python如何使用jacobi方法求解矩阵的特征值与特征向量
时间: 2024-04-30 10:19:23 浏览: 14
Jacobi方法是一种经典的求解实对称矩阵特征值和特征向量的方法。下面是Python实现Jacobi方法求解矩阵特征值和特征向量的代码:
```python
import numpy as np
def jacobi(A, eps):
n = A.shape[0]
B = np.eye(n)
while True:
p, q = 0, 0
for i in range(n):
for j in range(i+1, n):
if abs(A[i, j]) > abs(A[p, q]):
p, q = i, j
if abs(A[p, q]) < eps:
break
phi = 0.5*np.arctan(2*A[p, q]/(A[p, p]-A[q, q]))
c, s = np.cos(phi), np.sin(phi)
J = np.eye(n)
J[p, p], J[q, q] = c, c
J[p, q], J[q, p] = -s, s
A = np.dot(np.dot(J.T, A), J)
B = np.dot(B, J)
return np.diag(A), B
# 测试
A = np.array([[4, -30, 60, -35], [-30, 300, -675, 420], [60, -675, 1620, -1050], [-35, 420, -1050, 700]])
eps = 1e-8
eigenvalues, eigenvectors = jacobi(A, eps)
print("特征值:", eigenvalues)
print("特征向量:\n", eigenvectors)
```
其中,A为待求解的实对称矩阵,eps为停机精度,jacobi函数返回特征值和特征向量。