PageRank
From Wikimization
(Difference between revisions)
| Line 1: | Line 1: | ||
| + | [[Image:Gleich.jpg|thumb|right|793px|CSUM in Digital Signal Processing terms]] | ||
<pre> | <pre> | ||
function s=csum(x) | function s=csum(x) | ||
% CSUM Sum of elements using a compensated summation algorithm | % CSUM Sum of elements using a compensated summation algorithm | ||
% | % | ||
| - | % For large vectors, the native sum command in Matlab does not appear to | + | % For large vectors, the native sum command in Matlab does |
| - | + | % not appear to use a compensated summation algorithm which | |
| - | + | % can cause significant roundoff errors. | |
% | % | ||
| - | % This code implements a variant of Kahan's compensated | + | % This code implements a variant of Kahan's compensated |
| - | % which often takes about twice as long, but produces more accurate sums | + | % summation algorithm which often takes about twice as long, |
| - | + | % but produces more accurate sums when the number of | |
| + | % elements is large. | ||
% | % | ||
% See also SUM | % See also SUM | ||
| Line 21: | Line 23: | ||
% David Gleich, Stanford University, 2008 | % David Gleich, Stanford University, 2008 | ||
| - | + | s_hat=0; y=0; e=0; | |
for i=1:numel(x) | for i=1:numel(x) | ||
| - | + | s_hat_old = s_hat; | |
y = x(i) + e; | y = x(i) + e; | ||
| - | + | s_hat = s_hat_old + y; | |
| - | e = ( | + | e = (s_hat_old - s_hat) + y; |
end | end | ||
</pre> | </pre> | ||
Revision as of 20:49, 17 February 2009
function s=csum(x)
% CSUM Sum of elements using a compensated summation algorithm
%
% For large vectors, the native sum command in Matlab does
% not appear to use a compensated summation algorithm which
% can cause significant roundoff errors.
%
% This code implements a variant of Kahan's compensated
% summation algorithm which often takes about twice as long,
% but produces more accurate sums when the number of
% elements is large.
%
% See also SUM
%
% Example:
% v=rand(1e7,1);
% sum1 = sum(v);
% sum2 = csum(v);
% fprintf('sum1 = %18.16e\nsum2 = %18.16e\n', sum1, sum2);
% David Gleich, Stanford University, 2008
s_hat=0; y=0; e=0;
for i=1:numel(x)
s_hat_old = s_hat;
y = x(i) + e;
s_hat = s_hat_old + y;
e = (s_hat_old - s_hat) + y;
end