category

language_learning/python/2021.10.26_eig_and_eigh/eig_and_eigh.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/17789
+"""
+
+import numpy as np
+
+def hamiltonian(width=2, length=2):
+    h00 = np.zeros((width*length, width*length))
+    for i0 in range(length):
+        for j0 in range(width-1):
+            h00[i0*width+j0, i0*width+j0+1] = 1
+            h00[i0*width+j0+1, i0*width+j0] = 1
+    for i0 in range(length-1):
+        for j0 in range(width):
+            h00[i0*width+j0, (i0+1)*width+j0] = 1
+            h00[(i0+1)*width+j0, i0*width+j0] = 1
+    return h00
+
+print('矩阵：\n', hamiltonian(), '\n')
+
+eigenvalue, eigenvector = np.linalg.eig(hamiltonian())
+print('eig求解特征值：', eigenvalue)
+print('eig求解特征向量：\n',eigenvector)
+print('判断特征向量是否正交：\n', np.dot(eigenvector.transpose(), eigenvector))
+
+print()
+
+eigenvalue, eigenvector = np.linalg.eigh(hamiltonian())
+print('eigh求解特征值：', eigenvalue)
+print('eigh求解特征向量：\n',eigenvector)
+print('判断特征向量是否正交：\n', np.dot(eigenvector.transpose(), eigenvector))