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The setting is here.

X: 6000x8000 non-sparse matrix

B: 8000x1 sparse vector with only tens of non-zeros

d: positive number

M: is sparsified X'X, i.e. thresholding the elements smaller than d in magnitude to be 0.
Only hundreds of elements are left. So (X' * X - M) have many small elements and is not sparse.

I want to compute the vector y=(X' * X - M)* B and can rewrite as y=X' * (X * B) - M*B. The first part is fast enough, but the second part involves X'*X, and is very very slow.

Could any one help me to accelerate this computation?

Thanks a million!

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  • $\begingroup$ I don't think MO is the right place for this question, maybe Stack Overflow stackoverflow.com is better. $\endgroup$
    – Zander
    Commented Mar 29, 2011 at 2:29
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    $\begingroup$ I agree that this is completely inappropriate, voting to close $\endgroup$
    – Igor Rivin
    Commented Mar 29, 2011 at 2:45

2 Answers 2

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Don't compute the entries that would be multiplied with the zero entries of $B$. That is, take the submatrix $X_{nz}$ of $X$ consisting of those columns corresponding with the nonzero entries of $B$, and take $B_{nz}$ to be the concatenation of all nonzero entries of $B$. Then compute the sparsification of $X^T \cdot X_{nz}$ and multiply that by $B_{nz}$.

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Matlab has a sparse matrix type.

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