ЛР 1 / lab1

from scipy import integrate
from math import *
import numpy as np
import random
import matplotlib.pyplot as plt

global all
all = 0
def punkt1():
    global all
    def integrals1(t):
        return 20/(t+1)

    def integrals2(t):
        return 10-40*(t-1)**2

    def integrals3(t):
        return -30*sin(2*pi*(t-2))-30

    a = integrate.quad(lambda t: abs(integrals1(t)), 0, 1)[0]
    b = integrate.quad(lambda t: abs(integrals2(t)), 1, 2)[0]
    c = integrate.quad(lambda t: abs(integrals3(t)), 2, 3)[0]
    all = (a + b + c)

    print('Значение интеграла встроенной функцией: ', all)



    x1 = np.arange(0, 1, 0.001)
    x2 = np.arange(1, 2, 0.001)
    x3 = np.arange(2, 3, 0.001)
    alina = []
    for i in x1:
        alina.append(integrals3(i))

    plt.plot(x1, integrals1(x1), label='20/(t+1)')
    plt.plot(x2, integrals2(x2), label='10-40*(t-1)**2')
    plt.plot(x3, alina, label='-30*sin(2*pi*(t-2))-30')
    plt.xlabel('x')
    plt.ylabel('y')

    plt.legend()
    plt.show()

    return all

def monte_karlo():
    mas_x = []
    mas_y = []

    for j in range(0, 15):
        n = 2 ** j

        count = 0

        for i in range(0, n):
            t = random.uniform(0.0, 3.0)
            weight = 1

            if t < 1:
                count += abs(20/(t+1))

            if 1 <= t <= 2:
                count += abs(10-40*(t-1)**2)

            if t > 2:
                count += abs(-30*sin(2*pi*(t-2))-30)

            if t < 1 or t > 2:
                weight = -weight

        integral_value = (3.0/n) * count

        print('При N =', n, 'значение F =', integral_value)

        mas_x.append(n)
        mas_y.append(integral_value)

    fig, ax = plt.subplots()
    ax.hlines(all, -5, 10000, color = 'blue')
    plt.plot(mas_x, mas_y)
    plt.legend(['истинное значение F'])

    plt.semilogx(basey=2)

    ax.set_xlabel('N повторений')
    ax.set_ylabel('значение F')
    plt.show()

if __name__ == '__main__':
    punkt1()
    monte_karlo()