PageRank
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(New page: <pre> 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 summa...) |
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% David Gleich, Stanford University, 2008 | % David Gleich, Stanford University, 2008 | ||
| - | + | shat=0; y=0; e=0; | |
for i=1:numel(x) | for i=1:numel(x) | ||
| - | + | shat_old = shat; | |
| + | y = x(i) + e; | ||
| + | shat = shat_old + y; | ||
| + | e = (shat_old - shat) + y; | ||
end | end | ||
</pre> | </pre> | ||
Revision as of 20:27, 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 round
% off 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
shat=0; y=0; e=0;
for i=1:numel(x)
shat_old = shat;
y = x(i) + e;
shat = shat_old + y;
e = (shat_old - shat) + y;
end