QuanTAlib/lib/trends/mama/Mama.cs

using System;
using System.Runtime.CompilerServices;

namespace QuanTAlib;

/// <summary>
/// MESA Adaptive Moving Average (MAMA)
/// A trend-following indicator that adapts to the market's phase rate of change.
/// </summary>
[SkipLocalsInit]
public sealed class Mama : ITValuePublisher
{
    public TValue Last { get; private set; }
    public TValue Fama { get; private set; }
    public bool IsHot => _state.Index > 6;
    public event Action<TValue>? Pub;

    private readonly double _fastLimit;
    private readonly double _slowLimit;

    private record struct State(
        double Period, double Phase, double Mama, double Fama, double SumPr,
        double I2, double Q2, double Re, double Im, double LastValidPrice, int Index
    );
    private State _state;
    private State _p_state;

    private readonly RingBuffer _priceBuffer;
    private readonly RingBuffer _smoothBuffer;
    private readonly RingBuffer _detrender;
    private readonly RingBuffer _I1_buffer;
    private readonly RingBuffer _Q1_buffer;

    private const double c1 = 0.0962;
    private const double c2 = 0.5769;
    private const double TWOPI = 2.0 * Math.PI;
    private const double RadToDeg = 180.0 / Math.PI;

    public Mama(double fastLimit = 0.5, double slowLimit = 0.05)
    {
        if (fastLimit <= slowLimit || fastLimit <= 0 || slowLimit <= 0)
        {
            throw new ArgumentException("FastLimit must be > SlowLimit and > 0");
        }
        _fastLimit = fastLimit;
        _slowLimit = slowLimit;

        _priceBuffer = new RingBuffer(7);
        _smoothBuffer = new RingBuffer(7);
        _detrender = new RingBuffer(7);
        _I1_buffer = new RingBuffer(7);
        _Q1_buffer = new RingBuffer(7);

        Name = $"Mama({fastLimit:F2},{slowLimit:F2})";
        Init();
    }

    public Mama(ITValuePublisher source, double fastLimit = 0.5, double slowLimit = 0.05) : this(fastLimit, slowLimit)
    {
        source.Pub += (item) => Update(item);
    }

    public void Init()
    {
        _state = default;
        _state.Mama = double.NaN;
        _state.Fama = double.NaN;
        _p_state = _state;

        _priceBuffer.Clear();
        _smoothBuffer.Clear();
        _detrender.Clear();
        _I1_buffer.Clear();
        _Q1_buffer.Clear();

        Last = new TValue(DateTime.MinValue, double.NaN);
        Fama = new TValue(DateTime.MinValue, double.NaN);
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public TValue Update(TValue input, bool isNew = true)
    {
        if (isNew)
        {
            _p_state = _state;
            _state.Index++;
        }
        else
        {
            _state = _p_state;
        }

        double price = input.Value;
        if (!double.IsFinite(price))
        {
            price = _state.LastValidPrice;
        }
        else
        {
            _state.LastValidPrice = price;
        }

        _priceBuffer.Add(price, isNew);

        if (_state.Index > 6)
        {
            double adj = (0.075 * _state.Period) + 0.54;

            // Smooth
            double smooth = (4.0 * _priceBuffer[^1] + 3.0 * _priceBuffer[^2] + 2.0 * _priceBuffer[^3] + _priceBuffer[^4]) * 0.1;
            _smoothBuffer.Add(smooth, isNew);

            // Detrender
            double dt = (c1 * _smoothBuffer[^1] + c2 * _smoothBuffer[^3] - c2 * _smoothBuffer[^5] - c1 * _smoothBuffer[^7]) * adj;
            _detrender.Add(dt, isNew);

            // Q1
            double q1 = (c1 * dt + c2 * _detrender[^3] - c2 * _detrender[^5] - c1 * _detrender[^7]) * adj;
            _Q1_buffer.Add(q1, isNew);

            // I1 = dt[3]
            double i1 = _detrender[^4];
            _I1_buffer.Add(i1, isNew);

            // Advance phases
            // jI = CalculateHilbertTransform(_i1, adj)
            double jI = (c1 * i1 + c2 * _I1_buffer[^3] - c2 * _I1_buffer[^5] - c1 * _I1_buffer[^7]) * adj;
            // jQ = CalculateHilbertTransform(_q1, adj)
            double jQ = (c1 * q1 + c2 * _Q1_buffer[^3] - c2 * _Q1_buffer[^5] - c1 * _Q1_buffer[^7]) * adj;

            // Phasor addition
            double i2_val = i1 - jQ;
            double q2_val = q1 + jI;

            // Smooth i2, q2
            _state.I2 = 0.2 * i2_val + 0.8 * _p_state.I2;
            _state.Q2 = 0.2 * q2_val + 0.8 * _p_state.Q2;

            // Homodyne discriminator
            double re_val = (_state.I2 * _p_state.I2) + (_state.Q2 * _p_state.Q2);
            double im_val = (_state.I2 * _p_state.Q2) - (_state.Q2 * _p_state.I2);

            // Smooth re, im
            _state.Re = 0.2 * re_val + 0.8 * _p_state.Re;
            _state.Im = 0.2 * im_val + 0.8 * _p_state.Im;

            // Calculate Period
            double period = (Math.Abs(_state.Im) > double.Epsilon && Math.Abs(_state.Re) > double.Epsilon)
                ? TWOPI / Math.Atan(_state.Im / _state.Re)
                : 0.0;

            // Adjust Period
            double periodCap = _p_state.Period * 1.5;
            double periodFloor = _p_state.Period * 0.67;

            if (period > periodCap) period = periodCap;
            if (period < periodFloor) period = periodFloor;

            if (period < 6.0) period = 6.0;
            if (period > 50.0) period = 50.0;

            // Smooth Period
            _state.Period = 0.2 * period + 0.8 * _p_state.Period;

            // Phase calculation
            _state.Phase = Math.Abs(i1) >= double.Epsilon ? Math.Atan(q1 / i1) * RadToDeg : 0.0;

            // Adaptive alpha
            double delta = Math.Max(_p_state.Phase - _state.Phase, 1.0);
            double alpha = _fastLimit / delta;
            alpha = Math.Clamp(alpha, _slowLimit, _fastLimit);

            // Final indicators
            _state.Mama = alpha * _priceBuffer[^1] + (1.0 - alpha) * _p_state.Mama;
            _state.Fama = 0.5 * alpha * _state.Mama + (1.0 - 0.5 * alpha) * _p_state.Fama;
        }
        else
        {
            // Initialization phase
            _state.SumPr += price;
            double avg = _state.Index > 0 ? _state.SumPr / _state.Index : price;
            _state.Mama = avg;
            _state.Fama = avg;
            
            // Initialize buffers with 0
            _smoothBuffer.Add(0, isNew);
            _detrender.Add(0, isNew);
            _I1_buffer.Add(0, isNew);
            _Q1_buffer.Add(0, isNew);
        }

        Last = new TValue(input.Time, _state.Mama);
        Fama = new TValue(input.Time, _state.Fama);
        Pub?.Invoke(Last);
        return Last;
    }

    public TSeries Update(TSeries source)
    {
        if (source.Count == 0) return [];

        int len = source.Count;
        var v = new List<double>(len);
        var t = new List<long>(len);

        for (int i = 0; i < len; i++)
        {
            var item = source[i];
            var result = Update(item);
            v.Add(result.Value);
            t.Add(item.Time);
        }

        return new TSeries(t, v);
    }

    public static void Calculate(ReadOnlySpan<double> source, Span<double> output, double fastLimit = 0.5, double slowLimit = 0.05)
    {
        var mama = new Mama(fastLimit, slowLimit);
        for (int i = 0; i < source.Length; i++)
        {
            output[i] = mama.Update(new TValue(DateTime.MinValue, source[i])).Value;
        }
    }

    public string Name { get; set; }
}