Matrix-vector operations without loops

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Valeri Aronov
Valeri Aronov on 14 Oct 2021
Edited: Valeri Aronov on 14 Oct 2021
How do I do this without loops:
HessW = rand(length(x), length(x), length(f));
GradW = rand(length(x), length(f));
A = zeros(length(x));
for i=1:length(f)
for j=1:length(x)
for k=1:length(x)
A(j) = A(j) + 2*HessW(j,k,i)*GradW(k,i);
end
end
end
Thanks

Accepted Answer

Matt J
Matt J on 14 Oct 2021
Edited: Matt J on 14 Oct 2021
A=2*(HessW(:,:)*GradW(:));
  1 Comment
Valeri Aronov
Valeri Aronov on 14 Oct 2021
!!! Hats off.
Further 'improvement' ;-)
A=2*HessW(:,:)*GradW(:);

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More Answers (1)

Rik
Rik on 14 Oct 2021
You can use permute to reshape the second array and use the implicit expansion to do the multiplication in one go. Then sum over two dimensions to get your vector.
Note that you shouldn't use length. Use numel or size instead.
x=rand(5,1);f=rand(3,1);
HessW = rand(numel(x), numel(x), numel(f));
GradW = rand(numel(x), numel(f));
A=2*HessW.*permute(GradW,[3 1 2]);
sum(A,[2 3])
ans = 5×1
9.8738 8.3109 7.6960 9.2496 9.0811
A = zeros(length(x));
for i=1:length(f)
for j=1:length(x)
for k=1:length(x)
A(j) = A(j) + 2*HessW(j,k,i)*GradW(k,i);
end
end
end
A
A = 5×5
9.8738 0 0 0 0 8.3109 0 0 0 0 7.6960 0 0 0 0 9.2496 0 0 0 0 9.0811 0 0 0 0
  2 Comments
Rik
Rik on 14 Oct 2021
You can split it up in steps. You should also include comments that explain why you are doing what you're doing.
%change the order of dimensions so this is a 1xNxN array
GradW_permuted=permute(GradW,[3 1 2]);
%do element-wise multiplication
A=2*HessW.*GradW_permuted;
%sum over the second and third dimension to get the vector
A=sum(A,[2 3])
These comments don't explain the purpose, because your question did not do so.
I would not suggest leaving in the loops, as they harm the performance of the code.
If you worry about readability of you code, make sure to write comments. Explain what you're doing. I often say half you text should be green. That is overdoing it, but your functions should have documentation and you code should have comments.

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