1 ## Copyright (C) 2000 Ben Sapp <bsapp@lanl.gov>
2 ## Copyright (C) 2002 Paul Kienzle <pkienzle@gmail.com>
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
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
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/>.
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.
23 ## Reference: David G Luenberger's Linear and Nonlinear Programming
25 function x = nrm(f,x,varargin)
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);