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maint: Update copyright dates in all source files.
author John W. Eaton <jwe@octave.org>
date Fri, 30 Mar 2018 09:19:05 -0400
parents 194eb4bd202b
children 00f796120a6d
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1 ## Copyright (C) 2013-2018 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
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8 ## (at 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
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13 ## GNU 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 ## <https://www.gnu.org/licenses/>.
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19 ## -*- texinfo -*-
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20 ## @deftypefn {} {@var{sum} =} kahan (@var{sum}, @var{comp}, @var{term})
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21 ## @deftypefnx {} {[@var{sum}, @var{comp}] =} kahan (@var{sum}, @var{comp}, @var{term})
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22 ##
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23 ## This function implements the Kahan summation algorithm, also known as
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24 ## compensated summation.
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25 ##
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26 ## The algorithm significantly reduces the numerical error in the total
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27 ## obtained by adding a sequence of finite precision floating point numbers,
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28 ## compared to the straightforward 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 by @code{integrate_adaptive} to better catch
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31 ## 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 ## This variable is also returned as the first output argument in order to
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35 ## reuse it in subsequent calls to @code{kahan} function.
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36 ##
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37 ## The second input argument contains the compensation term and is returned
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38 ## as the second output argument so that it can be reused in future calls of
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39 ## the same summation.
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40 ##
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41 ## The third input argument @var{term} is the variable to be added to
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42 ## @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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52 endfunction