Best way to speed up (parallelize) a large function that take three large 3D arrays as input

I have a function that I generated that is the doubled integral evaluated via trapezoidal rule using 1000 segments of another function in x and y:

. I have this very large function saved to a file, and the input I'm now feeding it, , are 3D arrays. As of right now, with arrays that are it takes roughly a minute for the computation to finish, and in future I'd like to potentially pass it far larger arrays (e.g. ). I've been trying to find away that I could speed this up using parallel processing. The issue is that all ways I've tried to implement any parallelization has slowed it down. What I start with is

s = 10;
xi = -1:2/(s-1):1;
[xi1,xi2,xi3] = ndgrid(xi,xi,xi);

I've tried the following things:

spmd with distributed()

XI1 = distributed(xi1);
XI2 = distributed(xi2);
XI3 = distributed(xi3);
spmd
    Z = myfunc(XI1,XI2,XI3);
end

However this made the processing take roughly 30 minutes.

spmd with codistributed()

spmd
    XI1 = codistributed(xi1);
    XI2 = codistributed(xi2);
    XI3 = codistributed(xi3);
    Z = myfunc(XI1,XI2,XI3);
end
Z = gather(Z);

This made the computation take roughly 40 minutes.

parfor loop with mat2tiles()

XI1 = mat2tiles(xi1,[2,2,2]);
XI2 = mat2tiles(xi2,[2,2,2]);
XI3 = mat2tiles(xi3,[2,2,2]);
Z = mat2tiles(zeros(s,s,s),[2,2,2]);

N = numel(XI1);

parfor i=1:N
    Z{i} = myfunc(XI1{I},XI2{I},XI3{i});
end

This took about 6 minutes to run. mat2tiles() is found here under file share: MAT2TILES: divide array into equal-sized sub-arrays - File Exchange - MATLAB Central (mathworks.com)

parfeval

work = parfeval(@myfunc,xi1,xi2,xi3);
Z = fetchOutputs(work);

This was evantually stopped because I waited over an hour for the the fetchOutputs to finish before cancelling.

I'm not too skilled with parallelization, but I imagine that there must be a faster way for me to have my different workers work on different parts of my array inputs. This is what I thought distributed() and codistributed() did, but the amount of time extra it took for them to finish was far too long to think it's that simple.

[Matt J]

mat2tiles() is found here under file share:

And what about cogather? Where did that come from?

[David Gillcrist]

Sorry, I mixed up my functions. I'm fixing the original post.

[Matt J]

How long does it take to process a single triplet xi1,xi2,xi3 without parallelization? How many workers, N, are you using?

Answer 1

[Matt J]

I think you need to extract the local part, like in the following:

XI1 = distributed(xi1);
XI2 = distributed(xi2);
XI3 = distributed(xi3);

glp=@getLocalPart;

spmd
    Z = myfunc(glp(XI1),glp(XI2),glp(XI3));
end