changeset
467 ## This one is classic. Note that we use scaled variables again,
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10201
diff changeset
468 ## but compare to scaled step, so nothing bad.
8395
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
469 if (sn <= tolx*xn)
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
470 info = 2;
21751
b571fc85953f maint: Use two spaces after period to indicate sentence break.
Rik <rik@octave.org>
parents: 21578
diff changeset
471 ## Again a classic one. It seems weird to use the same tolf
10549
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10201
diff changeset
472 ## for two different tests, but that's what M*b manual appears
95c3e38098bf Untabify .m scripts
Rik <code@nomad.inbox5.com>
parents: 10201
diff changeset
473 ## to say.
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
474 elseif (actred < tolf)
8383
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
475 info = 3;
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
476 endif
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
477 endif
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
478
10821
693e22af08ae Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents: 10793
diff changeset
479 ## Criterion for recalculating Jacobian.
8986
22c8272af34b improvements to fsolve & family
Jaroslav Hajek <highegg@gmail.com>
parents: 8857
diff changeset
480 if (! updating || nfail == 2 || nsuciter < 2)
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
481 break;
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
482 endif
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
483
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8468
diff changeset
484 ## Compute the scaled Broyden update.
8590
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
485 if (useqr)
26075
5d28fc32a7c7 doc: Consistent use of "fval" for optimization functions.
Kai T. Ohlhus <k.ohlhus@gmail.com>
parents: 25828
diff changeset
486 u = (fval1 - q*w) / sn;
8590
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
487 v = dg .* ((dg .* s) / sn);
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
488
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
489 ## Update the QR factorization.
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
490 [q, r] = qrupdate (q, r, u, v);
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
491 else
26075
5d28fc32a7c7 doc: Consistent use of "fval" for optimization functions.
Kai T. Ohlhus <k.ohlhus@gmail.com>
parents: 25828
diff changeset
492 u = (fval1 - w);
8590
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
493 v = dg .* ((dg .* s) / sn);
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
494
10821
693e22af08ae Grammarcheck documentation of m-files
Rik <octave@nomad.inbox5.com>
parents: 10793
diff changeset
495 ## update the Jacobian
8590
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
496 fjac += u * v';
8395
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
497 endif
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
498 endwhile
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
499 endwhile
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
500
8507
cadc73247d65 style fixes
John W. Eaton <jwe@octave.org>
parents: 8468
diff changeset
501 ## Restore original shapes.
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
502 x = reshape (x, xsiz);
26075
5d28fc32a7c7 doc: Consistent use of "fval" for optimization functions.
Kai T. Ohlhus <k.ohlhus@gmail.com>
parents: 25828
diff changeset
503 fval = reshape (fval, fsiz);
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
504
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
505 output.iterations = niter;
8986
22c8272af34b improvements to fsolve & family
Jaroslav Hajek <highegg@gmail.com>
parents: 8857
diff changeset
506 output.successful = nsuciter;
8590
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
507 output.funcCount = nfev;
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
508
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
509 endfunction
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
510
21759
b002b4331a12 maint: Use two newlines after endfunction and start of BIST tests.
Rik <rik@octave.org>
parents: 21758
diff changeset
511 ## A helper function that evaluates a function and checks for bad results.
30893
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files.
Rik <rik@octave.org>
parents: 30875
diff changeset
512 function [fx, jx] = guarded_eval (fcn, x, complexeqn)
21758
ffad2baa90f7 maint: Use newlines to make code more readable.
Rik <rik@octave.org>
parents: 21751
diff changeset
513
8693
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
514 if (nargout > 1)
30893
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files.
Rik <rik@octave.org>
parents: 30875
diff changeset
515 [fx, jx] = fcn (x);
8693
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
516 else
30893
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files.
Rik <rik@octave.org>
parents: 30875
diff changeset
517 fx = fcn (x);
8997
187a9d9c2f04 simplifications to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8991
diff changeset
518 jx = [];
8693
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
519 endif
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
520
8997
187a9d9c2f04 simplifications to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8991
diff changeset
521 if (! complexeqn && ! (isreal (fx) && isreal (jx)))
27069
0a62d9a6aa2d Place Octave's warning and error IDs in to the "Octave" namespace (bug #56213).
Rik <rik@octave.org>
parents: 26376
diff changeset
522 error ("Octave:fsolve:notreal", "fsolve: non-real value encountered");
14868
5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory
Rik <octave@nomad.inbox5.com>
parents: 14386
diff changeset
523 elseif (complexeqn && ! (isnumeric (fx) && isnumeric (jx)))
27069
0a62d9a6aa2d Place Octave's warning and error IDs in to the "Octave" namespace (bug #56213).
Rik <rik@octave.org>
parents: 26376
diff changeset
524 error ("Octave:fsolve:notnum", "fsolve: non-numeric value encountered");
8693
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
525 elseif (any (isnan (fx(:))))
27069
0a62d9a6aa2d Place Octave's warning and error IDs in to the "Octave" namespace (bug #56213).
Rik <rik@octave.org>
parents: 26376
diff changeset
526 error ("Octave:fsolve:isnan", "fsolve: NaN value encountered");
14386
59aab666f2bf Extend "FunValCheck" option to optimization routines to detect Inf values.
Rik <octave@nomad.inbox5.com>
parents: 14363
diff changeset
527 elseif (any (isinf (fx(:))))
27069
0a62d9a6aa2d Place Octave's warning and error IDs in to the "Octave" namespace (bug #56213).
Rik <rik@octave.org>
parents: 26376
diff changeset
528 error ("Octave:fsolve:isinf", "fsolve: Inf value encountered");
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
529 endif
21758
ffad2baa90f7 maint: Use newlines to make code more readable.
Rik <rik@octave.org>
parents: 21751
diff changeset
530
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
531 endfunction
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
532
10050
dc88a0b6472c support old style jacobian for fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 9899
diff changeset
533 function [fx, jx] = make_fcn_jac (x, fcn, fjac)
21758
ffad2baa90f7 maint: Use newlines to make code more readable.
Rik <rik@octave.org>
parents: 21751
diff changeset
534
10050
dc88a0b6472c support old style jacobian for fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 9899
diff changeset
535 fx = fcn (x);
dc88a0b6472c support old style jacobian for fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 9899
diff changeset
536 if (nargout == 2)
dc88a0b6472c support old style jacobian for fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 9899
diff changeset
537 jx = fjac (x);
dc88a0b6472c support old style jacobian for fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 9899
diff changeset
538 endif
21758
ffad2baa90f7 maint: Use newlines to make code more readable.
Rik <rik@octave.org>
parents: 21751
diff changeset
539
10050
dc88a0b6472c support old style jacobian for fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 9899
diff changeset
540 endfunction
dc88a0b6472c support old style jacobian for fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 9899
diff changeset
541
25730
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
542 ## Solve the double dogleg trust-region least-squares problem:
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
543 ## Minimize norm (r*x-b) subject to the constraint norm (d.*x) <= delta,
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
544 ## x being a convex combination of the gauss-newton and scaled gradient.
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
545
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
546 ## FIXME: error checks
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
547 ## FIXME: handle singularity, or leave it up to mldivide?
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
548
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
549 function x = __dogleg__ (r, b, d, delta)
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
550
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
551 ## Get Gauss-Newton direction.
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
552 x = r \ b;
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
553 xn = norm (d .* x);
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
554 if (xn > delta)
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
555 ## GN is too big, get scaled gradient.
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
556 s = (r' * b) ./ d;
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
557 sn = norm (s);
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
558 if (sn > 0)
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
559 ## Normalize and rescale.
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
560 s = (s / sn) ./ d;
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
561 ## Get the line minimizer in s direction.
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
562 tn = norm (r*s);
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
563 snm = (sn / tn) / tn;
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
564 if (snm < delta)
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
565 ## Get the dogleg path minimizer.
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
566 bn = norm (b);
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
567 dxn = delta/xn; snmd = snm/delta;
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
568 t = (bn/sn) * (bn/xn) * snmd;
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
569 t -= dxn * snmd^2 - sqrt ((t-dxn)^2 + (1-dxn^2)*(1-snmd^2));
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
570 alpha = dxn*(1-snmd^2) / t;
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
571 else
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
572 alpha = 0;
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
573 endif
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
574 else
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
575 alpha = delta / xn;
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
576 snm = 0;
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
577 endif
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
578 ## Form the appropriate convex combination.
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
579 x = alpha * x + ((1-alpha) * min (snm, delta)) * s;
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
580 endif
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
581
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
582 endfunction
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
583
17338
1c89599167a6 maint: End m-files with 1 blank line.
Rik <rik@octave.org>
parents: 17290
diff changeset
584
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13027
diff changeset
585 %!function retval = __f (p)
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
586 %! x = p(1);
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
587 %! y = p(2);
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
588 %! z = p(3);
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
589 %! retval = zeros (3, 1);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
590 %! retval(1) = sin (x) + y^2 + log (z) - 7;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
591 %! retval(2) = 3*x + 2^y -z^3 + 1;
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
592 %! retval(3) = x + y + z - 5;
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13027
diff changeset
593 %!endfunction
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
594 %!test
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
595 %! x_opt = [ 0.599054;
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
596 %! 2.395931;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
597 %! 2.005014 ];
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
598 %! tol = 1.0e-5;
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13027
diff changeset
599 %! [x, fval, info] = fsolve (@__f, [ 0.5; 2.0; 2.5 ]);
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
600 %! assert (info > 0);
8383
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
601 %! assert (norm (x - x_opt, Inf) < tol);
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
602 %! assert (norm (fval) < tol);
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
603
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13027
diff changeset
604 %!function retval = __f (p)
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
605 %! x = p(1);
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
606 %! y = p(2);
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
607 %! z = p(3);
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
608 %! w = p(4);
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
609 %! retval = zeros (4, 1);
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
610 %! retval(1) = 3*x + 4*y + exp (z + w) - 1.007;
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
611 %! retval(2) = 6*x - 4*y + exp (3*z + w) - 11;
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
612 %! retval(3) = x^4 - 4*y^2 + 6*z - 8*w - 20;
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
613 %! retval(4) = x^2 + 2*y^3 + z - w - 4;
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13027
diff changeset
614 %!endfunction
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
615 %!test
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
616 %! x_opt = [ -0.767297326653401, 0.590671081117440, ...
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
617 %! 1.47190018629642, -1.52719341133957 ];
25730
bf89eea6652e Overhaul fsolve for better performance and Matlab compatibility (bug #41146).
Rik <rik@octave.org>
parents: 25606
diff changeset
618 %! tol = 1.0e-4;
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13027
diff changeset
619 %! [x, fval, info] = fsolve (@__f, [-1, 1, 2, -1]);
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
620 %! assert (info > 0);
8383
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
621 %! assert (norm (x - x_opt, Inf) < tol);
8306
43795cf108d0 initial implementation of fsolve
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
622 %! assert (norm (fval) < tol);
8383
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
623
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13027
diff changeset
624 %!function retval = __f (p)
8383
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
625 %! x = p(1);
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
626 %! y = p(2);
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
627 %! z = p(3);
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
628 %! retval = zeros (3, 1);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
629 %! retval(1) = sin (x) + y^2 + log (z) - 7;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
630 %! retval(2) = 3*x + 2^y -z^3 + 1;
8383
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
631 %! retval(3) = x + y + z - 5;
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
632 %! retval(4) = x*x + y - z*log (z) - 1.36;
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13027
diff changeset
633 %!endfunction
8383
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
634 %!test
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
635 %! x_opt = [ 0.599054;
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
636 %! 2.395931;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
637 %! 2.005014 ];
8383
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
638 %! tol = 1.0e-5;
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13027
diff changeset
639 %! [x, fval, info] = fsolve (@__f, [ 0.5; 2.0; 2.5 ]);
8383
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
640 %! assert (info > 0);
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
641 %! assert (norm (x - x_opt, Inf) < tol);
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
642 %! assert (norm (fval) < tol);
a762d9daa700 allow overdetermined systems in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8306
diff changeset
643
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13027
diff changeset
644 %!function retval = __f (p)
8395
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
645 %! x = p(1);
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
646 %! y = p(2);
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
647 %! z = p(3);
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
648 %! retval = zeros (3, 1);
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
649 %! retval(1) = sin (x) + y^2 + log (z) - 7;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
650 %! retval(2) = 3*x + 2^y -z^3 + 1;
8395
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
651 %! retval(3) = x + y + z - 5;
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13027
diff changeset
652 %!endfunction
8395
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
653 %!test
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
654 %! x_opt = [ 0.599054;
14363
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
655 %! 2.395931;
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
Rik <octave@nomad.inbox5.com>
parents: 14143
diff changeset
656 %! 2.005014 ];
8395
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
657 %! tol = 1.0e-5;
8590
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
658 %! opt = optimset ("Updating", "qrp");
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13027
diff changeset
659 %! [x, fval, info] = fsolve (@__f, [ 0.5; 2.0; 2.5 ], opt);
8395
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
660 %! assert (info > 0);
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
661 %! assert (norm (x - x_opt, Inf) < tol);
88fd356b0d95 optionally allow pivoting in fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8383
diff changeset
662 %! assert (norm (fval) < tol);
8590
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
663
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
664 %!test
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
665 %! b0 = 3;
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
666 %! a0 = 0.2;
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
667 %! x = 0:.5:5;
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
668 %! noise = 1e-5 * sin (100*x);
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
669 %! y = exp (-a0*x) + b0 + noise;
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
670 %! c_opt = [a0, b0];
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
671 %! tol = 1e-5;
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
672 %!
21568
3d60ed163b70 maint: Eliminate bad spacing around '='.
Rik <rik@octave.org>
parents: 21546
diff changeset
673 %! [c, fval, info, output] = fsolve (@(c) (exp(-c(1)*x) + c(2) - y), [0, 0]);
8590
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
674 %! assert (info > 0);
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
675 %! assert (norm (c - c_opt, Inf) < tol);
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
676 %! assert (norm (fval) < norm (noise));
c136d313206a improvements to fsolve
Jaroslav Hajek <highegg@gmail.com>
parents: 8562
diff changeset
677
30893
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files.
Rik <rik@octave.org>
parents: 30875
diff changeset
678 %!function y = cfcn (x)
8693
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
679 %! y(1) = (1+i)*x(1)^2 - (1-i)*x(2) - 2;
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
680 %! y(2) = sqrt (x(1)*x(2)) - (1-2i)*x(3) + (3-4i);
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
681 %! y(3) = x(1) * x(2) - x(3)^2 + (3+2i);
13305
63463570d9fe Add %!endfunction block keyword to test.m
Rik <octave@nomad.inbox5.com>
parents: 13027
diff changeset
682 %!endfunction
8693
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
683
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
684 %!test
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
685 %! x_opt = [-1+i, 1-i, 2+i];
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
686 %! x = [i, 1, 1+i];
11587
c792872f8942 all script files: untabify and strip trailing whitespace
John W. Eaton <jwe@octave.org>
parents: 11523
diff changeset
687 %!
30893
e1788b1a315f maint: Use "fcn" as preferred abbreviation for "function" in m-files.
Rik <rik@octave.org>
parents: 30875
diff changeset
688 %! [x, f, info] = fsolve (@cfcn, x, optimset ("ComplexEqn", "on"));
8693
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
689 %! tol = 1e-5;
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
690 %! assert (norm (f) < tol);
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
691 %! assert (norm (x - x_opt, Inf) < tol);
e5ffb52c9c61 improve fsolve and add ComplexEqn option
Jaroslav Hajek <highegg@gmail.com>
parents: 8661
diff changeset
692
25499
c29a2107c559 fsolve.m: Add BIST test for bug #53991.
Rik <rik@octave.org>
parents: 25486
diff changeset
693 %!test <*53991>
c29a2107c559 fsolve.m: Add BIST test for bug #53991.
Rik <rik@octave.org>
parents: 25486
diff changeset
694 %! A = @(lam) [0 1 0 0; 0 0 1 0; 0 0 0 1; 0 0 -lam^2 0];
c29a2107c559 fsolve.m: Add BIST test for bug #53991.
Rik <rik@octave.org>
parents: 25486
diff changeset
695 %! C = [1 0 0 0; 0 0 1 0];
c29a2107c559 fsolve.m: Add BIST test for bug #53991.
Rik <rik@octave.org>
parents: 25486
diff changeset
696 %! B = @(lam) [C*expm(A(lam)*0); C*expm(A(lam)*1)];
c29a2107c559 fsolve.m: Add BIST test for bug #53991.
Rik <rik@octave.org>
parents: 25486
diff changeset
697 %! detB = @(lam) det (B(lam));
25606
959657cab846 maint: Strip trailing whitespace from source files.
John W. Eaton <jwe@octave.org>
parents: 25500
diff changeset
698 %!
26075
5d28fc32a7c7 doc: Consistent use of "fval" for optimization functions.
Kai T. Ohlhus <k.ohlhus@gmail.com>
parents: 25828
diff changeset
699 %! [x, fval, info] = fsolve (detB, 0);
25499
c29a2107c559 fsolve.m: Add BIST test for bug #53991.
Rik <rik@octave.org>
parents: 25486
diff changeset
700 %! assert (x == 0);
26075
5d28fc32a7c7 doc: Consistent use of "fval" for optimization functions.
Kai T. Ohlhus <k.ohlhus@gmail.com>
parents: 25828
diff changeset
701 %! assert (fval == -1);
25499
c29a2107c559 fsolve.m: Add BIST test for bug #53991.
Rik <rik@octave.org>
parents: 25486
diff changeset
702 %! assert (info == -2);
c29a2107c559 fsolve.m: Add BIST test for bug #53991.
Rik <rik@octave.org>
parents: 25486
diff changeset
703
25500
b3c35a130f94 fsolve.m: Return info=1 when initial guess (x0) is correct (bug #53991).
Rik <rik@octave.org>
parents: 25499
diff changeset
704 %!test <*53991>
26075
5d28fc32a7c7 doc: Consistent use of "fval" for optimization functions.
Kai T. Ohlhus <k.ohlhus@gmail.com>
parents: 25828
diff changeset
705 %! [x, fval, info] = fsolve (@(x) 5*x, 0);
25500
b3c35a130f94 fsolve.m: Return info=1 when initial guess (x0) is correct (bug #53991).
Rik <rik@octave.org>
parents: 25499
diff changeset
706 %! assert (x == 0);
26075
5d28fc32a7c7 doc: Consistent use of "fval" for optimization functions.
Kai T. Ohlhus <k.ohlhus@gmail.com>
parents: 25828
diff changeset
707 %! assert (fval == 0);
25500
b3c35a130f94 fsolve.m: Return info=1 when initial guess (x0) is correct (bug #53991).
Rik <rik@octave.org>
parents: 25499
diff changeset
708 %! assert (info == 1);