# coding:utf-8

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import math

# 牛顿迭代法 x[n+1]=(x[n]+a/x[n])/2 
def func(a):
    if a < 1e-6:
        return 0
    last = a
    c = a / 2
    while math.fabs(c - last) > 1e-6: # math.fabs()返回绝对值;while一直循环直到不满足条件为止
        last = c
        c = (c + a/c) / 2
    return c


if __name__ == '__main__':
    mpl.rcParams['font.sans-serif'] = [u'SimHei']
    mpl.rcParams['axes.unicode_minus'] = False
    x = np.linspace(0, 30, num=50)
    print('x=', x)
    func_ = np.frompyfunc(func, 1, 1)
    y = func_(x)
    print('y=', y)
    # y = np.sqrt(x)
    plt.figure(figsize=(10, 5), facecolor='w')
    plt.plot(x, y, 'ro-', lw=2, markersize=6)
    plt.grid(b=True, ls=':')
    plt.xlabel('X', fontsize=16)
    plt.ylabel('Y', fontsize=16)
    plt.title(u'求二次根', fontsize=18)
    plt.show()