torch.tile 手动实现 kron+矩阵乘法

1. tile

torch.tile 是对矩阵进行指定维度的复制数据，为了实现矩阵复制，使用kron 算子将对角矩阵I 复制后形成基于行变换和列变换的矩阵

2. pytorch

import torch
import torch.nn as nn
import torch.nn.functional as F

torch.set_printoptions(precision=3, sci_mode=False)

if __name__ == "__main__":
    run_code = 0
    a_matrix = torch.randn(2, 3)
    dim0 = 4
    dim1 = 3
    tile_matrix = torch.tile(a_matrix, dims=(dim0, dim1))
    print(f"a_matrix.shape=\n{a_matrix.shape}")
    print(f"tile_matrix.shape=\n{tile_matrix.shape}")
    print(f"a_matrix=\n{a_matrix}")
    print(f"tile_matrix=\n{tile_matrix}")
    my_one = torch.zeros(2 * dim0, 2)
    my_one[0::2, 0] = 1
    my_one[1::2, 1] = 1
    print(f"my_one=\n{my_one}")
    a_one = torch.ones(2).reshape(-1, 1)
    a_row = torch.eye(2)
    a_kron = torch.kron(a_one, a_row)
    print(f"a_kron=\n{a_kron}")
    a_co_one = torch.ones(3).reshape(1, -1)
    a_column = torch.eye(3)
    b_kron = torch.kron(a_co_one, a_column)
    print(f"b_kron=\n{b_kron}")
    my_one_result = my_one @ a_matrix @ b_kron
    print(f"my_one_result=\n{my_one_result}")
    m_check_result = torch.allclose(my_one_result,tile_matrix)
    print(f"m_check_result={m_check_result}")

• 结果：

a_matrix.shape=
torch.Size([2, 3])
tile_matrix.shape=
torch.Size([8, 9])
a_matrix=
tensor([[0.340, 0.766, 0.622],
        [0.366, 1.425, 0.886]])
tile_matrix=
tensor([[0.340, 0.766, 0.622, 0.340, 0.766, 0.622, 0.340, 0.766, 0.622],
        [0.366, 1.425, 0.886, 0.366, 1.425, 0.886, 0.366, 1.425, 0.886],
        [0.340, 0.766, 0.622, 0.340, 0.766, 0.622, 0.340, 0.766, 0.622],
        [0.366, 1.425, 0.886, 0.366, 1.425, 0.886, 0.366, 1.425, 0.886],
        [0.340, 0.766, 0.622, 0.340, 0.766, 0.622, 0.340, 0.766, 0.622],
        [0.366, 1.425, 0.886, 0.366, 1.425, 0.886, 0.366, 1.425, 0.886],
        [0.340, 0.766, 0.622, 0.340, 0.766, 0.622, 0.340, 0.766, 0.622],
        [0.366, 1.425, 0.886, 0.366, 1.425, 0.886, 0.366, 1.425, 0.886]])
my_one=
tensor([[1., 0.],
        [0., 1.],
        [1., 0.],
        [0., 1.],
        [1., 0.],
        [0., 1.],
        [1., 0.],
        [0., 1.]])
a_kron=
tensor([[1., 0.],
        [0., 1.],
        [1., 0.],
        [0., 1.]])
b_kron=
tensor([[1., 0., 0., 1., 0., 0., 1., 0., 0.],
        [0., 1., 0., 0., 1., 0., 0., 1., 0.],
        [0., 0., 1., 0., 0., 1., 0., 0., 1.]])
my_one_result=
tensor([[0.340, 0.766, 0.622, 0.340, 0.766, 0.622, 0.340, 0.766, 0.622],
        [0.366, 1.425, 0.886, 0.366, 1.425, 0.886, 0.366, 1.425, 0.886],
        [0.340, 0.766, 0.622, 0.340, 0.766, 0.622, 0.340, 0.766, 0.622],
        [0.366, 1.425, 0.886, 0.366, 1.425, 0.886, 0.366, 1.425, 0.886],
        [0.340, 0.766, 0.622, 0.340, 0.766, 0.622, 0.340, 0.766, 0.622],
        [0.366, 1.425, 0.886, 0.366, 1.425, 0.886, 0.366, 1.425, 0.886],
        [0.340, 0.766, 0.622, 0.340, 0.766, 0.622, 0.340, 0.766, 0.622],
        [0.366, 1.425, 0.886, 0.366, 1.425, 0.886, 0.366, 1.425, 0.886]])
m_check_result=True