# -*- coding: utf-8 -*-

#Program 0.5 Hermite Interpolation

import matplotlib.pyplot as plt

import numpy as np

#计算基函数的导数值

def dl(i, xi):

	result = 0.0

	for j in range(0,len(xi)):

		if j!=i:

			result += 1/(xi[i]-xi[j])

	result *= 2

	return result

#计算基函数值

def l(i, xi, x):

	deno = 1.0

	nu = 1.0

	for j in range(0, len(xi)):

		if j!= i:

			deno *= (xi[i]-xi[j])

			nu *= (x-xi[j])

	return nu/deno

#Hermite插值函数

def get_Hermite(xi, yi, dyi):

	def he(x):

		result = 0.0

		for i in range(0, len(xi)):

			result += (yi[i]+(x-xi[i])*(dyi[i]-2*yi[i]*dl(i, xi))) * ((l(i,xi,x))**2)

		return result

	return he

import math

sr_x = [(i * math.pi) + (math.pi / 2) for i in range(-3, 3)]

sr_fx = [math.sin(i) for i in sr_x]

deriv = [0 for i in sr_x]                           # 导数都为 0

Hx = get_Hermite(sr_x, sr_fx, deriv)  # 获得插值函数

tmp_x = [i * 0.1 * math.pi for i in range(-20, 20)] # 测试用例

tmp_y = [Hx(i) for i in tmp_x]                      # 根据插值函数获得测试用例的纵坐标

#画图

plt.plot(sr_x, sr_fx, 'ro')

plt.plot(tmp_x, tmp_y, 'b-')

plt.title('Hermite Interpolation')

plt.show()