R: Efficiently calculate double summation of product

Question

[learnBioinformatics]

Hello everyone,

I have a drug-target matrix A (5000 rows(target) X 6000 columns (drugs)), in which each element is a_ij, The second matrix is S, which is 6000 X 6000 matrix (drug-drug similarity matrix), where each element is s_lk. I would like to calculate the following formula: m_ij = sum(k=1..m, l=1..m) (a_il*a_jk*s_lk), [i.e., https://www.dropbox.com/s/5nw7ha5j8pkgcr9/sum.pdf?dl=0] which should a 5000 * 5000 matrix. Here m_ij will be used to calculate the target-target similarity as described in Bioinformatics Journal <<Drug-target interaction prediction through domain-tuned network-based inference>>

What is the efficient way to calculate such summation of product?

Can you give me a tip to calculate such formula, or some course to give a presentation to deal with such formula efficiently.

Thanks

[komal.rathi]

If I am not wrong, the method described in the paper is available as an R package DT-Hybrid.

[learnBioinformatics]

Thanks. Yes, I got it.

[Ram]

While we have many R experts here, I think this question is a better fit for stack overflow. If you were to provide some context on how this pertains to bioinformatics, this question might belong better here.

[learnBioinformatics]

Thanks RamRS. I have revised my poster and added the bioinformatics information.

[Ram]

Thank you for adding details. I'm not great with R and your question needs some expert insight so I guess we'll have to wait for some of them to take a look at it :)

[learnBioinformatics]

Thank you RamRS. I am also working on it.

[russhh]

are either of the matrices sparse?

[learnBioinformatics]

Matrice A is sparse and Matrice S is similarity matrix, which is not sparse.

Answer 1

[learnBioinformatics]

This answer should be: A %*% S %*% t(A)