coloring lines generated from numerical points

Question

I calculate the eigenvalues of large matrices depending on a parameter and would like to plot the eigenvalues in different colors. So I do not have functions where I can conveniently plot different functions in different colors, but instead I just have a set of points which just get connected as interpolation. My problem is that the lines should be intersecting, but that cannot be achieved with this numerical approach.

Maybe it is best explained with a small example.

import numpy as np
import numpy.linalg
import matplotlib.pyplot as plt

def mat(x):
    #return np.array([[np.sin(x), 0], [0, -np.sin(x)]])
    return np.array([[np.sin(x), 0, 0], [0, -np.sin(x), 0], [0, 0, np.sin(10*x)+x]])

fig=plt.figure()
fig.suptitle('wrong colors')
ax=fig.add_subplot(111)
# x = np.linspace(-1,1,100)  # no, not that easy, the intersection points are difficult to find
x = np.sort(np.random.uniform(low=-1, high=1, size=1000))
#evs = np.zeros((2, len(x)))
evs = np.zeros((3, len(x)))
for i in range(len(x)):
    evs[:, i] = np.linalg.eigvalsh(mat(x[i]))
print(np.shape(evs))
ax.plot(x, evs[0,:], color='C0')
ax.plot(x, evs[1,:], color='C1')
ax.plot(x, evs[2,:], color='C2')

# just reference plot, this is how it should look like
fig2 = plt.figure()
fig2.suptitle('correct colors')
ax2 = fig2.add_subplot(111)
ax2.plot(x, np.sin(x), color='C0')
ax2.plot(x, -np.sin(x), color='C1')
ax2.plot(x, np.sin(10*x)+x, color='C2')
plt.show()

So what I get is this:

What I would like to have is this:

One difficulty is that the intersection point is difficult to calculate and usually not included. That's ok, I don't need the point, as the graphics is purely informative. But the colors should be shown correctly. Any suggestions how I could achieve something like this easily?

To give you an idea of where this is to be used, have a look at the following picture. Here, the straight lines in the middle should have a different color than the curved ones. Besides the matrix being a lot more complex, the image is created in the same way as above.

EDIT: My example was not good and clear, I have come up with one which is closer to my real problem. The matrix is numeric and I cannot diagonalize it analytically, i.e. I cannot know whether it is sin, cos or maybe some mean np.sin(2*x+0.2)+np.cos(x)**2.

Answer 1

Here you go: Just concatenate the first part of one signal with the last part of the other

import numpy as np
import numpy.linalg
import matplotlib.pyplot as plt

def mat(x):
    return np.array([[np.sin(x), 0], [0, -np.sin(x)]])

fig=plt.figure()
fig.suptitle('wrong colors')
ax=fig.add_subplot(111)
x = np.linspace(-1,1,100)
evs = np.zeros((2, len(x)))
for i in range(len(x)):
    evs[:, i] = np.linalg.eigvalsh(mat(x[i]))
print(np.shape(evs))
ax.plot(x, np.concatenate((evs[0,:int(len(x)//2)],evs[1,int(len(x)//2):])), color='C0')
ax.plot(x, np.concatenate((evs[1,:int(len(x)//2)],evs[0,int(len(x)//2):])), color='C1')

plt.show()