method_Gaussian

import matplotlib.pyplot as plt
import numpy as np
from sympy import Symbol, Integral, exp, log
from scipy.special import roots_legendre

def function(x):
    f = 4 * np.sin(x * x) - np.log(x + 4)
    return f


def foo():
    _x = Symbol('x')
    return Integral(exp(_x) * log(_x), (_x, 1, 2))

def method_Gaussian(a, b, n):
    b_a_half_size = (b - a) / 2
    a_b_half_sum = (a + b) / 2

    roots, weights = roots_legendre(n)

    _sum = 0
    for i in range(n):
        _sum += weights[i] * function(a_b_half_sum + b_a_half_size * roots[i])
    _sum *= b_a_half_size

    print(str('Gaussian quadrature: ') + str(_sum))


def draw_function():
    x = np.arange(0.1, 2.5, 0.07)
    f = function(x)

    line = plt.plot(x, f, color='limegreen')

    plt.fill_between(x, f, color='palegreen', where=(x < 2) & (f > 0))
    plt.grid()

    plt.setp(line, color="limegreen", linewidth=1.5)
    plt.gca().spines["left"].set_position("zero")
    plt.gca().spines["bottom"].set_position("zero")
    plt.gca().spines["top"].set_visible(False)
    plt.gca().spines["right"].set_visible(False)

    plt.show()


def main():
    _a = 1
    _b = 2
    _n = 6

    method_Gaussian(_a, _b, _n)
    draw_function()

if __name__ == '__main__':
    main()