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

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

If input is a (a0×a1××an)(a_0 \times a_1 \times \dots \times a_n) tensor and other is a (b0×b1××bn)(b_0 \times b_1 \times \dots \times b_n) tensor, the result will be a (a0b0×a1b1××anbn)(a_0*b_0 \times a_1*b_1 \times \dots \times a_n*b_n) tensor with the following entries:

(inputother)k0,k1,,kn=inputi0,i1,,inotherj0,j1,,jn,(\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 kt=itbt+jtk_t = i_t * b_t + j_t for 0tn0 \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.


This function generalizes the typical definition of the Kronecker product for two matrices to two tensors, as described above. When input is a (m×n)(m \times n) matrix and other is a (p×q)(p \times q) matrix, the result will be a (pm×qn)(p*m \times q*n) block matrix:

AB=[a11Ba1nBam1BamnB]\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 A\mathbf{A} and other is B\mathbf{B}.

Keyword Arguments

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


>>> 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.]])


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