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Multiplying certain dimensions of two 3D matrices

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Michael
Michael 2012-5-14
编辑： Comrun Yousefzadeh 2020-6-17
Hi
I've got two matrices, one 30x30x50 and one 30x30x80
I would like to multiply them in such a way that the result is a 50x80 matrix ie. an implicit sum over all of the 30x30 common elements.
eg. A*B = C
C(k,l) = A(i,j,k)*B(i,j,l) summed over all i, j
Is there a simple way to write this? I would rather avoid complications using "reshape".
Thanks, Mike

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采纳的回答

Andrei Bobrov
Andrei Bobrov 2012-5-14
Idea of Sean de Wolski
C = squeeze(sum(sum(bsxfun(@times,a,permute(b,[1 2 4 3])))))
or
s = size(a)
C = squeeze(sum(bsxfun(@times,reshape(a,s(1)*s(2),[])',reshape(b,1,s(1)*s(2),[])),2))

更多回答（2 个）

Teja Muppirala
Teja Muppirala 2012-5-14
A = rand(30,30,50);
B = rand(30,30,80);
C = reshape(A,900,[])'*reshape(B,900,[]);
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Michael
Michael 2012-5-14
I have one more related question,
I'm also trying to compute D = C*A, I think A must be transposed for this to make sense: the (i,j,l) element of D is = (k,l) of C times (i,j,k) of A summed over k. I've experimented a bit and found this,
reshape(reshape(A,900,[])*C,30,30,[]);
Is it the best method? I haven't found a general rule to do these automatically yet and I'm not sure if the 'outer' reshape is preserving the form of my 30x30 matrix and not inadvertently flipping it about a diagonal.
Thanks very much for any help

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Comrun Yousefzadeh
Comrun Yousefzadeh 2020-6-17
编辑：Comrun Yousefzadeh 2020-6-17
I have a related questoin. I'm trying to multiply a two dimentioanl array to a specific dimension of a 3-D matrix. For example, A=2000*2000*72, B=72*3 and I'm trying to reach C=2000*2000*3. In other words B should be multiplied to the 3rd dimension of A and repeated (element wise) for 2000*2000 points in the first two dimensions. Currently I'm using a loop like this:
for ii=1:size(A,1)
for jj=1:size(A,2)
A1=A(ii,jj,:);
A1=A1(:);
C1=B'*A1; % C1 has dimension of 3*1
C2=D*C1; %D is a 3-3 matrix therefore, C2 has the same dimension as C1
C(ii,jj,:)=C2(:,1);
end
end
What is the better way to avoid the loop?
Thanks,

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