|
|
|
|
|
import numpy as np
|
|
|
|
|
|
from scipy.optimize import approx_fprime
|
|
|
|
|
|
import matplotlib.pyplot as plt
|
|
|
|
|
|
|
|
|
|
|
|
# 调整梯度下降法以动态适应参数数量
|
|
|
|
|
|
def gradient_descent_adjusted(func, sx, sy, learning_rate=0.001, iterations=5000):
|
|
|
|
|
|
# 动态确定func需要的参数数量（减去sx）
|
|
|
|
|
|
params_count = func.__code__.co_argcount - 1
|
|
|
|
|
|
# 基于参数数量初始化theta
|
|
|
|
|
|
theta = np.random.randn(params_count) * 0.01
|
|
|
|
|
|
|
|
|
|
|
|
# 定义损失函数和梯度的计算
|
|
|
|
|
|
def loss_grad(theta):
|
|
|
|
|
|
pred = func(sx, *theta)
|
|
|
|
|
|
error = pred - sy
|
|
|
|
|
|
loss = np.mean(error ** 2)
|
|
|
|
|
|
grad = approx_fprime(theta, lambda t: np.mean((func(sx, *t) - sy) ** 2), epsilon=1e-6)
|
|
|
|
|
|
return loss, grad
|
|
|
|
|
|
|
|
|
|
|
|
# 梯度下降循环
|
|
|
|
|
|
for _ in range(iterations):
|
|
|
|
|
|
_, grad = loss_grad(theta)
|
|
|
|
|
|
theta -= learning_rate * grad
|
|
|
|
|
|
|
|
|
|
|
|
return theta
|
|
|
|
|
|
|
|
|
|
|
|
# 示例函数：简单的线性函数
|
|
|
|
|
|
def example_func(sx,c, a, b):
|
|
|
|
|
|
return c*sx**2 + a * sx + b
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
# 生成模拟数据
|
|
|
|
|
|
np.random.seed(0)
|
|
|
|
|
|
sx = np.linspace(-1, 1, 100)
|
|
|
|
|
|
sy = 0.1*sx**2+ 3 * sx + 2 + np.random.randn(100) * 0.5
|
|
|
|
|
|
# 使用调整后的梯度下降法拟合模型
|
|
|
|
|
|
params_adjusted = gradient_descent_adjusted(example_func, sx, sy)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
# 绘制调整后的结果
|
|
|
|
|
|
plt.scatter(sx, sy, label="Data Points")
|
|
|
|
|
|
plt.plot(sx, example_func(sx, *params_adjusted), color="red", label="Fitted Line Adjusted")
|
|
|
|
|
|
plt.legend()
|
|
|
|
|
|
plt.xlabel("sx")
|
|
|
|
|
|
plt.ylabel("sy")
|
|
|
|
|
|
plt.title("Fitting with Adjusted Gradient Descent")
|
|
|
|
|
|
plt.show()
|
|
|
|
|
|
|
|
|
|
|
|
|
