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