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R: Compute multiplication efficiently

If I have a matrix A (5000-by-6000), which means it has n rows and m columns, it a_ij

is an element. I would like to calculate sum (k=1..m, l=1..m) (a[i,l]*a[j,k])

(ie this formula ) that is 5000 by 5000. What is the efficient way to calculate such a formula?

Thanks in advance.

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1 answer


You can simplify your expression so that the double sum of products becomes the product of two lines i

and j

. So your inference matrix is ​​essentially a Kronecker product of rows:



x <- rowSums(a)
x %o% x
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