std for a growing data range
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Hello :),
i am looking for an effective way to calculate following problem:
for i=1:1000
tmp=data(1:i,:);
rsStd(i)=std(tmp(:));
end
"data" is a matrix with k rows and j columns. What i dont want is to calculate the std for every column. What i would need is the std for a growing data range. By each loop step the data range for the calculation of the std grows as you can see in the code snippet.
Does anyone know probably a faster solution and could give me a hint? I am thinking something with vectorization but currently i have no idea. Many thanks!
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Roger Stafford
2014년 4월 25일
편집: Roger Stafford
2014년 4월 25일
n = (1:size(data,1))'*size(data,2);
sq = cumsum(sum(data.^2,2));
sm = cumsum(sum(data,2));
rsStd = sqrt((sq-sm.^2./n)./(n-1)); % <-- Corrected
(I'm assuming you want the unbiased version of standard deviation.)
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추가 답변 (2개)
Jos (10584)
2014년 4월 25일
편집: Jos (10584)
2014년 4월 25일
Here is the completely vectored code for the running sample standard deviation across the rows of a matrix X:
X = ceil(10*rand(13,4)) % example data
N = cumsum(ones(size(X)),1)
S1 = cumsum(X,1)
S2 = cumsum(X.^2,1)
R = sqrt((N.*S2 - S1.^2) ./ (N.*(N-1)))
% this can be a one-liner if you insist ..
% check
k = 4 ; [R(k,:) ; std(X(1:k,:))] % the same
Use it to your advantage!
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