# PageRank

### From Wikimization

(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