octave-libgccjit: scripts/optimization/fminunc.m annotate

annotate scripts/optimization/fminunc.m @ 18609:923614060f1d stable

fminunc.m: Improve documentation. * fminunc.m: Improve documentation.

author	Rik <rik@octave.org>
date	Tue, 01 Apr 2014 07:06:55 -0700
parents	cdcf66f4e244
children	e275d15c27b5

rev	line source
17744 d63878346099 maint: Update copyright notices for release. John W. Eaton <jwe@octave.org> parents: 17338 diff changeset	1 ## Copyright (C) 2008-2013 VZLU Prague, a.s.
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	2 ##
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	3 ## This file is part of Octave.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	4 ##
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	6 ## under the terms of the GNU General Public License as published by
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	8 ## your option) any later version.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	9 ##
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	13 ## General Public License for more details.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	14 ##
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	15 ## You should have received a copy of the GNU General Public License
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	16 ## along with Octave; see the file COPYING. If not, see
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	17 ## <http://www.gnu.org/licenses/>.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	18 ##
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	19 ## Author: Jaroslav Hajek <highegg@gmail.com>
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	20
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	21 ## -- texinfo --
10687 a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	22 ## @deftypefn {Function File} {} fminunc (@var{fcn}, @var{x0})
a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	23 ## @deftypefnx {Function File} {} fminunc (@var{fcn}, @var{x0}, @var{options})
18608 cdcf66f4e244 fminunc.m: Fix typo in header documentation (bug #42011). Massimiliano Fasi <mogrob.sanit@gmail.com> parents: 17744 diff changeset	24 ## @deftypefnx {Function File} {[@var{x}, @var{fval}, @var{info}, @var{output}, @var{grad}, @var{hess}] =} fminunc (@var{fcn}, @dots{})
10793 be55736a0783 Grammarcheck the documentation from m-files. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	25 ## Solve an unconstrained optimization problem defined by the function
be55736a0783 Grammarcheck the documentation from m-files. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	26 ## @var{fcn}.
14895 e0525ecf156e Add new function fminsearch.m Andy Adler <andy@analyti.ca> parents: 14868 diff changeset	27 ##
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	28 ## @var{fcn} should accept a vector (array) defining the unknown variables,
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	29 ## and return the objective function value, optionally with gradient.
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	30 ## @code{fminunc} attempts to determine a vector @var{x} such that
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	31 ## @code{@var{fcn} (@var{x})} is a local minimum. @var{x0} determines a
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	32 ## starting guess. The shape of @var{x0} is preserved in all calls to
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	33 ## @var{fcn}, but otherwise is treated as a column vector.
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	34 ## @var{options} is a structure specifying additional options.
9212 6feb27c38da1 support central differences in fminunc and fsolve Jaroslav Hajek <highegg@gmail.com> parents: 9207 diff changeset	35 ## Currently, @code{fminunc} recognizes these options:
17281 bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 14895 diff changeset	36 ## @qcode{"FunValCheck"}, @qcode{"OutputFcn"}, @qcode{"TolX"},
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 14895 diff changeset	37 ## @qcode{"TolFun"}, @qcode{"MaxIter"}, @qcode{"MaxFunEvals"},
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 14895 diff changeset	38 ## @qcode{"GradObj"}, @qcode{"FinDiffType"},
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 14895 diff changeset	39 ## @qcode{"TypicalX"}, @qcode{"AutoScaling"}.
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	40 ##
17281 bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 14895 diff changeset	41 ## If @qcode{"GradObj"} is @qcode{"on"}, it specifies that @var{fcn},
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	42 ## when called with 2 output arguments, also returns the Jacobian matrix
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	43 ## of partial first derivatives at the requested point.
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	44 ## @code{TolX} specifies the termination tolerance for the unknown variables
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	45 ## @var{x}, while @code{TolFun} is a tolerance for the objective function
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	46 ## value @var{fval}. The default is @code{1e-7} for both options.
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	47 ##
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	48 ## For a description of the other options, see @code{optimset}.
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	49 ##
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	50 ## On return, @var{x} is the location of the minimum and @var{fval} contains
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	51 ## the value of the objective function at @var{x}. @var{info} may be one of the
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	52 ## following values:
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	53 ##
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	54 ## @table @asis
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	55 ## @item 1
10793 be55736a0783 Grammarcheck the documentation from m-files. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	56 ## Converged to a solution point. Relative gradient error is less than
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	57 ## specified by @code{TolFun}.
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	58 ##
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	59 ## @item 2
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	60 ## Last relative step size was less than @code{TolX}.
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	61 ##
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	62 ## @item 3
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	63 ## Last relative change in function value was less than @code{TolFun}.
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	64 ##
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	65 ## @item 0
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	66 ## Iteration limit exceeded---either maximum numer of algorithm iterations
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	67 ## @code{MaxIter} or maximum number of function evaluations @code{MaxFunEvals}.
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	68 ##
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	69 ## @item -1
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	70 ## Alogrithm terminated by @code{OutputFcn}.
10821 693e22af08ae Grammarcheck documentation of m-files Rik <octave@nomad.inbox5.com> parents: 10793 diff changeset	71 ##
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	72 ## @item -3
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	73 ## The trust region radius became excessively small.
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	74 ## @end table
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	75 ##
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	76 ## Optionally, @code{fminunc} can return a structure with convergence statistics
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	77 ## (@var{output}), the output gradient (@var{grad}) at the solution @var{x},
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	78 ## and approximate Hessian (@var{hess}) at the solution @var{x}.
9627 5bcfa0b346e8 fix extra outputs in fminunc Jaroslav Hajek <highegg@gmail.com> parents: 9623 diff changeset	79 ##
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	80 ## Notes: If have only a single nonlinear equation of one variable then using
923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	81 ## @code{fminbnd} is usually a much better idea. The algorithm used is a
14895 e0525ecf156e Add new function fminsearch.m Andy Adler <andy@analyti.ca> parents: 14868 diff changeset	82 ## gradient search which depends on the objective function being differentiable.
e0525ecf156e Add new function fminsearch.m Andy Adler <andy@analyti.ca> parents: 14868 diff changeset	83 ## If the function has discontinuities it may be better to use a derivative-free
e0525ecf156e Add new function fminsearch.m Andy Adler <andy@analyti.ca> parents: 14868 diff changeset	84 ## algorithm such as @code{fminsearch}.
e0525ecf156e Add new function fminsearch.m Andy Adler <andy@analyti.ca> parents: 14868 diff changeset	85 ## @seealso{fminbnd, fminsearch, optimset}
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	86 ## @end deftypefn
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	87
13027 b9a89ca0fb75 prevent optimization functions from setting ans in workspace at startup John W. Eaton <jwe@octave.org> parents: 12578 diff changeset	88 ## PKG_ADD: ## Discard result to avoid polluting workspace with ans at startup.
b9a89ca0fb75 prevent optimization functions from setting ans in workspace at startup John W. Eaton <jwe@octave.org> parents: 12578 diff changeset	89 ## PKG_ADD: [~] = __all_opts__ ("fminunc");
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	90
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	91 function [x, fval, info, output, grad, hess] = fminunc (fcn, x0, options = struct ())
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	92
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	93 ## Get default options if requested.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	94 if (nargin == 1 && ischar (fcn) && strcmp (fcn, 'defaults'))
14552 86854d032a37 maint: miscellaneous style fixes for .m files John W. Eaton <jwe@octave.org> parents: 14386 diff changeset	95 x = optimset ("MaxIter", 400, "MaxFunEvals", Inf,
86854d032a37 maint: miscellaneous style fixes for .m files John W. Eaton <jwe@octave.org> parents: 14386 diff changeset	96 "GradObj", "off", "TolX", 1e-7, "TolFun", 1e-7,
86854d032a37 maint: miscellaneous style fixes for .m files John W. Eaton <jwe@octave.org> parents: 14386 diff changeset	97 "OutputFcn", [], "FunValCheck", "off",
86854d032a37 maint: miscellaneous style fixes for .m files John W. Eaton <jwe@octave.org> parents: 14386 diff changeset	98 "FinDiffType", "central",
86854d032a37 maint: miscellaneous style fixes for .m files John W. Eaton <jwe@octave.org> parents: 14386 diff changeset	99 "TypicalX", [], "AutoScaling", "off");
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	100 return;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	101 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	102
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	103 if (nargin < 2 \|\| nargin > 3 \|\| ! ismatrix (x0))
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	104 print_usage ();
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	105 endif
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	106
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	107 if (ischar (fcn))
9464 e598248a060d safer str2func use in optim functions Jaroslav Hajek <highegg@gmail.com> parents: 9212 diff changeset	108 fcn = str2func (fcn, "global");
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	109 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	110
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	111 xsiz = size (x0);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	112 n = numel (x0);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	113
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	114 has_grad = strcmpi (optimget (options, "GradObj", "off"), "on");
9212 6feb27c38da1 support central differences in fminunc and fsolve Jaroslav Hajek <highegg@gmail.com> parents: 9207 diff changeset	115 cdif = strcmpi (optimget (options, "FinDiffType", "central"), "central");
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	116 maxiter = optimget (options, "MaxIter", 400);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	117 maxfev = optimget (options, "MaxFunEvals", Inf);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	118 outfcn = optimget (options, "OutputFcn");
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	119
10201 5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	120 ## Get scaling matrix using the TypicalX option. If set to "auto", the
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	121 ## scaling matrix is estimated using the jacobian.
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	122 typicalx = optimget (options, "TypicalX");
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	123 if (isempty (typicalx))
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	124 typicalx = ones (n, 1);
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	125 endif
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	126 autoscale = strcmpi (optimget (options, "AutoScaling", "off"), "on");
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	127 if (! autoscale)
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	128 dg = 1 ./ typicalx;
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	129 endif
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	130
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	131 funvalchk = strcmpi (optimget (options, "FunValCheck", "off"), "on");
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	132
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	133 if (funvalchk)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	134 ## Replace fcn with a guarded version.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	135 fcn = @(x) guarded_eval (fcn, x);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	136 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	137
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	138 ## These defaults are rather stringent. I think that normally, user
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	139 ## prefers accuracy to performance.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	140
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	141 macheps = eps (class (x0));
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	142
10201 5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	143 tolx = optimget (options, "TolX", 1e-7);
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	144 tolf = optimget (options, "TolFun", 1e-7);
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	145
9623 bc0739d02724 update initial TR step for fsolve and fminunc Jaroslav Hajek <highegg@gmail.com> parents: 9464 diff changeset	146 factor = 0.1;
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	147 ## FIXME: TypicalX corresponds to user scaling (???)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	148 autodg = true;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	149
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	150 niter = 1;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	151 nfev = 0;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	152
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	153 x = x0(:);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	154 info = 0;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	155
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	156 ## Initial evaluation.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	157 fval = fcn (reshape (x, xsiz));
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	158 n = length (x);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	159
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	160 if (! isempty (outfcn))
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	161 optimvalues.iter = niter;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	162 optimvalues.funccount = nfev;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	163 optimvalues.fval = fval;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	164 optimvalues.searchdirection = zeros (n, 1);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	165 state = 'init';
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	166 stop = outfcn (x, optimvalues, state);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	167 if (stop)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	168 info = -1;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	169 break;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	170 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	171 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	172
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	173 nsuciter = 0;
9199 399884c9d4a1 import the step adaptation strategy from fsolve to fminunc Jaroslav Hajek <highegg@gmail.com> parents: 9084 diff changeset	174 lastratio = 0;
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	175
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	176 grad = [];
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	177
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	178 ## Outer loop.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	179 while (niter < maxiter && nfev < maxfev && ! info)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	180
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	181 grad0 = grad;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	182
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	183 ## Calculate function value and gradient (possibly via FD).
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	184 if (has_grad)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	185 [fval, grad] = fcn (reshape (x, xsiz));
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	186 grad = grad(:);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	187 nfev ++;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	188 else
10201 5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	189 grad = __fdjac__ (fcn, reshape (x, xsiz), fval, typicalx, cdif)(:);
9212 6feb27c38da1 support central differences in fminunc and fsolve Jaroslav Hajek <highegg@gmail.com> parents: 9207 diff changeset	190 nfev += (1 + cdif) * length (x);
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	191 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	192
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	193 if (niter == 1)
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	194 ## Initialize by identity matrix.
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	195 hesr = eye (n);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	196 else
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	197 ## Use the damped BFGS formula.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	198 y = grad - grad0;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	199 sBs = sumsq (w);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	200 Bs = hesr'*w;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	201 sy = y'*s;
9633 ecc2c556f844 simplify damped BFGS formula Jaroslav Hajek <highegg@gmail.com> parents: 9631 diff changeset	202 theta = 0.8 / max (1 - sy / sBs, 0.8);
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	203 r = theta * y + (1-theta) * Bs;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	204 hesr = cholupdate (hesr, r / sqrt (s'*r), "+");
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	205 [hesr, info] = cholupdate (hesr, Bs / sqrt (sBs), "-");
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	206 if (info)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	207 hesr = eye (n);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	208 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	209 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	210
10201 5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	211 if (autoscale)
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	212 ## Second derivatives approximate the hessian.
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	213 d2f = norm (hesr, 'columns').';
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	214 if (niter == 1)
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	215 dg = d2f;
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	216 else
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	217 ## FIXME: maybe fixed lower and upper bounds?
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	218 dg = max (0.1*dg, d2f);
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	219 endif
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	220 endif
5c66978f3fdf support TypicalX and AutoScaling in fsolve/fminunc, don't autoscale by default Jaroslav Hajek <highegg@gmail.com> parents: 9899 diff changeset	221
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	222 if (niter == 1)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	223 xn = norm (dg .* x);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	224 ## FIXME: something better?
9628 73e6ad869f08 further correct initial TR step strategy Jaroslav Hajek <highegg@gmail.com> parents: 9627 diff changeset	225 delta = factor * max (xn, 1);
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	226 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	227
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	228 ## FIXME: why tolfnxn? If abs (e) ~ abs(x) * eps is a vector
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	229 ## of perturbations of x, then norm (hesre) <= epsxn, i.e. by
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	230 ## tolf ~ eps we demand as much accuracy as we can expect.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	231 if (norm (grad) <= tolfnxn)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	232 info = 1;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	233 break;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	234 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	235
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	236 suc = false;
9207 25f50d2d76b3 improve TR updating strategy for fminunc and fsolve Jaroslav Hajek <highegg@gmail.com> parents: 9199 diff changeset	237 decfac = 0.5;
25f50d2d76b3 improve TR updating strategy for fminunc and fsolve Jaroslav Hajek <highegg@gmail.com> parents: 9199 diff changeset	238
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	239 ## Inner loop.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	240 while (! suc && niter <= maxiter && nfev < maxfev && ! info)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	241
9631 00958d0c4e3c split __dogleg__ > __doglegm__ Jaroslav Hajek <highegg@gmail.com> parents: 9628 diff changeset	242 s = - __doglegm__ (hesr, grad, dg, delta);
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	243
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	244 sn = norm (dg .* s);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	245 if (niter == 1)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	246 delta = min (delta, sn);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	247 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	248
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	249 fval1 = fcn (reshape (x + s, xsiz)) (:);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	250 nfev ++;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	251
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	252 if (fval1 < fval)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	253 ## Scaled actual reduction.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	254 actred = (fval - fval1) / (abs (fval1) + abs (fval));
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	255 else
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	256 actred = -1;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	257 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	258
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	259 w = hesr*s;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	260 ## Scaled predicted reduction, and ratio.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	261 t = 1/2 * sumsq (w) + grad'*s;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	262 if (t < 0)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	263 prered = -t/(abs (fval) + abs (fval + t));
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	264 ratio = actred / prered;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	265 else
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	266 prered = 0;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	267 ratio = 0;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	268 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	269
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	270 ## Update delta.
14868 5d3a684236b0 maint: Use Octave coding conventions for cuddling parentheses in scripts directory Rik <octave@nomad.inbox5.com> parents: 14552 diff changeset	271 if (ratio < min (max (0.1, 0.8*lastratio), 0.9))
9207 25f50d2d76b3 improve TR updating strategy for fminunc and fsolve Jaroslav Hajek <highegg@gmail.com> parents: 9199 diff changeset	272 delta *= decfac;
25f50d2d76b3 improve TR updating strategy for fminunc and fsolve Jaroslav Hajek <highegg@gmail.com> parents: 9199 diff changeset	273 decfac ^= 1.4142;
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	274 if (delta <= 1e1machepsxn)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	275 ## Trust region became uselessly small.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	276 info = -3;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	277 break;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	278 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	279 else
9199 399884c9d4a1 import the step adaptation strategy from fsolve to fminunc Jaroslav Hajek <highegg@gmail.com> parents: 9084 diff changeset	280 lastratio = ratio;
9207 25f50d2d76b3 improve TR updating strategy for fminunc and fsolve Jaroslav Hajek <highegg@gmail.com> parents: 9199 diff changeset	281 decfac = 0.5;
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	282 if (abs (1-ratio) <= 0.1)
9207 25f50d2d76b3 improve TR updating strategy for fminunc and fsolve Jaroslav Hajek <highegg@gmail.com> parents: 9199 diff changeset	283 delta = 1.4142*sn;
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	284 elseif (ratio >= 0.5)
9207 25f50d2d76b3 improve TR updating strategy for fminunc and fsolve Jaroslav Hajek <highegg@gmail.com> parents: 9199 diff changeset	285 delta = max (delta, 1.4142*sn);
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	286 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	287 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	288
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	289 if (ratio >= 1e-4)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	290 ## Successful iteration.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	291 x += s;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	292 xn = norm (dg .* x);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	293 fval = fval1;
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	294 nsuciter++;
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	295 suc = true;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	296 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	297
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	298 niter ++;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	299
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	300 ## FIXME: should outputfcn be called only after a successful iteration?
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	301 if (! isempty (outfcn))
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	302 optimvalues.iter = niter;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	303 optimvalues.funccount = nfev;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	304 optimvalues.fval = fval;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	305 optimvalues.searchdirection = s;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	306 state = 'iter';
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	307 stop = outfcn (x, optimvalues, state);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	308 if (stop)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	309 info = -1;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	310 break;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	311 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	312 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	313
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	314 ## Tests for termination conditions. A mysterious place, anything
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	315 ## can happen if you change something here...
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	316
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	317 ## The rule of thumb (which I'm not sure M*b is quite following)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	318 ## is that for a tolerance that depends on scaling, only 0 makes
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	319 ## sense as a default value. But 0 usually means uselessly long
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	320 ## iterations, so we need scaling-independent tolerances wherever
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	321 ## possible.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	322
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	323 ## The following tests done only after successful step.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	324 if (ratio >= 1e-4)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	325 ## This one is classic. Note that we use scaled variables again,
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	326 ## but compare to scaled step, so nothing bad.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	327 if (sn <= tolx*xn)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	328 info = 2;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	329 ## Again a classic one.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	330 elseif (actred < tolf)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	331 info = 3;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	332 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	333 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	334
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	335 endwhile
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	336 endwhile
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	337
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	338 ## Restore original shapes.
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	339 x = reshape (x, xsiz);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	340
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	341 output.iterations = niter;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	342 output.successful = nsuciter;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	343 output.funcCount = nfev;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	344
9627 5bcfa0b346e8 fix extra outputs in fminunc Jaroslav Hajek <highegg@gmail.com> parents: 9623 diff changeset	345 if (nargout > 5)
5bcfa0b346e8 fix extra outputs in fminunc Jaroslav Hajek <highegg@gmail.com> parents: 9623 diff changeset	346 hess = hesr'*hesr;
5bcfa0b346e8 fix extra outputs in fminunc Jaroslav Hajek <highegg@gmail.com> parents: 9623 diff changeset	347 endif
5bcfa0b346e8 fix extra outputs in fminunc Jaroslav Hajek <highegg@gmail.com> parents: 9623 diff changeset	348
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	349 endfunction
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	350
18609 923614060f1d fminunc.m: Improve documentation. Rik <rik@octave.org> parents: 18608 diff changeset	351 ## A helper function that evaluates a function and checks for bad results.
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	352 function [fx, gx] = guarded_eval (fun, x)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	353 if (nargout > 1)
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	354 [fx, gx] = fun (x);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	355 else
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	356 fx = fun (x);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	357 gx = [];
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	358 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	359
14383 07c55bceca23 Fix guarded_eval() subfunction in fminunc (bug #35534). Olaf Till <olaf.till@uni-jena.de> parents: 14138 diff changeset	360 if (! (isreal (fx) && isreal (gx)))
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	361 error ("fminunc:notreal", "fminunc: non-real value encountered");
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	362 elseif (any (isnan (fx(:))))
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	363 error ("fminunc:isnan", "fminunc: NaN value encountered");
14386 59aab666f2bf Extend "FunValCheck" option to optimization routines to detect Inf values. Rik <octave@nomad.inbox5.com> parents: 14383 diff changeset	364 elseif (any (isinf (fx(:))))
59aab666f2bf Extend "FunValCheck" option to optimization routines to detect Inf values. Rik <octave@nomad.inbox5.com> parents: 14383 diff changeset	365 error ("fminunc:isinf", "fminunc: Inf value encountered");
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	366 endif
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	367 endfunction
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	368
14386 59aab666f2bf Extend "FunValCheck" option to optimization routines to detect Inf values. Rik <octave@nomad.inbox5.com> parents: 14383 diff changeset	369
13305 63463570d9fe Add %!endfunction block keyword to test.m Rik <octave@nomad.inbox5.com> parents: 13027 diff changeset	370 %!function f = __rosenb (x)
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	371 %! n = length (x);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	372 %! f = sumsq (1 - x(1:n-1)) + 100 * sumsq (x(2:n) - x(1:n-1).^2);
13305 63463570d9fe Add %!endfunction block keyword to test.m Rik <octave@nomad.inbox5.com> parents: 13027 diff changeset	373 %!endfunction
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	374 %!test
13305 63463570d9fe Add %!endfunction block keyword to test.m Rik <octave@nomad.inbox5.com> parents: 13027 diff changeset	375 %! [x, fval, info, out] = fminunc (@__rosenb, [5, -5]);
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	376 %! tol = 2e-5;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	377 %! assert (info > 0);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	378 %! assert (x, ones (1, 2), tol);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	379 %! assert (fval, 0, tol);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	380 %!test
13305 63463570d9fe Add %!endfunction block keyword to test.m Rik <octave@nomad.inbox5.com> parents: 13027 diff changeset	381 %! [x, fval, info, out] = fminunc (@__rosenb, zeros (1, 4));
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	382 %! tol = 2e-5;
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	383 %! assert (info > 0);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	384 %! assert (x, ones (1, 4), tol);
b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	385 %! assert (fval, 0, tol);
14386 59aab666f2bf Extend "FunValCheck" option to optimization routines to detect Inf values. Rik <octave@nomad.inbox5.com> parents: 14383 diff changeset	386 %% Test FunValCheck works correctly
59aab666f2bf Extend "FunValCheck" option to optimization routines to detect Inf values. Rik <octave@nomad.inbox5.com> parents: 14383 diff changeset	387 %!assert (fminunc (@(x) x^2, 1, optimset ("FunValCheck", "on")), 0, eps)
59aab666f2bf Extend "FunValCheck" option to optimization routines to detect Inf values. Rik <octave@nomad.inbox5.com> parents: 14383 diff changeset	388 %!error <non-real value> fminunc (@(x) x + i, 1, optimset ("FunValCheck", "on"))
59aab666f2bf Extend "FunValCheck" option to optimization routines to detect Inf values. Rik <octave@nomad.inbox5.com> parents: 14383 diff changeset	389 %!error <NaN value> fminunc (@(x) x + NaN, 1, optimset ("FunValCheck", "on"))
59aab666f2bf Extend "FunValCheck" option to optimization routines to detect Inf values. Rik <octave@nomad.inbox5.com> parents: 14383 diff changeset	390 %!error <Inf value> fminunc (@(x) x + Inf, 1, optimset ("FunValCheck", "on"))
59aab666f2bf Extend "FunValCheck" option to optimization routines to detect Inf values. Rik <octave@nomad.inbox5.com> parents: 14383 diff changeset	391
9084 b7210faa3ed0 implement fminunc using factored trust-region BFGS Jaroslav Hajek <highegg@gmail.com> parents: diff changeset	392
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	393 ## Solve the double dogleg trust-region minimization problem:
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	394 ## Minimize 1/2norm(rx)^2 subject to the constraint norm(d.*x) <= delta,
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	395 ## x being a convex combination of the gauss-newton and scaled gradient.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	396
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	397 ## TODO: error checks
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	398 ## TODO: handle singularity, or leave it up to mldivide?
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	399
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	400 function x = __doglegm__ (r, g, d, delta)
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	401 ## Get Gauss-Newton direction.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	402 b = r' \ g;
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	403 x = r \ b;
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	404 xn = norm (d .* x);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	405 if (xn > delta)
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	406 ## GN is too big, get scaled gradient.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	407 s = g ./ d;
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	408 sn = norm (s);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	409 if (sn > 0)
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	410 ## Normalize and rescale.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	411 s = (s / sn) ./ d;
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	412 ## Get the line minimizer in s direction.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	413 tn = norm (r*s);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	414 snm = (sn / tn) / tn;
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	415 if (snm < delta)
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 10201 diff changeset	416 ## Get the dogleg path minimizer.
9899 9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	417 bn = norm (b);
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	418 dxn = delta/xn; snmd = snm/delta;
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	419 t = (bn/sn) * (bn/xn) * snmd;
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	420 t -= dxn * snmd^2 - sqrt ((t-dxn)^2 + (1-dxn^2)*(1-snmd^2));
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	421 alpha = dxn*(1-snmd^2) / t;
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	422 else
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	423 alpha = 0;
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	424 endif
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	425 else
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	426 alpha = delta / xn;
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	427 snm = 0;
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	428 endif
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	429 ## Form the appropriate convex combination.
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	430 x = alpha * x + ((1-alpha) * min (snm, delta)) * s;
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	431 endif
9f25290a35e8 more private function and subfunction changes John W. Eaton <jwe@octave.org> parents: 9758 diff changeset	432 endfunction
17338 1c89599167a6 maint: End m-files with 1 blank line. Rik <rik@octave.org> parents: 17281 diff changeset	433