test.py

import numpy as np
import matplotlib.pyplot as plt


x_for_f = np.linspace(-1.5, 1.5, 500)
y_for_f = np.array([np.tan(x_for_f[i]) for i in range(len(x_for_f))], dtype = float)






        
print("Enter count:")
n = int(input())


x = np.linspace(-1.5, 1.5, num = n)
y = np.array([np.tan(x[i]) for i in range(len(x))], dtype = float)


x_cheb = np.array([(3/2)*np.cos((2*i+1)/(2*n+2)*np.pi) for i in range(n+1)], dtype = float)
y_cheb = np.array([np.tan(x_cheb[i]) for i in range(len(x_cheb))], dtype = float)


def lagranz(x,y,t):
    z = 0
    for j in range(len(y)):
        p1=1
        p2=1
        for i in range(len(x)):
            if i == j:
                p1 *=1
                p2 *=1
            else:
                p1 *= (t-x[i])
                p2 *= x[j]-x[i]
        z = z+y[j]*p1/p2
    return z


xnew = []
ynew = [lagranz(x,y,i) for i in xnew]


x_cheb_new = np.linspace(np.min(x_cheb), np.max(x_cheb), 100)
y_cheb_new = [lagranz(x_cheb, y_cheb, i) for i in x_cheb_new]


y_dev = np.array([y_for_f[i] - ynew[i] for i in range(len(xnew))], dtype = float)


y_dev_cheb = np.array([y_for_f[i] - y_cheb_new[i] for i in range(len(x_cheb_new))], dtype = float)


plt.xlabel(r'$x$')
plt.ylabel(r'$f(x)$')
plt.title(r'$f(x)=2+sin(x)$')


plt.plot(x_for_f, y_for_f, label = "f(x)=2+sin(x)")             


plt.plot(x, y, 'o', xnew, ynew, label = "g(x), equidistant nodes")


plt.plot(x_cheb, y_cheb, 'o', x_cheb_new, y_cheb_new, label = "h(x), Chebyshev nodes") 


plt.plot(xnew, y_dev, "--", label = "f(x)-g(x)")



plt.plot(x_cheb_new, y_dev_cheb, "-.", label = "f(x)-h(x)")
plt.legend()

plt.grid(True)
plt.show()