Matlab 两张量之间的Kronecker积

我有两个张量：x是2×2×3，y也是2×2×3。定义张量的每个正面切片为x1x2x3，y1，y2，y3。席或彝是2×2矩阵。如何在matlab中实现x和y之间的kronecker乘积？我想要得到的是matlab中的kron（x1，y1），kron（x2，y2），kron（x3，y3），没有任何循环。

这适用于任意大小的

x

和

y

：

构建一个5D阵列

z

。前两个维度包含

x

和

y

行组合的乘积；接下来的两个包含

x

和

y

列组合的乘积；第五个是原始的三维空间

该阵列将被重塑，一方面折叠第一个和第二个维度，另一方面折叠第三个和第四个维度，以生成最终结果：

代码：

---

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

---

因此，在MATLAB中，您需要高效地找到一种方法来调用

kron

三次：

kron（x1，y1）；克朗（x2，y2）；克朗（x3，y3）对于来自每个张量的每对2D切片
kron
只能接受2D矩阵-我不知道如何在没有任何循环的情况下将其矢量化。为什么转义循环对应用程序如此重要。。。尤其是当张量很小的时候？哦，它只是3维！那么我对你的代码就更不了解了：-）@LuisMendo是的，有很多事情在发生！添加评论：）@迪瓦卡。这真是太神奇了。。。。。你怎么会对matlab中的bxsfun（）如此熟悉？。。。。。。谢谢Divakar。@meng对它上瘾了，康复不会带我去的！；）@迪瓦卡。我会仔细阅读你的代码，并在下次尝试自己解决这种索引问题。哇，真的很好！紧凑的代码！您需要将
2*m
更改为
m^2
，但
n
也需要更改。嘿，谢谢！更正。我想这是我第一次在5D中使用
bsxfun
：）通常情况下，3D已经足够了，恭喜太有趣了！！对绝对是最有趣的功能！
%// 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