Fastest way for page-wise computation - FOR vs ARRAYFUN vs PAGEFUN

I'd like to know the fastest way to deal with a 3D array in a page-wise way. Suppose I have the following data:

rng(0); 
data = randi([1, 10], 10, 10, 1000); % sample data 

and I want to know the inverse matrix of each page of this data. I compared three approaches to compute this:

% Approach1 - FOR loop 
tic; 
data_inv1 = zeros(10,10,1000); 
for ii = 1:size(data,3)
    data_inv1(:,:,ii) = inv(data(:,:,ii)); 
end
time1 = toc;

% Approach2 - Arrayfun 
tic; 
data_inv2 = arrayfun(@(ii)inv(data(:,:,ii)), 1:size(data,3), 'UniformOutput', false); 
time2 = toc; 

% Approach3 - Pagefun
tic; 
data_gpu = gpuArray(data); 
data_inv3 = pagefun(@inv, data_gpu); 
time3 = toc; 

% Comparison of elapsed times 
fprintf('FOR-loop: %.8f sec\n', time1); 
fprintf('Arrayfun: %.8f sec\n', time2); 
fprintf('Pagefun:  %.8f sec\n', time3); 

The results on my computer are shown below:

FOR-loop: 0.01121580 sec

Arrayfun: 0.01491200 sec

Pagefun: 0.01317000 sec

Surprisingly, the use of the for-loop was the fastest. I expected that pagefun will give me the fastest computation but that was not the case.

Has anyone tried different approaches to speedup the page-wise computation? Is there anyway to make a good use of pagefun?

[dpb]

Why the surprise?

The for loop is dead-ahead code with no overhead and no function handles.

The alternatives are higher-level abstractions for the convenience of writing code, but that convenicence comes with a cost.

This is a pretty general conclusion; if you can't directly vectorize something immediately to get into the use of buitin code, the plainest, most straightforward code you can write will generally also be the fastest.

[James Tursa]

"... with no overhead ..."

There is overhead involved with the above code. Namely the deep data copying of the pages. This can potentially be avoided in a mex routine.

[dpb]

Yes...sorry, I intended as the additional overhead with the higher-level constructs, not the inherent memcopy of addressing planes.

In theory, MATLAB should be able to address data(:,:,ii) in place without the explicit copy.

[Joss Knight]

What GPU do you have? I suspect pagefun will be faster if you process in single precision.