Create one_example_of_orthogonalization.py

2021.03.19_Schmidt_orthogonalization/one_example_of_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
+
+a = [[ 0 , 0  ,  1.5 ,  0.32635182-0.98480775j],
+ [0  ,   0  , -0.32635182-0.98480775j, 1.5  ],
+ [ 1.5 ,    -0.32635182+0.98480775j ,0, 0 ],
+ [ 0.32635182+0.98480775j , 1.5 ,  0, 0 ]]
+
+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
+
+def verify_orthogonality(vectors):
+    identity = np.eye(vectors.shape[1])
+    product = np.dot(vectors.T.conj(), vectors)
+    return np.allclose(abs(product), identity)
+
+# 对 np.linalg.eigh() 的特征向量正交化
+
+E, v = np.linalg.eigh(a)
+print(verify_orthogonality(v))
+
+v1 = Schmidt_orthogonalization(v)
+print(verify_orthogonality(v1))
+
+from scipy.linalg import orth
+v2 = orth(v)
+print(verify_orthogonality(v2))
+
+v3, S, Vt = np.linalg.svd(v)
+print(verify_orthogonality(v3))
+
+v4, R = np.linalg.qr(v)
+print(verify_orthogonality(v4))
+
+print()
+
+
+# 对 np.linalg.eig() 的特征向量正交化
+
+E, v = np.linalg.eig(a)
+print(verify_orthogonality(v))
+
+v1 = Schmidt_orthogonalization(v)
+print(verify_orthogonality(v1))
+
+from scipy.linalg import orth
+v2 = orth(v)
+print(verify_orthogonality(v2))
+
+v3, S, Vt = np.linalg.svd(v)
+print(verify_orthogonality(v3))
+
+v4, R = np.linalg.qr(v)
+print(verify_orthogonality(v4))