mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-04 04:07:42 +00:00
Miha Kralj
356 lines
10 KiB
C#
356 lines
10 KiB
C#
using System.Runtime.CompilerServices;
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using System.Runtime.InteropServices;
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namespace QuanTAlib;
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/// <summary>
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/// BINOMDIST: Binomial Distribution CDF
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/// Computes P(X ≤ k) for X ~ Binomial(n, p), where p is derived from the
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/// min-max normalized position of the input price within its rolling window.
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/// </summary>
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/// <remarks>
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/// Key properties:
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/// - Output always in [0, 1]
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/// - Rolling window tracks min/max for normalization; flat range returns P(X≤k|p=0.5)
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/// - p ≤ 0: returns 1.0 (all probability mass at X=0, P(X≤k)=1 for k≥0)
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/// - p ≥ 1: returns 1.0 if k≥n, else 0.0 (all mass at X=n)
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/// - Log-space computation via Lanczos log-gamma avoids factorial overflow for large n
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/// </remarks>
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[SkipLocalsInit]
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public sealed class Binomdist : AbstractBase
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{
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private readonly int _period;
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private readonly int _trials;
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private readonly int _threshold;
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private readonly RingBuffer _buffer;
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// Lanczos g=7, 9 coefficients (Numerical Recipes 3rd Ed., Table 6.1)
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private static ReadOnlySpan<double> LanczosCoeff =>
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[
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0.99999999999980993,
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676.5203681218851,
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-1259.1392167224028,
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771.32342877765313,
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-176.61502916214059,
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12.507343278686905,
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-0.13857109526572012,
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9.9843695780195716e-6,
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1.5056327351493116e-7
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];
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[StructLayout(LayoutKind.Auto)]
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private record struct State(double LastValid);
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private State _state, _p_state;
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public override bool IsHot => _buffer.Count >= _period;
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/// <summary>
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/// Initializes a new Binomdist indicator.
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/// </summary>
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/// <param name="period">Lookback window for min-max normalization (default 50)</param>
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/// <param name="trials">Number of Bernoulli trials n (default 20)</param>
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/// <param name="threshold">Success threshold k — computes P(X ≤ k) (default 10)</param>
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public Binomdist(int period = 50, int trials = 20, int threshold = 10)
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{
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if (period < 1)
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{
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throw new ArgumentException("Period must be >= 1", nameof(period));
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}
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if (trials < 1)
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{
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throw new ArgumentException("Trials must be >= 1", nameof(trials));
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}
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if (threshold < 0)
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{
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throw new ArgumentException("Threshold must be >= 0", nameof(threshold));
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}
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_period = period;
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_trials = trials;
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_threshold = threshold;
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_buffer = new RingBuffer(period);
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Name = $"Binomdist({period},{trials},{threshold})";
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WarmupPeriod = period;
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_state = new State(BinomCdf(0.5, trials, threshold));
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_p_state = _state;
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}
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/// <summary>
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/// Initializes a new Binomdist indicator with source for event-based chaining.
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/// </summary>
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/// <param name="source">Source indicator for chaining</param>
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/// <param name="period">Lookback window (default 50)</param>
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/// <param name="trials">Number of Bernoulli trials n (default 20)</param>
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/// <param name="threshold">Success threshold k (default 10)</param>
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public Binomdist(ITValuePublisher source, int period = 50, int trials = 20, int threshold = 10)
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: this(period, trials, threshold)
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{
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source.Pub += HandleUpdate;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private void HandleUpdate(object? sender, in TValueEventArgs e) => Update(e.Value, e.IsNew);
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/// <summary>
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/// Lanczos approximation of ln(Gamma(z)) for z > 0.
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/// g=7, 9 coefficients — accurate to ~15 significant digits.
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static double LnGamma(double z)
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{
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double x = z - 1.0;
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double t = x + 7.5; // g + 0.5 where g = 7
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double ser = LanczosCoeff[0];
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for (int k = 1; k <= 8; k++)
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{
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ser += LanczosCoeff[k] / (x + k);
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}
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return 0.5 * Math.Log(2.0 * Math.PI)
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+ (x + 0.5) * Math.Log(t)
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- t
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+ Math.Log(ser);
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}
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/// <summary>
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/// Log of binomial coefficient: ln C(n, i) = lnGamma(n+1) - lnGamma(i+1) - lnGamma(n-i+1).
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static double LnBinom(int n, int i)
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=> LnGamma(n + 1.0) - LnGamma(i + 1.0) - LnGamma(n - i + 1.0);
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/// <summary>
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/// Binomial CDF P(X ≤ k) for X ~ Binomial(n, p) via log-space summation.
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/// Avoids factorial overflow for large n.
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/// </summary>
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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internal static double BinomCdf(double p, int n, int k)
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{
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if (p <= 0.0)
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{
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return k >= 0 ? 1.0 : 0.0;
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}
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if (p >= 1.0)
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{
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return k >= n ? 1.0 : 0.0;
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}
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double lnP = Math.Log(p);
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double lnQ = Math.Log(1.0 - p);
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double cdf = 0.0;
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int kk = Math.Min(k, n);
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for (int i = 0; i <= kk; i++)
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{
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double lnTerm = Math.FusedMultiplyAdd(i, lnP, Math.FusedMultiplyAdd(n - i, lnQ, LnBinom(n, i)));
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cdf += Math.Exp(lnTerm);
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}
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return Math.Min(cdf, 1.0);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private static (double min, double max) FindMinMax(ReadOnlySpan<double> values)
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{
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if (values.Length == 0)
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{
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return (double.MaxValue, double.MinValue);
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}
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double min = values[0];
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double max = values[0];
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for (int i = 1; i < values.Length; i++)
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{
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double v = values[i];
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if (v < min)
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{
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min = v;
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}
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if (v > max)
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{
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max = v;
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}
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}
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return (min, max);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public override TValue Update(TValue input, bool isNew = true)
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{
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if (isNew)
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{
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_p_state = _state;
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}
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else
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{
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_state = _p_state;
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}
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double value = input.Value;
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double result;
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if (double.IsFinite(value))
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{
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_buffer.Add(value, isNew);
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var (min, max) = FindMinMax(_buffer.GetSpan());
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double range = max - min;
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// Flat range → neutral p=0.5
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double p = range > 0.0 ? (value - min) / range : 0.5;
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result = BinomCdf(p, _trials, _threshold);
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_state = new State(result);
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}
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else
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{
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result = _state.LastValid;
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}
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Last = new TValue(input.Time, result);
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PubEvent(Last, isNew);
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return Last;
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}
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public override TSeries Update(TSeries source)
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{
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var result = new TSeries(source.Count);
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ReadOnlySpan<double> values = source.Values;
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ReadOnlySpan<long> times = source.Times;
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for (int i = 0; i < source.Count; i++)
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{
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var tv = Update(new TValue(new DateTime(times[i], DateTimeKind.Utc), values[i]), true);
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result.Add(tv, true);
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}
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return result;
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}
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public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
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{
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TimeSpan interval = step ?? TimeSpan.FromSeconds(1);
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DateTime time = DateTime.UtcNow - (interval * source.Length);
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for (int i = 0; i < source.Length; i++)
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{
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Update(new TValue(time, source[i]), true);
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time += interval;
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}
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}
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public static TSeries Batch(TSeries source, int period = 50, int trials = 20, int threshold = 10)
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{
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var indicator = new Binomdist(period, trials, threshold);
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return indicator.Update(source);
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}
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/// <summary>
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/// Calculates Binomial Distribution CDF over a span of values.
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/// Uses a sliding window min-max normalization identical to the streaming path.
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/// </summary>
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public static void Batch(
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ReadOnlySpan<double> source, Span<double> output,
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int period = 50, int trials = 20, int threshold = 10)
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{
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if (source.Length == 0)
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{
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throw new ArgumentException("Source cannot be empty", nameof(source));
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}
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if (output.Length < source.Length)
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{
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throw new ArgumentException("Output length must be >= source length", nameof(output));
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}
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if (period < 1)
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{
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throw new ArgumentException("Period must be >= 1", nameof(period));
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}
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if (trials < 1)
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{
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throw new ArgumentException("Trials must be >= 1", nameof(trials));
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}
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if (threshold < 0)
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{
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throw new ArgumentException("Threshold must be >= 0", nameof(threshold));
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}
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double lastValid = BinomCdf(0.5, trials, threshold);
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for (int i = 0; i < source.Length; i++)
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{
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double val = source[i];
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if (!double.IsFinite(val))
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{
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output[i] = lastValid;
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continue;
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}
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int start = Math.Max(0, i - period + 1);
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double min = double.PositiveInfinity;
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double max = double.NegativeInfinity;
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for (int j = start; j <= i; j++)
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{
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double v = source[j];
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if (double.IsFinite(v))
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{
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if (v < min)
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{
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min = v;
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}
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if (v > max)
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{
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max = v;
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}
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}
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}
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if (!double.IsFinite(min) || !double.IsFinite(max))
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{
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output[i] = lastValid;
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continue;
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}
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double range = max - min;
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double p = range > 0.0 ? (val - min) / range : 0.5;
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double result = BinomCdf(p, trials, threshold);
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lastValid = result;
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output[i] = result;
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}
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}
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/// <summary>
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/// Exposes the Binomial CDF directly for testing and downstream consumers.
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/// </summary>
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public static double BinomialCdf(double p, int n, int k)
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=> BinomCdf(p, n, k);
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public static (TSeries Results, Binomdist Indicator) Calculate(
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TSeries source, int period = 50, int trials = 20, int threshold = 10)
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{
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var indicator = new Binomdist(period, trials, threshold);
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TSeries results = indicator.Update(source);
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return (results, indicator);
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}
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public override void Reset()
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{
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_buffer.Clear();
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_state = new State(BinomCdf(0.5, _trials, _threshold));
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_p_state = _state;
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Last = default;
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}
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}
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