Nrthugu

I want to use matplotlib to draw a picture of Newton interpolation, but I met with some difficulties. My figure don't through the last some points. Can you help me? If my code is wrong, please tell me the details, thank you.

import numpy as np

import matplotlib.pyplot as plt





def coef(x, y):

    '''x : array of data points

       y : array of f(x)  '''

    x.astype(float)

    y.astype(float)

    n = len(x)

    a = 

    for i in range(n):

        a.append(y[i])



    for j in range(1, n):



        for i in range(n - 1, j - 1, -1):

            a[i] = float(a[i] - a[i - 1]) / float(x[i] - x[i - j])



    return np.array(a)  # return an array of coefficient





def Eval(a, x, r):

    ''' a : array returned by function coef()

       x : array of data points

       r : the node to interpolate at  '''

    x.astype(float)

    n = len(a) - 1

    temp = a[n]

    for i in range(n - 1, -1, -1):

        temp = temp * (r - x[i]) + a[i]

    return temp  # return the y_value interpolation





if __name__ == '__main__':

    x = np.linspace(0, 20, 11)

    y = np.random.randint(0, 10, 11)

    # y = np.asarray([i ** 2 for i in x])



    a = coef(x, y)

    tmp_x = np.linspace(0, 21, 21)

    tmp_y = [Eval(a, tmp_x, i) for i in tmp_x]



    plt.plot(x, y, linestyle='', marker='o', color='b')

    plt.plot(tmp_x, tmp_y, linestyle='--', color='r')

    plt.show()

picture of code

OK， I had solve my problem after reading some paper about Newton Interprolation. But the comments are written in Chinese， when I have time, I will translate it into Engilsh.
image of Newton Interpolation

import numpy as np

import matplotlib.pyplot as plt





class Newton(object):

def __init__(self, x, y):

    self.x = x

    self.y = y



def run(self, tmp_x):

    # 构造差商表

    table = np.zeros([len(self.x), len(self.x) + 1], dtype=float)



    for i in range(len(self.x)):  # 将x 和 y 放入 差商表的前两列

        table[i][0] = self.x[i]

        table[i][1] = self.y[i]

    # 计算差商

    for i in range(2, table.shape[1]):  # i is 2 to 5

        for j in range(i - 1, table.shape[0]):  # j is

            table[j][i] = (table[j][i - 1] - table[j - 1][i - 1]) / (self.x[j] - self.x[j - i + 1])



    # print(table)  # 输出差商表

    # for i in range(table.shape[0]):

    #     for j in range(table.shape[1]):

    #         print(table[i][j], end=' ')

    #     print('n')

    # print('nn')



    # 由牛顿插值函数求给出的x序列对应的y序列

    tmp_y = 

    for ans_x in tmp_x:  # 遍历每个x

        ans_y = 0  # 对应于输入序列每个x的相应y值

        for i in range(table.shape[0]):

            tmp = table[i][i + 1]  # 求值多项式第 i 项， tab[i][i + 1]为其系数

            for j in range(i):

                tmp *= (ans_x - self.x[j])

            ans_y += tmp

        tmp_y.append(ans_y)

    return tmp_y





if __name__ == '__main__':

    plt.rcParams['font.sans-serif'] = ['SimHei']

    plt.rcParams['axes.unicode_minus'] = False



    sr_x = np.linspace(0, 20, 11)

    sr_fx = np.random.randint(0, 20, 11)



    tmp_x = np.linspace(0, 20)



    demo = Newton(sr_x, sr_fx)

    tmp_y = demo.run(tmp_x)



    print(tmp_x)

    print(tmp_y)



    plt.plot(sr_x, sr_fx, 'ro', label='插值节点')

    plt.plot(tmp_x, tmp_y, label='牛顿插值')

    enter code here

    plt.xlabel('x')

    plt.ylabel('y')

    plt.legend()

    plt.show()