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梯度下降法是神经网络计算的基础，下面我们用python编程来体验它！

代码

# -*- coding: utf-8 -*-"""@File    : 梯度下降法求函数最小值.py@Time    : 2020/5/17 21:30@Author  : Dontla@Email   : sxana@qq.com@Software: PyCharm"""# 函数def f(a, b):    return a ** 2 + b ** 2# 梯度def calcu_gra_f2x(a, b):    return 2 * adef calcu_gra_f2y(a, b):    return 2 * b# 位移向量def calcu_delta_x(gra_x, ita):    return gra_x * -itadef calcu_delta_y(gra_y, ita):    return gra_y * -itaif __name__ == '__main__':    # 学习率    eta = 0.1    # 初始参数    x, y = 3.00, 2.00    gra_f2x, gra_f2y = calcu_gra_f2x(x, y), calcu_gra_f2y(x, y)    delta_x, delta_y = calcu_delta_x(gra_f2x, eta), calcu_delta_y(gra_f2y, eta)    z = f(x, y)    # 执行梯度下降法    for i in range(0, 20):        print(            '第{:0>2d}轮\tx={:.2f}\ty={:.2f}\tgra_f2x={:.2f}\tgra_f2y={:.2f}\tdelta_x={:.2f}\tdelta_y={:.2f}\tz={:.2f}'.format(                i, x, y, gra_f2x, gra_f2y, delta_x, delta_y, z))        # 更新变量        x = x + delta_x        y = y + delta_y        gra_f2x = calcu_gra_f2x(x, y)        gra_f2y = calcu_gra_f2y(x, y)        delta_x = calcu_delta_x(gra_f2x, eta)        delta_y = calcu_delta_y(gra_f2y, eta)        z = f(x, y)

结果：

D:\20200228_play_with_pytorch\python\python.exe C:/Users/SIQI/Desktop/20200511_用Excel体验梯度下降法（改成用python体验）/梯度下降法求函数最小值/梯度下降法求函数最小值.py第00轮	x=3.00	y=2.00	gra_f2x=6.00	gra_f2y=4.00	delta_x=-0.60	delta_y=-0.40	z=13.00第01轮	x=2.40	y=1.60	gra_f2x=4.80	gra_f2y=3.20	delta_x=-0.48	delta_y=-0.32	z=8.32第02轮	x=1.92	y=1.28	gra_f2x=3.84	gra_f2y=2.56	delta_x=-0.38	delta_y=-0.26	z=5.32第03轮	x=1.54	y=1.02	gra_f2x=3.07	gra_f2y=2.05	delta_x=-0.31	delta_y=-0.20	z=3.41第04轮	x=1.23	y=0.82	gra_f2x=2.46	gra_f2y=1.64	delta_x=-0.25	delta_y=-0.16	z=2.18第05轮	x=0.98	y=0.66	gra_f2x=1.97	gra_f2y=1.31	delta_x=-0.20	delta_y=-0.13	z=1.40第06轮	x=0.79	y=0.52	gra_f2x=1.57	gra_f2y=1.05	delta_x=-0.16	delta_y=-0.10	z=0.89第07轮	x=0.63	y=0.42	gra_f2x=1.26	gra_f2y=0.84	delta_x=-0.13	delta_y=-0.08	z=0.57第08轮	x=0.50	y=0.34	gra_f2x=1.01	gra_f2y=0.67	delta_x=-0.10	delta_y=-0.07	z=0.37第09轮	x=0.40	y=0.27	gra_f2x=0.81	gra_f2y=0.54	delta_x=-0.08	delta_y=-0.05	z=0.23第10轮	x=0.32	y=0.21	gra_f2x=0.64	gra_f2y=0.43	delta_x=-0.06	delta_y=-0.04	z=0.15第11轮	x=0.26	y=0.17	gra_f2x=0.52	gra_f2y=0.34	delta_x=-0.05	delta_y=-0.03	z=0.10第12轮	x=0.21	y=0.14	gra_f2x=0.41	gra_f2y=0.27	delta_x=-0.04	delta_y=-0.03	z=0.06第13轮	x=0.16	y=0.11	gra_f2x=0.33	gra_f2y=0.22	delta_x=-0.03	delta_y=-0.02	z=0.04第14轮	x=0.13	y=0.09	gra_f2x=0.26	gra_f2y=0.18	delta_x=-0.03	delta_y=-0.02	z=0.03第15轮	x=0.11	y=0.07	gra_f2x=0.21	gra_f2y=0.14	delta_x=-0.02	delta_y=-0.01	z=0.02第16轮	x=0.08	y=0.06	gra_f2x=0.17	gra_f2y=0.11	delta_x=-0.02	delta_y=-0.01	z=0.01第17轮	x=0.07	y=0.05	gra_f2x=0.14	gra_f2y=0.09	delta_x=-0.01	delta_y=-0.01	z=0.01第18轮	x=0.05	y=0.04	gra_f2x=0.11	gra_f2y=0.07	delta_x=-0.01	delta_y=-0.01	z=0.00第19轮	x=0.04	y=0.03	gra_f2x=0.09	gra_f2y=0.06	delta_x=-0.01	delta_y=-0.01	z=0.00Process finished with exit code 0

貌似这么简单的计算也用不着使用函数吧？？徒增代码量？？