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annotate scripts/ode/private/kahan.m @ 20584:eb9e2d187ed2

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maint: Use Octave coding conventions in scripts/ode/private dir. * AbsRel_Norm.m, fuzzy_compare.m, hermite_quartic_interpolation.m, integrate_adaptive.m, integrate_const.m, integrate_n_steps.m, kahan.m, ode_struct_value_check.m, odepkg_event_handle.m, odepkg_structure_check.m, runge_kutta_45_dorpri.m, starting_stepsize.m: Wrap long lines to < 80 chars. Use double quotes rather than single quotes where possible. Use ';' at end of keywords "return;" and "break;" Use '##" for stand-alone comments and '#' for end-of-line comments. Use two spaces after period before starting new sentence. Use '!' instead of '~' for logical negation. Use specific form of end (endif, endfor, etc.). Don't use line continuation marker '...' unless necessary.
author Rik <rik@octave.org>
date Sun, 04 Oct 2015 22:18:54 -0700
parents 25623ef2ff4f
children
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1 ## Copyright (C) 2013, Roberto Porcu' <roberto.porcu@polimi.it>
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {@var{sum} =} kahan (@var{sum}, @var{comp}, @var{temp})
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21 ## @deftypefnx {Function File} {[@var{sum}, @var{comp}] =} kahan (@var{sum}, @var{comp}, @var{temp})
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22 ##
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23 ## This function is the implementation of the Kahan summation algorithm,
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24 ## also known as compensated summation.
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25 ##
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26 ## It significantly reduces the numerical error in the total obtained by adding
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27 ## a sequence of finite precision floating point numbers, compared to the
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28 ## obvious approach. For more details
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29 ## see @url{http://en.wikipedia.org/wiki/Kahan_summation_algorithm}.
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30 ## This function is called in @command{integrate_adaptive} and in
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31 ## @command{integrate_const} to better catch equality comparisons.
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32 ##
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33 ## The first input argument is the variable that will contain the summation,
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34 ## so that is also returned as first output argument in order to reuse it in
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35 ## next calls to kahan function.
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36 ##
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37 ## The second input argument contains the compensation term and it is returned
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38 ## as second output argument so that it can be reused in the next calls of the
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39 ## same computation.
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40 ##
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41 ## The third input argument is the variable that contains the term to be added
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42 ## to @var{Sum}.
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43 ## @end deftypefn
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44
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45 function [Sum, comp] = kahan (Sum, comp, term)
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46
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47 y = term - comp;
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48 t = Sum + y;
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49 comp = (t - Sum) - y;
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50 Sum = t;
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51
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52 endfunction
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53