两个张量之间的克罗内克积 [英] Kronecker product between two tensors

问题描述

我有两个张量:x是2×2×3，y也是2×2×3.定义每个张量的正面切片为x1 x2 x3，y1，y2，y3. xi或yi是2 x 2矩阵.在Matlab中，如何在x和y之间创建kronecker积?我想要得到的是同时在matlab中进行kron(x1，y1)，kron(x2，y2)，kron(x3，y3)而没有任何循环.

I have two tensor: x is 2-by-2-by-3, y is also 2-by-2-by-3. Define each frontal slice of tensor is x1 x2 x3,y1,y2,y3. xi or yi are 2-by-2 matrix. How can I do kronecker product between x and y in matlab? What I want to get is kron(x1,y1),kron(x2,y2),kron(x3,y3) in matlab simultaneously without any looping.

推荐答案

这可能是一种方法-

%// Pre-processing part
[m,n,r] = size(x) %// Get size
N = m*n %// number of elements in one 3D slice

%// ------------- PART 1: Get indices for each 3D slice

%// Get the first mxm block of kron-corresponding indices and then add to
%// each such block for the indices corresponding to the kron multiplications
%// of each iteration
a1 = bsxfun(@plus,reshape([0:N-1]*N+1,m,m),permute([0:N-1],[1 3 2]))

%// Now, a1 is a 3D array, we need to make 2D array out of it.
%// So, concatenate along rows to make it a "slimish" 2D array
a2 = reshape(permute(a1,[1 3 2]),size(a1,1)*size(a1,3),[])

%// Cut after every N rows to make it a square 2D array.
%// These are the indices for each frontal tensor of kron muliplications
slice_idx = reshape(permute(reshape(a2,N,size(a2,1)/N,[]),[1 3 2]),N,N)

%// -------------  PART 2: Get kron equivalent output

%// Perform x:(Nx1) x y:(1xN) multiplications
vals = bsxfun(@times,reshape(x,m*n,1,r),reshape(y,1,m*n,r)) %//multiplications

%// Get indices for all 3D slices and then index into those multiplications
%// with these for the final kron equivalent output
all_idx=bsxfun(@plus,slice_idx,permute([0:r-1]*m*m*n*n,[1 3 2])) %//all indices
out = vals(all_idx) %// final output of kron equivalent multiplications

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