Faster matmul for case sparse.coo * np.ndarray

[HatPdotS]

I am using this module quite heavily in a recent project and found that sparse.matmul could work faster.
I have implemented a faster version for the case matmul(sparse.coo, np.ndarray) using numba for the case of 2D arrays (cut be generalized). I also implemented a parallellized Version. The single threaded version is roughly 3 times faster than sparse.matmul in this case and scales linearly with the number of entries in the sparse matrix. The multi-threaded Version has some overhead but scales well for very large matrices (10000000+ entries).

Here is the code:

@numba.njit()
def matmul_fast(dim1:np.ndarray,dim2:np.ndarray,V:np.ndarray,Arr: np.ndarray,out: np.ndarray):
    for i in range(V.shape[0]):
        out[dim1[i]] += V[i] * Arr[dim2[i]]
    return out

@numba.njit(parallel=True,fastmath=True,boundscheck=False)
def matmul_fast_parallel(dim1:np.ndarray,dim2:np.ndarray,V:np.ndarray,Arr: np.ndarray,out: np.ndarray,n: np.int64 = 100000):
    f = V.shape[0]
    s = out.shape
    out_loc = np.zeros(s,dtype=np.float64)
    g = 0
    i = 0
    for i_0 in numba.prange(0,f//n+1):
        i = i_0 * n
        out_loc = np.zeros(s,dtype=np.float64)
        for g in range(i,i+n):
            if g>=f:
                break
            out_loc[dim1[g]] += V[g] * Arr[dim2[g]]
        out += out_loc
    return out

These functions can be driven by a non numba function that unpacks the sparse array object into coordinates, data and shape.

def matmul_sparse(Arr_sparse, Arr):
    out = np.zeros((Arr_sparse.shape[0],Arr.shape[1]))
    return matmul_fast_parallel(Arr_sparse.coords[0],Arr_sparse.coords[1],Arr_sparse.data,Arr,out)

Are there any optimizations planned that improve the performance of sparse.matmul?
If not would there be interest in introducing specific solutions like this as an option in the current implementation?

[Hameer Abbasi]

Hello, there's no precedent for multithreaded ops in this library, but please don't hesitate to make a PR for the single-threaded version. I'd be quite happy to accept it.