create_plot.py

import matplotlib.pyplot as plt
import numpy as np
import math

# Параметры построения графиков функций
N = 3000
a1, b1 = -12.0, 120.0
h1 = abs(a1 - b1) / N
x1 = [a1 + h1]
if x1[0] > 0.0:
    y1 = [x1[0] ** (1.0 / 3.0)]
else:
    y1 = [-((-x1[0]) ** (1.0 / 3.0))]

a2, b2 = -2.0, 120.0
h2 = abs(a2 - b2) / N
x2 = [a2 + h2]
y2 = [math.log(x2[0] + 2.0)]

for i in range(1, N):
    x1.append(x1[i-1] + h1)
    val = x1[i]
    if val > 0.0:
        y1.append(val ** (1.0 / 3.0))
    else:
        y1.append(-((-val) ** (1.0 / 3.0)))

    x2.append(x2[i-1] + h2)
    y2.append(math.log(x2[i] + 2.0))

roots_x = [-1.696595, 97.07366]
roots_y = [-1.192686, 4.59586]

# Функция невязки для линий уровня
def F(x, y):
    return (x - y**3)**2 + (np.log(x + 2) - y)**2

# Область вокруг первого корня
res_x1 = np.linspace(-1.89569, 5.0, 200)
res_y1 = np.linspace(-1.7, 2.0, 200)
X1, Y1 = np.meshgrid(res_x1, res_y1)
Z1 = F(X1, Y1)

# Область вокруг второго корня
res_x2 = np.linspace(91.0, 102.0, 200)
res_y2 = np.linspace(4.1, 5.0, 200)
X2, Y2 = np.meshgrid(res_x2, res_y2)
Z2 = F(X2, Y2)

fig, ax = plt.subplots(figsize=(10, 6))
ax.contour(X1, Y1, Z1, levels=25, cmap='viridis', alpha=0.6)
ax.contour(X2, Y2, Z2, levels=25, cmap='viridis', alpha=0.6)
ax.plot(x1, y1, color='green', linewidth=1.5, label='y = x^(1/3)')
ax.plot(x2, y2, color='red', linewidth=1.5, label='y = ln(x+2)')
ax.plot(roots_x, roots_y, 'o', color='black', markersize=8, label='roots')

ax.set_xlabel('x', fontsize=12)
ax.set_ylabel('y', fontsize=12)
ax.set_title('Graphs of functions and level lines of residual', fontsize=14)
ax.grid(True, linestyle='--', alpha=0.5)
ax.legend(loc='best')

plt.savefig('plot.png', dpi=150, bbox_inches='tight')
print("Plot saved as plot.png")
plt.show()