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# Laguerre Momentum Professional
## 1. Summary (Introduction)
> **Part of the Laguerre Indicator Family**
>
> This indicator is a member of a family of tools based on John Ehlers' Laguerre filter.
>
> * [Laguerre Filter Pro](./Laguerre_Filter_Pro.md): A fast, responsive moving average.
> * [Laguerre RSI Pro](./Laguerre_RSI_Pro.md): A smooth, noise-filtered momentum oscillator.
> * **Laguerre Momentum Pro:** A Laguerre-smoothed oscillator of the bar-by-bar momentum.
The Laguerre Momentum Pro is an oscillator that applies the powerful, low-lag **Laguerre Filter** to a **momentum source (Close - Open)** instead of the price.
While the standard `Laguerre_Filter_Pro` provides a smoothed representation of the trend, this indicator isolates and smooths the raw bar-by-bar momentum. The `gamma` parameter allows the user to precisely control the trade-off between responsiveness and smoothness of the final oscillator.
The result is a flexible, zero-mean oscillator that can be tuned to identify the underlying strength and direction of price velocity.
## 2. Mathematical Foundations and Calculation Logic
The indicator is a Laguerre-filtered average of the `Close - Open` value of each bar.
### Calculation Steps (Algorithm)
1. **Calculate Momentum Source:** For each bar, the source data is calculated as `Momentum = Close - Open`.
2. **Apply Laguerre Filter:** A full, weighted Laguerre Filter is calculated on this `Momentum` data series, using the user-defined `gamma` to control the smoothing.
## 3. MQL5 Implementation Details
* **Unified Engine (`Laguerre_Engine.mqh`):** This indicator uses the exact same, powerful calculation engine as the `Laguerre_Filter_Pro` and `Laguerre_RSI_Pro`. The only difference is that it is initialized in `SOURCE_MOMENTUM` mode.
* **Heikin Ashi Integration:** The indicator fully supports calculation on smoothed Heikin Ashi data (`HA Close - HA Open`).
* **Stability via Full Recalculation:** The indicator employs a full recalculation on every `OnCalculate` call to ensure the stateful, recursive calculation is always stable.
## 4. Parameters
* **Gamma (`InpGamma`):** The Laguerre filter coefficient (0.0 to 1.0). This parameter controls the indicator's speed and smoothness.
* **High Gamma (e.g., 0.7 - 0.9):** Results in a **slower, smoother** oscillator.
* **Low Gamma (e.g., 0.1 - 0.3):** Results in a **faster, more volatile** oscillator.
* **Candle Source (`InpCandleSource`):** Selects between `Standard` and `Heikin Ashi` candles for the `Close - Open` calculation.
## 5. Usage and Interpretation
The Laguerre Momentum is a classic zero-mean oscillator used for identifying momentum shifts and potential reversals.
### Standalone Usage
* **Zero-Line Crossover:**
* A cross **above the zero line** indicates that bullish momentum is taking control.
* A cross **below the zero line** indicates that bearish momentum is dominant.
* **Divergence:**
* **Bullish Divergence:** Price makes a **new lower low**, but the Laguerre Momentum makes a **higher low**.
* **Bearish Divergence:** Price makes a **new higher high**, but the Laguerre Momentum makes a **lower high**.
### Combined Strategy with Laguerre Filter (Primary Use)
This oscillator is designed to be used in conjunction with its companion indicator, the `Laguerre_Filter_Pro`.
* **The Zero-Cross Predicts the Filter's Turning Point:**
* **Buy Signal:** When the **Laguerre Momentum** line crosses **above the zero line**, it provides a leading signal that the `Laguerre_Filter` on the main chart is forming a **trough (a bottom)**.
* **Sell Signal:** When the **Laguerre Momentum** line crosses **below the zero line**, it provides a leading signal that the `Laguerre_Filter` is forming a **peak (a top)**.