plot_smoothing.py

"""
Figures 2 & 3 from the thesis:
- Smoothing of the indicator function for different r (Figure 2)
- Smoothing of the indicator function for different delta (Figure 3)
"""

import numpy as np
import matplotlib.pyplot as plt
from core import construct_smoothing_polynomial, smoothing_function


# --- Figure 2: Different r values, fixed delta = 0.5 ---
h = 0.001
T_vals = np.arange(3.5, 4.5 + h, h)
s0 = 4.0
delta = 0.5

fig1, ax1 = plt.subplots(figsize=(8, 5))

for r, color in [(20, 'red'), (10, 'blue'), (5, 'green')]:
    coeffs = construct_smoothing_polynomial(r)
    y = smoothing_function(T_vals, s0, delta, coeffs)
    ax1.plot(T_vals, y, color=color, label=f'r = {r}')

# Indicator function
ax1.plot(T_vals[T_vals <= 4.0], np.ones(np.sum(T_vals <= 4.0)), 'k', linewidth=1.5)
ax1.plot(T_vals[T_vals >= 4.0], np.zeros(np.sum(T_vals >= 4.0)), 'k', linewidth=1.5,
         label=r'$\mathbb{1}_{(-\infty, 4]}$')

ax1.set_ylim(-0.2, 1.2)
ax1.legend()
ax1.set_title(r'Smoothing of the indicator function for different $r$')
fig1.tight_layout()
fig1.savefig('plot_smoothing_r.png', dpi=150)
print("Saved: plot_smoothing_r.png")


# --- Figure 3: Different delta values, fixed r = 20 ---
r = 20
coeffs = construct_smoothing_polynomial(r)

fig2, ax2 = plt.subplots(figsize=(8, 5))

for delta_val, color in [(0.1, 'red'), (0.5, 'blue')]:
    y = smoothing_function(T_vals, s0, delta_val, coeffs)
    ax2.plot(T_vals, y, color=color, label=rf'$\delta = {delta_val}$')

# Indicator function
ax2.plot(T_vals[T_vals <= 4.0], np.ones(np.sum(T_vals <= 4.0)), 'k', linewidth=1.5)
ax2.plot(T_vals[T_vals >= 4.0], np.zeros(np.sum(T_vals >= 4.0)), 'k', linewidth=1.5,
         label=r'$\mathbb{1}_{(-\infty, 4]}$')

ax2.set_ylim(-0.2, 1.2)
ax2.legend()
ax2.set_title(r'Smoothing of the indicator function for different $\delta$')
fig2.tight_layout()
fig2.savefig('plot_smoothing_delta.png', dpi=150)
print("Saved: plot_smoothing_delta.png")

plt.show()