import numpy
from math import sqrt
import sys
from sympy import *


T = 20
N = 200
x0 = 3
eps = 1e-4

#x[i]=x[i-1]+h*f(x[i-1], t[i-1])

def ExplicitSchemeMethod1(N, T, x0):
    h = T/N
    x1 = x0
    t = numpy.linspace(0, T, N+1)
    x_exact = exactSolution(t[0])
    header = str('%4s| %9s| %8s| %9s| %8s|' % ('N', 't', 'x_exact', 'x1', 'x2'))
    table = []

    for i in range(len(t)):
        table.append(
            str('%4d| %8.4f |%8.4f | %8.4f | %8.4f|' % (i, t[i], x_exact, x1, x1))
        )
        if (i != 0):
            x1 = x1 + h * f(x1, t[i-1])
            x_exact = exactSolution(t[i])

    return header, table
#x[i+1]=x[i-1]+ 2*h*f(x[i], t[i])


def ExplicitSchemeMethod2(N, T, x0):
    table = []
    h = T/N
    t = numpy.linspace(0, T, N+1)
    x2 = x0
    header = str('%3s| %8s | %8s |' % ('N', 't', 'x3') + '\n')

    for i in range(len(t)):
        table.append(
            str('%4d| %8.4f |%8.4f |' % (i, t[i],  x2))
        )
        if (i == 0):
            x2_prev_i = x0
            continue

        if (i == 1):
            x2 = x0
            continue

        if (i > 1):
            x2_prev_i_1 = x2  # c предыдущего шага нашли и запомнили

            x2 = x2_prev_i + 2*h*f(x2, t[i])

            x2_prev_i = x2_prev_i_1  # запомнили как последующий для вычисления

    return header, table
# Implicit Scheme


def ImplicitScheme(N, T, x0, eps):

    h = T/N
    x_next, x_prev, i = x0, x0+1, 0
    while(numpy.abs(x_next-x_prev) > eps) and i <= N:
        t = i*h
        x_next = x_prev - f(x_prev, t)
        i = i+1
    return x_next, t

def f(x, t):
    return pow(t, 2)/x


def df(x, t):
    return diff(f(x, t), x)


def exactSolution(t):
    return sqrt(2/3*pow(t, 3)+9)


def printTable(header1, header2, leftHalth, rightHalth):
    delimeter = '  :)   '
    print(header1, delimeter, header2)

    for i in range(len(leftHalth)):
        print(leftHalth[i], delimeter, rightHalth[i])

if __name__ == '__main__':
    leftHeader, leftHalth = ExplicitSchemeMethod1(N, T, x0)
    rightHeader, rightHalth = ExplicitSchemeMethod2(N, T, x0)
    printTable(leftHeader, rightHeader, leftHalth, rightHalth)