Optimization of column shifting of large matrices (Circshift, etc.) - matlab

Question

I am currently looking for the most efficient way to shift and rearrange large matrices. Essentially, I have data with some parabolic shift that needs to be corrected in order to shift the "signal" to a linear event.
I have currently tried the following solutions and tried timing them. Is there any other method that may prove to be more efficient?
DATA = ones(100000,501);
DATA(10000,251) = 100;
for i=1:250
DATA(10000+i^2-1000:10000+i^2+1000,251-i) = 100;
DATA(10000+i^2-1000:10000+i^2+1000,251+i) = 100;
end
k = abs(-250:1:250).^2;
d = size(DATA,1);
figure(99)
imagesc(DATA)
t_INDEX = timeit(#()fun_INDEX(DATA,k))
t_SNIPPET = timeit(#()fun_SNIPPET(DATA,k))
t_CIRCSHIFT = timeit(#()fun_CIRCSHIFT(DATA,k))
t_INDEX_clean = timeit(#()fun_INDEX_clean(DATA,k))
t_SPARSE = timeit(#()fun_SPARSE(DATA,k))
t_BSXFUN = timeit(#()fun_BSXFUN(DATA,k))
function fun_INDEX(DATA,k)
DATA_1 = zeros(size(DATA));
for i=1:size(DATA,2)
DATA_1(:,i) = DATA([k(i)+1:end 1:k(i)],i);
end
figure(1)
imagesc(DATA_1)
end
function fun_SNIPPET(DATA,k)
kmax = max(k);
DATA_2 = zeros(size(DATA,1)-kmax,size(DATA,2));
for i=1:size(DATA,2)
DATA_2(:,i) = DATA(k(i)+1:end-kmax+k(i),i);
end
figure(2)
imagesc(DATA_2)
end
function fun_CIRCSHIFT(DATA,k)
DATA_3 = zeros(size(DATA));
for i=1:size(DATA,2)
DATA_3(:,i) = circshift(DATA(:,i),-k(i),1);
end
figure(3)
imagesc(DATA_3)
end
function fun_INDEX_clean(DATA,k)
[m, n] = size(DATA);
k = size(DATA,1)-k;
DATA_4 = zeros(m, n);
for i = (1 : n)
DATA_4(:, i) = [DATA((m - k(i) + 1 : m), i); DATA((1 : m - k(i) ), i)];
end
figure(4)
imagesc(DATA_4)
end
function fun_SPARSE(DATA,k)
[m,n] = size(DATA);
k = -k;
S = full(sparse(mod(k,m)+1,1:n,1,m,n));
DATA_5 = ifft(fft(DATA).*fft(S),'symmetric');
figure(5)
imagesc(DATA_5)
end
function fun_BSXFUN(DATA,k)
DATA = DATA';
k = -k;
[m,n] = size(DATA);
idx0 = mod(bsxfun(#plus,n-k(:),1:n)-1,n);
DATA_6 = DATA(bsxfun(#plus,(idx0*m),(1:m)'));
figure(6)
imagesc(DATA_6)
end
Is there any way to decrease computation time for this kind of problem?
Thanks in advance for any tips!

Answer 1

One option would be to use MATLAB's GPU functions, if your workstation has a GPU. Depending on if the entire data fits on the GPU at once, it will start to outperform CPU circshift at 1000 X 1000 matrix size.
The implementation only requires you to copy your data to the GPU with a single statement, and then operate circshift on the newly created you array.
A small discussion on its performance can be found here: https://www.mathworks.com/matlabcentral/answers/274619-circshift-slower-on-gpu . Especially, the last post describes a much faster GPU implementation if you actually don't need to circularly shift, but can get away with zero passing on one side, which might be relevant.