2213

#!/usr/bin/env python
# -*- coding: UTF-8 -*-
import math
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider, Button

fig, ax = plt.subplots()
exa, = plt.plot(-5, 5)
appr, = plt.plot(-5, 5)
plt.xlim(-5, 5)
plt.ylim(-5, 5)
plt.subplots_adjust(bottom=0.2)
plt.grid(True)
axes_slider_N = plt.axes([0.1, 0.08, 0.7, 0.04])
slider_N = Slider(axes_slider_N,
                      label='N',
                      valmin=1,
                      valmax=20,
                      valinit=2,
                      valfmt='%1.0f'
                      )

axprev = plt.axes([0.85, 0.08, 0.04, 0.04])
axnext = plt.axes([0.90, 0.08, 0.04, 0.04])
bnext = Button(axnext, '+')
bprev = Button(axprev, '-')

dx = 0.1
a = 0
b = 1
p = 0
q = -9
alpha1 = 1
beta1 = 0
gammma1 = 0
alpha2 = 1
beta2 = 1
gammma2 = 1

class M_piu():
    U = [0, 1]
    V = [1, 0]
    W = [0, 0]
    n = 2
    h = (b - a) / n
    d = q * h ** 2 - p * h - 2
    e = 1 + p * h
    X1 = (beta1) / (beta1 - alpha1 * h)
    Nu1 = (gammma1 * h) / (alpha1 * h - beta1)
    X2 = (beta2) / (alpha2 * h + beta2)
    Nu2 = (gammma2 * h) / (alpha2 * h + beta2)
    def __init__(self):
        self.func_approximate()
        self.func_exact()
    def clear_U_V_W(self):
        self.U = [0, 1]
        self.V = [1, 0]
        self.W = [0, 0]
    def get_vectors_value(self):
        self.clear_U_V_W()
        for i in range(2, self.n + 1):
            self.U.append((-self.U[i - 2] - self.d * self.U[i - 1]) / self.e)
            self.V.append((-self.V[i - 2] - self.d * self.V[i - 1]) / self.e)
            self.W.append(((-2 * np.exp(3 * i * self.h) * self.h ** 2) - self.W[i - 2] - self.d * self.W[i - 1]) / self.e)
    def change_n_count_slider(self, count):

        self.n = int(count)
        self.h = (b - a) / self.n
        h = self.h

        self.d = q * h ** 2 - p * h - 2
        self.e = 1 + p * h
        self.X1 = (-beta1) / (alpha1 * h - beta1)
        self.Nu1 = (gammma1 * h) / (alpha1 * h - beta1)

        self.X2 = (beta2) / (alpha2 * h + beta2)
        self.Nu2 = (gammma2 * h) / (alpha2 * h + beta2)

        self.func_approximate()
        self.func_exact()
    def change_n_count(self, count):
        self.n += count
        self.h = (b - a) / self.n
        h = self.h

        self.d = q * h ** 2 - p * h - 2
        self.e = 1 + p * h
        self.X1 = (-beta1) / (alpha1 * h - beta1)
        self.Nu1 = (gammma1 * h) / (alpha1 * h - beta1)

        self.X2 = (beta2) / (alpha2 * h + beta2)
        self.Nu2 = (gammma2 * h) / (alpha2 * h + beta2)

        self.func_exact()
        self.func_approximate()
        slider_N.set_val(self.n)
    def get_coefficients(self):
        W, V, U = self.W, self.V, self.U
        X1, X2, Nu1, Nu2 = self.X1, self.X2, self.Nu1, self.Nu2
        '''C1 = (X2 * Nu1 * V[n - 1] + X2 * W[n - 1] + Nu2 - V[n] * Nu1 - W[n]) / (
                            U[n] + X1 * V[n] - X2 * U[n - 1] - X1 * X2 * V[n - 1])'''
        n = self.n

        C1 = (X2 * Nu1 * V[n - 1] + X2 * W[n - 1] + Nu2 - Nu1 * V[n] - W[n]) / (
                    U[n] + X1 * V[n] - X2 * U[n - 1] - X1 * X2 * V[n - 1])
        C2 = C1 * X1 + Nu1

        return C1, C2
    def func_approximate(self):#приближенное
        self.get_vectors_value()
        C1, C2 = self.get_coefficients()
        ylist = []
        for i in range(0, self.n + 1):
            ylist.append(C1 * self.U[i] + C2 * self.V[i] + self.W[i])

        xlist = np.arange(0, 1 + ((b - a) / (self.n)), (b - a) / (self.n))
        appr.set_ydata(ylist)
        appr.set_xdata(xlist)
        plt.draw()
    def func_exact(self):#точное
        xlist = np.arange(a, b + dx, dx)
        ylist = [((3 * math.exp(3 * x) + (5 - 4 * x) * (math.exp(3 + 3 * x)) - 3 * math.exp(-3 * x)
                   - 5 * math.exp(3 - 3 * x) - 2 * x * math.exp(3 * x - 3)) / (12 * math.exp(3) + 6 * math.exp(-3)))
                 for x in xlist]
        exa.set_ydata(ylist)
        exa.set_xdata(xlist)
        plt.draw()


vizovem = M_piu()
bprev.on_clicked(lambda x: vizovem.change_n_count(-1))
bnext.on_clicked(lambda x: vizovem.change_n_count(1))
slider_N.on_changed(lambda x: vizovem.change_n_count_slider(slider_N.val))
plt.show()

if __name__ == "__main__":
    pass