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feat: add new indicators (Decay, Edecay, MinusDi, MinusDm, PlusDi, PlusDm, Maxindex, Minindex, Sarext) and update pine scripts, core libs, validation tests, and python bindings
This commit is contained in:
Miha Kralj
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using System.Runtime.CompilerServices;
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namespace QuanTAlib;
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/// <summary>
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/// MININDEX: Rolling Minimum Index
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/// Returns the position of the minimum value within a rolling window.
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/// Streaming mode: bars-ago offset (0=current, period-1=oldest).
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/// Batch span mode: absolute array index (TA-Lib compatible).
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/// </summary>
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/// <remarks>
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/// Key properties:
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/// - Returns the index/position of the lowest value, not the value itself
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/// - Streaming output is "bars-ago" offset for natural streaming consumption
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/// - Batch(ReadOnlySpan) output is absolute array index matching TA-Lib MININDEX
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/// - Tie-breaking: last occurrence wins (most recent bar, using <= comparison)
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/// - Can be cross-validated: source[Minindex.Batch[i]] == Lowest.Batch[i]
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/// </remarks>
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[SkipLocalsInit]
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public sealed class Minindex : AbstractBase
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{
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private readonly int _period;
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private readonly RingBuffer _buffer;
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private record struct State(double LastValid);
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private State _state, _p_state;
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public override bool IsHot => _buffer.Count >= _period;
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/// <summary>
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/// Initializes a new Minindex indicator with specified lookback period.
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/// </summary>
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/// <param name="period">Lookback window size (must be >= 2)</param>
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public Minindex(int period)
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{
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if (period < 2)
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{
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throw new ArgumentException("Period must be >= 2", nameof(period));
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}
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_period = period;
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_buffer = new RingBuffer(period);
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Name = $"Minindex({period})";
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WarmupPeriod = period;
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}
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/// <summary>
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/// Initializes a new Minindex indicator with source for event-based chaining.
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/// </summary>
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/// <param name="source">Source indicator for chaining</param>
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/// <param name="period">Lookback window size</param>
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public Minindex(ITValuePublisher source, int period) : this(period)
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{
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source.Pub += HandleUpdate;
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}
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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private void HandleUpdate(object? sender, in TValueEventArgs e) => Update(e.Value, e.IsNew);
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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public override TValue Update(TValue input, bool isNew = true)
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{
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if (isNew)
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{
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_p_state = _state;
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}
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else
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{
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_state = _p_state;
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}
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double value = double.IsFinite(input.Value) ? input.Value : _state.LastValid;
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_state = new State(value);
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_buffer.Add(value, isNew);
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// Scan the ring buffer to find the bars-ago index of the minimum value.
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// Tie-breaking: <= means last occurrence (most recent) wins.
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ReadOnlySpan<double> span = _buffer.GetSpan();
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int len = span.Length;
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double minVal = span[0];
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int minPos = 0;
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for (int i = 1; i < len; i++)
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{
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if (span[i] <= minVal)
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{
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minVal = span[i];
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minPos = i;
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}
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}
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// Convert to bars-ago: newest element is at index (len - 1), oldest at 0.
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// bars-ago = (len - 1) - minPos
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double result = (len - 1) - minPos;
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Last = new TValue(input.Time, result);
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PubEvent(Last, isNew);
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return Last;
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}
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public override TSeries Update(TSeries source)
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{
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var result = new TSeries(source.Count);
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ReadOnlySpan<double> values = source.Values;
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ReadOnlySpan<long> times = source.Times;
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for (int i = 0; i < source.Count; i++)
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{
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var tv = Update(new TValue(new DateTime(times[i], DateTimeKind.Utc), values[i]), true);
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result.Add(tv, true);
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}
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return result;
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}
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public override void Prime(ReadOnlySpan<double> source, TimeSpan? step = null)
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{
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TimeSpan interval = step ?? TimeSpan.FromSeconds(1);
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DateTime time = DateTime.UtcNow - (interval * source.Length);
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for (int i = 0; i < source.Length; i++)
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{
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Update(input: new TValue(time, source[i]), isNew: true);
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time += interval;
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}
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}
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public static TSeries Batch(TSeries source, int period)
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{
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var indicator = new Minindex(period);
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return indicator.Update(source);
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}
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/// <summary>
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/// Calculates rolling minimum index over a span of values.
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/// Output contains ABSOLUTE array indices (TA-Lib MININDEX compatible).
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/// </summary>
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public static void Batch(ReadOnlySpan<double> source, Span<double> output, int period)
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{
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if (source.Length == 0)
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{
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throw new ArgumentException("Source cannot be empty", nameof(source));
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}
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if (output.Length < source.Length)
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{
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throw new ArgumentException("Output length must be >= source length", nameof(output));
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}
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if (period < 2)
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{
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throw new ArgumentException("Period must be >= 2", nameof(period));
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}
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int len = source.Length;
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// Use monotonic deque algorithm — same as Lowest but output index, not value.
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int[]? rentedDeque = null;
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double[]? rentedValues = null;
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#pragma warning disable S1121 // Assignments should not be made from within sub-expressions
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Span<int> deque = period <= 256
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? stackalloc int[period]
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: (rentedDeque = System.Buffers.ArrayPool<int>.Shared.Rent(period)).AsSpan(0, period);
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Span<double> values = len <= 256
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? stackalloc double[len]
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: (rentedValues = System.Buffers.ArrayPool<double>.Shared.Rent(len)).AsSpan(0, len);
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#pragma warning restore S1121
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try
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{
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// First pass: store corrected values (handle NaN/Infinity)
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double lastValid = 0.0;
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for (int i = 0; i < len; i++)
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{
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double val = source[i];
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if (double.IsFinite(val))
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{
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lastValid = val;
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values[i] = val;
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}
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else
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{
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values[i] = lastValid;
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}
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}
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// Second pass: compute rolling min index using monotonic deque.
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// Circular buffer indexing — branch-based wrapping is faster than modulo.
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int head = 0; // front of deque (oldest/min)
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int tail = 0; // back of deque (newest)
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int count = 0; // number of elements in deque
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int capacity = deque.Length;
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for (int i = 0; i < len; i++)
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{
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double value = values[i];
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// Remove indices outside window from front
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while (count > 0 && deque[head] <= i - period)
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{
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head++;
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if (head >= capacity)
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{
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head -= capacity;
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}
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count--;
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}
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// Remove larger-or-equal values from back (<= tie-breaking: last occurrence wins)
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while (count > 0)
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{
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int backIdx = tail - 1;
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if (backIdx < 0)
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{
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backIdx += capacity;
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}
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if (values[deque[backIdx]] >= value)
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{
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tail = backIdx;
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count--;
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}
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else
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{
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break;
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}
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}
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// Add current index at tail
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deque[tail] = i;
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tail++;
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if (tail >= capacity)
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{
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tail -= capacity;
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}
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count++;
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// Output the ABSOLUTE index of the minimum (not the value)
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output[i] = deque[head];
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}
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}
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finally
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{
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if (rentedDeque != null)
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{
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System.Buffers.ArrayPool<int>.Shared.Return(rentedDeque);
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}
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if (rentedValues != null)
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{
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System.Buffers.ArrayPool<double>.Shared.Return(rentedValues);
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}
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}
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}
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public static (TSeries Results, Minindex Indicator) Calculate(TSeries source, int period)
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{
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var indicator = new Minindex(period);
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TSeries results = indicator.Update(source);
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return (results, indicator);
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}
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public override void Reset()
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{
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_buffer.Clear();
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_state = default;
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_p_state = default;
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Last = default;
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}
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}
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@@ -0,0 +1,167 @@
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# MININDEX: Rolling Minimum Index
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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| **Inputs** | Source (close) |
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| **Parameters** | `period` (default=14, min=2) |
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| **Outputs** | Single series (Minindex) |
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| **Output range** | Streaming: 0 to period-1 (bars-ago); Batch span: absolute array index |
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| **Warmup** | `period` bars |
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### TL;DR
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- MININDEX finds the position (index) of the minimum value within a rolling lookback window.
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- Parameterized by `period` (minimum 2).
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- Streaming mode outputs bars-ago offset (0 = current bar holds the min, period-1 = oldest bar).
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- Batch span mode outputs absolute array indices (TA-Lib MININDEX compatible).
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- Tie-breaking: last occurrence wins (most recent bar, `<=` comparison).
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- Requires `period` bars of warmup before first valid output (IsHot = true).
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- Cross-validation: `source[Minindex.Batch[i]] == Lowest.Batch[i]` for all bars after warmup.
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> "Finding support isn't just about the price — it's about *when* the floor was set."
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MININDEX identifies the position of the minimum value within a rolling window. While LOWEST tells you the trough *value*, MININDEX tells you *where* that trough is relative to the current bar. This is essential for support analysis, timing studies, and detecting how "stale" a low is.
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## Historical Context
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The MININDEX function originates from TA-Lib (TA_MININDEX), used in quantitative trading systems to identify when the lowest price in a lookback window occurred. This timing information is critical for:
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- **Support freshness**: A min at position 0 means support is being tested *now*; at position period-1, the low is stale and potentially irrelevant.
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- **Pattern detection**: Identifying double bottoms, inverse head-and-shoulders, and other formations requires knowing *when* troughs occurred.
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- **Exhaustion analysis**: The position of the low within the window indicates whether selling pressure is current or historical.
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## Architecture & Physics
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### 1. Streaming Mode — Bars-Ago Offset
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In streaming mode, the output represents how many bars ago the minimum occurred:
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$$
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\text{Minindex}_t = t - \arg\min_{t-n+1 \leq k \leq t} V_k
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$$
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where $n$ is the lookback period. A value of 0 means the current bar is the minimum; a value of $n-1$ means the oldest bar in the window holds the minimum.
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### 2. Batch Span Mode — Absolute Index
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In the `Batch(ReadOnlySpan)` method, output is the absolute array index:
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$$
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\text{output}[i] = \arg\min_{i-n+1 \leq k \leq i} V_k
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$$
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This matches TA-Lib's MININDEX convention and enables direct array lookup: `source[output[i]]` yields the minimum value.
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### 3. Tie-Breaking
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When multiple values in the window are equal to the minimum, the **most recent** (rightmost) occurrence wins:
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$$
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\text{Minindex}_t = \max \{ k : V_k = \min(\text{window}) \}
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$$
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This is achieved using `<=` comparison, matching TA-Lib behavior.
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### 4. Monotonic Deque (Batch Mode)
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The batch span method uses the same O(n) monotonic deque algorithm as Lowest, but outputs the index stored at the deque head rather than the value at that index:
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```
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// Lowest: output[i] = values[deque.PeekHead()] → the VALUE
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// Minindex: output[i] = deque.PeekHead() → the INDEX
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```
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### 5. Bar Correction via Rollback
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When `isNew=false`, the indicator:
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1. Restores previous state (`_state = _p_state`)
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2. Replaces the last value in the buffer
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3. Re-scans the buffer to find the new minimum position
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## Mathematical Foundation
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### Rolling Minimum Index Definition
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$$
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\text{Minindex}_t = \arg\min_{t-n+1 \leq k \leq t} V_k
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$$
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where $n$ is the lookback period and ties are broken in favor of the most recent occurrence.
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### Partial Window Behavior
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Before the window is full:
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$$
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\text{Minindex}_t = \arg\min_{0 \leq k \leq t} V_k \quad \text{for } t < n
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$$
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### Complexity Analysis
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| Operation | Streaming | Batch (Deque) |
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| :--- | :---: | :---: |
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| Per-update (worst) | O(n) | O(n) |
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| Per-update (amortized) | O(n) | O(1) |
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| Total for N updates | O(N×n) | O(N) |
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Streaming uses a linear scan of the RingBuffer, which is O(period) per bar — acceptable for typical periods (5–30). Batch mode uses the monotonic deque for O(1) amortized.
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## Performance Profile
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### Streaming Mode (Linear Scan)
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| Operation | Count | Cost (cycles) | Subtotal |
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| :--- | :---: | :---: | :---: |
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| CMP (scan) | period | 1 | period |
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| Array access | period | 3 | 3×period |
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| Index arithmetic | 2 | 1 | 2 |
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| **Total** | — | — | **~4×period cycles** |
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### Batch Mode (Monotonic Deque)
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| Operation | Count | Cost (cycles) | Subtotal |
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| :--- | :---: | :---: | :---: |
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| CMP (expired check) | 1 | 1 | 1 |
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| CMP (monotonicity) | ~2 avg | 1 | 2 |
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| Array access | 3 | 3 | 9 |
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| Index arithmetic | 2 | 1 | 2 |
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| **Total** | **~8** | — | **~14 cycles** |
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### Quality Metrics
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| Metric | Score | Notes |
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| :--- | :---: | :--- |
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| **Accuracy** | 10/10 | Exact index of minimum |
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| **Timeliness** | 10/10 | Zero lag for index detection |
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| **Smoothness** | 2/10 | Discrete jumps as window slides |
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| **Computational Cost** | 8/10 | O(period) streaming, O(1) batch |
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| **Memory** | 7/10 | O(n) for buffer + deque |
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## Validation
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| Library | Status | Notes |
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| :--- | :---: | :--- |
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| **TA-Lib MININDEX** | ✅ | Batch span output matches absolute indices |
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| **Cross-validation** | ✅ | `source[Minindex[i]] == Lowest[i]` for all valid bars |
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| **Known Values** | ✅ | Manual verification |
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## Common Pitfalls
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1. **Two Output Modes**: Streaming returns bars-ago offset; Batch(ReadOnlySpan) returns absolute array index. Do not mix them up.
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2. **Period Minimum is 2**: Unlike Lowest (which accepts period=1), Minindex requires period >= 2, since the index of a single element is trivially 0.
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3. **Tie-Breaking**: Uses `<=` so the most recent (rightmost) occurrence wins ties. This matches TA-Lib convention.
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4. **Window Boundary Effects**: When the previous min expires from the window, the index can jump abruptly. This is expected behavior.
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5. **Warmup Period**: `IsHot` becomes true after `period` values. Before warmup, returns index within available data.
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6. **Using isNew Incorrectly**: Use `isNew: false` only when correcting the current bar. New bars must use `isNew: true`.
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## References
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- TA-Lib: MININDEX function documentation.
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- Lemire, Daniel. (2006). "Streaming Maximum-Minimum Filter Using No More than Three Comparisons per Element."
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- Tarjan, Robert E. (1985). "Amortized Computational Complexity." SIAM Journal on Algebraic Discrete Methods.
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