PageRank

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[[Image:Gleich.jpg|thumb|right|429px|CSUM() in Digital Signal Processing terms:
 
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z<sup>-1</sup> is a unit delay, Q is a floating-point quantizer to 64 bits,
 
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q<sub>i</sub> represents error due to quantization (additive by definition). <br>-Jon Dattorro]]
 
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<pre>
 
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function s_hat=csum(x)
 
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% CSUM Sum of elements using a compensated summation algorithm.
 
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% David Gleich, Stanford University, 2008
 
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%
 
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% For large vectors, the native sum command in Matlab does
 
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% not appear to use a compensated summation algorithm which
 
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% can cause significant roundoff errors.
 
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%
 
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% This code implements a variant of Kahan's compensated
 
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% summation algorithm which often takes about twice as long,
 
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% but produces more accurate sums when the number of
 
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% elements is large.
 
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%
 
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% See also SUM
 
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%
 
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% Example:
 
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% v=rand(1e7,1);
 
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% sum1 = sum(v);
 
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% sum2 = csum(v);
 
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% fprintf('sum1 = %18.16e\nsum2 = %18.16e\n', sum1, sum2);
 
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s_hat=0; y=0; e=0;
 
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for i=1:numel(x)
 
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s_hat_old = s_hat;
 
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y = x(i) + e;
 
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s_hat = s_hat_old + y;
 
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e = (s_hat_old - s_hat) + y; %calculate difference first (Higham)
 
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end
 
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</pre>
 
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=== links ===
 
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[http://www.google.com/books?id=FJyBjjtHREQC&dq=Accuracy+and+Stability+of+Numerical+Algorithms&printsec=frontcover&source=bn#PPA92,M1 Accuracy and Stability of Numerical Algorithms, Nicholas J. Higham, 1996]
 
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For multiplier error feedback, see:
 
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[http://www.stanford.edu/~dattorro/HiFi.pdf Implementation of Recursive Digital Filters for High-Fidelity Audio]
 
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[http://www.stanford.edu/~dattorro/CorrectionsHiFi.pdf Comments on the above...]
 

Revision as of 15:25, 5 March 2009

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