How Can I replace the following for loop by vectorization?

2016 11 22
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更新时间：2016 11 24
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Hi Guys,
I have a set of large sparse matrices:
W ,size=(1,10,m)
V ,size=(10,1,m)
Y ,size=(10,10,n)
and I need the output matrix P as follow:
P(i,j)=W(:,:,i)*Y(:,:,j)*V(:,:,i)
e.g if m=2 & n=3
P=[
W(:,:,1)*Y(:,:,1)*V(:,:,1) W(:,:,1)*Y(:,:,2)*V(:,:,1);
W(:,:,1)*Y(:,:,2)*V(:,:,1) W(:,:,2)*Y(:,:,2)*V(:,:,2);
W(:,:,1)*Y(:,:,3)*V(:,:,1) W(:,:,2)*Y(:,:,3)*V(:,:,2)
]
I want to see if you have any suggestion how to write this by a single line code. I have written the code with "two for loop" but because of the large size of matrices, it is almost slow. Any faster idea is really appreciated.
Thank you in advance,
Alireza

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Jan
Jan 2016-11-22
Please post your code and typical input data. It matters if m=1e3 and n=1e7 or the other way around. Perhaps your code is slow due to a forgotten pre-allocation.
What does "sparse" mean? Do the arrays contain a lot of zeros or do you sue the type sparse, which does not work for 3D-arrays?
Alireza Barzegar
Alireza Barzegar 2016-11-23
编辑：Walter Roberson 2016-11-23
Actually, the size of matrices may be very large depend on the size of my problem, even 3000, and matrix Y is a sparse matrix, anyway we can ignore it now. As a simple example:
W(1,:)=[5 3 1];
W(2,:)=[0 1 4];
V(:,1)=[1;8;2];
V(:,2)=[6;4;7];
Y(:,:,1)=[3 1 5 ; 2 1 2 ; 0 3 1];
Y(:,:,2)=[5 0 2 ; 8 1 0 ; 2 3 7];
Y(:,:,3)=[7 0 4 ; 1 3 5 ; 7 2 0];
for i=1:2
for j=1:3
P(i,j) = ( ( (W(i,:))*Y(:,:,j)*V(:,i) ) );
end
end

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Roger Stafford
Roger Stafford 2016-11-23
编辑：Roger Stafford 2016-11-24

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Here's a single line code, but I'm not sure it's faster than, or even as fast as, your two nested for-loop solution:
Corrected:
P = (reshape(repmat(W,10,1,1).*repmat(V,1,10,1),[],m)).’*reshape(permute(Y,[2,1,3]),[],n);

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Alireza Barzegar
Alireza Barzegar 2016-11-23
would you update it for the example that I have added?
W(1,:)=[5 3 1];
W(2,:)=[0 1 4];
V(:,1)=[1;8;2];
V(:,2)=[6;4;7];
Y(:,:,1)=[3 1 5 ; 2 1 2 ; 0 3 1];
Y(:,:,2)=[5 0 2 ; 8 1 0 ; 2 3 7];
Y(:,:,3)=[7 0 4 ; 1 3 5 ; 7 2 0];
for i=1:2
for j=1:3
P(i,j) = ( ( (W(i,:))*Y(:,:,j)*V(:,i) ) );
end
end
Roger Stafford
Roger Stafford 2016-11-24
I see I have made a mistake in my solution. It should have read:
P = (reshape(repmat(W,10,1,1).*repmat(V,1,10,1),[],m)).’*reshape(permute(Y,[2,1,3]),[],n);
Roger Stafford
Roger Stafford 2016-11-24
In your example in keeping with your original statement you ought to have:
W(1,:,1) = [5 3 1];
W(1,:,2) = [0 1 4];
V(:,1,1) = [1;8;2];
V(:,1,2) = [6;4;7];
Then my code would read:
P = (reshape(repmat(W,3,1,1).*repmat(V,1,3,1),[],2)).’*reshape(permute(Y,[2,1,3]),[],3);
Alireza Barzegar
Alireza Barzegar 2016-11-24
Thanks, great idea and also much faster than for loop :)
Roger Stafford
Roger Stafford 2016-11-24
I'm glad to hear it. I was afraid it would be too slow. Sorry about the earlier error.

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