QuanTAlib/lib/errors/rmsle/Rmsle.cs

using System.Runtime.CompilerServices;

namespace QuanTAlib;

/// <summary>
/// RMSLE: Root Mean Squared Logarithmic Error
/// </summary>
/// <remarks>
/// RMSLE is the square root of MSLE, providing an error metric in log-scale units.
/// Like MSLE, it's robust to outliers and suited for data spanning multiple orders of magnitude.
///
/// Formula:
/// RMSLE = √[(1/n) * Σ(log(1 + actual) - log(1 + predicted))²]
///
/// Key properties:
/// - Same units as log-transformed data (more interpretable than MSLE)
/// - Robust to outliers (logarithmic compression)
/// - Requires non-negative values
/// - Scale-independent for multiplicative relationships
/// </remarks>
[SkipLocalsInit]
public sealed class Rmsle : BiInputIndicatorBase
{
    /// <summary>
    /// Creates RMSLE with specified period.
    /// </summary>
    /// <param name="period">Number of values to average (must be > 0)</param>
    public Rmsle(int period) : base(period, $"Rmsle({period})") { }

    /// <inheritdoc/>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected override double ComputeError(double actual, double predicted)
    {
        // Ensure non-negative (RMSLE requires non-negative values)
        double act = actual < 0 ? 0 : actual;
        double pred = predicted < 0 ? 0 : predicted;

        // Same as MSLE: (log(1 + actual) - log(1 + predicted))²
        double logActual = Math.Log(1.0 + act);
        double logPredicted = Math.Log(1.0 + pred);
        double logError = logActual - logPredicted;
        return logError * logError;
    }

    /// <inheritdoc/>
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    protected override double PostProcess(double mean) => Math.Sqrt(mean);

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

    /// <summary>
    /// Batch calculation using log squared error computation with rolling mean sqrt.
    /// </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];

        ComputeLogSquaredErrors(actual, predicted, errors);
        ErrorHelpers.ApplyRollingMeanSqrt(errors, output, period);
    }

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

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

        // Find first valid non-negative values
        for (int i = 0; i < len; i++)
        {
            if (double.IsFinite(actual[i]) && actual[i] >= 0)
            {
                lastValidActual = actual[i];
                break;
            }
        }

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

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

            // Handle NaN/Infinity and negative values
            if (double.IsFinite(act) && act >= 0)
            {
                lastValidActual = act;
            }
            else
            {
                act = lastValidActual;
            }

            if (double.IsFinite(pred) && pred >= 0)
            {
                lastValidPredicted = pred;
            }
            else
            {
                pred = lastValidPredicted;
            }

            double logActual = Math.Log(1.0 + act);
            double logPredicted = Math.Log(1.0 + pred);
            double logError = logActual - logPredicted;
            output[i] = logError * logError;
        }
    }
}