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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
-
s=0; e=0; temp=0; y=0;
+
shat=0; y=0; e=0;
for i=1:numel(x)
for i=1:numel(x)
-
temp=s; y=x(i)+e; s=temp+y; e=(temp-s)+y;
+
shat_old = shat;
 +
y = x(i) + e;
 +
shat = shat_old + y;
 +
e = (shat_old - shat) + y;
end
end
</pre>
</pre>

Revision as of 19:27, 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
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