PageRank
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(Difference between revisions)
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+ | [[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 | ||
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% 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