从线性代数到张量分解

Made by Xinyu Chen • 🌐 https://xinychen.github.io

目录

• Kronecker分解

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Kronecker分解

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例. 计算Kronecker积并求Kronecker分解。

• 计算Kronecker积

import numpy as np

A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6, 7], [8, 9, 10]])
X = np.kron(A, B)
print('X = ')
print(X)

• 求Kronecker分解

def permute(mat, A_dim1, A_dim2, B_dim1, B_dim2):
    ans = np.zeros((A_dim1 * A_dim2, B_dim1 * B_dim2))
    for j in range(A_dim2):
        for i in range(A_dim1):
            ans[A_dim1 * j + i, :] = mat[i * B_dim1 : (i + 1) * B_dim1,
                                         j * B_dim2 : (j + 1) * B_dim2].reshape(B_dim1 * B_dim2, order = 'F')
    return ans

X_tilde = permute(X, 2, 2, 2, 3)
print('X_tilde = ')
print(X_tilde)
print()
u, s, v = np.linalg.svd(X_tilde, full_matrices = False)
A_hat = np.sqrt(s[0]) * u[:, 0].reshape(2, 2, order = 'F')
B_hat = np.sqrt(s[0]) * v[0, :].reshape(2, 3, order = 'F')
print('A_hat = ')
print(A_hat)
print()
print('B_hat = ')
print(B_hat)