Intersection of two graphs in Python, find the x value

You can use np.sign in combination with np.diff and np.argwhere to obtain the indices of points where the lines cross (in this case, the points are [ 0, 149, 331, 448, 664, 743]):

import numpy as np
import matplotlib.pyplot as plt

x = np.arange(0, 1000)
f = np.arange(0, 1000)
g = np.sin(np.arange(0, 10, 0.01) * 2) * 1000

plt.plot(x, f, '-')
plt.plot(x, g, '-')

idx = np.argwhere(np.diff(np.sign(f - g))).flatten()
plt.plot(x[idx], f[idx], 'ro')
plt.show()

First it calculates f - g and the corresponding signs using np.sign. Applying np.diff reveals all the positions, where the sign changes (e.g. the lines cross). Using np.argwhere gives us the exact indices.

For those who are using or open to use the Shapely library for geometry-related computations, getting the intersection will be much easier. You just have to construct LineString from each line and get their intersection as follows:

import numpy as np
import matplotlib.pyplot as plt
from shapely.geometry import LineString

x = np.arange(0, 1000)
f = np.arange(0, 1000)
g = np.sin(np.arange(0, 10, 0.01) * 2) * 1000

plt.plot(x, f)
plt.plot(x, g)

first_line = LineString(np.column_stack((x, f)))
second_line = LineString(np.column_stack((x, g)))
intersection = first_line.intersection(second_line)

if intersection.geom_type == 'MultiPoint':
    plt.plot(*LineString(intersection).xy, 'o')
elif intersection.geom_type == 'Point':
    plt.plot(*intersection.xy, 'o')

And to get the x and y values as NumPy arrays you would just write:

x, y = LineString(intersection).xy
# x: array('d', [0.0, 149.5724669847373, 331.02906176584617, 448.01182730277833, 664.6733061190541, 743.4822641140581])
# y: array('d', [0.0, 149.5724669847373, 331.02906176584617, 448.01182730277833, 664.6733061190541, 743.4822641140581])

or if an intersection is only one point:

x, y = intersection.xy