import numpy as np
import matplotlib.pyplot as plt
class Optimizer:
def __init__(self,
epsilon = 1e-10, # 误差
iters = 100000, # 最大迭代次数
lamb = 0.01, # 学习率
gamma = 0.0, # 动量项系数
):
self.epsilon = epsilon
self.iters = iters
self.lamb = lamb
self.gamma = gamma
def momentum(self, x_0 = 0.5, y_0 = 0.5):
f1, f2 = self.fn(x_0, y_0), 0
w = np.array([x_0, y_0]) # 每次迭代后的函数值，用于绘制梯度曲线
k = 0 # 当前迭代次数
v_t = 0.0
while True:
if abs(f1 - f2) <= self.epsilon or k > self.iters:
break
f1 = self.fn(x_0, y_0)
g = np.array([self.dx(x_0, y_0), self.dy(x_0, y_0)])
v_t = self.gamma * v_t + self.lamb * g
x_0, y_0 = np.array([x_0, y_0]) - v_t
f2 = self.fn(x_0, y_0)
w = np.vstack((w, (x_0, y_0)))
k += 1
self.print_info(k, x_0, y_0, f2)
self.draw_process(w)
def print_info(self, k, x_0, y_0, f2):
print('迭代次数：{}'.format(k))
print('极值点：【x_0】：{} 【y_0】：{}'.format(x_0, y_0))
print('函数的极值：{}'.format(f2))
def draw_process(self, w):
X = np.arange(0, 1.5, 0.01)
Y = np.arange(-1, 1, 0.01)
[x, y] = np.meshgrid(X, Y)
f = x**3 - y**3 + 3 * x**2 + 3 * y**2 - 9 * x
plt.contour(x, y, f, 20)
plt.plot(w[:, 0],w[:, 1], 'g*', w[:, 0], w[:, 1])
plt.show()
def fn(self, x, y):
return x**3 - y**3 + 3 * x**2 + 3 * y**2 - 9 * x
def dx(self, x, y):
return 3 * x**2 + 6 * x - 9
def dy(self, x, y):
return - 3 * y**2 + 6 * y
"""
函数: f(x) = x**3 - y**3 + 3 * x**2 + 3 * y**2 - 9 * x
最优解: x = 1, y = 0
极小值: f(x,y) = -5
"""
optimizer = Optimizer()
optimizer.momentum()
