Something wrong about matplotlib.pyplot.contour

Question

I used matplotlib.pyplot.contour to draw a line, but the result is strange.
My python code:

import numpy as np
from matplotlib import pyplot as plt

N = 1000

E = np.linspace(-5,0,N)
V = np.linspace(0, 70,N)
E, V = np.meshgrid(E, V)

L = np.sqrt(-E)
R = -np.sqrt(E+V)/np.tan(np.sqrt(E+V))

plt.contour(V, E,(L-R),levels=[0])
plt.show()

The result is:

But when I use Mathematica, the result is different.
Mathematica code is:

ContourPlot[Sqrt[-en] == -Sqrt[en + V]/Tan[Sqrt[en + V]], {V, 0, 70}, {en, -5, 0}]

The result is:

The result that I want is Mathematica's result.

Why does matplotlib.pyplot.contour give the wrong result? I am very confused!

It would be very appreciate if you can give me some idea! Thank you very much!

Answer 1

matplotlib.pyplot.contour给出的结果在数值上是正确的，但在数学上是错误的。

如果仅绘制tan(x)，请检查会发生什么情况：

import numpy as np
from matplotlib import pyplot as plt

x = np.linspace(0,2*np.pi,1000)
y = np.tan(x)

plt.plot(x,y)
plt.show()

您将在两极得到一条线。这是因为后续点已连接。

您可以使用np.inf来处理大于特定数量的点，从而规避这一问题。例如。添加

y[np.abs(y)> 200] = np.inf

将导致

相同的方法可用于轮廓。

import numpy as np
from matplotlib import pyplot as plt

N = 1000

x = np.linspace(0, 70,N)
y = np.linspace(-5,0,N)
X,Y = np.meshgrid(x, y)

F = np.sqrt(-Y) + np.sqrt(Y+X)/np.tan(np.sqrt(Y+X))
F[np.abs(F) > 200] = np.inf

plt.contour(X, Y, F, levels=[0])
plt.show()