import numpy as np
from scipy.optimize import curve_fit

def hyperbola(x, s_1, s_2, o_x, o_y, c):
    # x > Input x values
    # s_1 > slope of line 1
    # s_2 > slope of line 2
    # o_x > x offset of crossing of asymptotes
    # o_y > y offset of crossing of asymptotes
    # c   > curvature of hyperbola

    b_2 = (s_1 + s_2) / 2
    b_1 = (s_2 - s_1) / 2

    return o_y + b_1 * (x - o_x) + b_2 * np.sqrt((x - o_x) ** 2 + c ** 2 / 4)

min_fit = np.array([-3.0, 0.0, -2.0, -10.0, 0.0])
max_fit = np.array([0.0, 3.0, 3.0, 0.0, 10.0])
guess = np.array([-2.5/3.0, 4/3.0, 1.0, -4.0, 0.5])

vars, covariance = curve_fit(f=hyperbola, xdata=n_step, ydata=n_mean, p0=guess, bounds=(min_fit, max_fit))