python 中的牛顿插值

Question

我必须使用现有代码进行二次插值并更改我的值。尽管如此，由于某种原因，当我继续绘制插值图时，函数突然停止（它不是连续的）。有人可以帮我弄清楚出了什么问题吗？我相信它与第 43 行（新数据点的评估）有关，但我不确定。

源代码：

import numpy as np
import matplotlib.pyplot as plt

plt.style.use('seaborn-poster')

%matplotlib inline

def divided_diff(x, y):
    '''
    function to calculate the divided
    differences table
    '''
    n = len(y)
    coef = np.zeros([n, n])
    # the first column is y
    coef[:,0] = y
    
    for j in range(1,n):
        for i in range(n-j):
            coef[i][j] = \
           (coef[i+1][j-1] - coef[i][j-1]) / (x[i+j]-x[i])
            
    return coef

def newton_poly(coef, x_data, x):
    '''
    evaluate the newton polynomial 
    at x
    '''
    n = len(x_data) - 1 
    p = coef[n]
    for k in range(1,n+1):
        p = coef[n-k] + (x -x_data[n-k])*p
    return p

x = np.array([-5, -1, 0, 2])
y = np.array([-2, 6, 1, 3])
# get the divided difference coef
a_s = divided_diff(x, y)[0, :]

# evaluate on new data points
x_new = np.arange(-5, 2.1, .1)
y_new = newton_poly(a_s, x, x_new)

plt.figure(figsize = (12, 8))
plt.plot(x, y, 'bo')
plt.plot(x_new, y_new)

我的代码（针对数据点进行了调整

(0,0);(6.4,1.9);(10.6,4.3)

）：

import numpy as np
import matplotlib.pyplot as plt

plt.style.use('seaborn-poster')

%matplotlib inline

def divided_diff(x, y):
    '''
    function to calculate the divided
    differences table
    '''
    n = len(y)
    coef = np.zeros([n, n])
    # the first column is y
    coef[:,0] = y
    
    for j in range(1,n):
        for i in range(n-j):
            coef[i][j] = \
           (coef[i+1][j-1] - coef[i][j-1]) / (x[i+j]-x[i])
            
    return coef

def newton_poly(coef, x_data, x):
    '''
    evaluate the newton polynomial 
    at x
    '''
    n = len(x_data) - 1 
    p = coef[n]
    for k in range(1,n+1):
        p = coef[n-k] + (x -x_data[n-k])*p
    return p

x = np.array([0, 6.4, 10.6])
y = np.array([0, 1.9, 4.3])
# get the divided difference coef
a_s = divided_diff(x, y)[0, :]

# evaluate on new data points
x_new = np.arange(-5, 2.1, .1)
y_new = newton_poly(a_s, x, x_new)

plt.figure(figsize = (12, 8))
plt.plot(x, y, 'bo')
plt.plot(x_new, y_new)