lab2_based

import numpy as np
import matplotlib.pyplot as plt
from scipy import integrate

T = 1.75418438
C = 1.03439984
g = 9.8
exactValue = (T - 1e-7) * np.sqrt(2 * C / g)
print(exactValue)


def Ft(t):
    return (1 / np.sqrt(g)) * np.sqrt((1 + ((np.sin(2 * t) ** 2) / (1 - np.cos(2 * t)) ** 2))/(C * (1 - np.cos(2 * t)))) \
            * C * (1 - np.cos(2 * t))


def compositeSimpson(a, b, n):
    # n - number of dots
    # n - 1 - number of intervals. Must be even
    # nodes sum via odd and even indexes
    if (n - 1) % 2 != 0:  # if number of intervals isn't even
        n = n + 1
    dotsNumber = n
    intervalsNumber = n - 1
    h = (b - a) / intervalsNumber
    nodesT = []

    for i in range(1, dotsNumber + 1):
        nodesT.append(a + (i - 1) * h)

    oddSum = evenSum = 0

    for index, item in enumerate(nodesT):
        if index == 0 or index == n - 1:
            continue
        if index % 2 != 0:   # for odd indexes
            # print(index, item)
            evenSum += Ft(item)
        else:       # for even indexes
            oddSum += Ft(item)
    oddSum *= 2
    evenSum *= 4
    return (Ft(nodesT[0]) + oddSum + evenSum + Ft(nodesT[n - 1])) * h / 3


def compositeTrapezoid(a, b, n):
    # n - number of dots
    # n - 1 - number of intervals.
    dotsNumber = n
    intervalsNumber = n - 1
    h = (b - a) / intervalsNumber
    nodesT = []
    sum = 0

    for i in range(1, dotsNumber + 1):
        nodesT.append(a + (i - 1) * h)
    # print(len(nodesT))
    for i in range(1, n - 1):
        sum += Ft(nodesT[i])

    sum *= 2

    return (Ft(nodesT[0]) + sum + Ft(nodesT[n - 1])) * h / 2


def calculateInaccuracy(a, b):
    # n - 1 - number of intervals
    # n - number of dots
    inaccuracyValuesSimpson = []
    inaccuracyValuesTrapezoid = []
    hValues = []
    for n in range(3, 10000, 100):
        inaccuracyValuesSimpson.append(np.abs(exactValue - compositeSimpson(a, b, n)))
        inaccuracyValuesTrapezoid.append(np.abs(exactValue - compositeTrapezoid(a, b, n)))
        hValues.append((b - a) / (n - 1))
    plt.loglog(hValues, inaccuracyValuesSimpson, 'o', color='black')
    plt.loglog(hValues, inaccuracyValuesTrapezoid, 'o', color='red')
    plt.title('Dependence of the absolute error of numerical integration on the integration step', color='grey')
    plt.legend(['Simpson method', 'Trapezoid method'], loc=0)
    plt.xlabel('Integration step', color='grey')
    plt.ylabel('Absolute inaccuracy', color='grey')
    plt.grid(True)
    plt.show()