#!/usr/bin/env python3
import numpy as np
import matplotlib.pyplot as plt

# Constants from the formula
C2 = 8
C3 = 1.4
U_ref = 0.5  # 50% of U_max (as a fraction)

# Voltage range from 1% to 100% of U_max
voltage_percent = np.linspace(1, 100, 1000)
voltage_fraction = voltage_percent / 100

# Calculate pi_U
pi_U = np.exp(C3 * ((voltage_fraction)**C2 - (U_ref)**C2))

# Create the plot
plt.figure(figsize=(10, 6))
plt.plot(voltage_percent, pi_U, 'b-', linewidth=2)
plt.title('Voltage Dependence Factor $\pi_U$')
plt.xlabel('Operating Voltage (% of $U_{\max}$)')
plt.ylabel('$\pi_U$')
plt.grid(True, linestyle='--', alpha=0.7)
plt.xlim(1, 100)
plt.xticks(np.arange(0, 101, 10))  # Percentage ticks every 10%

# Mark the reference voltage (50%)
plt.axvline(x=50, color='r', linestyle='--', label=f'$U_{{ref}} = 50\%$ of $U_{{max}}$')
plt.legend()

plt.savefig('pi_U_voltage_dependence.svg')