torch.kron

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

Computes the Kronecker product, denoted by $\otimes$, of input and other.

If input is a $(a_0\times a_1\times \cdots \times a_n)$ tensor and other is a $(b_0\times b_1\times \cdots \times b_n)$ tensor, the result will be a $(a_0\ast b_0\times a_1\ast b_1\times \cdots \times a_n\ast b_n)$ tensor with the following entries:

$$(\text{input}\otimes \text{other}{)}_{k_0,k_1,\dots ,k_n}={\text{input}}_{i_0,i_1,\dots ,i_n}\ast {\text{other}}_{j_0,j_1,\dots ,j_n},$$

where $k_t=i_t\ast b_t+j_t$ for $0\le t\le n$. 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. When input is a $(m\times n)$ matrix and other is a $(p\times q)$ matrix, the result will be a $(p\ast m\times q\ast n)$ block matrix:

A⊗B=​a11​B⋮am1​B​⋯⋱⋯​a1n​B⋮amn​B​​

where input is $\mathbf{A}$ and other is $\mathbf{B}$.

Parameters

• input (Tensor) –

• other (Tensor) –

Keyword Arguments

out (Tensor, optional) – The output tensor. Ignored if None. 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.]])