How can I help Julia better allocate memory on sparse matrix operations?



I have a function in a for loop along the lines of this:

function spmat_ops!(B, C, D, E, F, G, b, x)
    # Upper case vars are SparseMatrixCSC and lower case are Vectors
    A = B*C + D*E*F + G
    x = somefastsolver(A,b)

function main()
    for i = 1:100
        spmat_ops!(B, C, D, E, F, G, b, x)
        b += x

The SparceMatrixCSC operation is causing a lot of large allocations thus slowing down the code quite a bit. Is there any way to alleviate this?


What’s going on here is a bunch of temporary matrices are being constructing in the process of calculating A. To make this explicit, the line A = B*C + D*E*F + G gets expanded into something like:

T1 = B*C
T2 = E*F
T3 = D*T2
T4 = T1 + T2
A = T4 + G

So you end up generating 4 temporaries matrices, allocating a bunch of memory. What to do about this, I’m not exactly sure. Julia uses UMFPACK/SuiteSparse for sparse matrix operations and there might be a way to provide the output matrix for each operation (possibly reusing a single temporary matrix several times), but then you have to figure out the sparsity pattern of the output matrix, which is non-trivial for matrix-matrix multiplication.

Bottom line, I would look at the SuiteSparse documentation, see if the capability exists there, then have a look at julia’s base/sparse/cholmod.jl and see if the capability is exposed in julia.


Thanks for the feedback. I’ll look at the SuiteSparse docs and look through cholmod.jl.

The temp array structures should be unchanging and I do know their sparsity pattern.

I’m curious, for example, if T1 is created, then directly modified? Or perhaps arrays I, J, V are created then T1 = sparse(I, J, V) in which case it seems like preallocating T1 would be waste of space.


First of all I suspect you want x[:] = ....

If somefastsolver is an iterative solver, then you are probably better off storing A as a type - say (I simplify because I don’t want to type so much)

type MyOperator

function (Base.*)(A::MyOperator, x::AbstractVector)
   # now perform in-place sparse matrix multiplications using `A_mul_B!`


Perfect, the in-place sparse functions were what I was looking for. The operator overloading is an interesting solution I might consider.