On Tue, Nov 29, 2011 at 11:49:51AM -0500, Nir Krakauer wrote:
> Dear Olaf,
>
> Here is a new version that addresses your remarks.
>
> To avoid eliciting a warning, I think optimset would need a new
> option, which I've called SearchDirections, to hold the initial set of
> direction vectors.
>
> Best,
>
> Nir
Looks nice. I've made some minor changes. When I made a patch, I saw
that almost each line was changed due to stylistic changes
(indentation). So I attach the whole changed file and describe the
changes here:
- inserted option handling formalism at the beginning (must be in)
- changed @ -> @@ for texinfo (one was forgotten)
- changed some .^ to ^, since scalar operation, dot not necessary
The rest is stylistic, but partially makes life easier for others:
- inserted space before (
- changed end to end<if|for|while|_try_catch>
- for emacs Octave mode: changed # to ## for comment on separate line,
and changed ' to "
- changed % -> #
- changed ~ -> !
- 'if' always with parantheses
- indentation only by 2
I could commit it. But for the case you want to make some changes or
fixes later, or produce additional code, have you thought of asking
for an SVN account to be able to do it yourself? Also, the SVN logfile
would list you at the first place then for the commit. (But the
decision on accounts is not mine.)
If you want to get an account, you have to ask on this list. Maybe it
is better to start a new thread for this, but a reference to the
current thread should be given so your code contributiton can be seen.
If you should commit yourself, please add a line 'powell' in the INDEX
file and change the 'Date:' entry in the DESCRIPTION file to current
date before the commit (the 'Version:' entry should only be changed
after a release).
Olaf
> On Sat, Nov 26, 2011 at 4:19 PM, Olaf Till <olaf.t...@uni-jena.de> wrote:
>
> > But a few remarks to some coding aspects.
> >
> > - It is now obsolete (and should
> > not be done in new code) to have an argument ('args' in your case) with
> > extra arguments for the user function. These extra arguments can be passed
> > using anonymous functions, e.g.
> >
> > optimizer (@ (x) user_function (x, extra_argument, ...), ...)
> >
> > and need not be cared for by the optimizer. Only the argument which is
> > optimized is to be cared for
> >
> > - For the optimization functions of core Octave, 'optimset' is now used
> > for handling optimization options. In the optim package, some functions
> > (which were programmed before Octaves 'optimset' was available)
> > have different mechanisms of option handling. But this makes things more
> > complicated. In new code as yours, we should stick to some standard of
> > option handling. And as things stand now, the standard is Octaves
> > 'optimset'.
> > So I think you should re-consider the handling of the 'control' argument.
> > Note that if there is a _good_ reason (which possibly should be discussed
> > on the list) new optimset options can be defined.
> >
> > Olaf
## Copyright (C) 2011 Nir Krakauer
##
## 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{obj_value}, @var{convergence},
@var{iters}, @var{nevs}] = powell (@var{f}, @var{p0}, @var{control})
##powell: implements a direction-set (Powell's) method for multidimensional
minimization of a function without calculation of the gradient [1, 2]
##
## @subheading Arguments
##
## @itemize @bullet
## @item
## @var{f}: name of function to minimize (string or handle), which should
accept one input variable (see example for how to pass on additional input
arguments)
##
## @item
## @var{p0}: An initial value of the function argument to minimize
##
## @item
## @var{options}: an optional structure, which can be generated by optimset,
with some or all of the following fields:
## @itemize @minus
## @item
## MaxIter: maximum iterations (positive integer, or -1 or Inf for
unlimited (default))
## @item
## TolFun: minimum amount by which function value must decrease in each
iteration to continue (default is 1E-8)
## @item
## MaxFunEvals: maximum function evaluations (positive integer, or -1 or
Inf for unlimited (default))
## @item
## SearchDirections: an n*n matrix whose columns contain the initial set
of (presumably orthogonal) directions to minimize along, where n is the number
of elements in the argument to be minimized for; or an n*1 vector of magnitudes
for the initial directions (defaults to the set of unit direction vectors)
## @end itemize
## @end itemize
##
## @subheading Examples
##
## @example
## @group
## y = @@(x, s) x(1) ^ 2 + x(2) ^ 2 + s;
## o = optimset('MaxIter', 100, 'TolFun', 1E-10);
## s = 1;
## [x_optim, y_min, conv, iters, nevs] = powell(@@(x) y(x, s), [1 0.5], o);
%pass y wrapped in an anonymous function so that all other arguments to y,
which are held constant, are set
## %should return something like x_optim = [4E-14 3E-14], y_min = 1, conv = 1,
iters = 2, nevs = 24
## @end group
##
## @end example
##
## @subheading Returns:
##
## @itemize @bullet
## @item
## @var{p}: the minimizing value of the function argument
## @item
## @var{obj_value}: the value of @var{f}() at @var{p}
## @item
## @var{convergence}: 1 if normal convergence, 0 if not
## @item
## @var{iters}: number of iterations performed
## @item
## @var{nevs}: number of function evaluations
## @end itemize
##
## @subheading References
##
## @enumerate
## @item
## Powell MJD (1964), An efficient method for finding the minimum of a function
of several variables without calculating derivatives, @cite{Computer Journal},
7 :155-162
##
## @item
## Press, WH; Teukolsky, SA; Vetterling, WT; Flannery, BP (1992).
@cite{Numerical Recipes in Fortran: The Art of Scientific Computing} (2nd Ed.).
New York: Cambridge University Press (Section 10.5)
## @end enumerate
## @end deftypefn
## Author: Nir Krakauer <nkraka...@ccny.cuny.edu>
## Description: Multidimensional minimization (direction-set method)
## PKG_ADD: __all_opts__ ("powell");
function [p, obj_value, convergence, iters, nevs] = powell (f, p0, options);
if (nargin == 1 && ischar (f) && strcmp (f, "defaults"))
p = optimset ("MaxIter", Inf, \
"TolFun", 1e-8, \
"MaxFunEvals", Inf, \
"SearchDirections", []);
return;
endif
## check number of arguments
if ((nargin < 2) || (nargin > 3))
usage('powell: you must supply 2 or 3 arguments');
endif
## default or input values
if (nargin < 3)
options = struct ();
endif
xi_set = 0;
xi = optimget (options, 'SearchDirections');
if (! isempty (xi))
if (isvector (xi)) # assume that xi is is n*1 or 1*n
xi = diag (x);
endif
xi_set = 1;
endif
MaxIter = optimget (options, 'MaxIter', Inf);
if (MaxIter < 0) MaxIter = Inf; endif
MaxFunEvals = optimget (options, 'MaxFunEvals', Inf);
TolFun = optimget (options, 'TolFun', 1E-8);
nevs = 0;
iters = 0;
convergence = 0;
p = p0; # initial value of the argument being minimized
try
obj_value = f(p);
catch
error ("function does not exist or cannot be evaluated");
end_try_catch
nevs++;
n = numel (p); # number of dimensions to minimize over
xit = zeros (n, 1);
if (! xi_set)
xi = eye(n);
endif
## do an iteration
while (iters <= MaxIter && nevs <= MaxFunEvals && ! convergence)
iters++;
pt = p; # best point as iteration begins
fp = obj_value; # value of the objective function as iteration begins
ibig = 0; # will hold direction along which the objective function
decreased the most in this iteration
dlt = 0; # will hold decrease in objective function value in this iteration
for i = 1:n
xit = reshape (xi(:, i), size(p));
fptt = obj_value;
[a, obj_value, nev] = line_min (f, xit, {p});
nevs = nevs + nev;
p = p + a*xit;
change = fptt - obj_value;
if (change > dlt)
dlt = change;
ibig = i;
endif
endfor
if ( 2*abs(fp-obj_value) <= TolFun*(abs(fp) + abs(obj_value)) )
convergence = 1;
return
endif
if (iters == MaxIter)
disp ("iteration maximum exceeded");
return
endif
## attempt parabolic extrapolation
ptt = 2*p - pt;
xit = p - pt;
fptt = f(ptt);
nevs++;
if (fptt < fp) # check whether the extrapolation actually makes the
objective function smaller
t = 2 * (fp - 2*obj_value + fptt) * (fp-obj_value-dlt)^2 - dlt *
(fp-fptt)^2;
if (t < 0)
p = ptt;
[a, obj_value, nev] = line_min (f, xit, {p});
nevs = nevs + nev;
p = p + a*xit;
## add the net direction from this iteration to the direction set
xi(:, ibig) = xi(:, n);
xi(:, n) = xit(:);
endif
endif
endwhile
------------------------------------------------------------------------------
All the data continuously generated in your IT infrastructure
contains a definitive record of customers, application performance,
security threats, fraudulent activity, and more. Splunk takes this
data and makes sense of it. IT sense. And common sense.
http://p.sf.net/sfu/splunk-novd2d
_______________________________________________
Octave-dev mailing list
Octave-dev@lists.sourceforge.net
https://lists.sourceforge.net/lists/listinfo/octave-dev
