How can I adapt arrayfun() to operate on vectors rather than scalars?

I have a 45-variable function for which I'm trying to speed up computation of the finite-differencing based gradient, as function evaluation is expensive. I'm currently doing this with parfor on my 4-core CPU, but I'd still like things to be faster by using arrayfun() on my GPU (1050 Ti).

So I was thinking of creating a 45x45 matrix P where the ith column has the ith variable incremented by a small step size for finite differencing, and then calling

z = arrayfun(@objectiveFunction, P), and having arrayfun apply objectiveFunction to each column of P at a time.

However, arrayfun doesn't seem configured to do this, and I couldn't find another answer on the forums addressing whether its possible to reconfigure somehow.

Any thoughts?

Thanks.

[Rik]

Usually it is easier to reshape the data to fit the needs of the function. You could also convert to a cell (with mat2cell) and use cellfun, or convert to a struct and use structfun (probably slower).

[Anish Potnis]

You're right -- I realized I can just pass the current variable values as a constant, and have the variable for parallelization to just be the index of the variable that we want to compute the partial derivative for. This works normally with arrayfun().

Thanks.

Answer 1

[Joss Knight]

Look at pagefun for mixing in calls to vector operations with your ordinary element-wise functions. Usually with the functions supported by pagefun, standard MATLAB functions on gpuArray data, and arrayfun, you can get the result you're after.

[Anish Potnis]

Hey Joss.

I'm trying to parallelize the computation of column norms of a matrix.

1) pagefun doesn't support norm or vecnorm, so that seems out.

2) arrayfun(@(idx) norm(A(:,idx)), 1:n) will work, but there's a ton of data overhead in pushing the entire matrix to every parallel worker that makes this very slow.

3) I don't seem to be able to call vecnorm on the matrix directly, since its a gpuArray, and I want to have everything run on the GPU for speed.

I'm probably missing something obvious, but any advice would be appreciated.

[Joss Knight]

Yeah, vecnorm isn't supported for gpuArray yet, but it's really simple piece of code:

norm_X = sqrt(sum(X.*X));