Finding x-coordinates of all the points that has a particular y- coordinate [duplicate]

Solution 1:

I did not find a good answer to the question of how to find the roots or zeros of a numpy array, so here is a solution, using simple linear interpolation.

import numpy as np
N = 750
x = .4+np.sort(np.random.rand(N))*3.5
y = (x-4)*np.cos(x*9.)*np.cos(x*6+0.05)+0.1


def find_roots(x,y):
    s = np.abs(np.diff(np.sign(y))).astype(bool)
    return x[:-1][s] + np.diff(x)[s]/(np.abs(y[1:][s]/y[:-1][s])+1)

z = find_roots(x,y)

import matplotlib.pyplot as plt

plt.plot(x,y)
plt.plot(z, np.zeros(len(z)), marker="o", ls="", ms=4)

plt.show()

enter image description here

Of course you can invert the roles of x and y to get

plt.plot(y,x)
plt.plot(np.zeros(len(z)),z, marker="o", ls="", ms=4)

enter image description here

Because people where asking how to get the intercepts at non-zero values y0, note that one may simply find the zeros of y-y0 then.

y0 = 1.4
z = find_roots(x,y-y0)
# ...
plt.plot(z, np.zeros(len(z))+y0)

enter image description here

People were also asking how to get the intersection between two curves. In that case it's again about finding the roots of the difference between the two, e.g.

x = .4 + np.sort(np.random.rand(N)) * 3.5
y1 = (x - 4) * np.cos(x * 9.) * np.cos(x * 6 + 0.05) + 0.1
y2 = (x - 2) * np.cos(x * 8.) * np.cos(x * 5 + 0.03) + 0.3

z = find_roots(x,y2-y1)

plt.plot(x,y1)
plt.plot(x,y2, color="C2")
plt.plot(z, np.interp(z, x, y1), marker="o", ls="", ms=4, color="C1")

enter image description here