Fastest way to differentiate only the sides of large matricies

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Nathan Zechar
Nathan Zechar on 2 Oct 2021
Commented: Nathan Zechar on 4 Oct 2021
I believe I have found one of the fastest ways to differentiate different portions of a large matrix using built in Matlab functions. However, there is a problem to my method, there is a remaining middle value between the side values. Allow me to demonstate with some simple code which makes use of gpuArray. For my case, I need the data on a gpu.
N = 300; % Number of points in x,y,z dimensions
S = 10; % Number of points from side of a dimension
for i = 1:20
B = gpuArray(rand(N,N,N)); % Load some random data
An = diff(B(1:S+1,:,:),1,1); % Differentation from left side
Ap = diff(B(end-S:end,:,:),1,1); % Differentation from right side
A1 = B([2:S+1,N-S+1:N],:,:)-B([1:S,N-S:N-1],:,:);
% The above is the finite difference which is applied to
% both sides of the matrix at the same time. This method
% however, is slower than using built in diff
A2 = diff(B([1:S+1,N-S:N],:,:),1,1);
% The above method is the fastest method, however there is one
% additional data point between S+1 and N - S. Deleting this
% point would add extra computational time
However diff is coded on the backend of Matlab, and would need to be modified for my application. If this is true, how would I go about learning how to code up my own diff function for this special case?
Thank you

Accepted Answer

Matt J
Matt J on 3 Oct 2021
Edited: Matt J on 3 Oct 2021
This seems to be about as fast, at least on the GTX 1080 Ti.
T=reshape(B([1:S+1,N-S:N],:) ,S+1,2*N^2 );
A3 = reshape( diff(T,1,1), 2*S,N,N);
Nathan Zechar
Nathan Zechar on 4 Oct 2021
@Matt J, thank you again. I was hung up on what was happening on the inside of the first line in the original method.
Reduces to 2 dimensions. I thought that was part of the magic and had to permute to that form to get everything to work. Thank you so much again.

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