Pointwise multiplication of 3d array with 2d matrix and 1d array and summation by vectorization

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K.E.
K.E. 2016-8-27
编辑： Stephen Jue 2016-8-31
I have a 2 by 2 matrix
A = rand(2,2)
and a 1 by 5 vector
v = [8 9 12 10 11];
I have a 3d array of dimension 2 by 2 by 5.
Call it D such that
D(:,:,1) = [1 2;3 4];
D(:,:,2) = [5 6;7 8];
D(:,:,3) = [12 11;10 9];
D(:,:,4) = [13 15;17 19];
D(:,:,5) = [21 22;23 28];
How can I do the operations of
J=zeros(2);
K=zeros(2);
for i = 1:5
J = J + D(:,:,i)'*A*D(:,:,i);
K = K + D(:,:,i)'*D(:,:,i);
end
and
Q = zeros(size(D));
for i = 1:5
Q(:,:,i) = v(i)*D(:,:,i);
end
by vectorization in the fastest way. I want to do it because the 3d array very huge dimension in general.

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回答（1 个）

Stephen Jue
Stephen Jue 2016-8-31
编辑：Stephen Jue 2016-8-31
Hi Jeff,
These operations all require multi-dimensional matrix multiplication, which is not a built-in feature of MATLAB. However, there is a File Exchange function called mtimesx which can be used instead. It makes use of MATLAB's vectorization optimization by calling the "mtimes" function internally. It can do many operations to n-dimensional arrays, for example:
C = mtimesx(A,B) % performs the calculation C = A * B
C = mtimesx(A,'T',B) % performs the calculation C = A.' * B
C = mtimesx(A,B,'g') % performs the calculation C = A * conj(B)
C = mtimesx(A,'c',B,'C') % performs the calculation C = A' * B'
To calculate the sum (J = J + ...), you can use the result from "mtimesx" as an argument to cumsum.
Another alternative if you have the Parallel Computing Toolbox is to use the pagefun function.
I hope that helps.

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