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51 lines
1.4 KiB
51 lines
1.4 KiB
import numpy as np
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import matplotlib.pyplot as plt
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# 定义待拟合的函数形式
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def func(x, coeffs):
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return coeffs[0] * x + coeffs[1]
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# 定义目标函数，即待拟合数据
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def target_func(x):
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return 2.5 * x + 1.2
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# 生成带噪声的待拟合数据
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np.random.seed(0)
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x_data = np.linspace(0, 10, 100)
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y_data = target_func(x_data) + np.random.normal(0, 0.5, 100)
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# 定义损失函数，即拟合函数与目标函数之间的差距
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def loss_func(coeffs, x, y):
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return np.mean((y - func(x, coeffs))**2)
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# 定义梯度计算函数，即损失函数对于系数的偏导数
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def gradient_func(coeffs, x, y):
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gradient = np.zeros_like(coeffs)
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gradient[0] = -2 * np.mean((y - func(x, coeffs)) * x)
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gradient[1] = -2 * np.mean(y - func(x, coeffs))
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return gradient
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# 初始化参数
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learning_rate = 0.01
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num_iterations = 1000
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initial_coeffs = np.array([1.0, 1.0], dtype=float)
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# 使用梯度下降法拟合函数
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coeffs = initial_coeffs
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for i in range(num_iterations):
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gradient = gradient_func(coeffs, x_data, y_data)
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coeffs -= learning_rate * gradient
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# 打印拟合得到的系数
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print("拟合得到的系数：", coeffs)
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# 绘制拟合结果
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x_fit = np.linspace(0, 10, 100)
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y_fit = func(x_fit, coeffs)
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plt.plot(x_data, y_data, 'bo', label='原始数据')
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plt.plot(x_fit, y_fit, 'r-', label='拟合曲线')
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plt.legend()
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plt.xlabel('x')
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plt.ylabel('y')
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plt.show() |