44 lines
1.6 KiB
Python
44 lines
1.6 KiB
Python
"""
|
|
This code is supported by the website: https://www.guanjihuan.com
|
|
The newest version of this code is on the web page: https://www.guanjihuan.com/archives/10890
|
|
"""
|
|
|
|
import numpy as np
|
|
|
|
|
|
def main():
|
|
A = np.array([[0, 1, 1, -1], [1, 0, -1, 1], [1, -1, 0, 1], [-1, 1, 1, 0]])
|
|
eigenvalue, eigenvector = np.linalg.eig(A)
|
|
print('矩阵：\n', A)
|
|
print('特征值:\n', eigenvalue)
|
|
print('特征向量:\n', eigenvector)
|
|
|
|
print('\n判断是否正交：\n', np.dot(eigenvector.transpose(), eigenvector))
|
|
print('判断是否正交：\n', np.dot(eigenvector, eigenvector.transpose()))
|
|
|
|
print('对角化验证：')
|
|
print(np.dot(np.dot(eigenvector.transpose(), A), eigenvector))
|
|
|
|
# 施密斯正交化
|
|
eigenvector = Schmidt_orthogonalization(eigenvector)
|
|
|
|
print('\n施密斯正交化后，特征向量：\n', eigenvector)
|
|
|
|
print('施密斯正交化后，判断是否正交：\n', np.dot(eigenvector.transpose(), eigenvector))
|
|
print('施密斯正交化后，判断是否正交：\n', np.dot(eigenvector, eigenvector.transpose()))
|
|
|
|
print('施密斯正交化后，对角化验证：')
|
|
print(np.dot(np.dot(eigenvector.transpose(), A), eigenvector))
|
|
|
|
|
|
def Schmidt_orthogonalization(eigenvector):
|
|
num = eigenvector.shape[1]
|
|
for i in range(num):
|
|
for i0 in range(i):
|
|
eigenvector[:, i] = eigenvector[:, i] - eigenvector[:, i0]*np.dot(eigenvector[:, i].transpose().conj(), eigenvector[:, i0])/(np.dot(eigenvector[:, i0].transpose().conj(),eigenvector[:, i0]))
|
|
eigenvector[:, i] = eigenvector[:, i]/np.linalg.norm(eigenvector[:, i])
|
|
return eigenvector
|
|
|
|
|
|
if __name__ == '__main__':
|
|
main() |