import numpy as npfrom sympy import *import matplotlib.pyplot as pltdef f(x): return 1 / (1 + x ** 2)def cal(begin, end): by = f(begin) ey = f(end) I = (n - end) / (begin - end) * by + (n - begin) / (end - begin) * ey return 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)) - 5 dx = [] 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'] = False x = np.linspace(-5, 5, 101) y = f(x) Ly = nfSub(x, nf) plt.plot(x, y, label='原函数') plt.plot(x, Ly, label='分段线性插值函数') 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 - y temp = abs(temp) print(temp.mean())if __name__ == '__main__': x = np.array(range(11)) - 5 y = f(x) n, m = symbols('n m') init_printing(use_unicode=True) nf = calnf(x) draw(nf) lossCal(nf) 
