/usr/share/octave/packages/3.2/optim-1.0.17/nrm.m is in octave-optim 1.0.17-1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 | ## Copyright (C) 2000 Ben Sapp. All rights reserved.
##
## 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 2, or (at your option) any
## later version.
##
## This 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.
## -*- 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
## Author: Ben Sapp <bsapp@lanl.gov>
## Reference: David G Luenberger's Linear and Nonlinear Programming
## 2002-01-28 Paul Kienzle
## * save two function evaluations by inlining the derivatives
## * pass through varargin{:} to the function
## 2002-03-13 Paul Kienzle
## * simplify update expression
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
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