#-*- coding:UTF-8 -*-
import math


from BuildPlot import create_plot


def function(x, y):
    return (y/(1+x))-0.5*y*y


def tabulate_function(a, b, tabulate_step):
    y = []
    x = []
    current_x = a
    while current_x <= b:
        y.append(function(current_x))
        x.append(current_x)
        current_x += tabulate_step
    return [x, y]


def method_runge_kutta_3(x, y, h):
    phi_0 = h * function(x, y)
    phi_1 = h * function(x + h / 2, y + phi_0 / 2)
    phi_2 = h * function(x + h, y - phi_0 + 2 * phi_1)
    return [x + h, (phi_0 + 4 * phi_1 + phi_2)/6 + y]

def method_runge_kutta_4(x, y, h):
    phi_0 = h * function(x, y)
    phi_1 = h * function(x + h / 3, y + phi_0 / 3)
    phi_2 = h * function(x + 2*h / 3, y - phi_0 / 3 + phi_1)
    phi_3 = h * function(x + h, y + phi_0+phi_1+phi_2)
    return [x + h, y+ (phi_0+3*phi_1+3*phi_2+phi_3)/8]

def method_prediction_and_correction(prev_x, prev_y, h):
    x = prev_x + h
    y = prev_y + h * function(prev_x, prev_y)
    y = prev_y + h * function(x, y) + (function(x, y) - function(prev_x, prev_y)) * h / 2
    return [x, y]


if __name__ == "__main__":


    h = 0.1
    x = 0  # float(input("Write a: "))
    y = 1  # float(input("Write b: "))
    data1 = [[x], [y]]
    data2 = [[x], [y]]
    data3 = [[x], [y]]
    print("Лабораторная работа №3, вариант 12, часть 2: "
          "Используя метод Рунге-Кутта третьего, четвертого порядка точности и\n" +
                "метод прогноза и коррекции, вычислить значения y1, y2, y3 приближенного\n" +
                "решения заданного дифференциального уравнения первого порядка. Вычис-\n" +
                "ления производить с пятью знаками после запятой. Шаг h = 0.1 . Результаты\n" +
                "вычислений отобразить на графике.\n")
    print("Method Runge Kutta 3")
    value = [x, y]
    for i in range(3):
        value = method_runge_kutta_3(value[0], value[1], h)
        print("x[{2}] = {0}\ny[{2}] = {1}".format(value[0], value[1], i))
        data1[0].append(value[0])
        data1[1].append(value[1])

    print("\nMethod Runge Kutta 4")
    value = [x, y]
    for i in range(3):
        value = method_runge_kutta_4(value[0], value[1], h)
        print("x[{2}] = {0}\ny[{2}] = {1}".format(value[0], value[1], i))
        data2[0].append(value[0])
        data2[1].append(value[1])

    print("\nMethod prediction and correction")
    value = [x, y]
    for i in range(3):
        value = method_prediction_and_correction(value[0], value[1], h)
        print("x[{2}] = {0}\ny[{2}] = {1}".format(value[0], value[1], i))
        data3[0].append(value[0])
        data3[1].append(value[1])

    create_plot(data1, data2, data3)