CODEWITHSUNDEEP
matlabsparse-matrix
user1189053
user1189053

Reputation: 131

Adding a sparse vector to a dense vector in Matlab

Suppose I have a high dimensional vector v which is dense and another high dimensional vector x which is sparse and I want to do an operation which looks like

v = v + x

Ideally since one needs to update only a few entries in v this operation should be fast but it is still taking a good amount of time even when I have declared x to be sparse. I have tried with v being in full as well as v being in sparse form and both are fairly slow.

I have also tried to extract the indices from the sparse vector x by calling a find and then updating the original vector in a for loop. This is faster than the above operations, but is there a way to achieve the same with much less code.

Thanks

Upvotes: 3

Views: 275

Answers (1)

TroyHaskin
TroyHaskin

Reputation: 8401

Quoting from the Matlab documentation (emphasis mine):

Binary operators yield sparse results if both operands are sparse, and full results if both are full. For mixed operands, the result is full unless the operation preserves sparsity. If S is sparse and F is full, then S+F, S*F, and F\S are full, while S.*F and S&F are sparse. In some cases, the result might be sparse even though the matrix has few zero elements.

Therefore, if you wish to keep x sparse, I think using logical indexing to update v with the nonzero values of x is best. Here is a sample function that shows either logical indexing or explicitly full-ing x is best (at least on my R2015a install):

function [] = blur()

    n = 5E6;
    v = rand(n,1);
    x = sprand(n,1,0.001);
    xf = full(x);
    vs = sparse(v);

    disp(['Full-Sparse:   ',num2str(timeit(@() v + x)      ,'%9.5f')]);
    disp(['Full-Full:     ',num2str(timeit(@() v + xf)     ,'%9.5f')]);
    disp(['Sparse-Sparse: ',num2str(timeit(@() vs + x)     ,'%9.5f')]);
    disp(['Logical Index: ',num2str(timeit(@() update(v,x)),'%9.5f')]);

end

function [] = update(v,x)

    mask = x ~= 0;
    v(mask) = v(mask) + x(mask);

end

Upvotes: 6

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