/usr/share/octave/packages/optim-1.3.0/nonlin_min.m is in octave-optim 1.3.0-1.
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##
## 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. 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{parallel_local}: logical scalar, default: false. Estimate
## gradient of objective function and of constraints in parallel
## processes. Works for default finite difference gradient function and
## for complex step derivatives. Due to overhead, a speed advantage can
## only be expected if objective function or constraint functions are
## time consuming enough.
##
## @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 column-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 parameters 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{f_inequc_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{df_inequc_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{f_equc_idx} and @code{df_equc_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 (termination criterium). Default: .0001.
##
## @code{MaxIter}: Maximum number of iterations (termination criterium).
## Default: backend-specific.
##
## @code{fract_prec}: Column Vector, minimum fractional change of
## parameters in an iteration (termination 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{grad_objf_pstruct} (gradient of objective function),
## @code{hessian_objf_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, ...
"grad_objf_pstruct", false, ...
"hessian_objf_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", [], ...
"f_inequc_idx", false, ...
"df_inequc_idx", false, ...
"f_equc_idx", false, ...
"df_equc_idx", false, ...
"TolFun", stol_default, ...
"MaxIter", [], ...
"Display", "off", ...
"Algorithm", "lm_feasible", ...
"parallel_local", false, ... # Matlabs UseParallel
# works differently
"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, "grad_objf_pstruct", f_pstruct);
hessian_pstruct = optimget (settings, "hessian_objf_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, "f_inequc_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, "f_equc_idx", false))
f_genecstr = @ (p, varargin) apply_idx_if_given ...
(f_genecstr (p, varargin{:}), varargin{:});
endif
if (user_df_gencstr)
if (! optimget (settings, "df_inequc_idx", false))
df_gencstr = @ (varargin) df_gencstr (varargin{:})(varargin{2}, :);
endif
else
df_inequc_pstruct = false;
endif
if (user_df_genecstr)
if (! optimget (settings, "df_equc_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
if (any (diffp <= 0))
error ("some elements of 'diffp' non-positive");
endif
if (cstep <= 0)
error ("'cstep' non-positive");
endif
if ((hook.TolFun = optimget (settings, "TolFun", stol_default)) < 0)
error ("'TolFun' negative");
endif
if (any (fract_prec < 0))
error ("some elements of 'fract_prec' negative");
endif
if (any (max_fract_change < 0))
error ("some elements of 'max_fract_change' negative");
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
parallel_local = optimget (settings, "parallel_local", false);
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, parallel_local}, ...
{"diffp", "diff_onesided", "lbound", "ubound", ...
"plabels", "fixed", "h", "parallel_local"}, ...
2, hook));
else
dfdp = @ (p, hook) ...
dfdp (p, cell2fields ...
({diffp, diff_onesided, orig_lbound, orig_ubound, ...
plabels, assign(orig_fixed, nonfixed, hook.fixed), ...
cstep, parallel_local}, ...
{"diffp", "diff_onesided", "lbound", "ubound", ...
"plabels", "fixed", "h", "parallel_local"}, ...
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, parallel_local}, ...
{"diffp", "diff_onesided", "lbound", "ubound", ...
"plabels", "fixed", "h", "parallel_local"}, ...
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, parallel_local}, ...
{"diffp", "diff_onesided", "lbound", "ubound", ...
"plabels", "fixed", "h", "parallel_local"}, ...
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, parallel_local}, ...
{"diffp", "diff_onesided", "lbound", "ubound", ...
"plabels", "fixed", "h", "parallel_local"}, ...
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, parallel_local}, ...
{"diffp", "diff_onesided", "lbound", "ubound", ...
"plabels", "fixed", "h", "parallel_local"}, ...
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")
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