from math import log, e, sqrt, exp
import numpy as np
import matplotlib.pyplot as plt


def func(x, y):
    return exp(x + y)


h = 0.005
a = 0
b = 0.5
y0 = 0

x = np.arange(a + h, b + h, h)
y = []
y.append(y0)
for xn, n in zip(x, range(len(x))):
    f1 = func(xn, y[n])
    f2 = func(xn + h / 2, y[n] + (h / 2) * f1)
    f3 = func(xn + h, y[n] - h * f1 + 2 * h * f2)
    y.append(y[n] + (h / 6) * (f1 + 4 * f2 + f3))

x = x.tolist()
x.insert(0, 0)

plt.plot(x, y)
plt.tick_params(length=4, width=2, labelsize=10)
r = [i for i in np.arange(0, 1.5, 0.1)]
plt.yticks(r)
plt.xticks(r)
plt.grid(True)
# plt.show()
for i, j in zip(x, y):
    print('x: ', round(i, 5), '  ', 'y: ', round(j, 5), sep='   ')
# def solv(func, a, b, h, y0, x0):

#     # valid(a, b, h, y0, x0)
#     x = np.arange(a+h, b+h, h)
#     y = []
#     y.append(y0)

#     for xn,n in zip(x,range(len(x))):
#         f1 = func(xn, y[n])
#         f2 = func(xn + h/2, y[n] + (h/2)*f1)
#         f3 = func(xn + h, y[n] - h*f1 + 2*h*f2)
#         y.append(y[n] + (h/6)*(f1 + 4*f2 + f3))

#     x = x.tolist()
#     x.insert(0, 0)
#     plt.plot(x, y)
#     plt.tick_params( length=4, width=2, labelsize=10)
#     r = [i for i in np.arange(0, 1.5,0.1)]
#     plt.yticks(r)
#     plt.xticks(r)
#     plt.grid(True)
#     # plt.show()

#     return round(y[int((x0 - a)*(1/h))], 5)

# print(solv(func, 0, 0.5, 0.0001, 0, 0.5))
# print(-log(2 - exp(0.5)))