Matlab GPU use with functions that take arguments of different dimensions

I am trying to use parallel computing with GPU in Matlab, and I would like to apply a function to a large array (to avoid the use of a for loop, which is quite slow). I have read Matlab's documentation, and I can use arrayfun, but only if I want to do elementwise operations. Maybe I am confused, but I would appreciate if someone can help me to use it. As an example of what I want to do, imagine that I would like to perform the following operation,

X_t = B Z_t + Qe_t

where X_t is 2x1, B is 2x5, and Z_t is 5x1, with Q 2x2.

I define a function,

    function X = propose(Z,B,Q)
    X=Z*B+Q*rand(2,1);
    end

Now, suppose that I have an array Z_p which is 5x1000. To each of the 1000 columns I would like to apply the previous function, for given matrices B and Q, to get an array X_p which is 2x1000.

Given the documentation for `arrayfun` I can not do this,

    Xp=arrayfun(@propose,Zp,B,Q)

So, is there any possibility to do it?

Thanks!

*PS*: Yes, I know that in this simple example I can just do the multiplication without a for loop, but the application I have in mind is more complicated and I cannot do it. I just put this example as an illustration.

Answer 1

[Joss Knight]

pagefun is what you're looking for. With it you can batch vector and matrix operations across pages of an array (the 3rd dimension). Obviously in your case simple vector algebra would do the trick but to force it to use pagefun you might do something like

 N = size(Zp,2);
 Zp = reshape(Zp, 5, 1, []);  % Stack Z-vectors along the 3rd dimension
 BZ = pagefun(@mtimes, B, Zp); % Assumes you wanted to multiply same B by every Z
 offset = pagefun(@mtimes, Q, gpuArray.rand(2,1,N));
 Xp = pagefun(@plus, BZ, offset); % Completely unnecessary, Xp = BZ+offset would work

[Carlos]

Ah I had no idea about this function!! I will give it a try, but it sounds like what I need! In principle this should be faster than doing a for loop for all the columns of Zp, right?

[Carlos]

Well...it does not work. I mean, it works for this simple illustration that I posted here, but my problem requires a user defined function, with some more complex algebra, and pagefun does not admit them, while arrayfun does :(

[Joss Knight]

pagefun can call any function that arrayfun can call, it just can't call lots of them in a single launch. Perhaps by breaking up your arrayfun function into multiple calls to pagefun, you can achieve what you're after.