Add Tukey's Biweight and WMAPE implementations with comprehensive tests and documentation

- Introduced Tukey's Biweight as a robust loss function, including mathematical foundation, usage patterns, and performance profile.
- Added WMAPE (Weighted Mean Absolute Percentage Error) implementation, emphasizing its advantages for intermittent demand forecasting.
- Created unit tests for WMAPE covering various scenarios including edge cases and batch calculations.
- Documented both Tukey's Biweight and WMAPE with detailed explanations, properties, and common use cases.

lib/errors/mdae/Mdae.cs

@@ -0,0 +1,223 @@
+using System.Runtime.CompilerServices;
+using System.Runtime.InteropServices;
+
+namespace QuanTAlib;
+
+/// <summary>
+/// MdAE: Median Absolute Error
+/// </summary>
+/// <remarks>
+/// MdAE is the median of absolute errors between actual and predicted values.
+/// Unlike MAE which uses the mean, MdAE is robust to outliers.
+///
+/// Formula:
+/// MdAE = Median(|actual - predicted|)
+///
+/// Key properties:
+/// - Robust to outliers (50% breakdown point)
+/// - Same units as the original data
+/// - Less sensitive to extreme errors than MAE
+/// - MdAE = 0 indicates at least half the predictions are perfect
+/// </remarks>
+[SkipLocalsInit]
+public sealed class Mdae : AbstractBase
+{
+    private readonly RingBuffer _buffer;
+    private readonly double[] _sortBuffer;
+
+    [StructLayout(LayoutKind.Auto)]
+    private record struct State(double LastValidActual, double LastValidPredicted, int TickCount);
+    private State _state;
+    private State _p_state;
+
+    public Mdae(int period)
+    {
+        if (period <= 0)
+            throw new ArgumentException("Period must be greater than 0", nameof(period));
+
+        _buffer = new RingBuffer(period);
+        _sortBuffer = new double[period];
+        Name = $"Mdae({period})";
+        WarmupPeriod = period;
+    }
+
+    public override bool IsHot => _buffer.IsFull;
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public TValue Update(TValue actual, TValue predicted, bool isNew = true)
+    {
+        double actualVal = actual.Value;
+        double predictedVal = predicted.Value;
+
+        if (!double.IsFinite(actualVal))
+            actualVal = double.IsFinite(_state.LastValidActual) ? _state.LastValidActual : 0.0;
+        else
+            _state.LastValidActual = actualVal;
+
+        if (!double.IsFinite(predictedVal))
+            predictedVal = double.IsFinite(_state.LastValidPredicted) ? _state.LastValidPredicted : 0.0;
+        else
+            _state.LastValidPredicted = predictedVal;
+
+        double absError = Math.Abs(actualVal - predictedVal);
+
+        if (isNew)
+        {
+            _p_state = _state;
+            _buffer.Add(absError);
+            _state.TickCount++;
+        }
+        else
+        {
+            _state = _p_state;
+            _buffer.UpdateNewest(absError);
+        }
+
+        // Calculate median
+        double result = CalculateMedian();
+
+        Last = new TValue(actual.Time, result);
+        PubEvent(Last, isNew);
+        return Last;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public TValue Update(double actual, double predicted, bool isNew = true)
+    {
+        return Update(new TValue(DateTime.UtcNow, actual), new TValue(DateTime.UtcNow, predicted), isNew);
+    }
+
+    public override TValue Update(TValue input, bool isNew = true)
+    {
+        throw new NotSupportedException("MdAE requires two inputs. Use Update(actual, predicted).");
+    }
+
+    public override TSeries Update(TSeries source)
+    {
+        throw new NotSupportedException("MdAE requires two inputs. Use Calculate(actualSeries, predictedSeries, period).");
+    }
+
+    public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
+    {
+        throw new NotSupportedException("MdAE requires two inputs.");
+    }
+
+    public override void Reset()
+    {
+        _buffer.Clear();
+        _state = default;
+        _p_state = default;
+        Last = default;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    private double CalculateMedian()
+    {
+        int count = _buffer.Count;
+        if (count == 0) return 0.0;
+
+        // Copy to sort buffer
+        for (int i = 0; i < count; i++)
+        {
+            _sortBuffer[i] = _buffer[i];
+        }
+
+        // Sort the portion we're using
+        Array.Sort(_sortBuffer, 0, count);
+
+        // Return median
+        if (count % 2 == 1)
+        {
+            return _sortBuffer[count / 2];
+        }
+        else
+        {
+            return (_sortBuffer[count / 2 - 1] + _sortBuffer[count / 2]) * 0.5;
+        }
+    }
+
+    public static TSeries Calculate(TSeries actual, TSeries predicted, int period)
+    {
+        if (actual.Count != predicted.Count)
+            throw new ArgumentException("Actual and predicted series must have the same length", nameof(predicted));
+
+        int len = actual.Count;
+        var t = new List<long>(len);
+        var v = new List<double>(len);
+        CollectionsMarshal.SetCount(t, len);
+        CollectionsMarshal.SetCount(v, len);
+
+        var tSpan = CollectionsMarshal.AsSpan(t);
+        var vSpan = CollectionsMarshal.AsSpan(v);
+
+        Batch(actual.Values, predicted.Values, vSpan, period);
+        actual.Times.CopyTo(tSpan);
+
+        return new TSeries(t, v);
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public static void Batch(ReadOnlySpan<double> actual, ReadOnlySpan<double> predicted, Span<double> output, int period)
+    {
+        if (actual.Length != predicted.Length || actual.Length != output.Length)
+            throw new ArgumentException("All spans must have the same length", nameof(output));
+        if (period <= 0)
+            throw new ArgumentException("Period must be greater than 0", nameof(period));
+
+        int len = actual.Length;
+        if (len == 0) return;
+
+        // Use heap allocation for batch - we need sorting per element
+        double[] buffer = new double[period];
+        double[] sortBuffer = new double[period];
+
+        double lastValidActual = 0;
+        double lastValidPredicted = 0;
+
+        for (int k = 0; k < len; k++)
+        {
+            if (double.IsFinite(actual[k])) { lastValidActual = actual[k]; break; }
+        }
+        for (int k = 0; k < len; k++)
+        {
+            if (double.IsFinite(predicted[k])) { lastValidPredicted = predicted[k]; break; }
+        }
+
+        int bufferIndex = 0;
+        int bufferCount = 0;
+
+        for (int i = 0; i < len; i++)
+        {
+            double act = actual[i];
+            double pred = predicted[i];
+
+            if (double.IsFinite(act)) lastValidActual = act; else act = lastValidActual;
+            if (double.IsFinite(pred)) lastValidPredicted = pred; else pred = lastValidPredicted;
+
+            double absError = Math.Abs(act - pred);
+
+            // Add to circular buffer
+            buffer[bufferIndex] = absError;
+            bufferIndex++;
+            if (bufferIndex >= period) bufferIndex = 0;
+            if (bufferCount < period) bufferCount++;
+
+            // Copy and sort for median
+            for (int j = 0; j < bufferCount; j++)
+            {
+                sortBuffer[j] = buffer[j];
+            }
+            Array.Sort(sortBuffer, 0, bufferCount);
+
+            // Calculate median
+            if (bufferCount % 2 == 1)
+            {
+                output[i] = sortBuffer[bufferCount / 2];
+            }
+            else
+            {
+                output[i] = (sortBuffer[bufferCount / 2 - 1] + sortBuffer[bufferCount / 2]) * 0.5;
+            }
+        }
+    }
+}