python写一个奇异值分解的代码
时间: 2024-03-02 07:22:39 浏览: 16
以下是Python中的奇异值分解代码:
```python
import numpy as np
from numpy.linalg import svd
# 假设我们有一个矩阵A
A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
# 使用numpy中的svd函数进行奇异值分解
U, S, V = svd(A)
# U和V是正交矩阵,S是奇异值向量
print("U = \n", U)
print("S = \n", S)
print("V = \n", V)
# 重构原始矩阵
D = np.zeros((A.shape[0], A.shape[1]))
for i in range(min(A.shape)):
D[i][i] = S[i]
A_reconstructed = np.dot(U, np.dot(D, V))
# 打印重构后的矩阵和原始矩阵
print("A_reconstructed = \n", A_reconstructed)
print("A = \n", A)
```
输出结果:
```
U =
[[-0.21483724 -0.88723069 0.40824829]
[-0.52058739 -0.24964395 -0.81649658]
[-0.82633754 0.38794278 0.40824829]]
S =
[1.68481034e+01 1.06836951e+00 3.33475287e-16]
V =
[[-0.47967113 -0.57236779 -0.66506446]
[-0.77669099 -0.07568654 0.62531791]
[-0.40824829 0.81649658 -0.40824829]]
A_reconstructed =
[[1. 2. 3.]
[4. 5. 6.]
[7. 8. 9.]]
A =
[[1 2 3]
[4 5 6]
[7 8 9]]
```
代码中的`svd`函数使用numpy.linalg模块中的SVD(奇异值分解)函数。它接受一个矩阵作为输入,并返回三个矩阵:U、S和V。其中,S是奇异值向量,U和V是正交矩阵。我们可以使用这些矩阵来重构原始矩阵。