// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Generalized Double Exponential Moving Average (GDEMA)", "GDEMA", overlay=true)

//@function Computes Generalized DEMA — extends standard DEMA with a tunable volume factor
//          that controls the aggressiveness of lag compensation.
//          GDEMA = (1 + v) * EMA1 - v * EMA2, where EMA2 = EMA(EMA1).
//          When v=1 → standard DEMA; v=0 → plain EMA; v>1 → more aggressive lag removal.
//@param source Series to analyze
//@param period Lookback period for both EMA stages
//@param vfactor Volume/gain factor controlling lag compensation aggressiveness
//@returns Generalized DEMA value from first bar with proper warmup compensation
//@reference Patrick G. Mulloy, "Smoothing Data with Faster Moving Averages" (TASC, Feb 1994)
//@optimized O(1) per bar; two cascaded EMA states with shared warmup compensator
gdema(series float source, simple int period, simple float vfactor) =>

    float a = 2.0 / (period + 1)
    float beta = 1.0 - a

    var bool warmup = true
    var float e = 1.0
    var float ema1_raw = 0.0
    var float ema2_raw = 0.0
    var float ema1 = source
    var float ema2 = source

    ema1_raw := a * (source - ema1_raw) + ema1_raw

    if warmup
        e *= beta
        float c = 1.0 / (1.0 - e)
        ema1 := c * ema1_raw
        ema2_raw := a * (ema1 - ema2_raw) + ema2_raw
        ema2 := c * ema2_raw
        warmup := e > 1e-10
    else
        ema1 := ema1_raw
        ema2_raw := a * (ema1 - ema2_raw) + ema2_raw
        ema2 := ema2_raw

    // Generalized DEMA: (1 + v) * EMA1 - v * EMA2
    // v=0 → EMA, v=1 → standard DEMA, v>1 → more lag reduction (more overshoot)
    (1.0 + vfactor) * ema1 - vfactor * ema2

// ---------- Main loop ----------

// Inputs
i_period  = input.int(10, "Period", minval=1)
i_vfactor = input.float(1.0, "Volume Factor (v)", minval=0.0, maxval=3.0, step=0.1,
     tooltip="0=EMA, 1=standard DEMA, >1=more aggressive lag removal")
i_source  = input.source(close, "Source")

// Calculation
gdema_value = gdema(i_source, i_period, i_vfactor)

// Plot
plot(gdema_value, "GDEMA", color=color.yellow, linewidth=2)