Accumulator Error Feedback
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% | % | ||
% % Matlab csum() example: | % % Matlab csum() example: | ||
- | % | + | % clear all |
- | % | + | % csumv = 0; |
- | % | + | % while ~csumv |
- | % | + | % v = randn(13e6,1); |
- | % | + | % rsumv = abs(sum(v) - sum(v(end:-1:1))); |
- | % | + | % disp(['rsumv = ' num2str(rsumv,'%18.16f')]); |
- | % | + | % csumv = abs(csum(v) - csum(v(end:-1:1))); |
- | % | + | % disp(['csumv = ' num2str(csumv,'%18.16e')]); |
- | + | % end | |
+ | [~, idx] = sort(abs(x),'descend'); | ||
+ | x = x(idx); | ||
s_hat=0; e=0; | s_hat=0; e=0; | ||
for i=1:numel(x) | for i=1:numel(x) | ||
Line 35: | Line 37: | ||
e = (s_hat_old - s_hat) + y; %calculate difference first (Higham) | e = (s_hat_old - s_hat) + y; %calculate difference first (Higham) | ||
end | end | ||
+ | return | ||
</pre> | </pre> | ||
Revision as of 15:29, 5 October 2017
function s_hat = 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. -David Gleich % % Also see SUM. % % % Matlab csum() example: % clear all % csumv = 0; % while ~csumv % v = randn(13e6,1); % rsumv = abs(sum(v) - sum(v(end:-1:1))); % disp(['rsumv = ' num2str(rsumv,'%18.16f')]); % csumv = abs(csum(v) - csum(v(end:-1:1))); % disp(['csumv = ' num2str(csumv,'%18.16e')]); % end [~, idx] = sort(abs(x),'descend'); x = x(idx); s_hat=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; %calculate difference first (Higham) end return
links
Accuracy and Stability of Numerical Algorithms 2e, ch.4.3, Nicholas J. Higham, 2002
For multiplier error feedback, see:
Implementation of Recursive Digital Filters for High-Fidelity Audio
Comments on Implementation of Recursive Digital Filters for High-Fidelity Audio