第三章课后习题3.2和3.3
习题3.2
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def X(n):
# 差分方程的解
return 2 * (-1)**(n + 1)
n_values = [0, 1, 2, 3, 4, 5]#根据需要自行调整
for n in n_values:
print(f"X({n}) = {X(n)}")
print("学号：3001")
习题3.3
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import numpy as np
from scipy.sparse.linalg import eigs
import pylab as plt
w = np.array([[0, 1, 0, 1, 1, 1],
[0, 0, 0, 1, 1, 1],
[1, 1, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 1],
[0, 0, 1, 0, 0, 1],
[0, 0, 1, 0, 0, 0]])
r = np.sum(w,axis=1,keepdims=True)
n = w.shape[0]
d = 0.85
P = (1-d)/n+d*w/r #利用矩阵广播
w,v = eigs(P.T,1) #求最大特征值及对应的特征向量
v = v/sum(v)
v = v.real
print("最大特征值为：",w.real)
print("归一化特征向量为：\n",np.round(v,4))
plt.bar(range(1,n+1),v.flatten(),width=0.6)
plt.show()
print("学号：3001")
