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(* $Id: partition.ml 759 2009-06-10 09:38:07Z ohl $
Copyright (C) 1999-2009 by
Wolfgang Kilian <kilian@hep.physik.uni-siegen.de>
Thorsten Ohl <ohl@physik.uni-wuerzburg.de>
Juergen Reuter <juergen.reuter@physik.uni-freiburg.de>
WHIZARD 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.
WHIZARD 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, write to the Free Software
Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. *)
let rcs = RCS.parse "Partition" ["Partitions"]
{ RCS.revision = "$Revision: 759 $";
RCS.date = "$Date: 2009-06-10 10:38:07 +0100 (Wed, 10 Jun 2009) $";
RCS.author = "$Author: ohl $";
RCS.source
= "$URL: file:///hepforge/repos/238/branches/ohl/omega-development/splitting-amplitudes/src/partition.ml $" }
(* All unordered pairs of integers with the same sum~$n$ in a given
range~$\{n_1,\ldots,n_2\}$:
\begin{equation}
\text{\ocwlowerid{pairs}}: (n, n_1, n_2) \to
\bigl\{ (i,j) \,\vert\, i+j=n
\land n_1\le i \le j \le n_2 \bigr\}
\end{equation} *)
let rec pairs' acc n1 n2 =
if n1 > n2 then
List.rev acc
else
pairs' ((n1, n2) :: acc) (succ n1) (pred n2)
let pairs sum min_n1 max_n2 =
let n1 = max min_n1 (sum - max_n2) in
let n2 = sum - n1 in
if n2 <= max_n2 then
pairs' [] n1 n2
else
[]
let rec tuples d sum n_min n_max =
if d <= 0 then
invalid_arg "tuples"
else if d > 1 then
tuples' d sum n_min n_max n_min
else if sum >= n_min && sum <= n_max then
[[sum]]
else
[]
and tuples' d sum n_min n_max n =
if n > n_max then
[]
else
List.fold_right (fun l ll -> (n :: l) :: ll)
(tuples (pred d) (sum - n) (max n_min n) n_max)
(tuples' d sum n_min n_max (succ n))
(* \begin{dubious}
When I find a little spare time, I can provide a dedicated implementation,
but we \emph{know} that [Impossible] is \emph{never} raised and the present
approach is just as good (except for a possible tiny inefficiency).
\end{dubious} *)
exception Impossible of string
let impossible name = raise (Impossible name)
let triples sum n_min n_max =
List.map (function [n1; n2; n3] -> (n1, n2, n3) | _ -> impossible "triples")
(tuples 3 sum n_min n_max)
(*i
* Local Variables:
* mode:caml
* indent-tabs-mode:nil
* page-delimiter:"^(\\* .*\n"
* End:
i*)

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