python画出e指数函数的图像

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 np
import math
import matplotlib as mpl
import 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()