MATLAB: Std for a growing data range

growing matrixMATLABmatrixstd

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!

Best Answer

 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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