Vectorize product into new dimension

Question

Frank Rosler 2021-12-13

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1610140-vectorize-product-into-new-dimension

评论： Frank Rosler 2021-12-14

I often run into for-loops like the following (minimal working example):

A = randn(1000);
b = randn(1,1000);
lA = size(A,1);
lb = length(b);
B = zeros(lA,lA,lb);
for k=1:lb
    B(:,:,k) = A*b(k);
end

Is there a good way to vectorize this to make it faster? I tried writing

B = reshape(kron(b,A),lA,lA,lb)

but this is not always faster and sometimes even substantially slower than the for-loop.

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Answer 1

Steven Lord 2021-12-13

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https://ww2.mathworks.cn/matlabcentral/answers/1610140-vectorize-product-into-new-dimension#answer_854350

在 MATLAB Online 中打开

Using slightly smaller arrays so these lines can run in Answers:

A = randn(100);
b = randn(1,100);
lA = size(A,1);
lb = length(b);
tic
B = zeros(lA,lA,lb);
for k=1:lb
    B(:,:,k) = A*b(k);
end
toc
Elapsed time is 0.007129 seconds.
tic
B2 = A.*reshape(b, 1, 1, []);
toc
Elapsed time is 0.003494 seconds.
max(abs(B-B2), [], 'all')
ans = 0

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Frank Rosler 2021-12-14

在 MATLAB Online 中打开

Thanks for that, I hadn't seen this before.

Oddly enough, the computation time seems to depend heavily on the sizes of A and b. If they're both of size 100, then indeed your method is faster than the for loop. But when I tried the same code with both A and b of size 1000, the computation times (for 4 runs on my laptop) were as follows:

'for loop:' 2.4059
'vectorized:' 5.0114
----------------------
'for loop:' 2.3183
'vectorized:' 4.8548
----------------------
'for loop:' 2.2921
'vectorized:' 4.9109
----------------------
'for loop:' 2.3115
'vectorized:' 4.6621
----------------------