函數

y=11+x2y=11+x2

圖像

可以看到，這里已經幾乎沒有任何差距了。。

代碼

import numpy as np from sympy import * import matplotlib.pyplot as pltdef f(x):return 1 / (1 + x ** 2)def cal(begin, end):by = f(begin)ey = f(end)Y = 1 / (1 + n ** 2)df = diff(Y)dfb = df.subs(n, begin)dfe = df.subs(n, end)oldFrac = ((n - end) / (begin - end))newFrac = ((n - begin) / (end - begin))I = (oldFrac ** 2) * (1 + 2 * newFrac) * by + (newFrac ** 2) * (1 + 2 * oldFrac) * ey + (oldFrac ** 2) * (n - begin) * dfb + (newFrac ** 2) * (n - end) * dfereturn Idef calnf(x):nf = []for i in range(len(x) - 1):nf.append(cal(x[i], x[i + 1]))return nfdef calf(f, x):y = []for i in x:y.append(f.subs(n, i))return ydef nfSub(x, nf):tempx = np.array(range(11)) - 5dx = []for i in range(10):labelx = []for j in range(len(x)):if x[j] >= tempx[i] and x[j] < tempx[i + 1]:labelx.append(x[j])elif i == 9 and x[j] >= tempx[i] and x[j] <= tempx[i + 1]:labelx.append(x[j])dx = dx + calf(nf[i], labelx)return np.array(dx)def draw(nf):plt.rcParams['font.sans-serif'] = ['SimHei']plt.rcParams['axes.unicode_minus'] = Falsex = np.linspace(-5, 5, 101)y = f(x)Ly = nfSub(x, nf)plt.plot(x, y, label='原函數')plt.plot(x, Ly, label='分段Hermite插值函數')plt.xlabel('x')plt.ylabel('y')plt.legend()plt.savefig('1.png')plt.show()def lossCal(nf):x = np.linspace(-5, 5, 101)y = f(x)Ly = nfSub(x, nf)Ly = np.array(Ly)temp = Ly - ytemp = abs(temp)print(temp.mean())if __name__ == '__main__':x = np.array(range(11)) - 5y = f(x)n, m = symbols('n m')init_printing(use_unicode=True)nf = calnf(x)draw(nf)lossCal(nf)

總結

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