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optim: upgrade license to GPLv3+ and mention on DESCRIPTION the other package licenses
author carandraug
date Fri, 30 Mar 2012 15:14:48 +0000
parents f80846665d3b
children fba8cdd5f9ad
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1 ## Copyright (C) 2010, 2011 Olaf Till <olaf.till@uni-jena.de>
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2 ##
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3 ## This program is free software; you can redistribute it and/or modify it under
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4 ## the terms of the GNU General Public License as published by the Free Software
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5 ## Foundation; either version 3 of the License, or (at your option) any later
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6 ## version.
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7 ##
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8 ## This program is distributed in the hope that it will be useful, but WITHOUT
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9 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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10 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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11 ## details.
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12 ##
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13 ## You should have received a copy of the GNU General Public License along with
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14 ## this program; if not, see <http://www.gnu.org/licenses/>.
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15
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16 ## -*- texinfo -*-
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17 ## @deftypefn {Function File} {[@var{p}, @var{resid}, @var{cvg}, @var{outp}] =} nonlin_residmin (@var{f}, @var{pin})
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18 ## @deftypefnx {Function File} {[@var{p}, @var{resid}, @var{cvg}, @var{outp}] =} nonlin_residmin (@var{f}, @var{pin}, @var{settings})
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19 ## Frontend for nonlinear minimization of residuals returned by a model
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20 ## function.
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21 ##
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22 ## The functions supplied by the user have a minimal
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23 ## interface; any additionally needed constants (e.g. observed values)
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24 ## can be supplied by wrapping the user functions into anonymous
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25 ## functions.
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26 ##
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27 ## The following description applies to usage with vector-based
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28 ## parameter handling. Differences in usage for structure-based
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29 ## parameter handling will be explained in a separate section below.
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30 ##
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31 ## @var{f}: function returning the array of residuals. It gets a column
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32 ## vector of real parameters as argument. In gradient determination,
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33 ## this function may be called with an informational second argument,
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34 ## whose content depends on the function for gradient determination.
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35 ##
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36 ## @var{pin}: real column vector of initial parameters.
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37 ##
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38 ## @var{settings}: structure whose fields stand for optional settings
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39 ## referred to below. The fields can be set by @code{optimset()} with
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40 ## Octave versions 3.3.55 or greater; with older Octave versions, the
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41 ## fields must be set directly as structure-fields in the correct case.
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42 ##
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43 ## The returned values are the column vector of final parameters
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44 ## @var{p}, the final array of residuals @var{resid}, an integer
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45 ## @var{cvg} indicating if and how optimization succeeded or failed, and
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46 ## a structure @var{outp} with additional information, curently with
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47 ## only one field: @var{niter}, the number of iterations. @var{cvg} is
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48 ## greater than zero for success and less than or equal to zero for
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49 ## failure; its possible values depend on the used backend and currently
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50 ## can be @code{0} (maximum number of iterations exceeded), @code{2}
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51 ## (parameter change less than specified precision in two consecutive
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52 ## iterations), or @code{3} (improvement in objective function --- e.g.
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53 ## sum of squares --- less than specified).
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54 ##
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55 ## @var{settings}:
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56 ##
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57 ## @code{Algorithm}: String specifying the backend. Default:
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58 ## @code{"lm_svd_feasible"}. The latter is currently the only backend
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59 ## distributed with this package. It is described in a separate section
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60 ## below.
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61 ##
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62 ## @code{dfdp}: Function computing the jacobian of the residuals with
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63 ## respect to the parameters, assuming residuals are reshaped to a
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64 ## vector. Default: finite differences. Will be called with the column
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65 ## vector of parameters and an informational structure as arguments. The
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66 ## structure has the fields @code{f}: value of residuals for current
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67 ## parameters, reshaped to a column vector, @code{fixed}: logical vector
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68 ## indicating which parameters are not optimized, so these partial
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69 ## derivatives need not be computed and can be set to zero,
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70 ## @code{diffp}, @code{diff_onesided}, @code{lbound}, @code{ubound}:
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71 ## identical to the user settings of this name, @code{plabels}:
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72 ## 1-dimensional cell-array of column-cell-arrays, each column with
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73 ## labels for all parameters, the first column contains the numerical
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74 ## indices of the parameters. The default jacobian function will call
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75 ## the model function with the second argument set with fields @code{f}:
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76 ## as the @code{f} passed to the jacobian function, @code{plabels}:
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77 ## cell-array of 1x1 cell-arrays with the entries of the
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78 ## column-cell-arrays of @code{plabels} as passed to the jacobian
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79 ## function corresponding to current parameter, @code{side}: @code{0}
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80 ## for one-sided interval, @code{1} or @code{2}, respectively, for the
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81 ## sides of a two-sided interval, and @code{parallel}: logical scalar
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82 ## indicating parallel computation of partial derivatives.
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83 ##
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84 ## @code{diffp}: column vector of fractional intervals (doubled for
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85 ## central intervals) supposed to be used by jacobian functions
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86 ## performing finite differencing. Default: @code{.001 * ones (size (parameters))}. The default jacobian function will use these as
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87 ## absolute intervals for parameters with value zero.
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88 ##
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89 ## @code{diff_onesided}: logical column vector indicating that one-sided
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90 ## intervals should be used by jacobian functions performing finite
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91 ## differencing. Default: @code{false (size (parameters))}.
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92 ##
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93 ## @code{complex_step_derivative}, @code{complex_step_derivative_inequc},
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94 ## @code{complex_step_derivative_equc}: logical scalars, default: false.
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95 ## Estimate Jacobian of model function, general inequality constraints,
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96 ## and general equality constraints, respectively, with complex step
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97 ## derivative approximation. Use only if you know that your model
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98 ## function, function of general inequality constraints, or function of
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99 ## general equality constraints, respectively, is suitable for this. No
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100 ## user function for the respective Jacobian must be specified.
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101 ##
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102 ## @code{cstep}: scalar step size for complex step derivative
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103 ## approximation. Default: 1e-20.
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104 ##
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105 ## @code{fixed}: logical column vector indicating which parameters
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106 ## should not be optimized, but kept to their inital value. Fixing is
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107 ## done independently of the backend, but the backend may choose to fix
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108 ## additional parameters under certain conditions.
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109 ##
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110 ## @code{lbound}, @code{ubound}: column vectors of lower and upper
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111 ## bounds for parameters. Default: @code{-Inf} and @code{+Inf},
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112 ## respectively. The bounds are non-strict, i.e. parameters are allowed
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113 ## to be exactly equal to a bound. The default jacobian function will
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114 ## respect bounds (but no further inequality constraints) in finite
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115 ## differencing.
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116 ##
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117 ## @code{inequc}: Further inequality constraints. Cell-array containing
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118 ## up to four entries, two entries for linear inequality constraints
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119 ## and/or one or two entries for general inequality constraints. Either
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120 ## linear or general constraints may be the first entries, but the two
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121 ## entries for linear constraints must be adjacent and, if two entries
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122 ## are given for general constraints, they also must be adjacent. The
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123 ## two entries for linear constraints are a matrix (say @code{m}) and a
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124 ## vector (say @code{v}), specifying linear inequality constraints of
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125 ## the form @code{m.' * parameters + v >= 0}. The first entry for
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126 ## general constraints must be a differentiable vector valued function
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127 ## (say @code{h}), specifying general inequality constraints of the form
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128 ## @code{h (p[, idx]) >= 0}; @code{p} is the column vector of optimized
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129 ## paraters and the optional argument @code{idx} is a logical index.
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130 ## @code{h} has to return the values of all constraints if @code{idx} is
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131 ## not given, and has to return only the indexed constraints if
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132 ## @code{idx} is given (so computation of the other constraints can be
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133 ## spared). In gradient determination, this function may be called with
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134 ## an informational third argument, whose content depends on the
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135 ## function for gradient determination. If a second entry for general
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136 ## inequality constraints is given, it must be a function computing the
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137 ## jacobian of the constraints with respect to the parameters. For this
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138 ## function, the description of @code{dfdp} above applies, except that
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139 ## it is called with 3 arguments since it has an additional argument
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140 ## @code{idx} --- a logical index --- at second position, indicating
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141 ## which rows of the jacobian must be returned, and except that the
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142 ## default function calls @code{h} with 3 arguments, since the argument
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143 ## @code{idx} is also supplied. Note that specifying linear constraints
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144 ## as general constraints will generally waste performance, even if
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145 ## further, non-linear, general constraints are also specified.
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146 ##
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147 ## @code{equc}: Equality constraints. Specified the same way as
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148 ## inequality constraints (see @code{inequc}).
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149 ##
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150 ## @code{cpiv}: Function for complementary pivoting, usable in
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151 ## algorithms for constraints. Default: @ cpiv_bard. Only the default
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152 ## function is supplied with the package.
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153 ##
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154 ## @code{weights}: Array of weights for the residuals. Dimensions must
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155 ## match.
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156 ##
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157 ## @code{TolFun}: Minimum fractional improvement in objective function
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158 ## (e.g. sum of squares) in an iteration (abortion criterium). Default:
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159 ## .0001.
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160 ##
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161 ## @code{MaxIter}: Maximum number of iterations (abortion criterium).
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162 ## Default: backend-specific.
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163 ##
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164 ## @code{fract_prec}: Column Vector, minimum fractional change of
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165 ## parameters in an iteration (abortion criterium if violated in two
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166 ## consecutive iterations). Default: backend-specific.
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167 ##
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168 ## @code{max_fract_change}: Column Vector, enforced maximum fractional
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169 ## change in parameters in an iteration. Default: backend-specific.
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170 ##
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171 ## @code{Display}: String indicating the degree of verbosity. Default:
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172 ## @code{"off"}. Possible values are currently @code{"off"} (no
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173 ## messages) and @code{"iter"} (some messages after each iteration).
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174 ## Support of this setting and its exact interpretation are
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175 ## backend-specific.
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176 ##
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177 ## @code{plot_cmd}: Function enabling backend to plot results or
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178 ## intermediate results. Will be called with current computed
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179 ## residualse. Default: plot nothing.
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180 ##
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181 ## @code{debug}: Logical scalar, default: @code{false}. Will be passed
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182 ## to the backend, which might print debugging information if true.
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183 ##
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184 ## Structure-based parameter handling
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185 ##
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186 ## The setting @code{param_order} is a cell-array with names of the
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187 ## optimized parameters. If not given, and initial parameters are a
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188 ## structure, all parameters in the structure are optimized. If initial
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189 ## parameters are a structure, it is an error if @code{param_order} is
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190 ## not given and there are any non-structure-based configuration items
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191 ## or functions.
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192 ##
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193 ## The initial parameters @var{pin} can be given as a structure
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194 ## containing at least all fields named in @code{param_order}. In this
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195 ## case the returned parameters @var{p} will also be a structure.
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196 ##
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197 ## Each user-supplied function can be called with the argument
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198 ## containing the current parameters being a structure instead of a
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199 ## column vector. For this, a corresponding setting must be set to
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200 ## @code{true}: @code{f_pstruct} (model function), @code{dfdp_pstruct}
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201 ## (jacobian of model function), @code{f_inequc_pstruct} (general
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202 ## inequality constraints), @code{df_inequc_pstruct} (jacobian of
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203 ## general inequality constraints), @code{f_equc_pstruct} (general
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204 ## equality constraints), and @code{df_equc_pstruct} (jacobian of
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205 ## general equality constraints). If a jacobian-function is configured
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206 ## in such a way, it must return the columns of the jacobian as fields
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207 ## of a structure under the respective parameter names.
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208 ##
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209 ## Similarly, for specifying linear constraints, instead of the matrix
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210 ## (called @code{m} above), a structure containing the rows of the
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211 ## matrix in fields under the respective parameter names can be given.
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212 ## In this case, rows containing only zeros need not be given.
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213 ##
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214 ## The vector-based settings @code{lbound}, @code{ubound},
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215 ## @code{fixed}, @code{diffp}, @code{diff_onesided}, @code{fract_prec},
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216 ## and @code{max_fract_change} can be replaced by the setting
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217 ## @code{param_config}. It is a structure that can contain fields named
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218 ## in @code{param_order}. For each such field, there may be subfields
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219 ## with the same names as the above vector-based settings, but
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220 ## containing a scalar value for the respective parameter. If
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221 ## @code{param_config} is specified, none of the above
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222 ## vector/matrix-based settings may be used.
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223 ##
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224 ## Additionally, named parameters are allowed to be non-scalar real
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225 ## arrays. In this case, their dimensions are given by the setting
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226 ## @code{param_dims}, a cell-array of dimension vectors, each containing
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227 ## at least two dimensions; if not given, dimensions are taken from the
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228 ## initial parameters, if these are given in a structure. Any
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229 ## vector-based settings or not structure-based linear constraints then
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230 ## must correspond to an order of parameters with all parameters
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231 ## reshaped to vectors and concatenated in the user-given order of
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232 ## parameter names. Structure-based settings or structure-based initial
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233 ## parameters must contain arrays with dimensions reshapable to those of
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234 ## the respective parameters.
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235 ##
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236 ## Description of backends (currently only one)
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237 ##
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238 ## "lm_svd_feasible"
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239 ##
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240 ## A Levenberg/Marquardt algorithm using singular value decomposition
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241 ## and featuring constraints which must be met by the initial parameters
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242 ## and are attempted to be kept met throughout the optimization.
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243 ##
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244 ## Parameters with identical lower and upper bounds will be fixed.
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245 ##
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246 ## Returned value @var{cvg} will be @code{0}, @code{2}, or @code{3}.
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247 ##
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248 ## Backend-specific defaults are: @code{MaxIter}: 20, @code{fract_prec}:
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249 ## @code{zeros (size (parameters))}, @code{max_fract_change}: @code{Inf}
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250 ## for all parameters.
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251 ##
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252 ## Interpretation of @code{Display}: if set to @code{"iter"}, currently
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253 ## @code{plot_cmd} is evaluated for each iteration, and some further
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254 ## diagnostics may be printed.
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255 ##
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256 ## Specific option: @code{lm_svd_feasible_alt_s}: if falling back to
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257 ## nearly gradient descent, do it more like original Levenberg/Marquardt
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258 ## method, with descent in each gradient component; for testing only.
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259 ##
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260 ## @seealso {nonlin_curvefit}
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261 ## @end deftypefn
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262
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263 function [p, resid, cvg, outp] = nonlin_residmin (varargin)
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264
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265 if (nargin == 1)
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266 p = __nonlin_residmin__ (varargin{1});
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267 return;
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268 endif
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269
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270 if (nargin < 2 || nargin > 3)
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271 print_usage ();
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272 endif
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273
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274 if (nargin == 2)
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275 varargin{3} = struct ();
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276 endif
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277
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278 varargin{4} = struct ();
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279
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280 [p, resid, cvg, outp] = __nonlin_residmin__ (varargin{:});
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281
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282 endfunction