efficient variable circshift on 3D matrix
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Hello,
I have a working method of circularly shifting every 60 element vector in a 3D matrix A (300x300x60) over its corresponding value in 2D shift matrix B (300x300) which is relatively slow. I hope there is a faster method than the methods I currently have.
The shifting works as follows: If B(1,1) for example is 10, I want to shift A(1, 1, :) over 10 samples. Every value in B can be different.
My first approach was the following:
for i=1:size(B, 1)
for j=1:size(B, 2)
A(i, j, :) = circshift(A(i, j, :), B(i, j));
end
end
which works, but is relatively slow (0.2s). A second approach was to first reshape matrices A and B to 2D and 1D respectively and get rid of the nested for loop.
a = reshape(A, size(A, 1)*size(A, 2), size(A, 3))';
b = reshape(B, size(B, 1)*size(B, 2), 1);
for i = 1:length(b)
a(:, i) = circshift(a(:, i), b(i));
end
A = reshape(a', size(fm2, 1), size(fm2, 2), size(fm2, 3));
Which also works and is already little bit faster (0.1s).
Is there any other method to do this that would be much faster?
Thanks.
5 个评论
I don't know of a good alternative. I was going to suggest reshaping, but you already got there. I don't think avoiding the multiple size() calls saves any meaningful amount of time, but it's more compact.
A = rand(300,300,60);
B = randi([-30 30],300,300);
% original method
a = timeit(@() testA(A,B))
% using simplified mcode
b = timeit(@() testB(A,B))
% time ratio
a/b
function testA(A,B)
for i=1:size(B, 1)
for j=1:size(B, 2)
A(i, j, :) = circshift(A(i, j, :), B(i, j));
end
end
end
function testB(A,B)
s = size(A);
a = reshape(A, [], s(3))';
b = reshape(B, [], 1);
for i = 1:length(b)
a(:, i) = circshift(a(:, i), b(i));
end
A = reshape(a', s);
end
There's probably something I'm forgetting, but I recall running into this same obstacle before.
Jona Gladines
2022-3-2
DGM
2022-3-2
Well, I'm still kind of hoping that someone else has another improvement. I was mostly just offering a (more) reliable timing method.
Providing inputs would be very useful. It matters e.g. if the values of B are unique or if there are typically many same values. Optimizing code can exploit such patterns of the input.
For the test data DGM hast provided, this is twice as fast:
s = size(A);
a = reshape(A, [], s(3))';
b = reshape(B, [], 1);
ub = unique(b);
for i = 1:numel(ub)
m = (b == ub(i));
a(:, m) = circshift(a(:, m), ub(i));
end
A = reshape(a', s);
Jona Gladines
2022-3-2
采纳的回答
Jan
2022-3-2
In this code:
s = size(A);
a = reshape(A, [], s(3))';
b = reshape(B, [], 1);
ub = unique(b);
for i = 1:numel(ub)
m = (b == ub(i));
a(:, m) = circshift(a(:, m), ub(i));
end
A = reshape(a', s);
40% of the computing time is spent for transposing. So if you store the data directly in a way, which let the operations work on the first dimension, the computing time is reduced also.
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