category

academic_codes/others/2021.03.19_Schmidt_orthogonalization/Schmidt_orthogonalization.py

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+"""
+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()