torch.kron#

torch.kron(input,other,*,out=None)→Tensor#

Computes the Kronecker product, denoted by$\otimes$⊗, ofinput andother.

Ifinput is a$(a_0\times a_1\times \cdots \times a_n)$(a0​×a1​×⋯×an​) tensor andother is a$(b_0\times b_1\times \cdots \times b_n)$(b0​×b1​×⋯×bn​) tensor, the result will be a$(a_0\ast b_0\times a_1\ast b_1\times \cdots \times a_n\ast b_n)$(a0​∗b0​×a1​∗b1​×⋯×an​∗bn​) tensor with the following entries:

$$(\text{input}\otimes \text{other}{)}_{k_0,k_1,\dots ,k_n}={\text{input}}_{i_0,i_1,\dots ,i_n}\ast {\text{other}}_{j_0,j_1,\dots ,j_n},$$(input⊗other)k0​,k1​,…,kn​​=inputi0​,i1​,…,in​​∗otherj0​,j1​,…,jn​​,

where$k_t=i_t\ast b_t+j_t$kt​=it​∗bt​+jt​ for$0\le t\le n$0≤t≤n.If one tensor has fewer dimensions than the other it is unsqueezed until it has the same number of dimensions.

Supports real-valued and complex-valued inputs.

Note

This function generalizes the typical definition of the Kronecker product for two matrices to two tensors,as described above. Wheninput is a$(m\times n)$(m×n) matrix andother is a$(p\times q)$(p×q) matrix, the result will be a$(p\ast m\times q\ast n)$(p∗m×q∗n) block matrix:

A⊗B=​a11​B⋮am1​B​⋯⋱⋯​a1n​B⋮amn​B​​

whereinput is$\mathbf{A}$A andother is$\mathbf{B}$B.

Parameters

• input (Tensor) –

• other (Tensor) –

Keyword Arguments

out (Tensor,optional) – The output tensor. Ignored ifNone. Default:None

Examples:

>>>mat1=torch.eye(2)>>>mat2=torch.ones(2,2)>>>torch.kron(mat1,mat2)tensor([[1., 1., 0., 0.],        [1., 1., 0., 0.],        [0., 0., 1., 1.],        [0., 0., 1., 1.]])>>>mat1=torch.eye(2)>>>mat2=torch.arange(1,5).reshape(2,2)>>>torch.kron(mat1,mat2)tensor([[1., 2., 0., 0.],        [3., 4., 0., 0.],        [0., 0., 1., 2.],        [0., 0., 3., 4.]])