namespace Monitor.Backend.Analysis;

/// <summary>
/// 估计两端的时钟偏移和线性漂移：单向时延 x(t) = 偏移 + 漂移·t + 真实的时延变化。
/// 最小二乘拟合出直线，残差再减去残差的低分位（时延“地板”），就是去除偏移和漂移之后的抖动。
/// </summary>
public static class ClockDriftFit
{
    public const int MinPoints = 8;

    /// <summary>拟合 y = a + b·x，x 先居中以保证数值稳定。样本不足或 x 全部相同时返回 false。</summary>
    public static bool TryFit(ReadOnlySpan<double> x, ReadOnlySpan<double> y, out double intercept, out double slope, out double xMean)
    {
        intercept = 0;
        slope = 0;
        xMean = 0;
        int n = x.Length;
        if (n < 2)
        {
            return false;
        }

        double sumX = 0;
        double sumY = 0;
        for (int i = 0; i < n; i++)
        {
            sumX += x[i];
            sumY += y[i];
        }

        xMean = sumX / n;
        double yMean = sumY / n;
        double sxx = 0;
        double sxy = 0;
        for (int i = 0; i < n; i++)
        {
            double dx = x[i] - xMean;
            sxx += dx * dx;
            sxy += dx * (y[i] - yMean);
        }

        if (sxx <= 0)
        {
            return false;
        }

        slope = sxy / sxx;
        intercept = yMean - (slope * xMean);
        return true;
    }

    /// <summary>
    /// 去除偏移和漂移后的时延变化（非负）。样本少于 <see cref="MinPoints"/> 时返回 null（不产生观测值）。
    /// </summary>
    public static double[]? Jitter(ReadOnlySpan<double> timesUs, ReadOnlySpan<double> delaysUs)
    {
        int n = timesUs.Length;
        if (n < MinPoints || !TryFit(timesUs, delaysUs, out double intercept, out double slope, out double xMean))
        {
            return null;
        }

        double[] residual = new double[n];
        for (int i = 0; i < n; i++)
        {
            residual[i] = delaysUs[i] - (intercept + (slope * (timesUs[i] - xMean)));
        }

        double[] sorted = (double[])residual.Clone();
        Array.Sort(sorted);
        double floor = sorted[(int)(0.05 * (n - 1))];
        for (int i = 0; i < n; i++)
        {
            residual[i] = Math.Max(0, residual[i] - floor);
        }

        return residual;
    }
}