QuanTAlib/lib/errors/mpe/Mpe.cs

using System.Runtime.CompilerServices;

namespace QuanTAlib;

/// <summary>
/// MPE: Mean Percentage Error
/// </summary>
/// <remarks>
/// MPE measures the average percentage error between actual and predicted values,
/// preserving the sign to detect directional bias. Unlike MAPE, it can reveal
/// systematic over- or under-prediction.
///
/// Formula:
/// MPE = (100/n) * Σ((actual - predicted) / actual)
///
/// Key properties:
/// - Scale-independent (expressed as percentage)
/// - Preserves sign: positive = under-prediction, negative = over-prediction
/// - Cannot be calculated when actual = 0
/// - Useful for detecting systematic bias in predictions
/// </remarks>
[SkipLocalsInit]
public sealed class Mpe : BiInputIndicatorBase
{
    private const double Epsilon = 1e-10;

    /// <summary>
    /// Creates MPE with specified period.
    /// </summary>
    /// <param name="period">Number of values to average (must be > 0)</param>
    public Mpe(int period) : base(period, $"Mpe({period})") { }

    /// <inheritdoc/>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected override double ComputeError(double actual, double predicted)
    {
        // MPE: 100 * (actual - predicted) / actual (preserves sign)
        // When actual is near zero, use signed epsilon to preserve the original sign
        double divisor;
        if (Math.Abs(actual) < Epsilon)
        {
            int sign = Math.Sign(actual);
            divisor = sign != 0 ? sign * Epsilon : Epsilon;
        }
        else
        {
            divisor = actual;
        }
        return 100.0 * (actual - predicted) / divisor;
    }

    /// <summary>
    /// Calculates MPE for entire series.
    /// </summary>
    public static TSeries Batch(TSeries actual, TSeries predicted, int period)
        => CalculateImpl(actual, predicted, period, Batch);

    /// <summary>
    /// Batch calculation using signed percentage error computation with rolling mean.
    /// </summary>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void Batch(ReadOnlySpan<double> actual, ReadOnlySpan<double> predicted, Span<double> output, int period)
    {
        ValidateBatchInputs(actual, predicted, output, period);

        int len = actual.Length;
        if (len == 0)
        {
            return;
        }

        const int StackAllocThreshold = 256;
        Span<double> errors = len <= StackAllocThreshold
            ? stackalloc double[len]
            : new double[len];

        ComputeSignedPercentageErrors(actual, predicted, errors);
        ErrorHelpers.ApplyRollingMean(errors, output, period);
    }

    public static (TSeries Results, Mpe Indicator) Calculate(TSeries actual, TSeries predicted, int period)
    {
        var indicator = new Mpe(period);
        TSeries results = Batch(actual, predicted, period);
        return (results, indicator);
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private static void ComputeSignedPercentageErrors(ReadOnlySpan<double> actual, ReadOnlySpan<double> predicted, Span<double> output)
    {
        int len = actual.Length;
        double lastValidActual = 1.0, lastValidPredicted = 0;

        for (int i = 0; i < len; i++)
        {
            if (double.IsFinite(actual[i]) && Math.Abs(actual[i]) >= Epsilon)
            {
                lastValidActual = actual[i];
                break;
            }
        }

        for (int i = 0; i < len; i++)
        {
            if (double.IsFinite(predicted[i]))
            {
                lastValidPredicted = predicted[i];
                break;
            }
        }

        for (int i = 0; i < len; i++)
        {
            double act = actual[i];
            double pred = predicted[i];

            if (double.IsFinite(act) && Math.Abs(act) >= Epsilon)
            {
                lastValidActual = act;
            }
            else
            {
                act = lastValidActual;
            }

            if (double.IsFinite(pred))
            {
                lastValidPredicted = pred;
            }
            else
            {
                pred = lastValidPredicted;
            }

            // Use signed epsilon to preserve the original sign when actual is near zero
            double divisor;
            if (Math.Abs(act) < Epsilon)
            {
                int sign = Math.Sign(act);
                divisor = sign != 0 ? sign * Epsilon : Epsilon;
            }
            else
            {
                divisor = act;
            }
            output[i] = 100.0 * (act - pred) / divisor;
        }
    }
}