--- /dev/null
+## Copyright (C) 2012 Olaf Till <i7tiol@t-online.de>
+##
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or
+## (at your option) any later version.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {[@var{p}, @var{objf}, @var{cvg}, @var{outp}] =} nonlin_min (@var{f}, @var{pin})
+## @deftypefnx {Function File} {[@var{p}, @var{objf}, @var{cvg}, @var{outp}] =} nonlin_min (@var{f}, @var{pin}, @var{settings})
+##
+## Frontend for constrained nonlinear minimization of a scalar objective
+## function. The functions supplied by the user have a minimal
+## interface; any additionally needed constants can be supplied by
+## wrapping the user functions into anonymous functions.
+##
+## The following description applies to usage with vector-based
+## parameter handling. Differences in usage for structure-based
+## parameter handling will be explained in a separate section below.
+##
+## @var{f}: objective function. It gets a column vector of real
+## parameters as argument. In gradient determination, this function may
+## be called with an informational second argument, whose content
+## depends on the function for gradient determination.
+##
+## @var{pin}: real column vector of initial parameters.
+##
+## @var{settings}: structure whose fields stand for optional settings
+## referred to below. The fields can be set by @code{optimset()} with
+## Octave versions 3.3.55 or greater; with older Octave versions, the
+## fields must be set directly as structure-fields in the correct case.
+##
+## The returned values are the column vector of final parameters
+## @var{p}, the final value of the objective function @var{objf}, an
+## integer @var{cvg} indicating if and how optimization succeeded or
+## failed, and a structure @var{outp} with additional information,
+## curently with only one field: @var{niter}, the number of iterations.
+## @var{cvg} is greater than zero for success and less than or equal to
+## zero for failure; its possible values depend on the used backend and
+## currently can be @code{0} (maximum number of iterations exceeded),
+## @code{1} (fixed number of iterations completed, e.g. in stochastic
+## optimizers), @code{2} (parameter change less than specified precision
+## in two consecutive iterations), @code{3} (improvement in objective
+## function less than specified), or @code{-4} (algorithm got stuck).
+##
+## @var{settings}:
+##
+## @code{Algorithm}: String specifying the backend. Currently available
+## are @code{"lm_feasible"} (default) and @code{"siman"}. They are
+## described in separate sections below.
+##
+## @code{objf_grad}: Function computing the gradient of the objective
+## function with respect to the parameters, assuming residuals are
+## reshaped to a vector. Default: finite differences. Will be called
+## with the column vector of parameters and an informational structure
+## as arguments. The structure has the fields @code{f}: value of
+## objective function for current parameters, @code{fixed}: logical
+## vector indicating which parameters are not optimized, so these
+## partial derivatives need not be computed and can be set to zero,
+## @code{diffp}, @code{diff_onesided}, @code{lbound}, @code{ubound}:
+## identical to the user settings of this name, @code{plabels}:
+## 1-dimensional cell-array of column-cell-arrays, each column with
+## labels for all parameters, the first column contains the numerical
+## indices of the parameters. The default gradient function will call
+## the objective function with the second argument set with fields
+## @code{f}: as the @code{f} passed to the gradient function,
+## @code{plabels}: cell-array of 1x1 cell-arrays with the entries of the
+## column-cell-arrays of @code{plabels} as passed to the jacobian
+## function corresponding to current parameter, @code{side}: @code{0}
+## for one-sided interval, @code{1} or @code{2}, respectively, for the
+## sides of a two-sided interval, and @code{parallel}: logical scalar
+## indicating parallel computation of partial derivatives.
+##
+## @code{objf_hessian}: Function computing the Hessian of the objective
+## function with respect to the parameters. The default is backend
+## specific. Will be called with the column vector of parameters as
+## argument.
+##
+## @code{diffp}: column vector of fractional intervals (doubled for
+## central intervals) supposed to be used by gradient functions
+## performing finite differencing. Default: @code{.001 * ones (size
+## (parameters))}. The default gradient function will use these as
+## absolute intervals for parameters with value zero.
+##
+## @code{diff_onesided}: logical column vector indicating that one-sided
+## intervals should be used by gradient functions performing finite
+## differencing. Default: @code{false (size (parameters))}.
+##
+## @code{complex_step_derivative_objf},
+## @code{complex_step_derivative_inequc},
+## @code{complex_step_derivative_equc}: logical scalars, default: false.
+## Estimate gradient of objective function, general inequality
+## constraints, and general equality constraints, respectively, with
+## complex step derivative approximation. Use only if you know that your
+## objective function, function of general inequality constraints, or
+## function of general equality constraints, respectively, is suitable
+## for this. No user function for the respective gradient must be
+## specified.
+##
+## @code{cstep}: scalar step size for complex step derivative
+## approximation. Default: 1e-20.
+##
+## @code{fixed}: logical column vector indicating which parameters
+## should not be optimized, but kept to their inital value. Fixing is
+## done independently of the backend, but the backend may choose to fix
+## additional parameters under certain conditions.
+##
+## @code{lbound}, @code{ubound}: column vectors of lower and upper
+## bounds for parameters. Default: @code{-Inf} and @code{+Inf},
+## respectively. The bounds are non-strict, i.e. parameters are allowed
+## to be exactly equal to a bound. The default gradient function will
+## respect bounds (but no further inequality constraints) in finite
+## differencing.
+##
+## @code{inequc}: Further inequality constraints. Cell-array containing
+## up to four entries, two entries for linear inequality constraints
+## and/or one or two entries for general inequality constraints. Either
+## linear or general constraints may be the first entries, but the two
+## entries for linear constraints must be adjacent and, if two entries
+## are given for general constraints, they also must be adjacent. The
+## two entries for linear constraints are a matrix (say @code{m}) and a
+## vector (say @code{v}), specifying linear inequality constraints of
+## the form @code{m.' * parameters + v >= 0}. The first entry for
+## general constraints must be a differentiable vector valued function
+## (say @code{h}), specifying general inequality constraints of the form
+## @code{h (p[, idx]) >= 0}; @code{p} is the column vector of optimized
+## paraters and the optional argument @code{idx} is a logical index.
+## @code{h} has to return the values of all constraints if @code{idx} is
+## not given. It may choose to return only the indexed constraints if
+## @code{idx} is given (so computation of the other constraints can be
+## spared); in this case, the additional setting @code{inequc_f_idx} has
+## to be set to @code{true}. In gradient determination, this function
+## may be called with an informational third argument, whose content
+## depends on the function for gradient determination. If a second entry
+## for general inequality constraints is given, it must be a function
+## computing the jacobian of the constraints with respect to the
+## parameters. For this function, the description of @code{dfdp} above
+## applies, with 2 exceptions: 1) it is called with 3 arguments since it
+## has an additional argument @code{idx} --- a logical index --- at
+## second position, indicating which rows of the jacobian must be
+## returned (if the function chooses to return only indexed rows, the
+## additional setting @code{inequc_df_idx} has to be set to
+## @code{true}). 2) the default jacobian function calls @code{h} with 3
+## arguments, since the argument @code{idx} is also supplied. Note that
+## specifying linear constraints as general constraints will generally
+## waste performance, even if further, non-linear, general constraints
+## are also specified.
+##
+## @code{equc}: Equality constraints. Specified the same way as
+## inequality constraints (see @code{inequc}). The respective additional
+## settings are named @code{equc_f_idx} and @code{equc_df_idx}.
+##
+## @code{cpiv}: Function for complementary pivoting, usable in
+## algorithms for constraints. Default: @ cpiv_bard. Only the default
+## function is supplied with the package.
+##
+## @code{TolFun}: Minimum fractional improvement in objective function
+## in an iteration (abortion criterium). Default: .0001.
+##
+## @code{MaxIter}: Maximum number of iterations (abortion criterium).
+## Default: backend-specific.
+##
+## @code{fract_prec}: Column Vector, minimum fractional change of
+## parameters in an iteration (abortion criterium if violated in two
+## consecutive iterations). Default: backend-specific.
+##
+## @code{max_fract_change}: Column Vector, enforced maximum fractional
+## change in parameters in an iteration. Default: backend-specific.
+##
+## @code{Display}: String indicating the degree of verbosity. Default:
+## @code{"off"}. Possible values are currently @code{"off"} (no
+## messages) and @code{"iter"} (some messages after each iteration).
+## Support of this setting and its exact interpretation are
+## backend-specific.
+##
+## @code{debug}: Logical scalar, default: @code{false}. Will be passed
+## to the backend, which might print debugging information if true.
+##
+## Structure-based parameter handling
+##
+## The setting @code{param_order} is a cell-array with names of the
+## optimized parameters. If not given, and initial parameters are a
+## structure, all parameters in the structure are optimized. If initial
+## parameters are a structure, it is an error if @code{param_order} is
+## not given and there are any non-structure-based configuration items
+## or functions.
+##
+## The initial parameters @var{pin} can be given as a structure
+## containing at least all fields named in @code{param_order}. In this
+## case the returned parameters @var{p} will also be a structure.
+##
+## Each user-supplied function can be called with the argument
+## containing the current parameters being a structure instead of a
+## column vector. For this, a corresponding setting must be set to
+## @code{true}: @code{objf_pstruct} (objective function),
+## @code{objf_grad_pstruct} (gradient of objective function),
+## @code{objf_hessian_pstruct} (hessian of objective function),
+## @code{f_inequc_pstruct} (general inequality constraints),
+## @code{df_inequc_pstruct} (jacobian of general inequality
+## constraints), @code{f_equc_pstruct} (general equality constraints),
+## and @code{df_equc_pstruct} (jacobian of general equality
+## constraints). If a gradient (jacobian) function is configured in such
+## a way, it must return the entries (columns) of the gradient
+## (jacobian) as fields of a structure under the respective parameter
+## names. If the hessian function is configured in such a way, it must
+## return a structure (say @code{h}) with fields e.g. as
+## @code{h.a.b = value} for @code{value} being the 2nd partial derivative
+## with respect to @code{a} and @code{b}. There is no need to also
+## specify the field @code{h.b.a} in this example.
+##
+## Similarly, for specifying linear constraints, instead of the matrix
+## (called @code{m} above), a structure containing the rows of the
+## matrix in fields under the respective parameter names can be given.
+## In this case, rows containing only zeros need not be given.
+##
+## The vector-based settings @code{lbound}, @code{ubound},
+## @code{fixed}, @code{diffp}, @code{diff_onesided}, @code{fract_prec},
+## and @code{max_fract_change} can be replaced by the setting
+## @code{param_config}. It is a structure that can contain fields named
+## in @code{param_order}. For each such field, there may be subfields
+## with the same names as the above vector-based settings, but
+## containing a scalar value for the respective parameter. If
+## @code{param_config} is specified, none of the above
+## vector/matrix-based settings may be used.
+##
+## Additionally, named parameters are allowed to be non-scalar real
+## arrays. In this case, their dimensions are given by the setting
+## @code{param_dims}, a cell-array of dimension vectors, each containing
+## at least two dimensions; if not given, dimensions are taken from the
+## initial parameters, if these are given in a structure. Any
+## vector-based settings or not structure-based linear constraints then
+## must correspond to an order of parameters with all parameters
+## reshaped to vectors and concatenated in the user-given order of
+## parameter names. Structure-based settings or structure-based initial
+## parameters must contain arrays with dimensions reshapable to those of
+## the respective parameters.
+##
+## Description of backends
+##
+## "lm_feasible"
+##
+## A Levenberg/Marquardt-like optimizer, attempting to honour
+## constraints throughout the course of optimization. This means that
+## the initial parameters must not violate constraints (to find an
+## initial feasible set of parameters, e.g. Octaves @code{sqp} can be
+## used, by specifying an objective function which is constant or which
+## returns the quadratic distance to the initial values). If the
+## constraints need only be honoured in the result of the optimization,
+## Octaves @code{sqp} may be preferable. The Hessian is either supplied
+## by the user or is approximated by the BFGS algorithm.
+##
+## Returned value @var{cvg} will be @code{2} or @code{3} for success and
+## @code{0} or @code{-4} for failure (see above for meaning).
+##
+## Backend-specific defaults are: @code{MaxIter}: 20, @code{fract_prec}:
+## @code{zeros (size (parameters))}, @code{max_fract_change}: @code{Inf}
+## for all parameters.
+##
+## Interpretation of @code{Display}: if set to @code{"iter"}, currently
+## only information on applying @code{max_fract_change} is printed.
+##
+## "siman"
+##
+## A simulated annealing (stochastic) optimizer, changing all parameters
+## at once in a single step, so being suitable for non-bound
+## constraints.
+##
+## No gradient or hessian of the objective function is used. The
+## settings @code{MaxIter}, @code{fract_prec}, @code{TolFun}, and
+## @code{max_fract_change} are not honoured.
+##
+## Accepts the additional settings @code{T_init} (initial temperature,
+## default 0.01), @code{T_min} (final temperature, default 1.0e-5),
+## @code{mu_T} (factor of temperature decrease, default 1.005),
+## @code{iters_fixed_T} (iterations within one temperature step, default
+## 10), @code{max_rand_step} (column vector or structure-based
+## configuration of maximum random steps for each parameter, default
+## 0.005 * @var{pin}), @code{stoch_regain_constr} (if @code{true},
+## regain constraints after a random step, otherwise take new random
+## value until constraints are met, default false), @code{trace_steps}
+## (set field @code{trace} of @var{outp} with a matrix with a row for
+## each step, first column iteration number, second column repeat number
+## within iteration, third column value of objective function, rest
+## columns parameter values, default false), and @code{siman_log} (set
+## field @code{log} of @var{outp} with a matrix with a row for each
+## iteration, first column temperature, second column value of objective
+## function, rest columns numbers of tries with decrease, no decrease
+## but accepted, and no decrease and rejected.
+##
+## Steps with increase @code{diff} of objective function are accepted if
+## @code{rand (1) < exp (- diff / T)}, where @code{T} is the temperature
+## of the current iteration.
+##
+## If regaining of constraints failed, optimization will be aborted and
+## returned value of @var{cvg} will be @code{0}. Otherwise, @var{cvg}
+## will be @code{1}.
+##
+## Interpretation of @code{Display}: if set to @code{"iter"}, an
+## informational line is printed after each iteration.
+##
+## @end deftypefn
+
+## disabled PKG_ADD: __all_opts__ ("nonlin_min");
+
+function [p, objf, cvg, outp] = nonlin_min (f, pin, settings)
+
+ if (compare_versions (version (), "3.3.55", "<"))
+ ## optimset mechanism was fixed for option names with underscores
+ ## sometime in 3.3.54+, if I remember right
+ optimget = @ __optimget__;
+ endif
+
+ if (compare_versions (version (), "3.2.4", "<="))
+ ## For bug #31484; but Octave 3.6... shows bug #36288 due to this
+ ## workaround. Octave 3.7... seems to be all right.
+ __dfdp__ = @ __dfdp__;
+ endif
+
+ ## some scalar defaults; some defaults are backend specific, so
+ ## lacking elements in respective constructed vectors will be set to
+ ## NA here in the frontend
+ diffp_default = .001;
+ stol_default = .0001;
+ cstep_default = 1e-20;
+
+ if (nargin == 1 && ischar (f) && strcmp (f, "defaults"))
+ p = optimset ("param_config", [], \
+ "param_order", [], \
+ "param_dims", [], \
+ "f_inequc_pstruct", false, \
+ "f_equc_pstruct", false, \
+ "objf_pstruct", false, \
+ "df_inequc_pstruct", false, \
+ "df_equc_pstruct", false, \
+ "objf_grad_pstruct", false, \
+ "objf_hessian_pstruct", false, \
+ "lbound", [], \
+ "ubound", [], \
+ "objf_grad", [], \
+ "objf_hessian", [], \
+ "cpiv", @ cpiv_bard, \
+ "max_fract_change", [], \
+ "fract_prec", [], \
+ "diffp", [], \
+ "diff_onesided", [], \
+ "complex_step_derivative_objf", false, \
+ "complex_step_derivative_inequc", false, \
+ "complex_step_derivative_equc", false, \
+ "cstep", cstep_default, \
+ "fixed", [], \
+ "inequc", [], \
+ "equc", [], \
+ "inequc_f_idx", false, \
+ "inequc_df_idx", false, \
+ "equc_f_idx", false, \
+ "equc_df_idx", false, \
+ "TolFun", stol_default, \
+ "MaxIter", [], \
+ "Display", "off", \
+ "Algorithm", "lm_feasible", \
+ "T_init", .01, \
+ "T_min", 1.0e-5, \
+ "mu_T", 1.005, \
+ "iters_fixed_T", 10, \
+ "max_rand_step", [], \
+ "stoch_regain_constr", false, \
+ "trace_steps", false, \
+ "siman_log", false, \
+ "debug", false);
+ return;
+ endif
+
+ if (nargin < 2 || nargin > 3)
+ print_usage ();
+ endif
+
+ if (nargin == 2)
+ settings = struct ();
+ endif
+
+ if (ischar (f))
+ f = str2func (f);
+ endif
+
+ if (! (pin_struct = isstruct (pin)))
+ if (! isvector (pin) || columns (pin) > 1)
+ error ("initial parameters must be either a structure or a column vector");
+ endif
+ endif
+
+ #### processing of settings and consistency checks
+
+ pconf = optimget (settings, "param_config");
+ pord = optimget (settings, "param_order");
+ pdims = optimget (settings, "param_dims");
+ f_inequc_pstruct = optimget (settings, "f_inequc_pstruct", false);
+ f_equc_pstruct = optimget (settings, "f_equc_pstruct", false);
+ f_pstruct = optimget (settings, "objf_pstruct", false);
+ dfdp_pstruct = optimget (settings, "objf_grad_pstruct", f_pstruct);
+ hessian_pstruct = optimget (settings, "objf_hessian_pstruct", f_pstruct);
+ df_inequc_pstruct = optimget (settings, "df_inequc_pstruct", \
+ f_inequc_pstruct);
+ df_equc_pstruct = optimget (settings, "df_equc_pstruct", \
+ f_equc_pstruct);
+ lbound = optimget (settings, "lbound");
+ ubound = optimget (settings, "ubound");
+ dfdp = optimget (settings, "objf_grad");
+ if (ischar (dfdp)) dfdp = str2func (dfdp); endif
+ hessian = optimget (settings, "objf_hessian");
+ max_fract_change = optimget (settings, "max_fract_change");
+ fract_prec = optimget (settings, "fract_prec");
+ diffp = optimget (settings, "diffp");
+ diff_onesided = optimget (settings, "diff_onesided");
+ fixed = optimget (settings, "fixed");
+ do_cstep = optimget (settings, "complex_step_derivative_objf", false);
+ cstep = optimget (settings, "cstep", cstep_default);
+ if (do_cstep && ! isempty (dfdp))
+ error ("both 'complex_step_derivative_objf' and 'objf_grad' are set");
+ endif
+ do_cstep_inequc = \
+ optimget (settings, "complex_step_derivative_inequc", false);
+ do_cstep_equc = optimget (settings, "complex_step_derivative_equc", \
+ false);
+ max_rand_step = optimget (settings, "max_rand_step");
+
+ any_vector_conf = ! (isempty (lbound) && isempty (ubound) && \
+ isempty (max_fract_change) && \
+ isempty (fract_prec) && isempty (diffp) && \
+ isempty (diff_onesided) && isempty (fixed) && \
+ isempty (max_rand_step));
+
+ ## collect constraints
+ [mc, vc, f_genicstr, df_gencstr, user_df_gencstr] = \
+ __collect_constraints__ (optimget (settings, "inequc"), \
+ do_cstep_inequc, "inequality constraints");
+ [emc, evc, f_genecstr, df_genecstr, user_df_genecstr] = \
+ __collect_constraints__ (optimget (settings, "equc"), \
+ do_cstep_equc, "equality constraints");
+ mc_struct = isstruct (mc);
+ emc_struct = isstruct (emc);
+
+ ## correct "_pstruct" settings if functions are not supplied, handle
+ ## constraint functions not honoring indices
+ if (isempty (dfdp)) dfdp_pstruct = false; endif
+ if (isempty (hessian)) hessian_pstruct = false; endif
+ if (isempty (f_genicstr))
+ f_inequc_pstruct = false;
+ elseif (! optimget (settings, "inequc_f_idx", false))
+ f_genicstr = @ (p, varargin) apply_idx_if_given \
+ (f_genicstr (p, varargin{:}), varargin{:});
+ endif
+ if (isempty (f_genecstr))
+ f_equc_pstruct = false;
+ elseif (! optimget (settings, "equc_f_idx", false))
+ f_genecstr = @ (p, varargin) apply_idx_if_given \
+ (f_genecstr (p, varargin{:}), varargin{:});
+ endif
+ if (user_df_gencstr)
+ if (! optimget (settings, "inequc_df_idx", false))
+ df_gencstr = @ (varargin) df_gencstr (varargin{:})(varargin{2}, :);
+ endif
+ else
+ df_inequc_pstruct = false;
+ endif
+ if (user_df_genecstr)
+ if (! optimget (settings, "equc_df_idx", false))
+ df_genecstr = @ (varargin) df_genecstr (varargin{:})(varargin{2}, :);
+ endif
+ else
+ df_equc_pstruct = false;
+ endif
+
+ ## some settings require a parameter order
+ if (pin_struct || ! isempty (pconf) || f_inequc_pstruct || \
+ f_equc_pstruct || f_pstruct || dfdp_pstruct || \
+ hessian_pstruct || df_inequc_pstruct || df_equc_pstruct || \
+ mc_struct || emc_struct)
+ if (isempty (pord))
+ if (pin_struct)
+ if (any_vector_conf || \
+ ! (f_pstruct && \
+ (f_inequc_pstruct || isempty (f_genicstr)) && \
+ (f_equc_pstruct || isempty (f_genecstr)) && \
+ (dfdp_pstruct || isempty (dfdp)) && \
+ (hessian_pstruct || isempty (hessian)) && \
+ (df_inequc_pstruct || ! user_df_gencstr) && \
+ (df_equc_pstruct || ! user_df_genecstr) && \
+ (mc_struct || isempty (mc)) && \
+ (emc_struct || isempty (emc))))
+ error ("no parameter order specified and constructing a parameter order from the structure of initial parameters can not be done since not all configuration or given functions are structure based");
+ else
+ pord = fieldnames (pin);
+ endif
+ else
+ error ("given settings require specification of parameter order or initial parameters in the form of a structure");
+ endif
+ endif
+ pord = pord(:);
+ if (pin_struct && ! all (isfield (pin, pord)))
+ error ("some initial parameters lacking");
+ endif
+ if ((nnames = rows (unique (pord))) < rows (pord))
+ error ("duplicate parameter names in 'param_order'");
+ endif
+ if (isempty (pdims))
+ if (pin_struct)
+ pdims = cellfun \
+ (@ size, fields2cell (pin, pord), "UniformOutput", false);
+ else
+ pdims = num2cell (ones (nnames, 2), 2);
+ endif
+ else
+ pdims = pdims(:);
+ if (pin_struct && \
+ ! all (cellfun (@ (x, y) prod (size (x)) == prod (y), \
+ struct2cell (pin), pdims)))
+ error ("given param_dims and dimensions of initial parameters do not match");
+ endif
+ endif
+ if (nnames != rows (pdims))
+ error ("lengths of 'param_order' and 'param_dims' not equal");
+ endif
+ pnel = cellfun (@ prod, pdims);
+ ppartidx = pnel;
+ if (any (pnel > 1))
+ pnonscalar = true;
+ cpnel = num2cell (pnel);
+ prepidx = cat (1, cellfun \
+ (@ (x, n) x(ones (1, n), 1), \
+ num2cell ((1:nnames).'), cpnel, \
+ "UniformOutput", false){:});
+ epord = pord(prepidx, 1);
+ psubidx = cat (1, cellfun \
+ (@ (n) (1:n).', cpnel, \
+ "UniformOutput", false){:});
+ else
+ pnonscalar = false; # some less expensive interfaces later
+ prepidx = (1:nnames).';
+ epord = pord;
+ psubidx = ones (nnames, 1);
+ endif
+ else
+ pord = []; # spares checks for given but not needed
+ endif
+
+ if (pin_struct)
+ np = sum (pnel);
+ else
+ np = length (pin);
+ if (! isempty (pord) && np != sum (pnel))
+ error ("number of initial parameters not correct");
+ endif
+ endif
+
+ plabels = num2cell (num2cell ((1:np).'));
+ if (! isempty (pord))
+ plabels = cat (2, plabels, num2cell (epord), \
+ num2cell (num2cell (psubidx)));
+ endif
+
+ ## some useful vectors
+ zerosvec = zeros (np, 1);
+ NAvec = NA (np, 1);
+ Infvec = Inf (np, 1);
+ falsevec = false (np, 1);
+ sizevec = [np, 1];
+
+ ## collect parameter-related configuration
+ if (! isempty (pconf))
+ ## use supplied configuration structure
+
+ ## parameter-related configuration is either allowed by a structure
+ ## or by vectors
+ if (any_vector_conf)
+ error ("if param_config is given, its potential items must not \
+ be configured in another way");
+ endif
+
+ ## supplement parameter names lacking in param_config
+ nidx = ! isfield (pconf, pord);
+ pconf = cell2fields ({struct()}(ones (1, sum (nidx))), \
+ pord(nidx), 2, pconf);
+
+ pconf = structcat (1, fields2cell (pconf, pord){:});
+
+ ## in the following, use reshape with explicit dimensions (instead
+ ## of x(:)) so that errors are thrown if a configuration item has
+ ## incorrect number of elements
+
+ lbound = - Infvec;
+ if (isfield (pconf, "lbound"))
+ idx = ! fieldempty (pconf, "lbound");
+ if (pnonscalar)
+ lbound (idx(prepidx), 1) = \
+ cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+ {pconf(idx).lbound}.', \
+ cpnel(idx), "UniformOutput", false){:});
+ else
+ lbound(idx, 1) = cat (1, pconf.lbound);
+ endif
+ endif
+
+ ubound = Infvec;
+ if (isfield (pconf, "ubound"))
+ idx = ! fieldempty (pconf, "ubound");
+ if (pnonscalar)
+ ubound (idx(prepidx), 1) = \
+ cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+ {pconf(idx).ubound}.', \
+ cpnel(idx), "UniformOutput", false){:});
+ else
+ ubound(idx, 1) = cat (1, pconf.ubound);
+ endif
+ endif
+
+ max_fract_change = fract_prec = NAvec;
+
+ if (isfield (pconf, "max_fract_change"))
+ idx = ! fieldempty (pconf, "max_fract_change");
+ if (pnonscalar)
+ max_fract_change(idx(prepidx)) = \
+ cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+ {pconf(idx).max_fract_change}.', \
+ cpnel(idx), \
+ "UniformOutput", false){:});
+ else
+ max_fract_change(idx) = [pconf.max_fract_change];
+ endif
+ endif
+
+ if (isfield (pconf, "fract_prec"))
+ idx = ! fieldempty (pconf, "fract_prec");
+ if (pnonscalar)
+ fract_prec(idx(prepidx)) = \
+ cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+ {pconf(idx).fract_prec}.', cpnel(idx), \
+ "UniformOutput", false){:});
+ else
+ fract_prec(idx) = [pconf.fract_prec];
+ endif
+ endif
+
+ diffp = zerosvec;
+ diffp(:) = diffp_default;
+ if (isfield (pconf, "diffp"))
+ idx = ! fieldempty (pconf, "diffp");
+ if (pnonscalar)
+ diffp(idx(prepidx)) = \
+ cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+ {pconf(idx).diffp}.', cpnel(idx), \
+ "UniformOutput", false){:});
+ else
+ diffp(idx) = [pconf.diffp];
+ endif
+ endif
+
+ diff_onesided = fixed = falsevec;
+
+ if (isfield (pconf, "diff_onesided"))
+ idx = ! fieldempty (pconf, "diff_onesided");
+ if (pnonscalar)
+ diff_onesided(idx(prepidx)) = \
+ logical \
+ (cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+ {pconf(idx).diff_onesided}.', cpnel(idx), \
+ "UniformOutput", false){:}));
+ else
+ diff_onesided(idx) = logical ([pconf.diff_onesided]);
+ endif
+ endif
+
+ if (isfield (pconf, "fixed"))
+ idx = ! fieldempty (pconf, "fixed");
+ if (pnonscalar)
+ fixed(idx(prepidx)) = \
+ logical \
+ (cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+ {pconf(idx).fixed}.', cpnel(idx), \
+ "UniformOutput", false){:}));
+ else
+ fixed(idx) = logical ([pconf.fixed]);
+ endif
+ endif
+
+ max_rand_step = NAvec;
+
+ if (isfield (pconf, "max_rand_step"))
+ idx = ! fieldempty (pconf, "max_rand_step");
+ if (pnonscalar)
+ max_rand_step(idx(prepidx)) = \
+ logical \
+ (cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+ {pconf(idx).max_rand_step}.',
+ cpnel(idx), \
+ "UniformOutput", false){:}));
+ else
+ max_rand_step(idx) = logical ([pconf.max_rand_step]);
+ endif
+ endif
+
+ else
+ ## use supplied configuration vectors
+
+ if (isempty (lbound))
+ lbound = - Infvec;
+ elseif (any (size (lbound) != sizevec))
+ error ("bounds: wrong dimensions");
+ endif
+
+ if (isempty (ubound))
+ ubound = Infvec;
+ elseif (any (size (ubound) != sizevec))
+ error ("bounds: wrong dimensions");
+ endif
+
+ if (isempty (max_fract_change))
+ max_fract_change = NAvec;
+ elseif (any (size (max_fract_change) != sizevec))
+ error ("max_fract_change: wrong dimensions");
+ endif
+
+ if (isempty (fract_prec))
+ fract_prec = NAvec;
+ elseif (any (size (fract_prec) != sizevec))
+ error ("fract_prec: wrong dimensions");
+ endif
+
+ if (isempty (diffp))
+ diffp = zerosvec;
+ diffp(:) = diffp_default;
+ else
+ if (any (size (diffp) != sizevec))
+ error ("diffp: wrong dimensions");
+ endif
+ diffp(isna (diffp)) = diffp_default;
+ endif
+
+ if (isempty (diff_onesided))
+ diff_onesided = falsevec;
+ else
+ if (any (size (diff_onesided) != sizevec))
+ error ("diff_onesided: wrong dimensions")
+ endif
+ diff_onesided(isna (diff_onesided)) = false;
+ diff_onesided = logical (diff_onesided);
+ endif
+
+ if (isempty (fixed))
+ fixed = falsevec;
+ else
+ if (any (size (fixed) != sizevec))
+ error ("fixed: wrong dimensions");
+ endif
+ fixed(isna (fixed)) = false;
+ fixed = logical (fixed);
+ endif
+
+ if (isempty (max_rand_step))
+ max_rand_step = NAvec;
+ elseif (any (size (max_rand_step) != sizevec))
+ error ("max_rand_step: wrong dimensions");
+ endif
+
+ endif
+
+ ## guaranty all (lbound <= ubound)
+ if (any (lbound > ubound))
+ error ("some lower bounds larger than upper bounds");
+ endif
+
+ #### consider whether initial parameters and functions are based on
+ #### parameter structures or parameter vectors; wrappers for call to
+ #### default function for jacobians
+
+ ## initial parameters
+ if (pin_struct)
+ if (pnonscalar)
+ pin = cat (1, cellfun (@ (x, n) reshape (x, n, 1), \
+ fields2cell (pin, pord), cpnel, \
+ "UniformOutput", false){:});
+ else
+ pin = cat (1, fields2cell (pin, pord){:});
+ endif
+ endif
+
+ ## objective function
+ if (f_pstruct)
+ if (pnonscalar)
+ f = @ (p, varargin) \
+ f (cell2struct \
+ (cellfun (@ reshape, mat2cell (p, ppartidx), \
+ pdims, "UniformOutput", false), \
+ pord, 1), varargin{:});
+ else
+ f = @ (p, varargin) \
+ f (cell2struct (num2cell (p), pord, 1), varargin{:});
+ endif
+ endif
+ f_pin = f (pin);
+
+ ## gradient of objective function
+ if (isempty (dfdp))
+ if (do_cstep)
+ dfdp = @ (p, hook) jacobs (p, f, hook);
+ else
+ dfdp = @ (p, hook) __dfdp__ (p, f, hook);
+ endif
+ endif
+ if (dfdp_pstruct)
+ if (pnonscalar)
+ dfdp = @ (p, hook) \
+ cat (2, \
+ fields2cell \
+ (dfdp (cell2struct \
+ (cellfun (@ reshape, mat2cell (p, ppartidx), \
+ pdims, "UniformOutput", false), \
+ pord, 1), hook), \
+ pord){:});
+ else
+ dfdp = @ (p, hook) \
+ cat (2, \
+ fields2cell \
+ (dfdp (cell2struct (num2cell (p), pord, 1), hook), \
+ pord){:});
+ endif
+ endif
+
+ ## hessian of objective function
+ if (hessian_pstruct)
+ if (pnonscalar)
+ hessian = @ (p) \
+ hessian_struct2mat \
+ (hessian (cell2struct \
+ (cellfun (@ reshape, mat2cell (p, ppartidx), \
+ pdims, "UniformOutput", false), \
+ pord, 1)), pord);
+ else
+ hessian = @ (p) \
+ hessian_struct2mat \
+ (hessian (cell2struct (num2cell (p), pord, 1)), pord);
+ endif
+ endif
+
+ ## function for general inequality constraints
+ if (f_inequc_pstruct)
+ if (pnonscalar)
+ f_genicstr = @ (p, varargin) \
+ f_genicstr (cell2struct \
+ (cellfun (@ reshape, mat2cell (p, ppartidx), \
+ pdims, "UniformOutput", false), \
+ pord, 1), varargin{:});
+ else
+ f_genicstr = @ (p, varargin) \
+ f_genicstr \
+ (cell2struct (num2cell (p), pord, 1), varargin{:});
+ endif
+ endif
+
+ ## note this stage
+ possibly_pstruct_f_genicstr = f_genicstr;
+
+ ## jacobian of general inequality constraints
+ if (df_inequc_pstruct)
+ if (pnonscalar)
+ df_gencstr = @ (p, func, idx, hook) \
+ cat (2, \
+ fields2cell \
+ (df_gencstr \
+ (cell2struct \
+ (cellfun (@ reshape, mat2cell (p, ppartidx), \
+ pdims, "UniformOutput", false), pord, 1), \
+ func, idx, hook), \
+ pord){:});
+ else
+ df_gencstr = @ (p, func, idx, hook) \
+ cat (2, \
+ fields2cell \
+ (df_gencstr (cell2struct (num2cell (p), pord, 1), \
+ func, idx, hook), \
+ pord){:});
+ endif
+ endif
+
+ ## function for general equality constraints
+ if (f_equc_pstruct)
+ if (pnonscalar)
+ f_genecstr = @ (p, varargin) \
+ f_genecstr (cell2struct \
+ (cellfun (@ reshape, mat2cell (p, ppartidx), \
+ pdims, "UniformOutput", false), \
+ pord, 1), varargin{:});
+ else
+ f_genecstr = @ (p, varargin) \
+ f_genecstr \
+ (cell2struct (num2cell (p), pord, 1), varargin{:});
+ endif
+ endif
+
+ ## note this stage
+ possibly_pstruct_f_genecstr = f_genecstr;
+
+ ## jacobian of general equality constraints
+ if (df_equc_pstruct)
+ if (pnonscalar)
+ df_genecstr = @ (p, func, idx, hook) \
+ cat (2, \
+ fields2cell \
+ (df_genecstr \
+ (cell2struct \
+ (cellfun (@ reshape, mat2cell (p, ppartidx), \
+ pdims, "UniformOutput", false), pord, 1), \
+ func, idx, hook), \
+ pord){:});
+ else
+ df_genecstr = @ (p, func, idx, hook) \
+ cat (2, \
+ fields2cell \
+ (df_genecstr (cell2struct (num2cell (p), pord, 1), \
+ func, idx, hook), \
+ pord){:});
+ endif
+ endif
+
+ ## linear inequality constraints
+ if (mc_struct)
+ idx = isfield (mc, pord);
+ if (rows (fieldnames (mc)) > sum (idx))
+ error ("unknown fields in structure of linear inequality constraints");
+ endif
+ smc = mc;
+ mc = zeros (np, rows (vc));
+ mc(idx(prepidx), :) = cat (1, fields2cell (smc, pord(idx)){:});
+ endif
+
+ ## linear equality constraints
+ if (emc_struct)
+ idx = isfield (emc, pord);
+ if (rows (fieldnames (emc)) > sum (idx))
+ error ("unknown fields in structure of linear equality constraints");
+ endif
+ semc = emc;
+ emc = zeros (np, rows (evc));
+ emc(idx(prepidx), :) = cat (1, fields2cell (semc, pord(idx)){:});
+ endif
+
+ ## parameter-related configuration for jacobian functions
+ if (dfdp_pstruct || df_inequc_pstruct || df_equc_pstruct)
+ if(pnonscalar)
+ s_diffp = cell2struct \
+ (cellfun (@ reshape, mat2cell (diffp, ppartidx), \
+ pdims, "UniformOutput", false), pord, 1);
+ s_diff_onesided = cell2struct \
+ (cellfun (@ reshape, mat2cell (diff_onesided, ppartidx), \
+ pdims, "UniformOutput", false), pord, 1);
+ s_orig_lbound = cell2struct \
+ (cellfun (@ reshape, mat2cell (lbound, ppartidx), \
+ pdims, "UniformOutput", false), pord, 1);
+ s_orig_ubound = cell2struct \
+ (cellfun (@ reshape, mat2cell (ubound, ppartidx), \
+ pdims, "UniformOutput", false), pord, 1);
+ s_plabels = cell2struct \
+ (num2cell \
+ (cat (2, cellfun \
+ (@ (x) cellfun \
+ (@ reshape, mat2cell (cat (1, x{:}), ppartidx), \
+ pdims, "UniformOutput", false), \
+ num2cell (plabels, 1), "UniformOutput", false){:}), \
+ 2), \
+ pord, 1);
+ s_orig_fixed = cell2struct \
+ (cellfun (@ reshape, mat2cell (fixed, ppartidx), \
+ pdims, "UniformOutput", false), pord, 1);
+ else
+ s_diffp = cell2struct (num2cell (diffp), pord, 1);
+ s_diff_onesided = cell2struct (num2cell (diff_onesided), pord, 1);
+ s_orig_lbound = cell2struct (num2cell (lbound), pord, 1);
+ s_orig_ubound = cell2struct (num2cell (ubound), pord, 1);
+ s_plabels = cell2struct (num2cell (plabels, 2), pord, 1);
+ s_orig_fixed = cell2struct (num2cell (fixed), pord, 1);
+ endif
+ endif
+
+ #### some further values and checks
+
+ if (any (fixed & (pin < lbound | pin > ubound)))
+ warning ("some fixed parameters outside bounds");
+ endif
+
+ ## dimensions of linear constraints
+ if (isempty (mc))
+ mc = zeros (np, 0);
+ vc = zeros (0, 1);
+ endif
+ if (isempty (emc))
+ emc = zeros (np, 0);
+ evc = zeros (0, 1);
+ endif
+ [rm, cm] = size (mc);
+ [rv, cv] = size (vc);
+ if (rm != np || cm != rv || cv != 1)
+ error ("linear inequality constraints: wrong dimensions");
+ endif
+ [erm, ecm] = size (emc);
+ [erv, ecv] = size (evc);
+ if (erm != np || ecm != erv || ecv != 1)
+ error ("linear equality constraints: wrong dimensions");
+ endif
+
+ ## note initial values of linear constraits
+ pin_cstr.inequ.lin_except_bounds = mc.' * pin + vc;
+ pin_cstr.equ.lin = emc.' * pin + evc;
+
+ ## note number and initial values of general constraints
+ if (isempty (f_genicstr))
+ pin_cstr.inequ.gen = [];
+ n_genicstr = 0;
+ else
+ n_genicstr = length (pin_cstr.inequ.gen = f_genicstr (pin));
+ endif
+ if (isempty (f_genecstr))
+ pin_cstr.equ.gen = [];
+ n_genecstr = 0;
+ else
+ n_genecstr = length (pin_cstr.equ.gen = f_genecstr (pin));
+ endif
+
+ #### collect remaining settings
+ hook.TolFun = optimget (settings, "TolFun", stol_default);
+ hook.MaxIter = optimget (settings, "MaxIter");
+ if (ischar (hook.cpiv = optimget (settings, "cpiv", @ cpiv_bard)))
+ hook.cpiv = str2func (hook.cpiv);
+ endif
+ hook.Display = optimget (settings, "Display", "off");
+ hook.testing = optimget (settings, "debug", false);
+ hook.siman.T_init = optimget (settings, "T_init", .01);
+ hook.siman.T_min = optimget (settings, "T_min", 1.0e-5);
+ hook.siman.mu_T = optimget (settings, "mu_T", 1.005);
+ hook.siman.iters_fixed_T = optimget (settings, "iters_fixed_T", 10);
+ hook.stoch_regain_constr = \
+ optimget (settings, "stoch_regain_constr", false);
+ hook.trace_steps = \
+ optimget (settings, "trace_steps", false);
+ hook.siman_log = \
+ optimget (settings, "siman_log", false);
+ backend = optimget (settings, "Algorithm", "lm_feasible");
+ backend = map_matlab_algorithm_names (backend);
+ backend = map_backend (backend);
+
+ #### handle fixing of parameters
+ orig_lbound = lbound;
+ orig_ubound = ubound;
+ orig_fixed = fixed;
+ if (all (fixed))
+ error ("no free parameters");
+ endif
+
+ nonfixed = ! fixed;
+ if (any (fixed))
+ ## backend (returned values and initial parameters)
+ backend = @ (f, pin, hook) \
+ backend_wrapper (backend, fixed, f, pin, hook);
+
+ ## objective function
+ f = @ (p, varargin) f (assign (pin, nonfixed, p), varargin{:});
+
+ ## gradient of objective function
+ dfdp = @ (p, hook) \
+ dfdp (assign (pin, nonfixed, p), hook)(nonfixed);
+
+ ## hessian of objective function
+ if (! isempty (hessian))
+ hessian = @ (p) \
+ hessian (assign (pin, nonfixed, p))(nonfixed, nonfixed);
+ endif
+
+ ## function for general inequality constraints
+ f_genicstr = @ (p, varargin) \
+ f_genicstr (assign (pin, nonfixed, p), varargin{:});
+
+ ## jacobian of general inequality constraints
+ df_gencstr = @ (p, func, idx, hook) \
+ df_gencstr (assign (pin, nonfixed, p), func, idx, hook) \
+ (:, nonfixed);
+
+ ## function for general equality constraints
+ f_genecstr = @ (p, varargin) \
+ f_genecstr (assign (pin, nonfixed, p), varargin{:});
+
+ ## jacobian of general equality constraints
+ df_genecstr = @ (p, func, idx, hook) \
+ df_genecstr (assign (pin, nonfixed, p), func, idx, hook) \
+ (:, nonfixed);
+
+ ## linear inequality constraints
+ vc += mc(fixed, :).' * (tp = pin(fixed));
+ mc = mc(nonfixed, :);
+
+ ## linear equality constraints
+ evc += emc(fixed, :).' * tp;
+ emc = emc(nonfixed, :);
+
+ ## _last_ of all, vectors of parameter-related configuration,
+ ## including "fixed" itself
+ lbound = lbound(nonfixed, :);
+ ubound = ubound(nonfixed, :);
+ max_fract_change = max_fract_change(nonfixed);
+ fract_prec = fract_prec(nonfixed);
+ max_rand_step = max_rand_step(nonfixed);
+ fixed = fixed(nonfixed);
+ endif
+
+ #### supplement constants to jacobian functions
+
+ ## gradient of objective function
+ if (dfdp_pstruct)
+ dfdp = @ (p, hook) \
+ dfdp (p, cell2fields \
+ ({s_diffp, s_diff_onesided, s_orig_lbound, \
+ s_orig_ubound, s_plabels, \
+ cell2fields(num2cell(hook.fixed), pord(nonfixed), \
+ 1, s_orig_fixed), cstep}, \
+ {"diffp", "diff_onesided", "lbound", "ubound", \
+ "plabels", "fixed", "h"}, \
+ 2, hook));
+ else
+ dfdp = @ (p, hook) \
+ dfdp (p, cell2fields \
+ ({diffp, diff_onesided, orig_lbound, orig_ubound, \
+ plabels, assign(orig_fixed, nonfixed, hook.fixed), \
+ cstep}, \
+ {"diffp", "diff_onesided", "lbound", "ubound", \
+ "plabels", "fixed", "h"}, \
+ 2, hook));
+ endif
+
+ ## jacobian of general inequality constraints
+ if (df_inequc_pstruct)
+ df_gencstr = @ (p, func, idx, hook) \
+ df_gencstr (p, func, idx, cell2fields \
+ ({s_diffp, s_diff_onesided, s_orig_lbound, \
+ s_orig_ubound, s_plabels, \
+ cell2fields(num2cell(hook.fixed), pord(nonfixed), \
+ 1, s_orig_fixed), cstep}, \
+ {"diffp", "diff_onesided", "lbound", "ubound", \
+ "plabels", "fixed", "h"}, \
+ 2, hook));
+ else
+ df_gencstr = @ (p, func, idx, hook) \
+ df_gencstr (p, func, idx, cell2fields \
+ ({diffp, diff_onesided, orig_lbound, \
+ orig_ubound, plabels, \
+ assign(orig_fixed, nonfixed, hook.fixed), cstep}, \
+ {"diffp", "diff_onesided", "lbound", "ubound", \
+ "plabels", "fixed", "h"}, \
+ 2, hook));
+ endif
+
+ ## jacobian of general equality constraints
+ if (df_equc_pstruct)
+ df_genecstr = @ (p, func, idx, hook) \
+ df_genecstr (p, func, idx, cell2fields \
+ ({s_diffp, s_diff_onesided, s_orig_lbound, \
+ s_orig_ubound, s_plabels, \
+ cell2fields(num2cell(hook.fixed), pord(nonfixed), \
+ 1, s_orig_fixed), cstep}, \
+ {"diffp", "diff_onesided", "lbound", "ubound", \
+ "plabels", "fixed", "h"}, \
+ 2, hook));
+ else
+ df_genecstr = @ (p, func, idx, hook) \
+ df_genecstr (p, func, idx, cell2fields \
+ ({diffp, diff_onesided, orig_lbound, \
+ orig_ubound, plabels, \
+ assign(orig_fixed, nonfixed, hook.fixed), cstep}, \
+ {"diffp", "diff_onesided", "lbound", "ubound", \
+ "plabels", "fixed", "h"}, \
+ 2, hook));
+ endif
+
+ #### interfaces to constraints
+
+ ## include bounds into linear inequality constraints
+ tp = eye (sum (nonfixed));
+ lidx = lbound != - Inf;
+ uidx = ubound != Inf;
+ mc = cat (2, tp(:, lidx), - tp(:, uidx), mc);
+ vc = cat (1, - lbound(lidx, 1), ubound(uidx, 1), vc);
+
+ ## concatenate linear inequality and equality constraints
+ mc = cat (2, mc, emc);
+ vc = cat (1, vc, evc);
+ n_lincstr = rows (vc);
+
+ ## concatenate general inequality and equality constraints
+ if (n_genecstr > 0)
+ if (n_genicstr > 0)
+ nidxi = 1 : n_genicstr;
+ nidxe = n_genicstr + 1 : n_genicstr + n_genecstr;
+ f_gencstr = @ (p, idx, varargin) \
+ cat (1, \
+ f_genicstr (p, idx(nidxi), varargin{:}), \
+ f_genecstr (p, idx(nidxe), varargin{:}));
+ df_gencstr = @ (p, idx, hook) \
+ cat (1, \
+ df_gencstr (p, @ (p, varargin) \
+ possibly_pstruct_f_genicstr \
+ (p, idx(nidxi), varargin{:}), \
+ idx(nidxi), \
+ setfield (hook, "f", \
+ hook.f(nidxi(idx(nidxi))))), \
+ df_genecstr (p, @ (p, varargin) \
+ possibly_pstruct_f_genecstr \
+ (p, idx(nidxe), varargin{:}), \
+ idx(nidxe), \
+ setfield (hook, "f", \
+ hook.f(nidxe(idx(nidxe))))));
+ else
+ f_gencstr = f_genecstr;
+ df_gencstr = @ (p, idx, hook) \
+ df_genecstr (p, \
+ @ (p, varargin) \
+ possibly_pstruct_f_genecstr \
+ (p, idx, varargin{:}), \
+ idx, \
+ setfield (hook, "f", hook.f(idx)));
+ endif
+ else
+ f_gencstr = f_genicstr;
+ df_gencstr = @ (p, idx, hook) \
+ df_gencstr (p, \
+ @ (p, varargin) \
+ possibly_pstruct_f_genicstr (p, idx, varargin{:}), \
+ idx, \
+ setfield (hook, "f", hook.f(idx)));
+ endif
+ n_gencstr = n_genicstr + n_genecstr;
+
+ ## concatenate linear and general constraints, defining the final
+ ## function interfaces
+ if (n_gencstr > 0)
+ nidxl = 1:n_lincstr;
+ nidxh = n_lincstr + 1 : n_lincstr + n_gencstr;
+ f_cstr = @ (p, idx, varargin) \
+ cat (1, \
+ mc(:, idx(nidxl)).' * p + vc(idx(nidxl), 1), \
+ f_gencstr (p, idx(nidxh), varargin{:}));
+ df_cstr = @ (p, idx, hook) \
+ cat (1, \
+ mc(:, idx(nidxl)).', \
+ df_gencstr (p, idx(nidxh), \
+ setfield (hook, "f", \
+ hook.f(nidxh))));
+ else
+ f_cstr = @ (p, idx, varargin) mc(:, idx).' * p + vc(idx, 1);
+ df_cstr = @ (p, idx, hook) mc(:, idx).';
+ endif
+
+ ## define eq_idx (logical index of equality constraints within all
+ ## concatenated constraints
+ eq_idx = false (n_lincstr + n_gencstr, 1);
+ eq_idx(n_lincstr + 1 - rows (evc) : n_lincstr) = true;
+ n_cstr = n_lincstr + n_gencstr;
+ eq_idx(n_cstr + 1 - n_genecstr : n_cstr) = true;
+
+ #### prepare interface hook
+
+ ## passed constraints
+ hook.mc = mc;
+ hook.vc = vc;
+ hook.f_cstr = f_cstr;
+ hook.df_cstr = df_cstr;
+ hook.n_gencstr = n_gencstr;
+ hook.eq_idx = eq_idx;
+ hook.lbound = lbound;
+ hook.ubound = ubound;
+
+ ## passed values of constraints for initial parameters
+ hook.pin_cstr = pin_cstr;
+
+ ## passed function for gradient of objective function
+ hook.dfdp = dfdp;
+
+ ## passed function for hessian of objective function
+ hook.hessian = hessian;
+
+ ## passed function for complementary pivoting
+ ## hook.cpiv = cpiv; # set before
+
+ ## passed value of objective function for initial parameters
+ hook.f_pin = f_pin;
+
+ ## passed options
+ hook.max_fract_change = max_fract_change;
+ hook.fract_prec = fract_prec;
+ ## hook.TolFun = ; # set before
+ ## hook.MaxIter = ; # set before
+ hook.fixed = fixed;
+ hook.max_rand_step = max_rand_step;
+
+ #### call backend
+
+ [p, objf, cvg, outp] = backend (f, pin, hook);
+
+ if (pin_struct)
+ if (pnonscalar)
+ p = cell2struct \
+ (cellfun (@ reshape, mat2cell (p, ppartidx), \
+ pdims, "UniformOutput", false), \
+ pord, 1);
+ else
+ p = cell2struct (num2cell (p), pord, 1);
+ endif
+ endif
+
+endfunction
+
+function backend = map_matlab_algorithm_names (backend)
+
+ ## nothing done here at the moment
+
+endfunction
+
+function backend = map_backend (backend)
+
+ switch (backend)
+ ## case "sqp_infeasible"
+ ## backend = "__sqp__";
+ ## case "sqp"
+ ## backend = "__sqp__";
+ case "lm_feasible"
+ backend = "__lm_feasible__";
+ case "siman"
+ backend = "__siman__";
+ otherwise
+ error ("no backend implemented for algorithm '%s'", backend);
+ endswitch
+
+ backend = str2func (backend);
+
+endfunction
+
+function [p, resid, cvg, outp] = backend_wrapper (backend, fixed, f, p, hook)
+
+ [tp, resid, cvg, outp] = backend (f, p(! fixed), hook);
+
+ p(! fixed) = tp;
+
+endfunction
+
+function lval = assign (lval, lidx, rval)
+
+ lval(lidx) = rval;
+
+endfunction
+
+function m = hessian_struct2mat (s, pord)
+
+ m = cell2mat (fields2cell \
+ (structcat (1, NA, fields2cell (s, pord){:}), pord));
+
+ idx = isna (m);
+
+ m(idx) = (m.')(idx);
+
+endfunction
+
+function ret = __optimget__ (s, name, default)
+
+ if (isfield (s, name))
+ ret = s.(name);
+ elseif (nargin > 2)
+ ret = default;
+ else
+ ret = [];
+ endif
+
+endfunction
+
+function ret = apply_idx_if_given (ret, varargin)
+
+ if (nargin > 1)
+ ret = ret(varargin{1});
+ endif
+
+endfunction
+
+%!demo
+%! ## Example for default optimization (Levenberg/Marquardt with
+%! ## BFGS), one non-linear equality constraint. Constrained optimum is
+%! ## at p = [0; 1].
+%! objective_function = @ (p) p(1)^2 + p(2)^2;
+%! pin = [-2; 5];
+%! constraint_function = @ (p) p(1)^2 + 1 - p(2);
+%! [p, objf, cvg, outp] = nonlin_min (objective_function, pin, optimset ("equc", {constraint_function}))
+
+%!demo
+%! ## Example for simulated annealing, two parameters, "trace_steps"
+%! ## is true;
+%! t_init = .2;
+%! t_min = .002;
+%! mu_t = 1.002;
+%! iters_fixed_t = 10;
+%! init_p = [2; 2];
+%! max_rand_step = [.2; .2];
+%! [p, objf, cvg, outp] = nonlin_min (@ (p) (p(1)/10)^2 + (p(2)/10)^2 + .1 * (-cos(4*p(1)) - cos(4*p(2))), init_p, optimset ("algorithm", "siman", "max_rand_step", max_rand_step, "t_init", t_init, "T_min", t_min, "mu_t", mu_t, "iters_fixed_T", iters_fixed_t, "trace_steps", true));
+%! p
+%! objf
+%! x = (outp.trace(:, 1) - 1) * iters_fixed_t + outp.trace(:, 2);
+%! x(1) = 0;
+%! plot (x, cat (2, outp.trace(:, 3:end), t_init ./ (mu_t .^ outp.trace(:, 1))))
+%! legend ({"objective function value", "p(1)", "p(2)", "Temperature"})
+%! xlabel ("subiteration")
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff