Divergence Indicator with Multi-Length Pivot Detection

This Pine Script, titled “Divergence Indicator with Multi-Length Pivot Detection”, tool that detects both regular and hidden divergences between price action and an oscillator (defaulting to close, but configurable). It features multi-length pivot logic, angle-based validation, no-cross filtering, and OB/OS region filtering, making it a robust and precise divergence engine. Below is a detailed breakdown:

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🔧 Inputs and Configuration
    •    osc_src: Oscillator source (e.g. close, RSI, MACD).
    •    show_hidden: Toggles detection of hidden divergences.
    •    min_*_angle settings: Control the minimum angle thresholds (in degrees) for confirming valid divergences (ensures momentum is strong enough).
    •    validate_no_cross: Ensures oscillator and price slopes don’t “cross” the actual values (i.e. filters out invalid or messy trends).
    •    oversold_level, overbought_level: Used when use_ob_os_filter is enabled to require oscillator to be in OS/OB zones for regular divergence.
    •    min_div_length: Minimum distance in bars between previous and current pivot points.

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🔁 Internal Engine Mechanics

1. Pivot Detection Engine (Phase 1: Historical Memory)
    •    For all combinations of left1 and right1 in the range [1, 10]:
    •    Records all valid pivot lows and pivot highs.
    •    Stores their:
    •    bar index
    •    price value
    •    oscillator value

This forms a “memory buffer” of past pivots that future price pivots are compared against.

2. Current Pivot Detection (Phase 2: Scanning)
    •    Loops through larger pivot configurations (left2 ∈ [5,15], right2 = 1) to detect new current pivots.
    •    For each new pivot, it compares against the historical pivots from phase 1.

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📐 Slope and Angle Calculation

For each matching pivot pair (historical vs current):
    •    Price and Oscillator Slopes are calculated via linear regression, producing:
    •    price_angle
    •    osc_angle
    •    These are converted using math.atan() and math.todegrees() to get proper angular direction and intensity of trend.

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🧠 Divergence Logic

✅ Bullish Divergence
    •    Regular Bullish: Price makes a lower low, oscillator makes a higher low.
    •    Hidden Bullish: Price makes a higher low, oscillator makes a lower low.
    •    Conditions:
    •    Must meet minimum angle thresholds.
    •    Optional: Must be in oversold region (osc_src < oversold_level).
    •    If validate_no_cross is enabled, linearly interpolated slope must not be violated.

✅ Bearish Divergence
    •    Regular Bearish: Price makes a higher high, oscillator makes a lower high.
    •    Hidden Bearish: Price makes a lower high, oscillator makes a higher high.
    •    Conditions mirror the bullish case (with polarity reversed).

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🖍️ Visualization
    •    Draws colored lines between pivots for visual clarity:
    •    Green: Regular Bullish
    •    Lime: Hidden Bullish
    •    Red: Regular Bearish
    •    Maroon: Hidden Bearish
    •    Uses plotshape() to mark divergence bars:
    •    Triangle-up for bullish
    •    Triangle-down for bearish

The lines and shapes help quickly identify divergence zones with strong momentum structure.

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🧪 Filtering Enhancements
    •    No Cross Slope Filter: Checks that oscillator and price values stay above/below their respective slope lines throughout the interval.
    •    OB/OS Filter: Restricts divergence signals to occur only in oversold/overbought conditions for regular divergences.
    •    Signal Thinning: Keeps line count to 100 using array.shift() and line.delete().

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🧬 Design Philosophy
    •    Built to mimic institutional-grade divergence detection, avoiding common false positives.
    •    Uses adaptive pivots, rigorous angle validation, and noise filtering.