How to sample from a distribution given the CDF in Python

I would like to draw samples from a probability distribution with CDF 1 - e^(-x^2).

Is there a method in python/scipy/etc. to enable you to sample from a probability distribution given only its CDF?

To create a custom random variable class given a CDF you could subclass scipy.rv_continuous and override rv_continuous._cdf. This will then automatically generate the corresponding PDF and other statistical information about your distribution, e.g.

import matplotlib.pyplot as plt
import numpy as np
from scipy import stats

class MyRandomVariableClass(stats.rv_continuous):
    def __init__(self, xtol=1e-14, seed=None):
        super().__init__(a=0, xtol=xtol, seed=seed)

    def _cdf(self, x):
        return 1-np.exp(-x**2)


if __name__ == "__main__":
    my_rv = MyRandomVariableClass()

    # sample distribution
    samples = my_rv.rvs(size = 1000)

    # plot histogram of samples
    fig, ax1 = plt.subplots()
    ax1.hist(list(samples), bins=50)

    # plot PDF and CDF of distribution
    pts = np.linspace(0, 5)
    ax2 = ax1.twinx()
    ax2.set_ylim(0,1.1)
    ax2.plot(pts, my_rv.pdf(pts), color='red')
    ax2.plot(pts, my_rv.cdf(pts), color='orange')

    fig.tight_layout()
    plt.show()