plot_rho_dist.py

import numpy as np #type: ignore
import matplotlib.pyplot as plt #type: ignore
import pandas as pd #type: ignore

# Load the CSV data
data = pd.read_csv('results.csv')

# Extract the 'Rho' column from the CSV
rho_values = data['Rho'].values

# Calculate the distribution of Rho values
rho_range = np.arange(1, 33)  # Rho values range from 1 to 32
rho_distribution = np.array([np.sum(rho_values == i) for i in rho_range])

# Normalize the distribution to get probabilities
total_values = len(rho_values)
rho_probabilities = rho_distribution / total_values

# Theoretical distribution Pr[ρ(y) = i] = 2^(-i)
theoretical_distribution = np.array([2.0**-i for i in rho_range])

# Plotting the empirical distribution and the theoretical distribution
plt.figure(figsize=(10, 6))

# Plot empirical distribution
plt.bar(rho_range, rho_probabilities, color='blue', alpha=0.6, label='Empirical Distribution')

# Plot theoretical distribution
plt.plot(rho_range, theoretical_distribution, color='red', marker='o', linestyle='-', label='Theoretical Distribution')

# Labels and title
plt.xlabel('Rho Value')
plt.ylabel('Probability (linear scale)')
#plt.yscale('log')
plt.title('Empirical vs Theoretical Distribution of Rho Values')
plt.legend()

# Show the plot
# plt.show()
plt.savefig('rho_distribution_plot_ylin.jpg', format='jpg', dpi=300)