# torch.kron¶

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

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

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

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

where $k_t = i_t * b_t + j_t$ for $0 \leq t \leq n$. 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 $(p*m \times q*n)$ block matrix:

$\mathbf{A} \otimes \mathbf{B}=\begin{bmatrix} a_{11} \mathbf{B} & \cdots & a_{1 n} \mathbf{B} \\ \vdots & \ddots & \vdots \\ a_{m 1} \mathbf{B} & \cdots & a_{m n} \mathbf{B} \end{bmatrix}$

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

Parameters
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.]])