--- /dev/null
+## Copyright (C) 2000 Ben Sapp <bsapp@lanl.gov>
+## Copyright (C) 2002 Etienne Grossmann <etienne@egdn.net>
+## Copyright (C) 2011 Nir Krakauer nkrakauer@ccny.cuny.edu
+##
+## 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/>.
+
+## [a,fx,nev] = line_min (f, dx, args, narg, h, nev_max) - Minimize f() along dx
+##
+## INPUT ----------
+## f : string : Name of minimized function
+## dx : matrix : Direction along which f() is minimized
+## args : cell : Arguments of f
+## narg : integer : Position of minimized variable in args. Default=1
+## h : scalar : Step size to use for centered finite difference
+## approximation of first and second derivatives. Default=1E-3.
+## nev_max : integer : Maximum number of function evaluations. Default=30
+##
+## OUTPUT ---------
+## a : scalar : Value for which f(x+a*dx) is a minimum (*)
+## fx : scalar : Value of f(x+a*dx) at minimum (*)
+## nev : integer : Number of function evaluations
+##
+## (*) The notation f(x+a*dx) assumes that args == {x}.
+##
+## Reference: David G Luenberger's Linear and Nonlinear Programming
+
+function [a,fx,nev] = line_min (f, dx, args, narg, h, nev_max)
+ velocity = 1;
+ acceleration = 1;
+
+ if (nargin < 4) narg = 1; endif
+ if (nargin < 5) h = 0.001; endif
+ if (nargin < 6) nev_max = 30; endif
+
+ nev = 0;
+ x = args{narg};
+ a = 0;
+
+ min_velocity_change = 0.000001;
+
+ while (abs (velocity) > min_velocity_change && nev < nev_max)
+ fx = feval (f,args{1:narg-1}, x+a*dx, args{narg+1:end});
+ fxph = feval (f,args{1:narg-1}, x+(a+h)*dx, args{narg+1:end});
+ fxmh = feval (f,args{1:narg-1}, x+(a-h)*dx, args{narg+1:end});
+ if (nev == 0)
+ fx0 = fx;
+ endif
+
+ velocity = (fxph - fxmh)/(2*h);
+ acceleration = (fxph - 2*fx + fxmh)/(h^2);
+ if abs(acceleration) <= eps, acceleration = 1; end # Don't do div by zero
+ # Use abs(accel) to avoid problems due to
+ # concave function
+ a = a - velocity/abs(acceleration);
+ nev += 3;
+ endwhile
+
+ fx = feval (f, args{1:narg-1}, x+a*dx, args{narg+1:end});
+ nev++;
+ if fx >= fx0 # if no improvement, return the starting value
+ a = 0;
+ fx = fx0;
+ endif
+
+ if (nev >= nev_max)
+ disp ("line_min: maximum number of function evaluations reached")
+ endif
+
+endfunction
+
+## Rem : Although not clear from the code, the returned a always seems to
+## correspond to (nearly) optimal fx.