Полином Лагранжа 2

import numpy as np
import matplotlib.pyplot as plt

import scipy.interpolate
import scipy.integrate

x = np.array([0, 1, 2, 3, 4, 5], dtype = float)
y = np.array([0.1, 0.5, 1, 6, 2, - 2.5], 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 = p1*1; p2 = p2*1
            else:
                p1 = p1*(t - x[i])
                p2 = p2*(x[j] - x[i])
        z = z + y[j]*p1/p2
    return z

def integr(a, b, dx):
    points = np.arange(a, b, dx)
    summ = 0
    for x_cur in points:
        summ += lagranz(x,y, x_cur)*dx
    return summ


xnew = np.linspace(np.min(x),np.max(x),100)
ynew = [lagranz(x,y,i) for i in xnew]
plt.plot(xnew,ynew, label='lagrange')
cubic_spline = scipy.interpolate.interp1d(x, y, kind='cubic')
ynew = cubic_spline(xnew)
plt.plot(xnew,ynew, label='cubic')
akima = scipy.interpolate.Akima1DInterpolator(x, y)
ynew = akima(xnew)
plt.plot(xnew,ynew, label='akima')
plt.grid(True)
plt.legend()
plt.show()


print integr(np.min(x), np.max(x), 0.1)
print integr(-2, 10, 0.01)



akima_1_2_integral_value,akima_1_2_integral_error = scipy.integrate.quad(akima, 1, 2)
print 'Value', akima_1_2_integral_value
print 'Error', akima_1_2_integral_error