具有适当符号的 Numpy 八函数

Question

我想计算 python 中二阶导数矩阵的特征向量。根据数学，第一个向量应该等于 0 到 pi 之间的 sin 函数，第二个向量应该等于 0 到 2*pi 之间的 sin 函数。因此我的代码看起来像

import numpy as np
from matplotlib import pyplot as plt
from scipy import sparse
import scipy.integrate as integrate
import scipy.special as special
import scipy

def create_second_deriv(size, h):
    delta_matrix_2_second_diff = (np.eye(size, dtype=np.float)*-2+np.eye(size, k=-1,dtype=np.float)*1+np.eye(size, k=1,dtype=np.float)*1)
    delta_matrix_2_second_diff /= (h*h)
    return -1*delta_matrix_2_second_diff

delta_x = 0.001
x = np.linspace(0, 1, (int)(1/delta_x))
delta_matrix = create_second_deriv(len(x), delta_x)
w, v = scipy.linalg.eigh(delta_matrix)

plt.plot(v.tolist()[0])
plt.show()
plt.plot(v.tolist()[1])
plt.show()

现在，我得到的输出是作为第一个特征向量的图，并且作为第二个特征向量的图。我已经知道不同值的符号是任意的，但在我的例子中，它们对以后的处理很重要。有没有办法 "flip" 符号使得结果值近似等于预期函数？在这种情况下，简单地使用 abs() 功能将无济于事。

Answer 1

There is a gotcha 与 scipy.linalg.eigh() 函数：

Be very careful using the eigh() routine to get eigenvalues, though. There's a "gotcha" buried in it.

The syntax is:
(eigenvalues, eigenvectors) = eigh(matrix)
This returns an array of eigenvalues and a 2D array of eigenvectors (each eigenvector consists of many components).

And there's the gotcha. Let's say you want the nth eigenvalue and eigenvector. I would write:
eigenvalues[n]
eigenvectors[n]
And I would be horribly wrong. The eigenvectors and eigenvalues do share an index, but the index on the eigenvector is SECOND column:
eigenvectors[:,n]

因此，您的代码的最后四行必须更改为：

plt.plot(v[:,0])
plt.show()
plt.plot(v[:,1])
plt.show()

具有适当符号的 Numpy 八函数

Numpy eigh-function with proper signs

python

numpy

eigenvector