1## Copyright (C) 2000 Ben Sapp <bsapp@lanl.gov>
2## Copyright (C) 2002 Paul Kienzle <pkienzle@gmail.com>
3##
4## This program is free software; you can redistribute it and/or modify it under
5## the terms of the GNU General Public License as published by the Free Software
6## Foundation; either version 3 of the License, or (at your option) any later
7## version.
8##
9## This program is distributed in the hope that it will be useful, but WITHOUT
10## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
11## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
12## details.
13##
14## You should have received a copy of the GNU General Public License along with
15## this program; if not, see <http://www.gnu.org/licenses/>.
16
17## -*- texinfo -*-
18## @deftypefn {Function File} {@var{xmin} =} nrm (@var{f},@var{x0})
19## Using @var{x0} as a starting point find a minimum of the scalar
20## function @var{f}.  The Newton-Raphson method is used.
21## @end deftypefn
22
23## Reference: David G Luenberger's Linear and Nonlinear Programming
24
25function x = nrm(f,x,varargin)
26  velocity = 1;
27  acceleration = 1;
28
29  h = 0.01;
30  while(abs(velocity) > 0.0001)
31    fx = feval(f,x,varargin{:});
32    fxph = feval(f,x+h,varargin{:});
33    fxmh = feval(f,x-h,varargin{:});
34    velocity = (fxph - fxmh)/(2*h);
35    acceleration = (fxph - 2*fx + fxmh)/(h^2);
36    x = x - velocity/abs(acceleration);
37  endwhile
38endfunction
39