Python: Use Polyval To Predict X Passing Y

I have 2 sets of points (X, Y). I want to: Use polifit to fit the line Given a Y predict an X This is the dataset: X Y -0.00001 5.400000e-08 -0.00001

Solution 1:

As I said in the comments, you can subtract the y value, fit an appropriate degree polynomial, then find it's roots. numpy is easily good enough for that task. Here is a simple example:

import numpy as np

x = np.arange(-10, 10.1, 0.3)
y = x ** 2

def find_x_from_y(x, y, deg, value, threshold=1E-6):

    # subtract the y value, fit a polynomial, then find the roots of it
    r = np.roots(np.polyfit(x, y - value, deg))

    # return only the real roots.. due to numerical errors, you
    # must introduce a threshold value to its complex part.
    return r.real[abs(r.imag) < threshold]

>>> find_x_from_y(x, y, 2, 0.5)
array([ 0.70710678, -0.70710678])

Finding roots is a numerical algorithm, it produces the numerical approximation of the actual roots. This might result in really small, but nonzero imaginary parts. To avoid this, you need a small threshold to distingush real and imaginary roots. This is why you can't really use np.isreal:

>>> np.isreal(3.2+1E-7j)
False

A visual example with a 3 degree polynomial:

import numpy as np
import matplotlib.pyplot as plt

x = np.arange(-10, 10.1, 0.3)
y = x ** 3 - 3 * x ** 2 - 9 * x

def find_x_from_y(x, y, deg, value, threshold=1E-6):
    r = np.roots(np.polyfit(x, y - value, deg))
    return r.real[abs(r.imag) < threshold]

value = -10
rts = find_x_from_y(x, y, 3, value)

fig = plt.figure(figsize=(10, 10))
plt.plot(x, y)
plt.axhline(value, color="r")
for r in rts:
    plt.axvline(r, color="k")