import numpy as np
from math import pi
from math import cos
from math import sqrt
import matplotlib.pyplot as plt

a = 0
b = 1.5
h = 0.15
countStep = int((b - a) / h + 1)
eps = 10 ** (-6)
arrX = np.arange(a, b + h, h)

#ТАБУЛИРОВАНИЕ
def tab(x):
    aN = x
    sum = aN
    i = 0
    while (abs(aN) > eps):
        aN *= - (((pi ** 2 ) * (4*i + 1) * (x**4)) / (4 * (2*i + 1) * (2*i + 2) * (4*i + 5)))
        i += 1
        sum += aN
    return(sum)

f = [None] * int((b - a) / h + 1)
for i in range(len(arrX)):
    arrX[i] = round(arrX[i], 5)
    f[i] = tab(arrX[i])

#ФУНКЦИЯ

def func(x):
    return cos(pi * x ** 2 / 2)

#ЛЕВЫЕ
print('Квадратурная формула левых прямоугольников')
def Pr(x, n):
    sum = 0
    hN = (x - a) / n
    i = 0
    for j in range(n + 1):
        sum += func(i) * hN
        i += hN
    return sum

for i in range(countStep):
    n = 2
    while True:
        In = Pr(arrX[i], n)
        I2n = Pr(arrX[i], 2*n)
        n *= 2
        if (abs(I2n - In) <= eps or n > 1024):
            break
    n = int(n / 2)
    #if (abs(I2n - In) > eps):
    print('{} {:<5} {:>10} {:<20} {:>5} {:<20} {:>15} {:<25} {:>15} {}'.format('x =', arrX[i], 'C(x) =', f[i], 'I =', Pr(arrX[i],n), 'Разность =', abs(f[i] - Pr(arrX[i], n)), 'n =', n))

print()

#ЦЕНТРАЛЬНЫХ
print('Квадратурная формула центральных прямоугольников')
def Centr(x, n):
    sum = 0
    hN = (x - a) / n
    i = hN
    for j in range(n):
        sum += func((2 * i - hN) / 2) * hN
        i += hN
    return sum

for i in range(countStep):
    n = 2
    while True:
        In = Centr(arrX[i], n)
        I2n = Centr(arrX[i], 2*n)
        n *= 2
        if (abs(I2n - In) <= eps or n > 1024):
            break
    n = int(n / 2)
    print('{} {:<5} {:>10} {:<20} {:>5} {:<20} {:>15} {:<25} {:>15} {}'.format('x =', arrX[i], 'C(x) =', f[i], 'I =', Centr(arrX[i],n), 'Разность =', abs(f[i] - Centr(arrX[i], n)), 'n =', n))

print()

#ТРАПЕЦИЙ
print('Квадратурная формула трапеций')
def Trap(x,n):
    sum = 0
    hN = (x - a) / n
    i = hN
    for j in range(n):
        sum += ((func(i) + func(i - hN)) * (hN / 2))
        i += hN
    return sum

for i in range(countStep):
    n = 2
    while True:
        In = Trap(arrX[i], n)
        I2n = Trap(arrX[i], 2*n)
        n *= 2
        if (abs(I2n - In) <= eps or n > 1024):
            break
    n = int(n / 2)
    print('{} {:<5} {:>10} {:<20} {:>5} {:<20} {:>15} {:<25} {:>15} {}'.format('x =', arrX[i], 'C(x) =', f[i], 'I =', Trap(arrX[i],n), 'Разность =', abs(f[i] - Trap(arrX[i], n)), 'n =', n))

print()

#СИМПСОНА
print('Квадратурная формула Симпсона')
def Simps(x,n):
    sum = 0
    hN = (x - a) / n
    i = hN
    for j in range(n):
        sum += (func(i) + 4 * func((2 * i - hN) / 2) + func(i - hN)) * hN/6
        i += hN
    return sum

for i in range(countStep):
    n = 2
    while True:
        In = Simps(arrX[i], n)
        I2n = Simps(arrX[i], 2*n)
        n *= 2
        if (abs(I2n - In) <= eps or n > 1024):
            break
    n = int(n / 2)
    print('{} {:<5} {:>10} {:<20} {:>5} {:<20} {:>15} {:<25} {:>15} {}'.format('x =', arrX[i], 'C(x) =', f[i], 'I =', Simps(arrX[i],n), 'Разность =', abs(f[i] - Simps(arrX[i], n)), 'n =', n))

print()

#ГАУССА
print('Квадратурная формула Гаусса')
def Gaus(x,n):
    sum = 0
    hN = (x - a) / n
    i = 0
    for j in range(n):
        sum += (func((i) + ((hN / 2) * (1 - 1 / sqrt(3)))) + func((i) + ((hN / 2) * (1 + 1 / sqrt(3))))) * hN / 2
        i += hN
    return sum

for i in range(countStep):
    n = 2
    while True:
        In = Gaus(arrX[i], n)
        I2n = Gaus(arrX[i], 2*n)
        n *= 2
        if (abs(I2n - In) <= eps or n > 1024):
            break
    n = int(n / 2)
    print('{} {:<5} {:>10} {:<20} {:>5} {:<20} {:>15} {:<25} {:>15} {}'.format('x =', arrX[i], 'C(x) =', f[i], 'I =', Gaus(arrX[i],n), 'Разность =', abs(f[i] - Gaus(arrX[i], n)), 'n =', n))

print()