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Add validation tests for various volume and momentum indicators
- Introduced Massi validation tests to ensure mathematical properties hold for the Mass Index indicator. - Added Va validation tests for Volume Accumulation, checking for finite outputs and correct accumulation behavior. - Implemented Vf validation tests for Volume Force, verifying outputs for rising and falling prices, and ensuring batch and streaming results match. - Created Vo validation tests for Volume Oscillator, confirming behavior with constant, increasing, and decreasing volumes. - Developed Vroc validation tests for Volume Rate of Change, validating outputs for constant volume and changes in volume. - Updated project file to include new momentum indicators (MACD and RSI) in the compilation.
This commit is contained in:
Miha Kralj
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using TradingPlatform.BusinessLayer;
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using QuanTAlib;
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namespace QuanTAlib.Tests;
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public sealed class WillrIndicatorTests
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{
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[Fact]
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public void WillrIndicator_Constructor_SetsDefaults()
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{
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var indicator = new WillrIndicator();
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Assert.Equal(14, indicator.Period);
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Assert.True(indicator.ShowColdValues);
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Assert.Contains("WILLR", indicator.Name, StringComparison.Ordinal);
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Assert.True(indicator.SeparateWindow);
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Assert.True(indicator.OnBackGround);
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}
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[Fact]
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public void WillrIndicator_MinHistoryDepths_EqualsZero()
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{
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var indicator = new WillrIndicator { Period = 14 };
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Assert.Equal(0, WillrIndicator.MinHistoryDepths);
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IWatchlistIndicator watchlistIndicator = indicator;
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Assert.Equal(0, watchlistIndicator.MinHistoryDepths);
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}
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[Fact]
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public void WillrIndicator_ShortName_IncludesParameters()
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{
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var indicator = new WillrIndicator { Period = 14 };
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indicator.Initialize();
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Assert.Contains("WILLR", indicator.ShortName, StringComparison.Ordinal);
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Assert.Contains("14", indicator.ShortName, StringComparison.Ordinal);
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}
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[Fact]
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public void WillrIndicator_SourceCodeLink_IsValid()
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{
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var indicator = new WillrIndicator();
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Assert.Contains("github.com", indicator.SourceCodeLink, StringComparison.Ordinal);
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Assert.Contains("Willr", indicator.SourceCodeLink, StringComparison.Ordinal);
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}
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[Fact]
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public void WillrIndicator_Initialize_CreatesInternalIndicator()
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{
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var indicator = new WillrIndicator { Period = 14 };
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indicator.Initialize();
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// After init, line series should exist (WillR + overbought + oversold)
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Assert.Equal(3, indicator.LinesSeries.Count);
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}
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[Fact]
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public void WillrIndicator_ProcessUpdate_HistoricalBar_ComputesValue()
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{
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var indicator = new WillrIndicator { Period = 5 };
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indicator.Initialize();
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var now = DateTime.UtcNow;
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for (int i = 0; i < 20; i++)
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{
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indicator.HistoricalData.AddBar(now.AddMinutes(i), 100 + i, 110 + i, 90 + i, 105 + i);
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var args = new UpdateArgs(UpdateReason.HistoricalBar);
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indicator.ProcessUpdate(args);
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}
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double willr = indicator.LinesSeries[0].GetValue(0);
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Assert.True(double.IsFinite(willr));
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Assert.True(willr >= -100.0 && willr <= 0.0);
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}
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[Fact]
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public void WillrIndicator_ProcessUpdate_NewBar_ComputesValue()
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{
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var indicator = new WillrIndicator { Period = 5 };
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indicator.Initialize();
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var now = DateTime.UtcNow;
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for (int i = 0; i < 10; i++)
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{
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indicator.HistoricalData.AddBar(now.AddMinutes(i), 100 + i, 110 + i, 90 + i, 105 + i);
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var args = new UpdateArgs(UpdateReason.HistoricalBar);
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indicator.ProcessUpdate(args);
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}
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// Simulate a new bar
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indicator.HistoricalData.AddBar(now.AddMinutes(10), 110, 120, 100, 115);
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var newArgs = new UpdateArgs(UpdateReason.NewBar);
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indicator.ProcessUpdate(newArgs);
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double willr = indicator.LinesSeries[0].GetValue(0);
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Assert.True(double.IsFinite(willr));
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Assert.True(willr >= -100.0 && willr <= 0.0);
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}
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[Fact]
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public void WillrIndicator_ReferenceLines_AreSet()
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{
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var indicator = new WillrIndicator { Period = 5 };
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indicator.Initialize();
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var now = DateTime.UtcNow;
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for (int i = 0; i < 10; i++)
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{
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indicator.HistoricalData.AddBar(now.AddMinutes(i), 100 + i, 110 + i, 90 + i, 105 + i);
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var args = new UpdateArgs(UpdateReason.HistoricalBar);
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indicator.ProcessUpdate(args);
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}
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// Overbought reference line at -20
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double overbought = indicator.LinesSeries[1].GetValue(0);
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Assert.Equal(-20.0, overbought, 1e-10);
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// Oversold reference line at -80
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double oversold = indicator.LinesSeries[2].GetValue(0);
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Assert.Equal(-80.0, oversold, 1e-10);
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}
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[Fact]
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public void WillrIndicator_CustomPeriod_IsUsed()
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{
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var indicator = new WillrIndicator { Period = 7 };
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indicator.Initialize();
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Assert.Contains("7", indicator.ShortName, StringComparison.Ordinal);
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}
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[Fact]
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public void WillrIndicator_Description_IsSet()
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{
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var indicator = new WillrIndicator();
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Assert.NotNull(indicator.Description);
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Assert.NotEmpty(indicator.Description);
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Assert.Contains("Williams", indicator.Description, StringComparison.OrdinalIgnoreCase);
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}
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}
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@@ -0,0 +1,59 @@
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using System.Drawing;
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using System.Runtime.CompilerServices;
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using TradingPlatform.BusinessLayer;
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namespace QuanTAlib;
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[SkipLocalsInit]
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public sealed class WillrIndicator : Indicator, IWatchlistIndicator
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{
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[InputParameter("Period", sortIndex: 0, 1, 500, 1, 0)]
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public int Period { get; set; } = 14;
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[InputParameter("Show cold values", sortIndex: 21)]
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public bool ShowColdValues { get; set; } = true;
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private Willr _indicator = null!;
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private readonly LineSeries _series;
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private readonly LineSeries _overbought;
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private readonly LineSeries _oversold;
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public static int MinHistoryDepths => 0;
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int IWatchlistIndicator.MinHistoryDepths => MinHistoryDepths;
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public override string ShortName => $"WILLR({Period})";
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public override string SourceCodeLink => "https://github.com/mihakralj/QuanTAlib/blob/main/lib/oscillators/willr/Willr.cs";
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public WillrIndicator()
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{
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OnBackGround = true;
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SeparateWindow = true;
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Name = "WILLR - Williams %R";
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Description = "Williams %R oscillator. Measures close position relative to highest high over lookback period. Range: -100 to 0.";
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_series = new LineSeries(name: "Williams %R", color: Color.Yellow, width: 2, style: LineStyle.Solid);
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_overbought = new LineSeries(name: "Overbought", color: Color.Gray, width: 1, style: LineStyle.Dash);
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_oversold = new LineSeries(name: "Oversold", color: Color.Gray, width: 1, style: LineStyle.Dash);
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AddLineSeries(_series);
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AddLineSeries(_overbought);
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AddLineSeries(_oversold);
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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protected override void OnInit()
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{
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_indicator = new Willr(Period);
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base.OnInit();
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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protected override void OnUpdate(UpdateArgs args)
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{
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_ = _indicator.Update(this.GetInputBar(args), args.IsNewBar());
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_series.SetValue(_indicator.Last.Value, _indicator.IsHot, ShowColdValues);
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_overbought.SetValue(-20.0, _indicator.IsHot, ShowColdValues);
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_oversold.SetValue(-80.0, _indicator.IsHot, ShowColdValues);
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}
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}
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@@ -0,0 +1,630 @@
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using Xunit;
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namespace QuanTAlib.Tests;
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public sealed class WillrConstructorTests
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{
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[Fact]
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public void DefaultPeriod_Is14()
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{
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var w = new Willr();
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Assert.Equal(14, w.Period);
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}
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[Fact]
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public void CustomPeriod_IsStored()
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{
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var w = new Willr(period: 20);
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Assert.Equal(20, w.Period);
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}
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[Theory]
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[InlineData(0)]
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[InlineData(-1)]
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[InlineData(-100)]
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public void InvalidPeriod_Throws(int period)
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{
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var ex = Assert.Throws<ArgumentException>(() => new Willr(period));
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Assert.Equal("period", ex.ParamName);
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}
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[Fact]
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public void MinimumPeriod_IsOne()
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{
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var w = new Willr(period: 1);
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Assert.Equal(1, w.Period);
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}
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[Fact]
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public void Name_IncludesPeriod()
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{
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var w = new Willr(period: 10);
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Assert.Contains("10", w.Name, StringComparison.Ordinal);
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}
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[Fact]
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public void WarmupPeriod_EqualsPeriod()
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{
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Assert.Equal(14, new Willr(14).WarmupPeriod);
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Assert.Equal(5, new Willr(5).WarmupPeriod);
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}
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}
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public sealed class WillrBasicTests
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{
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[Fact]
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public void Update_Returns_TValue()
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{
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var w = new Willr();
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var result = w.Update(new TValue(DateTime.UtcNow.Ticks, 100.0));
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Assert.True(double.IsFinite(result.Value));
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}
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[Fact]
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public void Last_IsAccessible()
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{
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var w = new Willr();
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_ = w.Update(new TValue(DateTime.UtcNow.Ticks, 100.0));
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Assert.True(double.IsFinite(w.Last.Value));
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}
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[Fact]
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public void IsHot_AfterWarmup()
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{
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var w = new Willr(period: 5);
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var time = DateTime.UtcNow;
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for (int i = 0; i < 4; i++)
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{
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w.Update(new TBar(time.AddMinutes(i), 100 + i, 105 + i, 95 + i, 102 + i, 100), isNew: true);
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}
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Assert.False(w.IsHot);
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w.Update(new TBar(time.AddMinutes(4), 104, 109, 99, 106, 100), isNew: true);
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Assert.True(w.IsHot);
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}
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[Fact]
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public void Name_IsNotNull()
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{
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var w = new Willr();
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Assert.NotNull(w.Name);
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Assert.NotEmpty(w.Name);
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}
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}
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public sealed class WillrRangeTests
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{
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[Fact]
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public void CloseAtHighest_ValueIsZero()
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{
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var w = new Willr(period: 5);
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var time = DateTime.UtcNow;
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for (int i = 0; i < 5; i++)
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{
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w.Update(new TBar(time.AddMinutes(i), 100, 110, 90, 100, 100), isNew: true);
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}
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// Close at highest high (110)
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w.Update(new TBar(time.AddMinutes(5), 110, 110, 90, 110, 100), isNew: true);
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Assert.Equal(0.0, w.Last.Value, 1e-10);
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}
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[Fact]
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public void CloseAtLowest_ValueIsNeg100()
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{
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var w = new Willr(period: 5);
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var time = DateTime.UtcNow;
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for (int i = 0; i < 5; i++)
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{
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w.Update(new TBar(time.AddMinutes(i), 100, 110, 90, 100, 100), isNew: true);
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}
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// Close at lowest low (90)
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w.Update(new TBar(time.AddMinutes(5), 90, 110, 90, 90, 100), isNew: true);
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Assert.Equal(-100.0, w.Last.Value, 1e-10);
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}
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[Fact]
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public void CloseAtMidpoint_ValueIsNeg50()
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{
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var w = new Willr(period: 5);
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var time = DateTime.UtcNow;
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for (int i = 0; i < 5; i++)
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{
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w.Update(new TBar(time.AddMinutes(i), 100, 110, 90, 100, 100), isNew: true);
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}
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// Close at midpoint of range (100 = midpoint of 90-110)
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w.Update(new TBar(time.AddMinutes(5), 100, 110, 90, 100, 100), isNew: true);
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Assert.Equal(-50.0, w.Last.Value, 1e-10);
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}
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[Fact]
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public void ConstantBars_ValueIsNeg50()
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{
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var w = new Willr(period: 5);
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var time = DateTime.UtcNow;
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for (int i = 0; i < 10; i++)
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{
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w.Update(new TBar(time.AddMinutes(i), 100, 100, 100, 100, 100), isNew: true);
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}
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// Range=0, should return -50
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Assert.Equal(-50.0, w.Last.Value, 1e-10);
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}
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[Fact]
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public void Rising_Produces_NearZero()
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{
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var w = new Willr(period: 5);
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var time = DateTime.UtcNow;
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for (int i = 0; i < 10; i++)
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{
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double price = 100.0 + (i * 2.0);
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w.Update(new TBar(time.AddMinutes(i), price, price + 1, price - 1, price + 1, 100), isNew: true);
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}
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// Close at recent high → WillR should be near 0 (> -20)
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Assert.True(w.Last.Value > -20.0);
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}
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[Fact]
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public void Falling_Produces_NearNeg100()
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{
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var w = new Willr(period: 5);
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var time = DateTime.UtcNow;
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for (int i = 0; i < 10; i++)
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{
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double price = 200.0 - (i * 2.0);
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w.Update(new TBar(time.AddMinutes(i), price, price + 1, price - 1, price - 1, 100), isNew: true);
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}
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// Close at recent low → WillR should be near -100 (< -80)
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Assert.True(w.Last.Value < -80.0);
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}
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}
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public sealed class WillrBarCorrectionTests
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{
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[Fact]
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public void IsNew_True_AdvancesState()
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{
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var w = new Willr(period: 5);
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var time = DateTime.UtcNow;
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var bar1 = new TBar(time, 100, 105, 95, 100, 100);
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var bar2 = new TBar(time.AddMinutes(1), 102, 108, 98, 104, 100);
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w.Update(bar1, isNew: true);
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var v1 = w.Last.Value;
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w.Update(bar2, isNew: true);
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var v2 = w.Last.Value;
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Assert.NotEqual(v1, v2);
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}
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[Fact]
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public void IsNew_False_RewritesCurrent()
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{
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var w = new Willr(period: 5);
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var time = DateTime.UtcNow;
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w.Update(new TBar(time, 100, 105, 95, 100, 100), isNew: true);
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w.Update(new TBar(time.AddMinutes(1), 102, 108, 98, 104, 100), isNew: true);
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var beforeCorrection = w.Last.Value;
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// Correct current bar (isNew=false)
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w.Update(new TBar(time.AddMinutes(1), 110, 115, 98, 112, 100), isNew: false);
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var afterCorrection = w.Last.Value;
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Assert.NotEqual(beforeCorrection, afterCorrection);
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}
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[Fact]
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public void IterativeCorrections_Restore()
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{
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var w = new Willr(period: 5);
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var time = DateTime.UtcNow;
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// Feed 3 bars
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for (int i = 0; i < 3; i++)
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{
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w.Update(new TBar(time.AddMinutes(i), 100 + i, 105 + i, 95 + i, 102 + i, 100), isNew: true);
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}
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// Add a new bar
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w.Update(new TBar(time.AddMinutes(3), 103, 108, 98, 105, 100), isNew: true);
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var original = w.Last.Value;
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// Correct it several times (isNew=false)
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w.Update(new TBar(time.AddMinutes(3), 110, 115, 98, 112, 100), isNew: false);
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w.Update(new TBar(time.AddMinutes(3), 90, 115, 85, 88, 100), isNew: false);
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// Correct back to original data
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w.Update(new TBar(time.AddMinutes(3), 103, 108, 98, 105, 100), isNew: false);
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var restored = w.Last.Value;
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Assert.Equal(original, restored, 1e-10);
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}
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}
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public sealed class WillrResetTests
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{
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[Fact]
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public void Reset_ClearsState()
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{
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var w = new Willr(period: 5);
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var time = DateTime.UtcNow;
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for (int i = 0; i < 10; i++)
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{
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w.Update(new TBar(time.AddMinutes(i), 100 + i, 105 + i, 95 + i, 102 + i, 100), isNew: true);
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}
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Assert.True(w.IsHot);
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w.Reset();
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|
||||
Assert.False(w.IsHot);
|
||||
Assert.Equal(default, w.Last);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Reset_AllowsReuse()
|
||||
{
|
||||
var w = new Willr(period: 5);
|
||||
var time = DateTime.UtcNow;
|
||||
|
||||
for (int i = 0; i < 10; i++)
|
||||
{
|
||||
w.Update(new TBar(time.AddMinutes(i), 100 + i, 105 + i, 95 + i, 102 + i, 100), isNew: true);
|
||||
}
|
||||
|
||||
w.Reset();
|
||||
|
||||
// Should be reusable after reset
|
||||
var result = w.Update(new TBar(time, 100, 105, 95, 100, 100), isNew: true);
|
||||
Assert.True(double.IsFinite(result.Value));
|
||||
Assert.False(w.IsHot);
|
||||
}
|
||||
}
|
||||
|
||||
public sealed class WillrRobustnessTests
|
||||
{
|
||||
[Fact]
|
||||
public void NaN_Uses_LastValid()
|
||||
{
|
||||
var w = new Willr(period: 5);
|
||||
var time = DateTime.UtcNow;
|
||||
|
||||
// Feed valid data
|
||||
for (int i = 0; i < 5; i++)
|
||||
{
|
||||
w.Update(new TBar(time.AddMinutes(i), 100, 105, 95, 100, 100), isNew: true);
|
||||
}
|
||||
|
||||
_ = w.Last.Value;
|
||||
|
||||
// Feed NaN bar
|
||||
w.Update(new TBar(time.AddMinutes(5), double.NaN, double.NaN, double.NaN, double.NaN, 100), isNew: true);
|
||||
|
||||
Assert.True(double.IsFinite(w.Last.Value));
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Infinity_Uses_LastValid()
|
||||
{
|
||||
var w = new Willr(period: 5);
|
||||
var time = DateTime.UtcNow;
|
||||
|
||||
for (int i = 0; i < 5; i++)
|
||||
{
|
||||
w.Update(new TBar(time.AddMinutes(i), 100, 105, 95, 100, 100), isNew: true);
|
||||
}
|
||||
|
||||
// Feed Infinity bar
|
||||
w.Update(new TBar(time.AddMinutes(5), double.PositiveInfinity, double.PositiveInfinity,
|
||||
double.NegativeInfinity, double.PositiveInfinity, 100), isNew: true);
|
||||
|
||||
Assert.True(double.IsFinite(w.Last.Value));
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void AllNaN_Returns_NaN()
|
||||
{
|
||||
var w = new Willr(period: 5);
|
||||
var time = DateTime.UtcNow;
|
||||
|
||||
// First data is NaN — no last-valid to substitute
|
||||
var result = w.Update(new TBar(time, double.NaN, double.NaN, double.NaN, double.NaN, 100), isNew: true);
|
||||
Assert.True(double.IsNaN(result.Value));
|
||||
}
|
||||
}
|
||||
|
||||
public sealed class WillrBatchTests
|
||||
{
|
||||
private static TBarSeries GenerateSeries(int count, int seed = 42)
|
||||
{
|
||||
var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.15, seed: seed);
|
||||
return gbm.Fetch(count, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Batch_TBarSeries_ProducesOutput()
|
||||
{
|
||||
var bars = GenerateSeries(100);
|
||||
var result = Willr.Batch(bars, period: 14);
|
||||
|
||||
Assert.Equal(100, result.Count);
|
||||
Assert.True(double.IsFinite(result[^1].Value));
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Calculate_Returns_ResultsAndIndicator()
|
||||
{
|
||||
var bars = GenerateSeries(100);
|
||||
var (results, indicator) = Willr.Calculate(bars, period: 14);
|
||||
|
||||
Assert.Equal(100, results.Count);
|
||||
Assert.True(indicator.IsHot);
|
||||
Assert.True(double.IsFinite(indicator.Last.Value));
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Streaming_Matches_Batch()
|
||||
{
|
||||
var bars = GenerateSeries(200);
|
||||
const int period = 14;
|
||||
|
||||
var w = new Willr(period);
|
||||
for (int i = 0; i < bars.Count; i++)
|
||||
{
|
||||
w.Update(bars[i]);
|
||||
}
|
||||
|
||||
var batch = Willr.Batch(bars, period);
|
||||
|
||||
Assert.Equal(w.Last.Value, batch[^1].Value, 1e-6);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Batch_Span_Empty_NoException()
|
||||
{
|
||||
var output = Array.Empty<double>();
|
||||
Willr.Batch(ReadOnlySpan<double>.Empty, ReadOnlySpan<double>.Empty,
|
||||
ReadOnlySpan<double>.Empty, output.AsSpan(), 14);
|
||||
Assert.Empty(output);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Batch_Span_InvalidPeriod_Throws()
|
||||
{
|
||||
var ex = Assert.Throws<ArgumentException>(() =>
|
||||
Willr.Batch(new double[10], new double[10], new double[10], new double[10], 0));
|
||||
Assert.Equal("period", ex.ParamName);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Batch_Span_MismatchedLengths_Throws()
|
||||
{
|
||||
var ex = Assert.Throws<ArgumentException>(() =>
|
||||
Willr.Batch(new double[10], new double[5], new double[10], new double[10], 14));
|
||||
Assert.Equal("high", ex.ParamName);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Batch_Span_OutputTooSmall_Throws()
|
||||
{
|
||||
var ex = Assert.Throws<ArgumentException>(() =>
|
||||
Willr.Batch(new double[10], new double[10], new double[10], new double[5], 14));
|
||||
Assert.Equal("output", ex.ParamName);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Update_TBarSeries_ProducesOutput()
|
||||
{
|
||||
var bars = GenerateSeries(100);
|
||||
var w = new Willr(14);
|
||||
var result = w.Update(bars);
|
||||
|
||||
Assert.Equal(100, result.Count);
|
||||
Assert.True(w.IsHot);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Batch_NullSource_ReturnsEmpty()
|
||||
{
|
||||
var result = Willr.Batch(null!, 14);
|
||||
Assert.Empty(result);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Batch_EmptySource_ReturnsEmpty()
|
||||
{
|
||||
var result = Willr.Batch(new TBarSeries(), 14);
|
||||
Assert.Empty(result);
|
||||
}
|
||||
}
|
||||
|
||||
public sealed class WillrEventTests
|
||||
{
|
||||
[Fact]
|
||||
public void Pub_Fires_OnUpdate()
|
||||
{
|
||||
var w = new Willr(period: 5);
|
||||
var eventRaised = false;
|
||||
|
||||
w.Pub += (object? _, in TValueEventArgs e) => { eventRaised = true; };
|
||||
|
||||
w.Update(new TBar(DateTime.UtcNow, 100, 105, 95, 100, 100), isNew: true);
|
||||
Assert.True(eventRaised);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Chaining_Works()
|
||||
{
|
||||
var bars = new TBarSeries();
|
||||
var w = new Willr(bars, period: 5);
|
||||
|
||||
TValue? lastValue = null;
|
||||
w.Pub += (object? _, in TValueEventArgs e) => { lastValue = e.Value; };
|
||||
|
||||
var time = DateTime.UtcNow;
|
||||
for (int i = 0; i < 10; i++)
|
||||
{
|
||||
bars.Add(new TBar(time.AddMinutes(i), 100 + i, 105 + i, 95 + i, 102 + i, 100));
|
||||
}
|
||||
|
||||
Assert.NotNull(lastValue);
|
||||
Assert.True(double.IsFinite(lastValue.Value.Value));
|
||||
}
|
||||
}
|
||||
|
||||
public sealed class WillrPrimeTests
|
||||
{
|
||||
[Fact]
|
||||
public void Prime_TBarSeries_SetsState()
|
||||
{
|
||||
var bars = new TBarSeries();
|
||||
var time = DateTime.UtcNow;
|
||||
|
||||
for (int i = 0; i < 20; i++)
|
||||
{
|
||||
bars.Add(new TBar(time.AddMinutes(i), 100 + i, 105 + i, 95 + i, 102 + i, 100));
|
||||
}
|
||||
|
||||
var w = new Willr(period: 5);
|
||||
w.Prime(bars);
|
||||
|
||||
Assert.True(w.IsHot);
|
||||
Assert.True(double.IsFinite(w.Last.Value));
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Prime_Span_SetsState()
|
||||
{
|
||||
var data = new double[50];
|
||||
for (int i = 0; i < 50; i++)
|
||||
{
|
||||
data[i] = 100.0 + i;
|
||||
}
|
||||
|
||||
var w = new Willr(period: 5);
|
||||
w.Prime(data.AsSpan());
|
||||
|
||||
Assert.True(w.IsHot);
|
||||
Assert.True(double.IsFinite(w.Last.Value));
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Prime_EmptySeries_NoError()
|
||||
{
|
||||
var w = new Willr(period: 5);
|
||||
w.Prime(new TBarSeries());
|
||||
|
||||
Assert.False(w.IsHot);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Prime_EmptySpan_NoError()
|
||||
{
|
||||
var w = new Willr(period: 5);
|
||||
w.Prime(ReadOnlySpan<double>.Empty);
|
||||
|
||||
Assert.False(w.IsHot);
|
||||
}
|
||||
}
|
||||
|
||||
public sealed class WillrConsistencyTests
|
||||
{
|
||||
private static TBarSeries GenerateSeries(int count, int seed = 42)
|
||||
{
|
||||
var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.15, seed: seed);
|
||||
return gbm.Fetch(count, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Span_Matches_TBarSeries()
|
||||
{
|
||||
var bars = GenerateSeries(200);
|
||||
const int period = 14;
|
||||
|
||||
var batchResult = Willr.Batch(bars, period);
|
||||
|
||||
var output = new double[bars.Count];
|
||||
Willr.Batch(bars.HighValues, bars.LowValues, bars.CloseValues, output.AsSpan(), period);
|
||||
|
||||
for (int i = 0; i < bars.Count; i++)
|
||||
{
|
||||
Assert.Equal(batchResult.Values[i], output[i], 12);
|
||||
}
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Different_Periods_Produce_Different_Results()
|
||||
{
|
||||
var bars = GenerateSeries(100);
|
||||
|
||||
var r5 = Willr.Batch(bars, period: 5);
|
||||
var r20 = Willr.Batch(bars, period: 20);
|
||||
|
||||
bool anyDifferent = false;
|
||||
for (int i = 20; i < 100; i++)
|
||||
{
|
||||
if (Math.Abs(r5.Values[i] - r20.Values[i]) > 0.01)
|
||||
{
|
||||
anyDifferent = true;
|
||||
break;
|
||||
}
|
||||
}
|
||||
Assert.True(anyDifferent);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Deterministic_Across_Runs()
|
||||
{
|
||||
var bars = GenerateSeries(200, seed: 99);
|
||||
const int period = 14;
|
||||
|
||||
var r1 = Willr.Batch(bars, period);
|
||||
var r2 = Willr.Batch(bars, period);
|
||||
|
||||
for (int i = 0; i < bars.Count; i++)
|
||||
{
|
||||
Assert.Equal(r1.Values[i], r2.Values[i], 15);
|
||||
}
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void WillR_Is_Inverse_Stoch()
|
||||
{
|
||||
var bars = GenerateSeries(200);
|
||||
const int period = 14;
|
||||
|
||||
var willr = Willr.Batch(bars, period);
|
||||
var (stochK, _) = Stoch.Batch(bars, kLength: period);
|
||||
|
||||
// WillR = -(100 - Stoch%K) = Stoch%K - 100
|
||||
// But only when range>0 (when range=0, Stoch returns 0, WillR returns -50)
|
||||
for (int i = period; i < bars.Count; i++)
|
||||
{
|
||||
double stochVal = stochK.Values[i];
|
||||
double willrVal = willr.Values[i];
|
||||
|
||||
if (Math.Abs(stochVal) > 1e-10 || Math.Abs(willrVal + 50.0) > 1e-10)
|
||||
{
|
||||
// Only compare when not at the degenerate range=0 case
|
||||
Assert.Equal(stochVal - 100.0, willrVal, 1e-9);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,360 @@
|
||||
using Skender.Stock.Indicators;
|
||||
using Xunit;
|
||||
using Xunit.Abstractions;
|
||||
|
||||
namespace QuanTAlib.Tests;
|
||||
|
||||
/// <summary>
|
||||
/// Williams %R validation tests.
|
||||
/// Cross-validates against Skender.Stock.Indicators.GetWilliamsR,
|
||||
/// TALib.NETCore, Tulip.NETCore, and self-consistency checks.
|
||||
/// </summary>
|
||||
public sealed class WillrValidationTests : IDisposable
|
||||
{
|
||||
private readonly ValidationTestData _data = new();
|
||||
private readonly ITestOutputHelper _output;
|
||||
private bool _disposed;
|
||||
|
||||
public WillrValidationTests(ITestOutputHelper output)
|
||||
{
|
||||
_output = output;
|
||||
}
|
||||
|
||||
public void Dispose()
|
||||
{
|
||||
Dispose(disposing: true);
|
||||
GC.SuppressFinalize(this);
|
||||
}
|
||||
|
||||
private void Dispose(bool disposing)
|
||||
{
|
||||
if (!_disposed && disposing)
|
||||
{
|
||||
_data.Dispose();
|
||||
_disposed = true;
|
||||
}
|
||||
}
|
||||
|
||||
private static TBarSeries GenerateSeries(int count, int seed = 42)
|
||||
{
|
||||
var gbm = new GBM(startPrice: 100.0, mu: 0.02, sigma: 0.15, seed: seed);
|
||||
return gbm.Fetch(count, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
|
||||
}
|
||||
|
||||
// --- A) Streaming vs Batch agreement ---
|
||||
|
||||
[Fact]
|
||||
public void Streaming_Matches_Batch()
|
||||
{
|
||||
var series = GenerateSeries(300);
|
||||
const int period = 14;
|
||||
|
||||
var willr = new Willr(period);
|
||||
for (int i = 0; i < series.Count; i++)
|
||||
{
|
||||
willr.Update(series[i]);
|
||||
}
|
||||
|
||||
var batch = Willr.Batch(series, period);
|
||||
|
||||
Assert.Equal(willr.Last.Value, batch[^1].Value, 1e-6);
|
||||
}
|
||||
|
||||
// --- B) Span matches TBarSeries ---
|
||||
|
||||
[Fact]
|
||||
public void Span_Matches_TBarSeries()
|
||||
{
|
||||
var series = GenerateSeries(200);
|
||||
const int period = 14;
|
||||
|
||||
var batchResult = Willr.Batch(series, period);
|
||||
|
||||
var output = new double[series.Count];
|
||||
Willr.Batch(series.HighValues, series.LowValues, series.CloseValues,
|
||||
output.AsSpan(), period);
|
||||
|
||||
for (int i = 0; i < series.Count; i++)
|
||||
{
|
||||
Assert.Equal(batchResult.Values[i], output[i], 12);
|
||||
}
|
||||
}
|
||||
|
||||
// --- C) Constant bars → WillR = -50 ---
|
||||
|
||||
[Fact]
|
||||
public void ConstantBars_ValueIs_Neg50()
|
||||
{
|
||||
const int period = 14;
|
||||
int count = 50;
|
||||
|
||||
var bars = new TBarSeries();
|
||||
for (int i = 0; i < count; i++)
|
||||
{
|
||||
bars.Add(new TBar(DateTime.UtcNow.AddMinutes(i), 50, 50, 50, 50, 100));
|
||||
}
|
||||
|
||||
var result = Willr.Batch(bars, period);
|
||||
|
||||
// When range=0 for all bars, WillR = -50
|
||||
for (int i = period - 1; i < count; i++)
|
||||
{
|
||||
Assert.Equal(-50.0, result.Values[i], 1e-10);
|
||||
}
|
||||
}
|
||||
|
||||
// --- D) Directional correctness ---
|
||||
|
||||
[Fact]
|
||||
public void Rising_Produces_NearZero()
|
||||
{
|
||||
const int period = 5;
|
||||
|
||||
var bars = new TBarSeries();
|
||||
for (int i = 0; i < 20; i++)
|
||||
{
|
||||
double price = 100.0 + (i * 2.0);
|
||||
bars.Add(new TBar(DateTime.UtcNow.AddMinutes(i), price, price + 1, price - 1, price + 1, 100));
|
||||
}
|
||||
|
||||
var willr = new Willr(period);
|
||||
for (int i = 0; i < bars.Count; i++)
|
||||
{
|
||||
willr.Update(bars[i]);
|
||||
}
|
||||
|
||||
// Close at recent high → WillR near 0 (> -20)
|
||||
Assert.True(willr.Last.Value > -20.0);
|
||||
}
|
||||
|
||||
[Fact]
|
||||
public void Falling_Produces_NearNeg100()
|
||||
{
|
||||
const int period = 5;
|
||||
|
||||
var bars = new TBarSeries();
|
||||
for (int i = 0; i < 20; i++)
|
||||
{
|
||||
double price = 200.0 - (i * 2.0);
|
||||
bars.Add(new TBar(DateTime.UtcNow.AddMinutes(i), price, price + 1, price - 1, price - 1, 100));
|
||||
}
|
||||
|
||||
var willr = new Willr(period);
|
||||
for (int i = 0; i < bars.Count; i++)
|
||||
{
|
||||
willr.Update(bars[i]);
|
||||
}
|
||||
|
||||
// Close at recent low → WillR near -100 (< -80)
|
||||
Assert.True(willr.Last.Value < -80.0);
|
||||
}
|
||||
|
||||
// --- E) Cross-validation with Skender ---
|
||||
|
||||
[Fact]
|
||||
public void Skender_Matches()
|
||||
{
|
||||
const int period = 14;
|
||||
|
||||
var qResult = Willr.Batch(_data.Bars, period);
|
||||
|
||||
var skResults = _data.SkenderQuotes.GetWilliamsR(period).ToList();
|
||||
|
||||
// Compare converged values (skip warmup)
|
||||
int start = period;
|
||||
int totalCompared = 0;
|
||||
int mismatches = 0;
|
||||
|
||||
for (int i = start; i < _data.Bars.Count; i++)
|
||||
{
|
||||
double? skWillR = skResults[i].WilliamsR;
|
||||
|
||||
if (skWillR.HasValue)
|
||||
{
|
||||
totalCompared++;
|
||||
double err = Math.Abs(qResult.Values[i] - skWillR.Value);
|
||||
|
||||
if (err > 1e-9)
|
||||
{
|
||||
mismatches++;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
Assert.True(totalCompared > 0, "No Skender results to compare");
|
||||
double mismatchRate = (double)mismatches / totalCompared;
|
||||
Assert.True(mismatchRate < 0.01,
|
||||
$"Mismatch rate {mismatchRate:P2} exceeds 1% threshold ({mismatches}/{totalCompared})");
|
||||
|
||||
_output.WriteLine($"Skender validation: {totalCompared} compared, {mismatches} mismatches ({mismatchRate:P2})");
|
||||
}
|
||||
|
||||
// --- F) Cross-validation with TA-Lib ---
|
||||
|
||||
[Fact]
|
||||
public void TALib_Matches()
|
||||
{
|
||||
const int period = 14;
|
||||
int len = _data.Bars.Count;
|
||||
|
||||
var qResult = Willr.Batch(_data.Bars, period);
|
||||
|
||||
double[] taOutput = new double[len];
|
||||
|
||||
var retCode = TALib.Functions.WillR(
|
||||
_data.HighPrices.Span, _data.LowPrices.Span, _data.ClosePrices.Span,
|
||||
0..^0, taOutput, out var outRange, period);
|
||||
Assert.Equal(TALib.Core.RetCode.Success, retCode);
|
||||
|
||||
int lookback = TALib.Functions.WillRLookback(period);
|
||||
|
||||
ValidationHelper.VerifyData(qResult, taOutput, outRange, lookback, tolerance: ValidationHelper.TalibTolerance);
|
||||
|
||||
_output.WriteLine("TA-Lib validation passed.");
|
||||
}
|
||||
|
||||
// --- G) Cross-validation with Tulip ---
|
||||
|
||||
[Fact]
|
||||
public void Tulip_Matches()
|
||||
{
|
||||
const int period = 14;
|
||||
int len = _data.Bars.Count;
|
||||
|
||||
var qResult = Willr.Batch(_data.Bars, period);
|
||||
|
||||
double[][] tulipInputs = [_data.HighPrices.ToArray(), _data.LowPrices.ToArray(), _data.ClosePrices.ToArray()];
|
||||
double[][] tulipOutputs = [new double[len - period + 1]];
|
||||
|
||||
_ = Tulip.Indicators.willr.Run(tulipInputs, [period], tulipOutputs);
|
||||
|
||||
int lookback = period - 1;
|
||||
ValidationHelper.VerifyData(qResult, tulipOutputs[0], lookback, tolerance: ValidationHelper.TulipTolerance);
|
||||
|
||||
_output.WriteLine("Tulip validation passed.");
|
||||
}
|
||||
|
||||
// --- H) Inverse Stochastic identity ---
|
||||
|
||||
[Fact]
|
||||
public void WillR_Is_Inverse_Stoch()
|
||||
{
|
||||
var series = GenerateSeries(500, seed: 77);
|
||||
const int period = 14;
|
||||
|
||||
var willr = Willr.Batch(series, period);
|
||||
var (stochK, _) = Stoch.Batch(series, kLength: period);
|
||||
|
||||
// WillR = Stoch%K - 100 when range > 0
|
||||
int totalCompared = 0;
|
||||
for (int i = period; i < series.Count; i++)
|
||||
{
|
||||
double stochVal = stochK.Values[i];
|
||||
double willrVal = willr.Values[i];
|
||||
|
||||
// Skip degenerate range=0 cases (Stoch returns 0, WillR returns -50)
|
||||
if (Math.Abs(stochVal) > 1e-10 || Math.Abs(willrVal + 50.0) > 1e-10)
|
||||
{
|
||||
Assert.Equal(stochVal - 100.0, willrVal, 1e-9);
|
||||
totalCompared++;
|
||||
}
|
||||
}
|
||||
|
||||
Assert.True(totalCompared > 0, "No valid comparison points");
|
||||
_output.WriteLine($"Inverse Stochastic identity: validated {totalCompared} points.");
|
||||
}
|
||||
|
||||
// --- I) Determinism ---
|
||||
|
||||
[Fact]
|
||||
public void Deterministic_Across_Runs()
|
||||
{
|
||||
var series = GenerateSeries(200, seed: 99);
|
||||
const int period = 14;
|
||||
|
||||
var r1 = Willr.Batch(series, period);
|
||||
var r2 = Willr.Batch(series, period);
|
||||
|
||||
for (int i = 0; i < series.Count; i++)
|
||||
{
|
||||
Assert.Equal(r1.Values[i], r2.Values[i], 15);
|
||||
}
|
||||
}
|
||||
|
||||
// --- J) Multi-period consistency ---
|
||||
|
||||
[Fact]
|
||||
public void Different_Periods_Produce_Different_Results()
|
||||
{
|
||||
var series = GenerateSeries(100);
|
||||
|
||||
var r5 = Willr.Batch(series, period: 5);
|
||||
var r20 = Willr.Batch(series, period: 20);
|
||||
|
||||
bool anyDifferent = false;
|
||||
for (int i = 20; i < 100; i++)
|
||||
{
|
||||
if (Math.Abs(r5.Values[i] - r20.Values[i]) > 0.01)
|
||||
{
|
||||
anyDifferent = true;
|
||||
break;
|
||||
}
|
||||
}
|
||||
Assert.True(anyDifferent);
|
||||
}
|
||||
|
||||
// --- K) Calculate returns consistent results ---
|
||||
|
||||
[Fact]
|
||||
public void Calculate_Produces_Consistent_Results()
|
||||
{
|
||||
var series = GenerateSeries(100);
|
||||
const int period = 14;
|
||||
|
||||
var (results, indicator) = Willr.Calculate(series, period);
|
||||
|
||||
Assert.Equal(100, results.Count);
|
||||
Assert.True(indicator.IsHot);
|
||||
Assert.True(double.IsFinite(indicator.Last.Value));
|
||||
}
|
||||
|
||||
// --- L) All outputs finite after warmup ---
|
||||
|
||||
[Fact]
|
||||
public void AllOutputsFinite_AfterWarmup()
|
||||
{
|
||||
const int period = 14;
|
||||
var willr = new Willr(period);
|
||||
|
||||
for (int i = 0; i < _data.Bars.Count; i++)
|
||||
{
|
||||
var result = willr.Update(_data.Bars[i]);
|
||||
|
||||
if (i >= period - 1)
|
||||
{
|
||||
Assert.True(double.IsFinite(result.Value),
|
||||
$"Non-finite output at bar {i}: {result.Value}");
|
||||
}
|
||||
}
|
||||
|
||||
_output.WriteLine("All outputs finite after warmup verified.");
|
||||
}
|
||||
|
||||
// --- M) Range bounded ---
|
||||
|
||||
[Fact]
|
||||
public void Output_Bounded_Neg100_To_Zero()
|
||||
{
|
||||
const int period = 14;
|
||||
var result = Willr.Batch(_data.Bars, period);
|
||||
|
||||
for (int i = period - 1; i < _data.Bars.Count; i++)
|
||||
{
|
||||
double val = result.Values[i];
|
||||
Assert.True(val >= -100.0 && val <= 0.0,
|
||||
$"WillR value {val} out of [-100, 0] range at bar {i}");
|
||||
}
|
||||
|
||||
_output.WriteLine("All WillR values within [-100, 0] range.");
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,329 @@
|
||||
using System.Buffers;
|
||||
using System.Runtime.CompilerServices;
|
||||
using System.Runtime.InteropServices;
|
||||
|
||||
namespace QuanTAlib;
|
||||
|
||||
/// <summary>
|
||||
/// WILLR: Williams %R.
|
||||
/// Measures close position relative to highest high over a lookback period.
|
||||
/// Range: -100 (lowest low) to 0 (highest high).
|
||||
/// Formula: WillR = -100 * (HighestHigh - Close) / (HighestHigh - LowestLow).
|
||||
/// When range is zero, returns -50 (midpoint).
|
||||
/// Uses monotonic deques for O(1) amortized highest/lowest tracking.
|
||||
/// </summary>
|
||||
[SkipLocalsInit]
|
||||
public sealed class Willr : ITValuePublisher
|
||||
{
|
||||
private const int DefaultPeriod = 14;
|
||||
|
||||
private readonly int _period;
|
||||
private readonly double[] _hBuf;
|
||||
private readonly double[] _lBuf;
|
||||
private readonly MonotonicDeque _maxDeque;
|
||||
private readonly MonotonicDeque _minDeque;
|
||||
|
||||
private int _count;
|
||||
private long _index;
|
||||
|
||||
[StructLayout(LayoutKind.Auto)]
|
||||
private record struct State(
|
||||
double LastValidHigh, double LastValidLow, double LastValidClose);
|
||||
|
||||
private State _s;
|
||||
private State _ps;
|
||||
|
||||
private readonly TBarPublishedHandler _barHandler;
|
||||
|
||||
public string Name { get; }
|
||||
public int Period => _period;
|
||||
public int WarmupPeriod => _period;
|
||||
public TValue Last { get; private set; }
|
||||
public bool IsHot => _count >= _period;
|
||||
|
||||
public event TValuePublishedHandler? Pub;
|
||||
|
||||
public Willr(int period = DefaultPeriod)
|
||||
{
|
||||
if (period <= 0)
|
||||
{
|
||||
throw new ArgumentException("Period must be greater than 0", nameof(period));
|
||||
}
|
||||
|
||||
_period = period;
|
||||
_hBuf = new double[_period];
|
||||
_lBuf = new double[_period];
|
||||
_maxDeque = new MonotonicDeque(_period);
|
||||
_minDeque = new MonotonicDeque(_period);
|
||||
_count = 0;
|
||||
_index = -1;
|
||||
_s = new State(double.NaN, double.NaN, double.NaN);
|
||||
_ps = _s;
|
||||
|
||||
Name = $"WillR({period})";
|
||||
_barHandler = HandleBar;
|
||||
}
|
||||
|
||||
public Willr(TBarSeries source, int period = DefaultPeriod) : this(period)
|
||||
{
|
||||
Prime(source);
|
||||
source.Pub += _barHandler;
|
||||
}
|
||||
|
||||
private void HandleBar(object? sender, in TBarEventArgs e) => Update(e.Value, e.IsNew);
|
||||
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
private void PubEvent(TValue value, bool isNew = true) =>
|
||||
Pub?.Invoke(this, new TValueEventArgs { Value = value, IsNew = isNew });
|
||||
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
public TValue Update(TBar input, bool isNew = true)
|
||||
{
|
||||
if (isNew)
|
||||
{
|
||||
_ps = _s;
|
||||
_index++;
|
||||
if (_count < _period)
|
||||
{
|
||||
_count++;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
_s = _ps;
|
||||
}
|
||||
|
||||
var s = _s;
|
||||
|
||||
// Validate inputs — substitute last-valid on NaN/Infinity
|
||||
double high = input.High;
|
||||
double low = input.Low;
|
||||
double close = input.Close;
|
||||
|
||||
if (double.IsFinite(high)) { s.LastValidHigh = high; }
|
||||
else { high = s.LastValidHigh; }
|
||||
|
||||
if (double.IsFinite(low)) { s.LastValidLow = low; }
|
||||
else { low = s.LastValidLow; }
|
||||
|
||||
if (double.IsFinite(close)) { s.LastValidClose = close; }
|
||||
else { close = s.LastValidClose; }
|
||||
|
||||
// If still no valid data, return NaN
|
||||
if (double.IsNaN(high) || double.IsNaN(low) || double.IsNaN(close))
|
||||
{
|
||||
_s = s;
|
||||
Last = new TValue(input.Time, double.NaN);
|
||||
PubEvent(Last, isNew);
|
||||
return Last;
|
||||
}
|
||||
|
||||
int bufIdx = _index < 0 ? 0 : (int)(_index % _period);
|
||||
_hBuf[bufIdx] = high;
|
||||
_lBuf[bufIdx] = low;
|
||||
|
||||
if (isNew)
|
||||
{
|
||||
_maxDeque.PushMax(_index, high, _hBuf);
|
||||
_minDeque.PushMin(_index, low, _lBuf);
|
||||
}
|
||||
else
|
||||
{
|
||||
_maxDeque.RebuildMax(_hBuf, _index, _count);
|
||||
_minDeque.RebuildMin(_lBuf, _index, _count);
|
||||
}
|
||||
|
||||
double highest = _maxDeque.GetExtremum(_hBuf);
|
||||
double lowest = _minDeque.GetExtremum(_lBuf);
|
||||
double range = highest - lowest;
|
||||
|
||||
double willr = range > 0.0 ? -100.0 * (highest - close) / range : -50.0;
|
||||
|
||||
_s = s;
|
||||
|
||||
Last = new TValue(input.Time, willr);
|
||||
PubEvent(Last, isNew);
|
||||
return Last;
|
||||
}
|
||||
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
public TValue Update(TValue input, bool isNew = true) =>
|
||||
Update(new TBar(input.Time, input.Value, input.Value, input.Value, input.Value, 0), isNew);
|
||||
|
||||
public TSeries Update(TBarSeries source)
|
||||
{
|
||||
if (source.Count == 0)
|
||||
{
|
||||
return new TSeries([], []);
|
||||
}
|
||||
|
||||
int len = source.Count;
|
||||
var t = new List<long>(len);
|
||||
var v = new List<double>(len);
|
||||
|
||||
CollectionsMarshal.SetCount(t, len);
|
||||
CollectionsMarshal.SetCount(v, len);
|
||||
|
||||
Batch(source.HighValues, source.LowValues, source.CloseValues,
|
||||
CollectionsMarshal.AsSpan(v), _period);
|
||||
|
||||
source.Times.CopyTo(CollectionsMarshal.AsSpan(t));
|
||||
|
||||
// Prime internal state for continued streaming
|
||||
Prime(source);
|
||||
|
||||
var lastTime = new DateTime(source.Times[^1], DateTimeKind.Utc);
|
||||
Last = new TValue(lastTime, CollectionsMarshal.AsSpan(v)[^1]);
|
||||
|
||||
return new TSeries(t, v);
|
||||
}
|
||||
|
||||
public void Prime(TBarSeries source)
|
||||
{
|
||||
Reset();
|
||||
|
||||
if (source.Count == 0)
|
||||
{
|
||||
return;
|
||||
}
|
||||
|
||||
for (int i = 0; i < source.Count; i++)
|
||||
{
|
||||
Update(source[i], isNew: true);
|
||||
}
|
||||
}
|
||||
|
||||
public void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
|
||||
{
|
||||
Reset();
|
||||
|
||||
if (source.Length == 0)
|
||||
{
|
||||
return;
|
||||
}
|
||||
|
||||
long t = DateTime.UtcNow.Ticks;
|
||||
long stepTicks = (step ?? TimeSpan.FromMinutes(1)).Ticks;
|
||||
|
||||
for (int i = 0; i < source.Length; i++)
|
||||
{
|
||||
double val = source[i];
|
||||
Update(new TBar(t, val, val, val, val, 0), isNew: true);
|
||||
t += stepTicks;
|
||||
}
|
||||
}
|
||||
|
||||
public void Reset()
|
||||
{
|
||||
Array.Clear(_hBuf);
|
||||
Array.Clear(_lBuf);
|
||||
_maxDeque.Reset();
|
||||
_minDeque.Reset();
|
||||
_count = 0;
|
||||
_index = -1;
|
||||
_s = new State(double.NaN, double.NaN, double.NaN);
|
||||
_ps = _s;
|
||||
Last = default;
|
||||
}
|
||||
|
||||
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
||||
public static void Batch(
|
||||
ReadOnlySpan<double> high,
|
||||
ReadOnlySpan<double> low,
|
||||
ReadOnlySpan<double> close,
|
||||
Span<double> output,
|
||||
int period)
|
||||
{
|
||||
if (period <= 0)
|
||||
{
|
||||
throw new ArgumentException("Period must be greater than 0", nameof(period));
|
||||
}
|
||||
if (high.Length != low.Length || high.Length != close.Length)
|
||||
{
|
||||
throw new ArgumentException("Input spans must have the same length", nameof(high));
|
||||
}
|
||||
if (output.Length < high.Length)
|
||||
{
|
||||
throw new ArgumentException("Output span must be at least as long as input", nameof(output));
|
||||
}
|
||||
|
||||
int len = high.Length;
|
||||
if (len == 0)
|
||||
{
|
||||
return;
|
||||
}
|
||||
|
||||
// Compute highest/lowest via Highest/Lowest batch helpers
|
||||
const int StackallocThreshold = 256;
|
||||
double[]? rentedUpper = null;
|
||||
double[]? rentedLower = null;
|
||||
scoped Span<double> upperBuf;
|
||||
scoped Span<double> lowerBuf;
|
||||
|
||||
if (len <= StackallocThreshold)
|
||||
{
|
||||
upperBuf = stackalloc double[len];
|
||||
lowerBuf = stackalloc double[len];
|
||||
}
|
||||
else
|
||||
{
|
||||
rentedUpper = ArrayPool<double>.Shared.Rent(len);
|
||||
rentedLower = ArrayPool<double>.Shared.Rent(len);
|
||||
upperBuf = rentedUpper.AsSpan(0, len);
|
||||
lowerBuf = rentedLower.AsSpan(0, len);
|
||||
}
|
||||
|
||||
try
|
||||
{
|
||||
Highest.Batch(high, upperBuf, period);
|
||||
Lowest.Batch(low, lowerBuf, period);
|
||||
|
||||
for (int i = 0; i < len; i++)
|
||||
{
|
||||
double range = upperBuf[i] - lowerBuf[i];
|
||||
output[i] = range > 0.0 ? -100.0 * (upperBuf[i] - close[i]) / range : -50.0;
|
||||
}
|
||||
}
|
||||
finally
|
||||
{
|
||||
if (rentedUpper != null)
|
||||
{
|
||||
ArrayPool<double>.Shared.Return(rentedUpper);
|
||||
}
|
||||
if (rentedLower != null)
|
||||
{
|
||||
ArrayPool<double>.Shared.Return(rentedLower);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
public static TSeries Batch(TBarSeries source, int period = DefaultPeriod)
|
||||
{
|
||||
if (source == null || source.Count == 0)
|
||||
{
|
||||
return new TSeries([], []);
|
||||
}
|
||||
|
||||
int len = source.Count;
|
||||
var t = new List<long>(len);
|
||||
var v = new List<double>(len);
|
||||
|
||||
CollectionsMarshal.SetCount(t, len);
|
||||
CollectionsMarshal.SetCount(v, len);
|
||||
|
||||
Batch(source.HighValues, source.LowValues, source.CloseValues,
|
||||
CollectionsMarshal.AsSpan(v), period);
|
||||
|
||||
source.Times.CopyTo(CollectionsMarshal.AsSpan(t));
|
||||
|
||||
return new TSeries(t, v);
|
||||
}
|
||||
|
||||
public static (TSeries Results, Willr Indicator) Calculate(
|
||||
TBarSeries source, int period = DefaultPeriod)
|
||||
{
|
||||
var indicator = new Willr(period);
|
||||
var results = indicator.Update(source);
|
||||
return (results, indicator);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,171 @@
|
||||
# WILLR: Williams %R
|
||||
|
||||
> "The market tells you where it closed relative to where it traded. That single fact contains more information than most traders realize." -- George Lane (on the principle shared with Williams %R)
|
||||
|
||||
## Overview
|
||||
|
||||
Williams %R measures where the closing price sits within the highest-high to lowest-low range over a lookback period, scaled to \(-100, 0\). It is the arithmetic inverse of the Fast Stochastic %K: identical math, different scale. A reading near 0 means the close is near the period high; a reading near \(-100\) means the close is near the period low.
|
||||
|
||||
Default period: 14 bars. Output range: \(-100\) to \(0\). Warmup: `period` bars.
|
||||
|
||||
## Historical Context
|
||||
|
||||
Larry Williams introduced Williams %R in his 1973 book *How I Made One Million Dollars Last Year Trading Commodities*. The indicator predates widespread computerized trading and was designed for quick manual calculation: find the highest high, find the lowest low, see where the close falls in that range.
|
||||
|
||||
Williams %R and the Stochastic Oscillator (George Lane, late 1950s) share the same core logic. The only difference is the output mapping:
|
||||
|
||||
$$\text{Stoch \%K} = 100 \times \frac{C - LL}{HH - LL}, \quad \text{Williams \%R} = -100 \times \frac{HH - C}{HH - LL}$$
|
||||
|
||||
This means $\text{Williams \%R} = \text{Stoch \%K} - 100$. The inverted scale places "overbought" at the top (near 0) and "oversold" at the bottom (near \(-100\)), which some traders find more intuitive for spotting reversals.
|
||||
|
||||
## Architecture and Physics
|
||||
|
||||
### 1. Streaming Path (O(1) Amortized)
|
||||
|
||||
The streaming implementation uses **MonotonicDeque** pairs for O(1) amortized highest-high and lowest-low tracking over the sliding window:
|
||||
|
||||
- **MonotonicDeque (max)**: Maintains decreasing order of high values. Front always holds the current window maximum.
|
||||
- **MonotonicDeque (min)**: Maintains increasing order of low values. Front always holds the current window minimum.
|
||||
- **Circular buffers** (`_hBuf`, `_lBuf`): Store raw high/low values for deque rebuild on bar correction.
|
||||
|
||||
Bar correction (`isNew=false`) triggers a full deque rebuild from the circular buffer, restoring correct state without allocation.
|
||||
|
||||
### 2. State Management
|
||||
|
||||
```text
|
||||
State record struct:
|
||||
LastValidHigh -- NaN/Infinity protection for high
|
||||
LastValidLow -- NaN/Infinity protection for low
|
||||
LastValidClose -- NaN/Infinity protection for close
|
||||
```
|
||||
|
||||
The standard `_s` / `_ps` pattern enables bar correction:
|
||||
|
||||
- `isNew=true`: `_ps = _s`, advance index/count
|
||||
- `isNew=false`: `_s = _ps`, recalculate from previous valid state
|
||||
|
||||
### 3. Batch Path
|
||||
|
||||
Static `Batch()` methods delegate to `Highest.Batch()` and `Lowest.Batch()` for vectorized min/max computation over the full series. Intermediate buffers use `stackalloc` for inputs up to 256 elements and `ArrayPool<double>` for larger inputs.
|
||||
|
||||
### 4. Edge Case: Zero Range
|
||||
|
||||
When $HH = LL$ (all bars in the window have identical high and low), the range is zero and division is undefined. The implementation returns $-50$ (midpoint of the \(-100, 0\) scale). This differs from the Stochastic Oscillator, which returns $0$ for zero range.
|
||||
|
||||
## Mathematical Foundation
|
||||
|
||||
### Core Formula
|
||||
|
||||
$$\text{Williams \%R} = -100 \times \frac{HH_n - C}{HH_n - LL_n}$$
|
||||
|
||||
Where:
|
||||
|
||||
- $HH_n = \max(H_i)$ for $i \in [t - n + 1, \, t]$
|
||||
- $LL_n = \min(L_i)$ for $i \in [t - n + 1, \, t]$
|
||||
- $C$ = current close price
|
||||
- $n$ = lookback period (default 14)
|
||||
|
||||
### Relationship to Stochastic
|
||||
|
||||
$$\text{Williams \%R} = \text{Stoch \%K} - 100$$
|
||||
|
||||
Proof:
|
||||
|
||||
$$\text{Stoch \%K} = 100 \times \frac{C - LL}{HH - LL}$$
|
||||
|
||||
$$\text{Williams \%R} = -100 \times \frac{HH - C}{HH - LL} = -100 \times \frac{(HH - LL) - (C - LL)}{HH - LL}$$
|
||||
|
||||
$$= -100 + 100 \times \frac{C - LL}{HH - LL} = \text{Stoch \%K} - 100$$
|
||||
|
||||
### Parameter Mapping
|
||||
|
||||
| Parameter | Symbol | Default | Constraint |
|
||||
|-----------|--------|---------|------------|
|
||||
| `period` | $n$ | 14 | $n \geq 1$ |
|
||||
|
||||
## Performance Profile
|
||||
|
||||
| Metric | Value |
|
||||
|--------|-------|
|
||||
| Time complexity (streaming) | O(1) amortized per bar |
|
||||
| Time complexity (batch) | O(n) total |
|
||||
| Space complexity | O(period) |
|
||||
| Warmup period | `period` bars |
|
||||
| Output range | \(-100\) to \(0\) |
|
||||
| Allocations in `Update()` | Zero |
|
||||
|
||||
### Operation Count (per bar, streaming)
|
||||
|
||||
| Operation | Count |
|
||||
|-----------|-------|
|
||||
| Comparisons | 2-3 (deque push) |
|
||||
| Divisions | 1 |
|
||||
| Multiplications | 1 |
|
||||
| NaN checks | 3 (high, low, close) |
|
||||
|
||||
### Quality Metrics
|
||||
|
||||
| Metric | Score (1-10) |
|
||||
|--------|-------------|
|
||||
| Noise rejection | 3 |
|
||||
| Lag | 2 (minimal) |
|
||||
| Sensitivity | 8 |
|
||||
| Computational cost | 2 (very cheap) |
|
||||
| Implementation complexity | 3 |
|
||||
|
||||
## Interpretation
|
||||
|
||||
### Overbought / Oversold Zones
|
||||
|
||||
| Zone | Williams %R Level | Interpretation |
|
||||
|------|-------------------|----------------|
|
||||
| Overbought | > \(-20\) | Close near period high. Potential reversal down. |
|
||||
| Neutral | \(-80\) to \(-20\) | Normal trading range. |
|
||||
| Oversold | < \(-80\) | Close near period low. Potential reversal up. |
|
||||
|
||||
### Signal Patterns
|
||||
|
||||
- **Overbought reversal**: %R rises above \(-20\) then drops back below. Bearish signal.
|
||||
- **Oversold reversal**: %R falls below \(-80\) then rises back above. Bullish signal.
|
||||
- **Divergence**: Price makes new highs while %R does not (or vice versa). Potential trend exhaustion.
|
||||
- **Failure swing**: %R reaches an extreme, pulls back, fails to re-reach the extreme, then reverses. Stronger signal than simple crossover.
|
||||
|
||||
### Practical Notes
|
||||
|
||||
In strong uptrends, Williams %R can remain above \(-20\) for extended periods. Treating every overbought reading as a sell signal in a bull market is a reliable way to underperform. Use trend filters (ADX, moving average slope) to contextualize overbought/oversold readings.
|
||||
|
||||
## Validation
|
||||
|
||||
| Library | Match | Notes |
|
||||
|---------|-------|-------|
|
||||
| Skender | ✔️ | `GetWilliamsR(lookbackPeriods)` -- `WilliamsR` property |
|
||||
| TA-Lib | ✔️ | `WillR(high, low, close, period)` |
|
||||
| Tulip | ✔️ | `willr(high, low, close, period)` |
|
||||
| Ooples | ❔ | Not validated |
|
||||
|
||||
All validated libraries agree within $1 \times 10^{-9}$ tolerance after warmup convergence.
|
||||
|
||||
## Common Pitfalls
|
||||
|
||||
1. **Inverted scale confusion**: Williams %R uses \(-100\) to \(0\), not 0 to 100. Overbought is near 0, oversold is near \(-100\). Reversing the mental model from Stochastic is the most common mistake.
|
||||
|
||||
2. **Zero range returns \(-50\)**: When all bars in the window share the same high and low (e.g., constant-price instruments), the range is zero. This implementation returns \(-50\) (midpoint). Other implementations may return 0 or NaN.
|
||||
|
||||
3. **Overbought does not equal sell**: In trending markets, %R stays overbought/oversold for long stretches. Fading the trend based solely on %R readings without a trend filter leads to significant drawdowns.
|
||||
|
||||
4. **Short lookback noise**: Period < 5 creates excessive whipsaws. The default 14 balances responsiveness and noise rejection for most timeframes.
|
||||
|
||||
5. **No signal line**: Unlike the Stochastic Oscillator, Williams %R traditionally has no %D signal line. Traders who want smoothed crossover signals should either use Stochastic or apply a separate SMA to Williams %R output.
|
||||
|
||||
6. **NaN propagation**: If the first bar contains NaN for all OHLC fields, the output is NaN until valid data arrives. After the first valid bar, subsequent NaN inputs are replaced with the last valid value.
|
||||
|
||||
7. **Bar correction with deque rebuild**: Correcting a bar (`isNew=false`) triggers a full deque rebuild from the circular buffer. This is O(period) worst case, not O(1). In practice this is negligible since bar corrections are infrequent, but batch-correcting thousands of bars in a tight loop would show the cost.
|
||||
|
||||
## References
|
||||
|
||||
- Williams, L. (1973). *How I Made One Million Dollars Last Year Trading Commodities*. Windsor Books.
|
||||
- Lane, G. C. (1984). "Lane's Stochastics." *Technical Analysis of Stocks & Commodities*.
|
||||
- Murphy, J. J. (1999). *Technical Analysis of the Financial Markets*. New York Institute of Finance.
|
||||
- Achelis, S. B. (2000). *Technical Analysis from A to Z*. McGraw-Hill.
|
||||
- [TradingView Williams %R](https://www.tradingview.com/support/solutions/43000502218/)
|
||||
- [StockCharts Williams %R](https://school.stockcharts.com/doku.php?id=technical_indicators:williams_r)
|
||||
Reference in New Issue
Block a user