power_method.py

power_method.py

"""べき乗則を用いて複素行列の最大固有値を求める"""
import numpy as np
import matplotlib.pyplot as plt

seed=1
ndim = 10
np.random.seed=seed
A = np.random.randn(ndim,ndim)+1.j*np.random.randn(ndim,ndim)
x = np.random.randn(ndim) + 1.j*np.random.randn(ndim)
niter = 300

eig_ary =[]
for i in range(niter):
	x_old = x[:]
	x = np.dot(A, x)
	x_norm = np.sqrt(np.sum(x**2))
	numer = np.dot(x_old, x)
	denom = np.dot(x_old, x_old)
	eigval = numer / denom
	print(eigval)
	eig_ary.append(eigval)
	x /= x_norm
	
eigvals = np.linalg.eigvals(A)
print(np.abs(eigvals))


fig = plt.figure(1)
ax = fig.add_subplot(111)
ax.plot(np.abs(eig_ary))
ax.axhline(np.sort(np.abs(eigvals))[-1], color='red')

plt.show()