梯度下降算法3维图像示例

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.pylab as mpl
from mpl_toolkits.mplot3d import Axes3D

# 画图中文显示：不报错
mpl.rcParams['font.sans-serif'] = [u'simHei']
mpl.rcParams['axes.unicode_minus'] = False

# 设置二维函数(有2个特征属性:x1, x2)
def f(x1, x2):
    return 0.6 * (x1 + x2) ** 2 - x1 * x2
# 2个特征属性的求导得theta1, theta2
def hx1(x1, x2):
    return 1.2 * (x1 + x2) - x2
def hx2(x1, x2):
    return 1.2 * (x1 + x2) - x1

# 使用梯度下降法求解
GD_x1 = []
GD_x2 = []
GD_Y = []

# 设置初始化参数
x1 = 7
x2 = 6
alpha = 0.5
f_change = f(x1, x2)
f_current = f_change
GD_x1.append(x1)
GD_x2.append(x2)
GD_Y.append(f_current)

# 设置迭代次数统计变量
iter_num = 0
# 设置迭代条件
while iter_num < 500 and f_change > 1e-10:
    iter_num += 1
    pre_x1 = x1
    pre_x2 = x2
    x1 = pre_x1 - alpha * hx1(pre_x1, pre_x2)
    x2 = pre_x2 - alpha * hx2(pre_x1, pre_x2)

    tmp = f(x1, x2)
    # 梯度差值的绝对值
    f_change = np.abs(f_current - tmp)
    f_current = tmp
    GD_x1.append(x1)
    GD_x2.append(x2)
    GD_Y.append(f_current)
print(u'最终结果为：（%.5f, %.5f, %.5f）' % (x1, x2, f_current))
print(u'最终迭代次数结果为：%d' % iter_num)
print(GD_Y)
# print()

# 构建原函数数据
X1 = np.arange(-8, 8.5, 0.1)
X2 = np.arange(-8, 8.5, 0.1)
X1, X2 = np.meshgrid(X1, X2)  # 绘制X1, X2网格点
Y = np.array(list(map(lambda t: f(t[0], t[1]), zip(X1.flatten(), X2.flatten()))))
Y.shape = X1.shape

# 准备3D画布
fig = plt.figure(facecolor='w')
ax = Axes3D(fig)
ax.plot_surface(X1, X2, Y, rstride=1, cstride=1, cmap=plt.cm.jet)
ax.plot(GD_x1, GD_x2, GD_Y, 'ko--')
ax.set_title(u'函数$0.6 * (x1 + x2) ^ 2 - x1 * x2$: \n学习率：%.3f; 最终解是：(%.3f, %.3f, %.3f); 迭代次数：%d' % (alpha, x1, x2, f_current, iter_num))
plt.show()

E:\myprogram\anaconda\python.exe E:/xx/机器学习/梯度下降操作/梯度下降算法3维图像示例.py
最终结果为：（0.00000, -0.00000, 0.00000）
最终迭代次数结果为：17
[59.39999999999999, 5.386000000000001, 0.4947399999999999, 0.04702659999999999, 0.004857394, 0.0005934154600000001, 9.246989140000004e-05, 1.8087915226000006e-05, 4.06931862034e-06, 9.765902383306002e-07, 2.40481012074754e-07, 5.979026374297786e-08, 1.491786690093051e-08, 3.726793812099371e-09, 9.314578908428496e-10, 2.3284282211433304e-10, 5.820875697490912e-11, 1.4552013873896607e-11]