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:
enter image description here

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:

enter image description here

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!

Have you tried not using the optional parameters for contour? Those could be causing these problems — NewEyes
– NewEyes, Commented Mar 19, 2019 at 15:46

ImportanceOfBeingErnest · Accepted Answer · 2019-03-19 16:02:24Z

1

The result given by matplotlib.pyplot.contour is numerically correct, but mathematically wrong.

Check what happens if you simply plot the tan(x):

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()

You will get a line at the poles. This is because subsequent points are connected.

You can circumvent this by using np.inf for points larger than a certain number. E.g. adding

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

would result in

The same approach can be used for the contour.

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()

answered Mar 19, 2019 at 16:02

ImportanceOfBeingErnest

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