plot generalized means

means.py

import numpy as np
import matplotlib.pyplot as plt


def agm(an, bn):
    while np.any(abs(an - bn) > 1.0e-15):
        an, bn = (an + bn) / 2, np.sqrt(an * bn)
    return an

x = np.linspace(0, 4, 401)


plt.plot(x, np.maximum(1, x), label="inf mean (maximum)")
plt.plot(x, np.cbrt((1 + x ** 3) / 2), label="cubic mean")
plt.plot(x, np.sqrt((1 + x ** 2) / 2), label="root mean square")
plt.plot(x, (1 + x) / 2, label="arithmetic mean")
plt.plot(x, agm(1, x), linestyle=":", label="arithmetic–geometric mean")
plt.plot(x, np.sqrt(x), label="geometric mean")
plt.plot(x, 2 / (1 + 1 / x), label="harmonic mean")
plt.plot(x, np.minimum(1, x), label="-inf mean (minimum)")

plt.legend()
plt.xlim(0, 4)
plt.ylim(0, 3)
plt.grid()
plt.gca().set_aspect("equal")

plt.title("means of 1 and x")
plt.xlabel("x")

plt.savefig("means.png")
plt.show()