Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / optim-1.2.0 / nrm.m

diff --git a/octave_packages/optim-1.2.0/nrm.m b/octave_packages/optim-1.2.0/nrm.m
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+## Copyright (C) 2000 Ben Sapp <bsapp@lanl.gov>
+## Copyright (C) 2002 Paul Kienzle <pkienzle@gmail.com>
+##
+## 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{xmin} =} nrm(@var{f},@var{x0})
+## Using @var{x0} as a starting point find a minimum of the scalar
+## function @var{f}.  The Newton-Raphson method is used.
+## @end deftypefn
+
+## Reference: David G Luenberger's Linear and Nonlinear Programming
+
+function x = nrm(f,x,varargin)
+  velocity = 1;
+  acceleration = 1;
+  
+  h = 0.01;
+  while(abs(velocity) > 0.0001)
+    fx = feval(f,x,varargin{:});
+    fxph = feval(f,x+h,varargin{:});
+    fxmh = feval(f,x-h,varargin{:});
+    velocity = (fxph - fxmh)/(2*h);
+    acceleration = (fxph - 2*fx + fxmh)/(h^2);
+    x = x - velocity/abs(acceleration);
+  endwhile
+endfunction