// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Zero-Lag Triple EMA (ZLTEMA)", "ZLTEMA", overlay=true)

//@function Calculates ZLTEMA using zero-lag price and triple exponential smoothing with compensator
//@doc https://github.com/mihakralj/pinescript/blob/main/indicators/trends_IIR/zltema.md
//@param source Series to calculate ZLTEMA from
//@param period Smoothing period
//@param alpha Optional smoothing factor (overrides period if provided)
//@returns ZLTEMA value with zero-lag effect applied
//@optimized Uses lag compensation buffer and exponential warmup compensator on all three EMA stages for O(1) complexity
zltema(series float source, simple int period=0, simple float alpha=0) =>
    if alpha <= 0 and period <= 0
        runtime.error("Alpha or period must be provided")
    float a1 = alpha > 0 ? alpha : 2.0 / (period + 1)
    float beta1 = 1.0 - a1
    float r = math.pow(1.0 / a1, 1.0 / 3.0)
    float a2 = a1 * r
    float a3 = a2 * r
    simple int lag = math.max(1, math.round((period - 1) / 2))
    var bool warmup = true
    var float e = 1.0
    var float ema1_raw = 0.0
    var float ema2_raw = 0.0
    var float ema3_raw = 0.0
    var float ema1 = na
    var float ema2 = na
    var float ema3 = na
    var priceBuffer = array.new<float>(lag + 1, na)
    if not na(source)
        if na(ema1)
            ema1 := source
            ema2 := source
            ema3 := source
            array.fill(priceBuffer, source)
        array.shift(priceBuffer)
        array.push(priceBuffer, source)
        float laggedPrice = nz(array.get(priceBuffer, 0), source)
        float signal = 2 * source - laggedPrice
        ema1_raw := a1 * (signal - ema1_raw) + ema1_raw
        if warmup
            e *= beta1
            float c = 1.0 / (1.0 - e)
            ema1 := c * ema1_raw
            ema2_raw := a2 * (ema1 - ema2_raw) + ema2_raw
            ema2 := c * ema2_raw
            ema3_raw := a3 * (ema2 - ema3_raw) + ema3_raw
            ema3 := c * ema3_raw
            warmup := e > 1e-10
        else
            ema1 := ema1_raw
            ema2_raw := a2 * (ema1 - ema2_raw) + ema2_raw
            ema2 := ema2_raw
            ema3_raw := a3 * (ema2 - ema3_raw) + ema3_raw
            ema3 := ema3_raw
        3 * ema1 - 3 * ema2 + ema3
    else
        na

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

// Inputs
i_period = input.int(10, "Period", minval=1)
i_source = input.source(close, "Source")

// Calculation
zltema_value = zltema(i_source, i_period)

// Plot
plot(zltema_value, "ZLTEMA", color=color.yellow, linewidth=2)