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A:
We came across this as well. We tried a number of different approaches for resolving this issue and the only consistent solution was to disable the FST. There is really no fix for this other than that.
Q:
How many threads of a single core is needed to solve large sparse matrix multiplication?
We know that if we have a large sparse matrix $A$ and $B$ of order $m\times n$ and $n\times m$ and the elements $A$ are non-zero with probability $p$. For each non-zero element, we randomly choose $K$ elements of $B$ to multiply with the ones of $A$ to give a result $C$.
Under what circumstances, do we need at least $m/p$ threads to multiply $A$ and $B$ to give $C$? We need to have O(n^3) copies of $A$ in memory and the threads all use the same copy of $A$.
Thank you!
A:
Suppose that $n,m,K,p\in\mathbb{N}$.
If you multiply a matrix $A\in\mathbb{R}^{m\times n}$ by a matrix $B\in\mathbb{R}^{n\times m}$, there are two stages of computation:
Load the matrix, apply the two different transforms $A,B\in\mathbb{R}^{m\times n}$ and save the result $C\in\mathbb{R}^{m\times n}$.
Form the product $A\cdot B\in\mathbb{R}^{m\times n}$.
Step 2 can be done in parallel or in series. It depends on the function that multiplies two matrices, but in general it is $O(mn)$. In step 1, the cost depends on the kind of sparsity, so $\text{sparsity}(A)\leq \text{sparsity}(C)\leq \text{sparsity}(A)+\text{sparsity}(B)$. That is, the cost per sparsity is $O(1)$. Then, if $A$ and $B$ have the same sparsity, multiplying two matrices is equivalent to matrix-matrix multiplication, which is in $O
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