I've made a number of changes to line_min for compatibility with the
current Octave command set as well as for more efficient operation.
Please see the attached.
Best,
Nir
18c18
< ## args : list : List of argument of f
---
> ## args : cell : Cell array of arguments of f
42c42,53
< function [a,fx,nev] = line_min (f, dx, args, narg)
---
> ## 2007-11-20 Nir Krakauer
> ## * modified to limit the number of function evaluations
> ## * added a check to ensure that the function value returned was never more
> than the initial value
> ## 2008-07-05 Nir Krakauer
> ## * randomized the step size h
> ## 2008-11-24 Nir Krakauer
> ## * modified to take args as a cell array rather than a list and to use
> feval rather than leval, since lists are deprecated in Octave 3
> ## 2011-08-24 Nir Krakauer
> ## * modified to no longer use the function splice, which doesn't exist in
> Octave 3.4
> ##
>
> function [a,fx,nev] = line_min(f, dx, args, narg);
47a59
> nev_max = 30;
49c61,62
< h = 0.001; # Was 0.01 here
---
> h = exp(rand() - 0.5)*0.001; %0.001; # Was 0.01 here
> %%x = nth (args,narg);
53,56c66,78
< while (abs (velocity) > 0.000001)
< 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});
---
> while (abs (velocity) > 0.000001) && (nev < nev_max)
> %%fx = feval (f,splice(args, narg, 1, {x+a*dx}){:} );
> args_new = args; args_new{narg} = x+a*dx;
> fx = feval (f, args_new{:} );
> if nev == 0
> fx0 = fx;
> end
> args_new{narg} = x+(a+h)*dx;
> fxph = feval (f, args_new{:} );
> args_new{narg} = x+(a-h)*dx;
> fxmh = feval (f, args_new{:} );
> %%fxph = feval (f,splice(args, narg,1,{x+(a+h)*dx}){:} );
> %%fxmh = feval (f,splice(args, narg,1,{x+(a-h)*dx}){:} );
61c83
< # Use abs(accel) to avoid problems due to
---
> # Use abs(acceleration) to avoid problems due to
65a88,101
>
> args_new = args; args_new{narg} = x+a*dx;
> fx = feval (f, args_new{:} );
> %%fx = feval (f, splice(args, narg, 1,{x+a*dx}){:} )
> nev++;
> if fx >= fx0 %if no improvement, return the starting value
> a = 0;
> fx = fx0;
> end
>
> if (nev >= nev_max)
> disp('my_line_min: maximum number of function evaluations exceeded')
> end
>
69c105
< ## correspond to (nearly) optimal fx.
\ No newline at end of file
---
> ## correspond to (nearly) optimal fx.
## 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.
## [a,fx,nev] = line_min (f, dx, args, narg) - Minimize f() along dx
##
## INPUT ----------
## f : string : Name of minimized function
## dx : matrix : Direction along which f() is minimized
## args : cell : Cell array of arguments of f
## narg : integer : Position of minimized variable in args. Default=1
##
## 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 == list (x).
## Author: Ben Sapp <bs...@lanl.gov>
## Reference: David G Luenberger's Linear and Nonlinear Programming
##
## Changelog : -----------
## 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
## 2002-04-17 Etienne Grossmann <etie...@isr.ist.utl.pt>
## * Rename nrm.m to line_min.m (in order not to break dfp, which uses nrm)
## * Use list of args, suppress call to __pseudo_func__
## * Add nargs argument, assume args is a list
## * Change help text
## 2007-11-20 Nir Krakauer
## * modified to limit the number of function evaluations
## * added a check to ensure that the function value returned was never more than the initial value
## 2008-07-05 Nir Krakauer
## * randomized the step size h
## 2008-11-24 Nir Krakauer
## * modified to take args as a cell array rather than a list and to use feval rather than leval, since lists are deprecated in Octave 3
## 2011-08-24 Nir Krakauer
## * modified to no longer use the function splice, which doesn't exist in Octave 3.4
##
function [a,fx,nev] = line_min(f, dx, args, narg);
velocity = 1;
acceleration = 1;
if nargin < 4, narg = 1; end
nev_max = 30;
nev = 0;
h = exp(rand() - 0.5)*0.001; %0.001; # Was 0.01 here
%%x = nth (args,narg);
x = args{narg};
a = 0;
# was 1e-4
while (abs (velocity) > 0.000001) && (nev < nev_max)
%%fx = feval (f,splice(args, narg, 1, {x+a*dx}){:} );
args_new = args; args_new{narg} = x+a*dx;
fx = feval (f, args_new{:} );
if nev == 0
fx0 = fx;
end
args_new{narg} = x+(a+h)*dx;
fxph = feval (f, args_new{:} );
args_new{narg} = x+(a-h)*dx;
fxmh = feval (f, args_new{:} );
%%fxph = feval (f,splice(args, narg,1,{x+(a+h)*dx}){:} );
%%fxmh = feval (f,splice(args, narg,1,{x+(a-h)*dx}){:} );
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(acceleration) to avoid problems due to
# concave function
a = a - velocity/abs(acceleration);
nev += 3;
endwhile
args_new = args; args_new{narg} = x+a*dx;
fx = feval (f, args_new{:} );
%%fx = feval (f, splice(args, narg, 1,{x+a*dx}){:} )
nev++;
if fx >= fx0 %if no improvement, return the starting value
a = 0;
fx = fx0;
end
if (nev >= nev_max)
disp('my_line_min: maximum number of function evaluations exceeded')
end
endfunction
## Rem : Although not clear from the code, the returned a always seems to
## correspond to (nearly) optimal fx.
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