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:

• 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.]])