Mercurial > octave-nkf
annotate scripts/ode/private/kahan.m @ 20570:6256f6e366ac
Fix copyright text in private ode functions
* script/ode/private/*.m: Fox the copyright text.
author | Carlo de Falco <carlo.defalco@polimi.it> |
---|---|
date | Fri, 02 Oct 2015 05:50:43 +0200 |
parents | fcb792acab9b |
children | 25623ef2ff4f |
rev | line source |
---|---|
20568
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
1 ## Copyright (C) 2013, Roberto Porcu' <roberto.porcu@polimi.it> |
20570
6256f6e366ac
Fix copyright text in private ode functions
Carlo de Falco <carlo.defalco@polimi.it>
parents:
20568
diff
changeset
|
2 ## |
6256f6e366ac
Fix copyright text in private ode functions
Carlo de Falco <carlo.defalco@polimi.it>
parents:
20568
diff
changeset
|
3 ## This file is part of Octave. |
20568
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
4 ## |
20570
6256f6e366ac
Fix copyright text in private ode functions
Carlo de Falco <carlo.defalco@polimi.it>
parents:
20568
diff
changeset
|
5 ## Octave is free software; you can redistribute it and/or modify it |
6256f6e366ac
Fix copyright text in private ode functions
Carlo de Falco <carlo.defalco@polimi.it>
parents:
20568
diff
changeset
|
6 ## under the terms of the GNU General Public License as published by |
6256f6e366ac
Fix copyright text in private ode functions
Carlo de Falco <carlo.defalco@polimi.it>
parents:
20568
diff
changeset
|
7 ## the Free Software Foundation; either version 3 of the License, or (at |
6256f6e366ac
Fix copyright text in private ode functions
Carlo de Falco <carlo.defalco@polimi.it>
parents:
20568
diff
changeset
|
8 ## your option) any later version. |
20568
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
9 ## |
20570
6256f6e366ac
Fix copyright text in private ode functions
Carlo de Falco <carlo.defalco@polimi.it>
parents:
20568
diff
changeset
|
10 ## Octave is distributed in the hope that it will be useful, but |
6256f6e366ac
Fix copyright text in private ode functions
Carlo de Falco <carlo.defalco@polimi.it>
parents:
20568
diff
changeset
|
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
6256f6e366ac
Fix copyright text in private ode functions
Carlo de Falco <carlo.defalco@polimi.it>
parents:
20568
diff
changeset
|
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
6256f6e366ac
Fix copyright text in private ode functions
Carlo de Falco <carlo.defalco@polimi.it>
parents:
20568
diff
changeset
|
13 ## General Public License for more details. |
20568
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
14 ## |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
15 ## You should have received a copy of the GNU General Public License |
20570
6256f6e366ac
Fix copyright text in private ode functions
Carlo de Falco <carlo.defalco@polimi.it>
parents:
20568
diff
changeset
|
16 ## along with Octave; see the file COPYING. If not, see |
6256f6e366ac
Fix copyright text in private ode functions
Carlo de Falco <carlo.defalco@polimi.it>
parents:
20568
diff
changeset
|
17 ## <http://www.gnu.org/licenses/>. |
20568
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
18 |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
19 ## -*- texinfo -*- |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
20 ## @deftypefn {Command} {[@var{sum}] =} kahan (@var{sum}, |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
21 ## @var{comp}, @var{temp}) |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
22 ## @deftypefnx {Command} {[@var{sum}, @var{comp}] =} kahan (@var{sum}, |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
23 ## @var{comp}, @var{temp}) |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
24 ## |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
25 ## This function is the implementation of the Kahan summation algorithm, |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
26 ## also known as compensated summation. It significantly reduces the numerical |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
27 ## error in the total obtained by adding a sequence of finite precision |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
28 ## floating point numbers, compared to the obvious approach. For more details |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
29 ## see @url{http://en.wikipedia.org/wiki/Kahan_summation_algorithm}. |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
30 ## This function is called in @command{integrate_adaptive} and in |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
31 ## @command{integrate_const} to better catch equality comparisons. |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
32 ## |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
33 ## The first input argument is the variable that will contain the summation, |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
34 ## so that is also returned as first output argument in order to reuse it in |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
35 ## next calls to kahan function. |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
36 ## |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
37 ## The second input argument contains the compensation term and it is returned |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
38 ## as second output argument so that it can be reused in the next calls |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
39 ## of the same computation. |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
40 ## |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
41 ## The third input argument is the variable that contains the term to |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
42 ## be added to @var{Sum}. |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
43 ## @end deftypefn |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
44 |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
45 function [Sum, comp] = kahan (Sum, comp, term) |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
46 |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
47 y = term - comp; |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
48 t = Sum + y; |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
49 comp = (t - Sum) - y; |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
50 Sum = t; |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
51 |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
52 endfunction |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
53 |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
54 ## Local Variables: *** |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
55 ## mode: octave *** |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
56 ## End: *** |