import numpy as np
import matplotlib.pyplot as plt

# F = exp
def F(x):
    return np.exp(x)

def dF(x):
    return np.exp(x)

x = np.linspace(-2, 2, 400)

# two points
q = -0.5
p = 1.0

Fq = F(q)
Fp = F(p)
dFq = dF(q)
dFp = dF(p)

tangent_q = Fq + dFq * (x - q)
tangent_p = Fp + dFp * (x - p)

plt.figure(figsize=(8, 6))
plt.plot(x, F(x), linewidth=2, label="F(x)=exp(x)")
plt.plot(x, tangent_q, "--", linewidth=1.2, label="Tangent at q")
plt.plot(x, tangent_p, ":", linewidth=1.2, label="Tangent at p")

# mark points
plt.scatter([q], [Fq], marker="o")
plt.scatter([p], [Fp], marker="s")

# vertical gaps showing asymmetry
plt.vlines(p, tangent_q[np.searchsorted(x, p)], Fp, linestyles="-", linewidth=2)
plt.vlines(q, tangent_p[np.searchsorted(x, q)], Fq, linestyles="-", linewidth=2)

plt.title("Bregman distance of F(x)=exp(x)")
plt.xlabel("x")
plt.ylabel("F(x)")
plt.grid()
plt.legend()
plt.tight_layout()
plt.savefig("bregman_exp.svg")
plt.show()