// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Adaptive Price Zone", "APZ", overlay=true)

//@function Calculates Adaptive Price Zone using double-smoothed EMA
//@param source Series to calculate middle line from
//@param period Lookback period (sqrt applied internally for smoothing)
//@param bandPct Band width multiplier
//@returns tuple with [middle, upper, lower] band values
//@optimized Uses compound warmup compensation for nested EMAs, O(1) complexity per bar
apz(series float source, simple int period, simple float bandPct) =>
    if period <= 0
        runtime.error("Period must be greater than 0")
    if period > 5000
        runtime.error("Period exceeds maximum of 5000")
    if bandPct <= 0.0
        runtime.error("Band multiplier must be greater than 0")

    float smoothPeriod = math.sqrt(period)
    float alpha = 2.0 / (smoothPeriod + 1.0)
    float beta = 1.0 - alpha

    var float ema1_price = 0.0
    var float ema2_price = 0.0
    var float ema1_range = 0.0
    var float ema2_range = 0.0
    var float e = 1.0
    var bool warmup = true

    float current_price = nz(source)
    float current_range = nz(high - low)

    ema1_price := alpha * current_price + beta * ema1_price
    ema2_price := alpha * ema1_price + beta * ema2_price

    ema1_range := alpha * current_range + beta * ema1_range
    ema2_range := alpha * ema1_range + beta * ema2_range

    float middle = ema2_price
    float adaptiveRange = ema2_range

    if warmup
        e *= beta * beta
        float compensator = 1.0 / (1.0 - e)
        middle := compensator * ema2_price
        adaptiveRange := compensator * ema2_range
        warmup := e > 1e-10

    float width = bandPct * adaptiveRange
    float upper = middle + width
    float lower = middle - width

    [middle, upper, lower]

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

// Inputs
i_period = input.int(20, "Period", minval=1, maxval=5000)
i_bandPct = input.float(2.0, "Band Multiplier", minval=0.001, step=0.1)
i_source = input.source(close, "Source")

// Calculation
[middle, upper, lower] = apz(i_source, i_period, i_bandPct)

// Plot
plot(middle, "Middle", color=color.yellow, linewidth=2)
p1 = plot(upper, "Upper", color=color.new(color.yellow, 50), linewidth=1)
p2 = plot(lower, "Lower", color=color.new(color.yellow, 50), linewidth=1)
fill(p1, p2, color=color.new(color.yellow, 90), title="Band Fill")