test_fitting.py

"""测试带偏置的幂律拟合功能"""
import numpy as np
from scipy.optimize import curve_fit

def power_law_with_offset(x, a, b, c):
    """带偏置的幂律函数: y = a * x^b + c"""
    return a * np.power(x, b) + c


def fit_power_law_with_offset(x_values, y_values):
    """
    使用带偏置的幂律拟合原始数据
    返回: (params, raw_rmse, log_rmse, fit_x, fit_y)
    """
    x_arr = np.array(x_values)
    y_arr = np.array(y_values)

    # 初始参数估计
    # 使用简单的幂律拟合作为初始值
    log_x = np.log10(x_arr)
    log_y = np.log10(y_arr)
    slope, intercept = np.polyfit(log_x, log_y, 1)

    a_init = 10**intercept
    b_init = slope
    c_init = 0  # 偏置初始值设为0

    try:
        # 使用curve_fit进行非线性拟合
        params, _ = curve_fit(
            power_law_with_offset,
            x_arr,
            y_arr,
            p0=[a_init, b_init, c_init],
            maxfev=10000
        )
        a, b, c = params

        # 计算预测值
        y_pred = power_law_with_offset(x_arr, a, b, c)

        # 计算原始空间 RMSE
        raw_rmse = np.sqrt(np.mean((y_arr - y_pred) ** 2))

        # 计算对数空间 RMSE
        log_y_actual = np.log10(y_arr)
        log_y_pred = np.log10(y_pred)
        log_rmse = np.sqrt(np.mean((log_y_actual - log_y_pred) ** 2))

        # 生成拟合曲线的点
        x_min, x_max = min(x_values), max(x_values)
        fit_x = np.linspace(x_min * 0.8, x_max * 1.2, 100)
        fit_y = power_law_with_offset(fit_x, a, b, c)

        return params, raw_rmse, log_rmse, fit_x, fit_y
    except Exception as e:
        print(f"Fitting failed: {e}")
        # 如果拟合失败，返回简单幂律拟合结果
        a = a_init
        b = b_init
        c = 0
        params = (a, b, c)

        y_pred = a * np.power(x_arr, b)

        # 计算原始空间 RMSE
        raw_rmse = np.sqrt(np.mean((y_arr - y_pred) ** 2))

        # 计算对数空间 RMSE
        log_y_actual = np.log10(y_arr)
        log_y_pred = np.log10(y_pred)
        log_rmse = np.sqrt(np.mean((log_y_actual - log_y_pred) ** 2))

        x_min, x_max = min(x_values), max(x_values)
        fit_x = np.linspace(x_min * 0.8, x_max * 1.2, 100)
        fit_y = a * np.power(fit_x, b)

        return params, raw_rmse, log_rmse, fit_x, fit_y


if __name__ == "__main__":
    # 测试数据：模拟一些模型参数和压缩率的关系
    # 假设真实关系为 y = 50 * x^(-0.1) + 10
    x_test = np.array([1, 3, 7, 13, 20, 30])
    y_true = 50 * np.power(x_test, -0.1) + 10
    # 添加一些噪声
    np.random.seed(42)
    y_test = y_true + np.random.normal(0, 0.5, len(x_test))

    print("测试数据:")
    print(f"x: {x_test}")
    print(f"y: {y_test}")
    print()

    # 进行拟合
    params, raw_rmse, log_rmse, fit_x, fit_y = fit_power_law_with_offset(x_test.tolist(), y_test.tolist())
    a, b, c = params

    print("拟合结果:")
    print(f"a = {a:.4f}")
    print(f"b = {b:.4f}")
    print(f"c = {c:.4f}")
    print(f"Raw RMSE = {raw_rmse:.4f}")
    print(f"Log-RMSE = {log_rmse:.4f}")
    print()
    print(f"拟合公式: y = {a:.2f} * x^{b:.3f} + {c:.2f}")
    print()
    print("真实参数: a=50, b=-0.1, c=10")
    print("拟合成功!" if raw_rmse < 2.0 else "拟合可能需要调整")