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## Copyright (C) 2010-2014 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{fy}, @var{cvg}, @var{outp}] =} nonlin_curvefit (@var{f}, @var{pin}, @var{x}, @var{y})
## @deftypefnx {Function File} {[@var{p}, @var{fy}, @var{cvg}, @var{outp}] =} nonlin_curvefit (@var{f}, @var{pin}, @var{x}, @var{y}, @var{settings})
## Frontend for nonlinear fitting of values, computed by a model
## function, to observed values.
##
## Please refer to the description of @code{nonlin_residmin}. The
## differences to @code{nonlin_residmin} are the additional arguments
## @var{x} (independent values, mostly, but not necessarily, an array of
## the same dimensions or the same number of rows as @var{y}) and
## @var{y} (array of observations), the returned value @var{fy} (final
## guess for observed values) instead of @var{resid}, that the model
## function has a second obligatory argument which will be set to
## @var{x} and is supposed to return guesses for the observations (with
## the same dimensions), and that the possibly user-supplied function
## for the jacobian of the model function has also a second obligatory
## argument which will be set to @var{x}.
##
## @c The following block will be cut out in the package info file.
## @c BEGIN_CUT_TEXINFO
##
## Also, if the setting @code{user_interaction} is given, additional
## information is passed to these functions. Type @code{optim_doc
## ("Common optimization options")} for this setting.
##
## @c END_CUT_TEXINFO
##
## @seealso {nonlin_residmin}
## @end deftypefn
function [p, fy, cvg, outp] = nonlin_curvefit (f, pin, x, y, settings)
if (nargin == 1)
p = __nonlin_residmin__ (f);
return;
endif
if (nargin < 4 || nargin > 5)
print_usage ();
endif
if (nargin == 4)
settings = struct ();
endif
if (! isempty (dfdp = optimget (settings, "dfdp")))
if (ischar (dfdp))
dfdp = str2func (dfdp);
endif
## settings = optimset \
## (settings, "dfdp", @ (p, varargin) dfdp (p, x, varargin{:}));
settings.dfdp = @ (p, varargin) dfdp (p, x, varargin{:});
endif
if (! isempty (uia = optimget (settings, "user_interaction", {})))
if (! iscell (uia))
uia = {uia};
endif
uia = cellfun (@ (f_handle) @ (p, v, s) ...
f_handle (p, cell2fields ({x, y},
{"model_x", "observations"},
2, v),
s),
uia(:), "UniformOutput", false);
settings.user_interaction = uia;
endif
[p, fy, cvg, outp] = __nonlin_residmin__ ...
(@ (p) f (p, x), pin, settings, struct ("observations", y));
fy += y;
endfunction
%!demo
%! ## Example for linear inequality constraints
%! ## (see also the same example in 'demo nonlin_residmin')
%!
%! ## independents and observations
%! indep = 1:5;
%! obs = [1, 2, 4, 7, 14];
%! ## model function:
%! f = @ (p, x) p(1) * exp (p(2) * x);
%! ## initial values:
%! init = [.25; .25];
%! ## linear constraints, A.' * parametervector + B >= 0
%! A = [1; -1]; B = 0; # p(1) >= p(2);
%! settings = optimset ("inequc", {A, B});
%!
%! ## start optimization
%! [p, model_values, cvg, outp] = nonlin_curvefit (f, init, indep, obs, settings)
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