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feat(dynamics): add PlusDI, MinusDI, PlusDM, MinusDM indicators
Complete thin Dx-composition wrapper indicators with full test coverage: - PlusDi/MinusDi: Directional Indicator wrappers (DiPlus/DiMinus from Dx) - PlusDm/MinusDm: Directional Movement wrappers (DmPlus/DmMinus from Dx) - Individual validation tests per indicator directory (TALib, Skender, bounds) - Combined unit tests (DiDm.Tests.cs) and validation tests (DiDm.Validation.Tests.cs) - Quantower wrappers + tests for all 4 indicators - PineScript v6 implementations with compensated RMA - Normalized .md documentation for all indicators and categories - 182 tests passing, 0 failures
This commit is contained in:
Miha Kralj
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# Numerics
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> "Price is raw signal. Transform exposes hidden structure. Derivative reveals momentum. Normalization enables comparison."
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Basic mathematical transforms and utility functions for time series. These building blocks convert raw price data into forms suitable for analysis, comparison, and downstream indicator consumption.
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| Indicator | Full Name | Description |
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# ACCEL: Second Derivative (Acceleration)
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> *Velocity tells you where you're going. Acceleration tells you if you're getting there faster or slower.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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- Requires `3` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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> "Velocity tells you where you're going. Acceleration tells you if you're getting there faster or slower."
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ACCEL measures the rate of change of velocity—the acceleration of a time series. As the second derivative, it reveals momentum shifts before they manifest in price direction. Positive acceleration means velocity is increasing (trend strengthening); negative means velocity is decreasing (trend weakening). This O(1) streaming implementation uses FMA optimization and SIMD batch processing.
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## Historical Context
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# BETADIST: Beta Distribution CDF
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> *The Beta distribution CDF maps values onto a flexible probability curve defined by two shape parameters — versatile enough to model any bounded outcome.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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# BINOMDIST: Binomial Distribution CDF
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> *Binomial distribution CDF counts the probability of success in fixed trials — discrete probability at its most fundamental.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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# CHANGE: Relative Price Change
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> *The simplest measure of movement is often the most powerful.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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- Requires `period + 1` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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> "The simplest measure of movement is often the most powerful."
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CHANGE calculates the percentage change between the current value and a value N periods ago. This fundamental indicator forms the basis for momentum analysis, rate of change calculations, and relative performance comparisons.
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## Mathematical Foundation
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# CWT: Continuous Wavelet Transform
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> *The continuous wavelet transform decomposes a signal across scale and time simultaneously — frequency analysis with temporal precision.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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# DECAY: Linear Decay
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> *A ratchet that only moves down slowly: price can push it up instantly, but gravity pulls it back at a steady, linear pace.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numerics |
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- Requires `1` bar of warmup before first valid output (IsHot = true).
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- Validated against Tulip Indicators `ti_decay` reference algorithm.
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> "A ratchet that only moves down slowly: price can push it up instantly, but gravity pulls it back at a steady, linear pace."
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DECAY implements the Tulip Indicators `ti_decay` function. When price is above the decayed level, output snaps to price. When price falls below, the output decays linearly at a rate of `1/period` per bar, creating a ceiling that gradually descends. This produces a one-sided envelope that hugs price from above.
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## Historical Context
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# DWT: Discrete Wavelet Transform
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> *The discrete wavelet transform splits a signal into approximation and detail at each scale — multiresolution analysis in action.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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# EDECAY: Exponential Decay
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> *A ratchet that only moves down gradually: price can push it up instantly, but gravity pulls it back at an exponential pace — faster when far from zero, slower as it approaches.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numerics |
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- Requires `1` bar of warmup before first valid output (IsHot = true).
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- Validated against Tulip Indicators `ti_edecay` reference algorithm.
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> "A ratchet that only moves down gradually: price can push it up instantly, but gravity pulls it back at an exponential pace — faster when far from zero, slower as it approaches."
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EDECAY implements the exponential decaying function. When price is above the decayed level, output snaps to price. When price falls below, the output decays exponentially by multiplying by `(period-1)/period` per bar, creating a ceiling that gradually descends. Unlike linear DECAY which subtracts a fixed amount, EDECAY's multiplicative factor produces a proportional decay rate.
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## Historical Context
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# EXPDIST: Exponential Distribution CDF
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> *The exponential distribution models the time between events — memoryless waiting distilled into a single rate parameter.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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# EXPTRANS: Exponential Function
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> *The exponential function is the only function that is its own derivative—a mathematical curiosity that makes it indispensable for modeling growth, decay, and everything compounding.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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- Requires `0` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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> "The exponential function is the only function that is its own derivative—a mathematical curiosity that makes it indispensable for modeling growth, decay, and everything compounding."
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The Exponential (EXP) transformer applies the natural exponential function $e^x$ to each value in a time series. As the inverse of the natural logarithm, it converts additive relationships back to multiplicative ones, making it essential for reconstructing price levels from log-returns and implementing models that assume log-normal distributions.
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## Mathematical Foundation
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# FDIST: F-Distribution CDF
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> *The F-distribution CDF tests variance ratios — a cornerstone of hypothesis testing built from two chi-squared variables.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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# FFT: Fast Fourier Transform (Dominant Cycle Detector)
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> *The FFT decomposes price into its constituent frequencies, revealing how much of each cycle lives inside the data.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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# GAMMADIST: Gamma Distribution CDF
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> *The Gamma distribution generalizes the exponential, modeling the sum of waiting times with a shape that bends to fit.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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# HIGHEST: Rolling Maximum
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> *What's the peak? The answer to that question defines support, resistance, and breakout levels.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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- Requires `period` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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> "What's the peak? The answer to that question defines support, resistance, and breakout levels."
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HIGHEST calculates the maximum value over a rolling lookback window. This O(1) amortized streaming implementation uses a monotonic deque algorithm, enabling real-time updates without re-scanning the entire window. Validated against TA-Lib MAX and Tulip max functions.
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## Historical Context
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# IFFT: Inverse Fast Fourier Transform (Spectral Low-Pass Filter)
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> *Inverse FFT reconstructs a time series from selected frequency components — a spectral scalpel for noise removal.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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# JERK: Third Derivative
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> *Acceleration tells you the trend is changing. Jerk tells you that change is itself changing—the earliest possible warning.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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- Requires `4` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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> "Acceleration tells you the trend is changing. Jerk tells you that change is itself changing—the earliest possible warning."
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JERK measures the rate of change of acceleration—called "jerk" in physics. As the third derivative, it detects changes in momentum dynamics before they appear in acceleration, velocity, or price. A positive jerk means acceleration is increasing; negative means acceleration is decreasing. This O(1) streaming implementation uses dual FMA optimization and SIMD batch processing for four-point calculations.
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## Historical Context
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# LINEARTRANS: Linear Scaling Transformer
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> *The simplest transformations are often the most powerful—linear scaling is the mathematical equivalent of adjusting the volume and tuning the dial.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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- Requires `0` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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> "The simplest transformations are often the most powerful—linear scaling is the mathematical equivalent of adjusting the volume and tuning the dial."
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The Linear transformer applies an affine transformation $y = \text{slope} \cdot x + \text{intercept}$ to each value in a time series. This fundamental operation enables scaling, offsetting, unit conversion, and normalization—the building blocks for preparing data for analysis or combining signals from different sources.
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## Mathematical Foundation
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# LOGNORMDIST: Log-Normal Distribution CDF
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> *The log-normal CDF models variables whose logarithm is normal — the natural distribution of prices and multiplicative processes.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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# LOGTRANS: Natural Logarithm Transformer
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> *The logarithm is one of the most useful mathematical functions, turning multiplicative relationships into additive ones—a property that makes many financial calculations tractable.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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- Requires `0` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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> "The logarithm is one of the most useful mathematical functions, turning multiplicative relationships into additive ones—a property that makes many financial calculations tractable."
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The LOG transformer applies the natural logarithm function $\ln(x)$ to input values. This point-wise transformation compresses large values and expands small ones, making it essential for analyzing multiplicative processes like compounded returns.
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## Mathematical Foundation
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# LOWEST: Rolling Minimum
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> *Know your floor. Support levels are just historical minimums waiting to be tested.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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- Requires `period` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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> "Know your floor. Support levels are just historical minimums waiting to be tested."
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LOWEST calculates the minimum value over a rolling lookback window. This O(1) amortized streaming implementation uses a monotonic deque algorithm, enabling real-time updates without re-scanning the entire window. Validated against TA-Lib MIN and Tulip min functions.
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## Historical Context
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# MAXINDEX: Rolling Maximum Index
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> *It's not just about the peak — it's about *when* the peak occurred.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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- Requires `period` bars of warmup before first valid output (IsHot = true).
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- Cross-validation: `source[Maxindex.Batch[i]] == Highest.Batch[i]` for all bars after warmup.
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> "It's not just about the peak — it's about *when* the peak occurred."
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MAXINDEX identifies the position of the maximum value within a rolling window. While HIGHEST tells you the peak *value*, MAXINDEX tells you *where* that peak is relative to the current bar. This is essential for pattern recognition, timing analysis, and detecting how "stale" a high is.
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## Historical Context
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# MININDEX: Rolling Minimum Index
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> *Finding support isn't just about the price — it's about *when* the floor was set.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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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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# NORMALIZE: Min-Max Normalization
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> *Normalization is the art of making apples and oranges comparable—by insisting that everything lives on the same scale from 0 to 1.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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- Requires `period` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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> "Normalization is the art of making apples and oranges comparable—by insisting that everything lives on the same scale from 0 to 1."
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The Normalize transformer applies min-max scaling to map any value series into the bounded range [0, 1] based on the observed minimum and maximum within a rolling lookback window. This technique is fundamental for feature scaling, creating bounded oscillators, and comparing series with different magnitudes.
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## Mathematical Foundation
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# NORMDIST: Normal Distribution CDF
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> *The normal distribution CDF is the bell curve's integral — the universal reference for probabilistic reasoning.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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# POISSONDIST: Poisson Distribution CDF
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> *Poisson distribution CDF counts rare events in fixed intervals — the mathematics of arrivals, defaults, and surprises.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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# RELU: Rectified Linear Unit
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> *The simplest non-linearity that works—ReLU's computational efficiency and gradient-friendly properties made deep learning practical.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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- Requires `0` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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> "The simplest non-linearity that works—ReLU's computational efficiency and gradient-friendly properties made deep learning practical."
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The Rectified Linear Unit (ReLU) activation function applies `max(0, x)` to each value, passing positive inputs unchanged while zeroing negative ones. Its simplicity belies its importance: ReLU enabled the training of deep neural networks by mitigating vanishing gradients, and its computational efficiency makes it the default activation for most architectures.
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## Mathematical Foundation
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# SIGMOID: Logistic Function
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> *The sigmoid function is the S-curve that turns messy reality into neat probabilities—a mathematical diplomat that insists every answer must be between 0 and 1.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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@@ -16,8 +18,6 @@
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- Requires `0` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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> "The sigmoid function is the S-curve that turns messy reality into neat probabilities—a mathematical diplomat that insists every answer must be between 0 and 1."
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The Sigmoid (Logistic) transformer maps any real-valued input to the bounded range (0, 1) using the standard logistic function. Its characteristic S-shaped curve makes it indispensable for probability estimation, neural network activations, and any scenario requiring bounded outputs from unbounded inputs.
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## Mathematical Foundation
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# SLOPE: First Derivative (Velocity)
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> *The simplest measure of change reveals the most: is it going up, or going down?*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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- Requires `2` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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> "The simplest measure of change reveals the most: is it going up, or going down?"
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SLOPE measures the instantaneous rate of change—the velocity of a time series. As the first derivative, it answers the fundamental question: how fast is the value changing right now? A positive slope means ascending; negative means descending; zero means flat. This O(1) streaming implementation uses SIMD optimization for batch calculations and handles bar corrections via state rollback.
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## Historical Context
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# SQRTTRANS: Square Root Transform
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> *The square root is nature's variance-stabilizing trick—halving the exponent space while preserving monotonicity. When price volatility scales with level, sqrt compresses the noise.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Numeric |
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@@ -16,8 +18,6 @@
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- Requires `0` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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> "The square root is nature's variance-stabilizing trick—halving the exponent space while preserving monotonicity. When price volatility scales with level, sqrt compresses the noise."
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The Square Root (SQRT) transformer applies $\sqrt{x}$ to each value in a time series. This variance-stabilizing transformation compresses ranges where volatility scales with magnitude, making it useful for heteroscedastic data where standard deviation increases with price level.
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## Mathematical Foundation
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# TDIST: Student's t-Distribution CDF
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> *Student's t-distribution CDF handles small samples with heavier tails than the normal — uncertainty acknowledged in the shape itself.*
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| Property | Value |
|
||||
| ---------------- | -------------------------------- |
|
||||
| **Category** | Numeric |
|
||||
|
||||
@@ -1,5 +1,7 @@
|
||||
# WEIBULLDIST: Weibull Distribution CDF
|
||||
|
||||
> *The Weibull distribution models failure rates that change over time — a flexible tool for reliability and survival analysis.*
|
||||
|
||||
| Property | Value |
|
||||
| ---------------- | -------------------------------- |
|
||||
| **Category** | Numeric |
|
||||
|
||||
Reference in New Issue
Block a user