Why is arrayfun for GPU slower than normal operations

Hi there,

Here goes a piece of testing code, yet arrayfun runs more slowly. Any thoughts? Many thanks.

function Test_GPU1()

EP = gpuArray(eps*ones(10000, 1, 'single'));
ONE = gpuArray(ones(10000, 1, 'single'));
ZERO = gpuArray(zeros(10000, 1, 'single'));
Cur_FF_Output = gpuArray(0.5*ones(10000, 1, 'single'));
Cur_Desired_Output = gpuArray(0.5*ones(10000, 1, 'single'));

for iter = 1:1000
% In output layer, Cur_Delta = Del(C)/Del(z) =  Del(C)/Del(a) * Del(a)/Del(z)
% [~, Cur_Delta0] = Cost_Function_GPU(Cur_FF_Output, Cur_Desired_Output, Hyper_Para);
temp00 = Cur_FF_Output + eps;
temp11 = log(temp00);
temp22 = log(1-Cur_FF_Output+eps);
temp33 = Cur_Desired_Output.*temp11;
temp44 = 1-Cur_FF_Output.*temp22;
Cur_Delta = Cur_FF_Output-Cur_Desired_Output;
Cost = 0-sum(temp33+temp44);

temp00 = arrayfun(@plus, Cur_FF_Output, EP);
temp11 = arrayfun(@log, temp00);
temp22 = arrayfun(@log, arrayfun(@minus, ONE, arrayfun(@plus, Cur_FF_Output, EP)));
temp33 = arrayfun(@times, Cur_Desired_Output, temp11);
temp44 = arrayfun(@minus, ONE, arrayfun(@times, Cur_FF_Output, temp22));
Cur_Delta = arrayfun(@minus, Cur_FF_Output, Cur_Desired_Output);
Cost = arrayfun(@minus, ZERO, sum(temp33+temp44));
end

end

[Jan]

Of course arrayfun has a certain overhead. It is expected to run slower than calling the operators directly.

Answer 1

[Joss Knight]

You are misunderstanding the use of arrayfun for gpuArray. Combine all those operations into a single function.

temp00 = arrayfun(@plus, Cur_FF_Output, EP);
temp11 = arrayfun(@log, temp00);
temp22 = arrayfun(@log, arrayfun(@minus, ONE, arrayfun(@plus, Cur_FF_Output, EP)));
temp33 = arrayfun(@times, Cur_Desired_Output, temp11);
temp44 = arrayfun(@minus, ONE, arrayfun(@times, Cur_FF_Output, temp22));
Cur_Delta = arrayfun(@minus, Cur_FF_Output, Cur_Desired_Output);
Cost = arrayfun(@minus, ZERO, sum(temp33+temp44));

becomes

function Cur_Delta = stuff(Cur_FF_Output, Cur_Desired_Output, EP)
    temp00 = Cur_FF_Output + EP;
    temp11 = log(temp00);
    temp22 = log(1 - (Cur_FF_Output + EP));
    temp33 = Cur_Desired_Output .* temp11;
    temp44 = 1 - (Cur_FF_Output .* temp22);
    Cur_Delta = Cur_FF_Output - Cur_Desired_Output;
end
Cur_Delta = arrayfun(@stuff, Cur_FF_Output, Cur_Desired_Output, EP);

Obviously, this can be extremely simplified. I've made a start, by removing the unnecessary ONE and ZERO variables.

After this, question whether you really need arrayfun, or should just call this function directly? MATLAB uses some clever optimisations that, for most sequences of element-wise operations, make using arrayfun unnecessary.

[Theron FARRELL]

Great! I compared two loops as follows

Cur_FF_Output = gpuArray(0.5*ones(10000, 1, 'single'));
Cur_Desired_Output = gpuArray(0.5*ones(10000, 1, 'single'));

tic
for iter = 1:1000
% In output layer, Cur_Delta = Del(C)/Del(z) =  Del(C)/Del(a) * Del(a)/Del(z)
% [~, Cur_Delta0] = Cost_Function_GPU(Cur_FF_Output, Cur_Desired_Output, Hyper_Para);
temp00 = Cur_FF_Output + eps;
temp11 = log(temp00);
temp22 = log(1-Cur_FF_Output+eps);
temp33 = Cur_Desired_Output.*temp11;
temp44 = 1-Cur_FF_Output.*temp22;
Cur_Delta = Cur_FF_Output-Cur_Desired_Output;
Cost = -sum(temp33+temp44);

end
toc

tic
for iter = 1:100
    [Cur_Delta, temp33, temp44] = arrayfun(@stuff, Cur_FF_Output, Cur_Desired_Output);
    Cost = -sum(temp33+temp44);;
end
toc

And the result is

Elapsed time is 1.595991 seconds.

Elapsed time is 0.476634 seconds.

The second one DID runs substantially faster. Wonderful!!! Thanks a lot for your generous succour!

So any practical guidelines for using or not using arrayfun() for gpu? I am afraid that they are not clear in official docs.

Also, if arrayfun() is not so helpful in @plus, @mius, and other basic element-wise operations but only so in user-built functions, will it be meaningful to provide the former any longer?

[Theron FARRELL]

At the same time, if I try the following as well

tic
Cost = -sum(Cur_Desired_Output .* log(Cur_FF_Output + eps) + (1 - Cur_Desired_Output) .* log(1 - Cur_FF_Output + eps));
Delta = (Cur_FF_Output-Cur_Desired_Output);

toc

This one runs the fastest.

Elapsed time is 1.246742 seconds.

Elapsed time is 0.333740 seconds.

Elapsed time is 0.002255 seconds.

Therefore, does it mean that arrayfun() has been a little bit outdated by now?

[Jan]

No, arrayfun is not outdated. It is efficient, if it is used for the purpose it is written for. It is definitely not designed to perform basic operations on elementary arrays. The practical guideline for using arrayfun is to avoid it, when it is not needed. All, what arrayfun does is to forward the data of the input arrays elementwise to the specified function. Functions, which accept arrays directly (so-called "vectorized" functions) are much more efficient. Example:

a = rand(1000, 1000);
b = rand(1000, 1000);

c = a + b;
d = arrayfun(@plus, a, b)

In the first case the function plus gets the arrays and can process all data in one step. In the second case arrayfunc extracts the data elementwise and call plus 1 million times to obtain the result. This is a severe overhead.

If a function does not accept arrays as input, I'd still prefer a loop. See the example given in the documentation of arrayfun:

S(1).f1 = rand(1,5);
S(2).f1 = rand(1,10);
S(3).f1 = rand(1,15);

A = arrayfun(@(x) mean(x.f1),S);

While this looks cute and compact, I prefer the old-fashioned and C-stylish:

A = zeros(size(A));
for k = 1:numel(S)
    A(k) = mean(S(k).f1);
end

This might contain more chances for typos. Then the compact arrayfun call. But as in the cases of cellfun and structfun , the loop approach is usually faster.

I avoid arrayfun completely in my codes.

[Joss Knight]

The answer is, it depends. MATLAB attempts to combine operations into GPU kernels for you, and that is more or less successful depending on your code. With GPU arrayfun, you can tell MATLAB exactly what code to run as a single kernel. Sometimes you can outwit MATLAB's ability to create good kernels automatically, and sometimes you can't. If you know what you're doing, you should always be able to create arrayfun kernels that are at least as fast as what MATLAB is creating for you, but there's no fun in that challenge.

Jan's info may be solid for non-GPU code, I'm not certain. gpuArray arrayfun is a completely customized implementation with special behaviour.

[Theron FARRELL]

I see. 'If you know what you're doing', 'At fast as', and 'no fun' are the key phrases, as I sense. *_^

To be candid, MATLAB, being the de facto most powerful, miraculous, as well as user-friendly scientific and technical SIMULATION and PROTOTYPING tool since 1984--I would not use the word computing here (let's forget MATLAB coder, embedded coder etc originally designed for auto industry at the moment), enjoys her AUTOMATIC optimisation without users' heavy involvement. One of the most typical examples is element-wise (vectorised) operations. That being said, my point is that a user should not take too many efforts on seeking THE most optimised code in lieu of concentrating on algorithmic designs and prototyping, which I do not think most users will do. Consequently, some notifications about pros and cons of using functions as well as PRACTICAL examples such as arrayfun() would be better to be given in the Help page, for example a more formal statement of your words above. Especially , in the advent of DNN, MATLAB would be better prepared for competing with loads of well-optimised, open-sourced code, tensorflow, theano, Caffe etc...

[Joss Knight]

I don't know how recently you viewed the latest documentation on GPU support. I think it's pretty comprehensive, and doesn't encourage you to use arrayfun unnecessarily. There's a great page that talks you through the various options for optimising your code which mentions arrayfun only as an advanced manoeuvre that might, but won't always, improve your performance. Generally we think of arrayfun as the way to 'write custom kernels in the MATLAB language', which many advanced users may look for. We rarely find it useful to document exactly what optimizations MATLAB is using. Usually it just confuses people, who start looking for performance improvements in the wrong place, or start blaming unexpected behaviour on the optimisations. Best to just do our best and leave ourselves the wiggle room to change the way things work from one release to the next.

[Theron FARRELL]

Understood! Thanks again for your great help and detailed explanation. I am always patient with MATLAB since 1997:-)

Answer 2

[Jan]

Of course arrayfun has a certain overhead. It is expected to run slower than calling the operators directly with arrays as inputs. In addition, in

Cur_FF_Output + eps

the second operand is a scalar, while in

arrayfun(@plus, Cur_FF_Output, EP)

Matlab has to process a vector. Addressing the elements of an array needs to access memory using a loop. Accessing a scalar is much cheaper.

What is the purpose of:

arrayfun(@minus, ZERO, sum(temp33+temp44))

? This is faster:

-sum(temp33+temp44)

[Theron FARRELL]

I tried

arrayfun(@minus, 0, sum(temp33+temp44))

yet MATLAB says the dimensions of the first and second operands do not match. So I had no choice but to use that patently clumsy way :-(

[Joss Knight]

If that is true, it is a bug. Are you sure that sum(temp33+temp44) is a gpuArray? What happens if you use gpuArray(0) instead?

[Theron FARRELL]

No, it is not a bug. Maybe somewhere I wrote the code mistakenly. My bad, sorry.

[Jan]

Even arrayfun(@minus, 0, sum(temp33+temp44)) is too complicated compared to

-sum(temp33+temp44)