这里用Python逼近函数y = exp(x);同样使用泰勒函数去逼近:

exp(x) = 1 + x + (x)^2/(2!) + .. + (x)^n/(n!) + ...

#!/usr/bin/python# -*- coding:utf-8 -*- import numpy as npimport mathimport matplotlib as mplimport matplotlib.pyplot as plt def calc_e_small(x): n = 10 f = np.arange(1, n+1).cumprod() b = np.array([x]*n).cumprod() return np.sum(b / f) + 1 def calc_e(x): reverse = False if x < 0: # 处理负数 x = -x reverse = True ln2 = 0.69314718055994530941723212145818 c = x / ln2 a = int(c+0.5) b = x - a*ln2 y = (2 ** a) * calc_e_small(b) if reverse: return 1/y return y if __name__ == "__main__": t1 = np.linspace(-2, 0, 10, endpoint=False) t2 = np.linspace(0, 3, 20) t = np.concatenate((t1, t2)) print(t) # 横轴数据 y = np.empty_like(t) for i, x in enumerate(t): y[i] = calc_e(x) print('e^', x, ' = ', y[i], '(近似值)\t', math.exp(x), '(真实值)') # print '误差：', y[i] - math.exp(x) plt.figure(facecolor='w') mpl.rcParams['font.sans-serif'] = [u'SimHei'] mpl.rcParams['axes.unicode_minus'] = False plt.plot(t, y, 'r-', t, y, 'go', linewidth=2) plt.title(u'Taylor展式的应用 - 指数函数', fontsize=18) plt.xlabel('X', fontsize=15) plt.ylabel('exp(X)', fontsize=15) plt.grid(True) plt.show()

以上这篇python实现画出e指数函数的图像就是小编分享给大家的全部内容了，希望能给大家一个参考，也希望大家多多支持。