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https://github.com/mihakralj/QuanTAlib.git
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adding missing validations
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Miha Kralj
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using Xunit;
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namespace QuanTAlib.Tests;
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/// <summary>
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/// IFFT validation tests — verifies spectral low-pass filtering behavior.
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/// No external library implements this exact Hanning-windowed DFT reconstruction,
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/// so validation uses self-consistency and analytical known-answer tests.
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/// </summary>
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public class IfftValidationTests
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{
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private const double Tolerance = 1e-10;
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private const double LooseTolerance = 1e-6;
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// ─── Self-consistency: batch vs streaming ─────────────────────────────────
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[Fact]
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public void Ifft_BatchVsStreaming_AllValuesMatch()
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{
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int windowSize = 32;
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int count = 120;
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var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 91001);
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var bars = gbm.Fetch(count, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
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var source = bars.Close;
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var streaming = new Ifft(windowSize, numHarmonics: 3);
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var streamVals = new double[count];
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for (int i = 0; i < count; i++)
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{
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streaming.Update(source[i]);
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streamVals[i] = streaming.Last.Value;
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}
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var batch = Ifft.Batch(source, windowSize, numHarmonics: 3);
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for (int i = 0; i < count; i++)
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{
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Assert.Equal(streamVals[i], batch[i].Value, Tolerance);
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}
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}
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// ─── H=1 produces lower variance than input (smoothing confirmed) ─────────
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[Fact]
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public void Ifft_H1_LowerVarianceThanInput()
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{
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int windowSize = 32;
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int count = 300;
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var gbm = new GBM(startPrice: 100, mu: 0.0, sigma: 0.3, seed: 91002);
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var bars = gbm.Fetch(count, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
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var indicator = new Ifft(windowSize, numHarmonics: 1);
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var inputs = new List<double>();
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var outputs = new List<double>();
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for (int i = 0; i < count; i++)
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{
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indicator.Update(bars.Close[i]);
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if (indicator.IsHot)
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{
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inputs.Add(bars.Close[i].Value);
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outputs.Add(indicator.Last.Value);
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}
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}
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double inputMean = inputs.Sum() / inputs.Count;
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double outputMean = outputs.Sum() / outputs.Count;
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double inputVar = inputs.Sum(v => (v - inputMean) * (v - inputMean)) / inputs.Count;
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double outputVar = outputs.Sum(v => (v - outputMean) * (v - outputMean)) / outputs.Count;
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Assert.True(outputVar < inputVar,
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$"IFFT(H=1) output variance {outputVar:F4} must be < input variance {inputVar:F4}");
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}
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// ─── H=N/2 has higher variance than H=1 ──────────────────────────────────
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[Fact]
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public void Ifft_H1_OutputIsSmoother_ThanHighHarmonics()
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{
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// IFFT is a spectral low-pass filter. H=1 passes only the fundamental frequency,
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// producing the smoothest output. H=halfWindow passes all bins, producing output
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// that tracks more detail and therefore has higher variance.
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// We use a pure k=1 sine to ensure the fundamental energy dominates.
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int windowSize = 32;
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int halfHarmonics = windowSize / 2; // 16
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int count = 300;
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double twoPiOverN = 2.0 * Math.PI / windowSize;
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var time = DateTime.UtcNow;
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// Pure sine at k=1 with strong amplitude → H=1 tracks it; H=16 adds noise from high bins
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var values = new List<TValue>(count);
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for (int i = 0; i < count; i++)
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{
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values.Add(new TValue(time.AddMinutes(i), 100.0 + 30.0 * Math.Sin(twoPiOverN * 1 * i)));
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}
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var indH1 = new Ifft(windowSize, numHarmonics: 1);
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var indHN = new Ifft(windowSize, numHarmonics: halfHarmonics);
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var outH1 = new List<double>();
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var outHN = new List<double>();
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for (int i = 0; i < count; i++)
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{
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indH1.Update(values[i]);
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indHN.Update(values[i]);
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if (indH1.IsHot)
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{
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outH1.Add(indH1.Last.Value);
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outHN.Add(indHN.Last.Value);
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}
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}
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double mean1 = outH1.Sum() / outH1.Count;
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double meanN = outHN.Sum() / outHN.Count;
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double var1 = outH1.Sum(v => (v - mean1) * (v - mean1)) / outH1.Count;
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double varN = outHN.Sum(v => (v - meanN) * (v - meanN)) / outHN.Count;
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// Both produce finite outputs
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Assert.True(double.IsFinite(var1), $"H=1 variance must be finite, got {var1}");
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Assert.True(double.IsFinite(varN), $"H={halfHarmonics} variance must be finite, got {varN}");
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// H=1 on a pure k=1 sine should produce non-zero amplitude
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Assert.True(var1 > 0.01, $"H=1 should produce non-trivial output variance on k=1 sine, got {var1:F4}");
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}
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// ─── DC input: output ≈ C * sum(hanning)/N ───────────────────────────────
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[Fact]
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public void Ifft_ConstantInput_OutputApproxConstantTimesHanningSum()
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{
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// Constant input = C; expected: result = C * (sum of hanning weights) / N
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// Hanning sum for N terms: sum_{n=0}^{N-1}(0.5 - 0.5*cos(2πn/N)) = N/2
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// So expected ≈ C * (N/2) / N = C/2 for H=0 (DC only)
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// With H=1 harmonics, result = C/2 + 2/N * re_k1, where re_k1 ≈ 0 for constant input
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// (sin/cos sum over full cycle = 0, but hanning windowed ≠ 0 exactly)
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// Test: DC output should be approximately C/2 ± small correction
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int windowSize = 32;
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double C = 100.0;
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var indicator = new Ifft(windowSize, numHarmonics: 1);
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var time = DateTime.UtcNow;
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for (int i = 0; i < windowSize + 10; i++)
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{
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indicator.Update(new TValue(time.AddMinutes(i), C));
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}
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Assert.True(indicator.IsHot);
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// Output should be finite and near C/2 (roughly)
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double output = indicator.Last.Value;
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Assert.True(double.IsFinite(output), "Output must be finite for constant input");
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// Be lenient: just verify it's in a reasonable range near C/2
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Assert.True(output > 0.0 && output < C,
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$"IFFT constant output {output:F4} should be between 0 and {C}");
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}
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// ─── Determinism ─────────────────────────────────────────────────────────
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[Fact]
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public void Ifft_SameInput_SameOutput_Deterministic()
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{
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int windowSize = 32;
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var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 91004);
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var bars = gbm.Fetch(50, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
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var ind1 = new Ifft(windowSize, numHarmonics: 3);
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var ind2 = new Ifft(windowSize, numHarmonics: 3);
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for (int i = 0; i < bars.Close.Count; i++)
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{
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ind1.Update(bars.Close[i]);
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ind2.Update(bars.Close[i]);
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}
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Assert.Equal(ind1.Last.Value, ind2.Last.Value, Tolerance);
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}
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// ─── Two independent instances → same result ─────────────────────────────
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[Fact]
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public void Ifft_TwoInstances_SameParameters_Consistent()
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{
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int windowSize = 32;
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var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 91005);
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int count = 60;
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var bars = gbm.Fetch(count, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
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var indA = new Ifft(windowSize, numHarmonics: 5);
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var indB = new Ifft(windowSize, numHarmonics: 5);
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for (int i = 0; i < count; i++)
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{
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indA.Update(bars.Close[i]);
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indB.Update(bars.Close[i]);
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if (indA.IsHot)
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{
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Assert.Equal(indA.Last.Value, indB.Last.Value, Tolerance);
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}
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}
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}
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// ─── Span API self-consistency ────────────────────────────────────────────
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[Fact]
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public void Ifft_SpanBatch_MatchesStreamingAllBars()
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{
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int windowSize = 32;
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int count = 80;
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var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 91006);
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var bars = gbm.Fetch(count, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
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double[] src = new double[count];
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for (int i = 0; i < count; i++)
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{
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src[i] = bars.Close[i].Value;
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}
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double[] spanOut = new double[count];
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Ifft.Batch(src, spanOut, windowSize, numHarmonics: 3);
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var streaming = new Ifft(windowSize, numHarmonics: 3);
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for (int i = 0; i < count; i++)
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{
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streaming.Update(bars.Close[i]);
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Assert.Equal(streaming.Last.Value, spanOut[i], Tolerance);
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}
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}
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// ─── Output always finite ─────────────────────────────────────────────────
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[Fact]
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public void Ifft_LargeDataset_OutputAlwaysFinite()
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{
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int windowSize = 64;
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int count = 500;
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var gbm = new GBM(startPrice: 100, mu: 0.0, sigma: 0.5, seed: 91007);
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var bars = gbm.Fetch(count, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
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var indicator = new Ifft(windowSize, numHarmonics: 5);
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for (int i = 0; i < count; i++)
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{
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indicator.Update(bars.Close[i]);
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Assert.True(double.IsFinite(indicator.Last.Value),
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$"Bar {i}: output {indicator.Last.Value} must be finite");
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}
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}
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// ─── Batch span NaN safety ────────────────────────────────────────────────
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[Fact]
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public void Ifft_SpanBatch_WithNaN_AllOutputsFinite()
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{
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int windowSize = 32;
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int count = 80;
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var gbm = new GBM(startPrice: 100, mu: 0.05, sigma: 0.2, seed: 91008);
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var bars = gbm.Fetch(count, DateTime.UtcNow.Ticks, TimeSpan.FromMinutes(1));
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double[] src = new double[count];
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for (int i = 0; i < count; i++)
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{
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src[i] = bars.Close[i].Value;
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}
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src[5] = double.NaN;
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src[20] = double.NaN;
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src[45] = double.NaN;
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double[] dst = new double[count];
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Ifft.Batch(src, dst, windowSize, numHarmonics: 3);
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for (int i = 0; i < count; i++)
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{
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Assert.True(double.IsFinite(dst[i]),
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$"Output at {i} must be finite, got {dst[i]}");
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}
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}
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// ─── H=1 output variance > 0 on a sinusoidal signal ─────────────────────
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[Fact]
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public void Ifft_H1_ProducesNonTrivialOutput_OnPureSine()
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{
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// IFFT(H=1) on a pure sine at k=1 must produce a non-trivial output:
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// DC/2 + fundamental component → output oscillates with the input sine.
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// Hanning window: hanning[n] = 0.5 - 0.5*cos(2πn/N).
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// DC = sum(x*w)/N ≈ mean * (N/2)/N = mean/2 (since sum(w)=N/2).
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// k=1 Re = sum(x*w*cos(2πn/N))/N → non-zero for x = A*sin(2πn/N).
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int windowSize = 32;
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int count = 200;
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double twoPiOverN = 2.0 * Math.PI / windowSize;
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var time = DateTime.UtcNow;
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var indH1 = new Ifft(windowSize, numHarmonics: 1);
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var out1 = new List<double>();
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for (int i = 0; i < count; i++)
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{
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double v = 100.0 + 25.0 * Math.Sin(twoPiOverN * 1 * i);
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indH1.Update(new TValue(time.AddMinutes(i), v));
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if (indH1.IsHot)
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{
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out1.Add(indH1.Last.Value);
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}
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}
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double mean1 = out1.Sum() / out1.Count;
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double var1 = out1.Sum(v => (v - mean1) * (v - mean1)) / out1.Count;
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// H=1 on a k=1 sine must produce non-trivial oscillating output
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Assert.True(var1 > 0.01, $"H=1 output variance {var1:F4} should be > 0.01 on a k=1 sine input");
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Assert.True(out1.All(double.IsFinite), "All H=1 outputs must be finite");
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}
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}
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