// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Jurik Volatility", "Jvolty", overlay=false)

//@function Jurik Volatility - extracted volatility component from JMA
//@param   source Series to calculate Jvolty from
//@param   period Number of bars used in the calculation (>= 1)
//@returns Normalized volatility measure (1 = low volatility, logParam = high volatility)
jvolty(series float source, simple int period) =>
    // ---- Precomputed length parameters (constant per series) ----
    simple float _LEN0       = period < 1.0000000002 ? 1e-10 : (period - 1.0) / 2.0
    simple float _LOG_PARAM  = math.max(math.log(math.sqrt(_LEN0)) / math.log(2.0) + 2.0, 0.0)
    simple float _SQRT_PARAM = math.sqrt(_LEN0) * _LOG_PARAM
    simple float _SQRT_DIV   = _SQRT_PARAM / (_SQRT_PARAM + 1.0)
    simple float _P_EXP      = math.max(_LOG_PARAM - 2.0, 0.5)

    // ---- Internal state (persists across bars) ----
    var float  upperBand    = na
    var float  lowerBand    = na
    var int    bars         = 0

    // 10-bar local deviation window
    var float  cycleDelta   = 0.0
    var int    volIndex     = 0
    var int    volCount     = 0
    var array<float> volWindow  = array.new_float(10, 0.0)

    // 128-bar volatility distribution
    var int    distIndex    = 0
    var int    distCount    = 0
    var array<float> distWindow = array.new_float(128, 0.0)
    var array<float> sorted     = array.new_float(0)

    float current_volty = na

    if not na(source)
        bars += 1

        // ---- First bar: initialize anchors ----
        if bars == 1
            upperBand := source
            lowerBand := source
            current_volty := 1.0
        else
            // 1) Local deviation vs. upperBand / lowerBand
            float diffA    = source - upperBand
            float diffB    = source - lowerBand
            float absA     = math.abs(diffA)
            float absB     = math.abs(diffB)
            float absValue = absA > absB ? absA : absB
            float dLocal   = absValue + 1e-10

            // 2) 10-bar SMA of local deviation -> highD
            float oldVol = array.get(volWindow, volIndex)
            cycleDelta  += dLocal - oldVol
            array.set(volWindow, volIndex, dLocal)
            volIndex += 1
            if volIndex >= 10
                volIndex := 0
            if volCount < 10
                volCount += 1
            float highD = volCount > 0 ? cycleDelta / (volCount < 10 ? volCount : 10) : dLocal

            // 3) 128-bar volatility distribution + trimmed mean
            array.set(distWindow, distIndex, highD)
            distIndex += 1
            if distIndex >= 128
                distIndex := 0
            if distCount < 128
                distCount += 1

            float dRef = highD
            if distCount >= 16
                int count = distCount
                array.clear(sorted)
                for i = 0 to count - 1
                    int idx = distIndex - 1 - i
                    if idx < 0
                        idx += 128
                    array.push(sorted, array.get(distWindow, idx))
                array.sort(sorted)

                int idxLo = 0
                int idxHi = 0
                if count >= 128
                    idxLo := 32
                    idxHi := 96
                else
                    int slice = int(math.max(5.0, math.round(count * 0.5)))
                    int drop  = (count - slice) / 2
                    idxLo := drop
                    idxHi := drop + slice - 1

                if idxLo < 0
                    idxLo := 0
                if idxHi >= count
                    idxHi := count - 1

                float sum = 0.0
                for i = idxLo to idxHi
                    sum += array.get(sorted, i)
                dRef := sum / float(idxHi - idxLo + 1)

            if dRef <= 0.0
                dRef := dLocal

            // 4) Jurik dynamic exponent
            float ratio = absValue / dRef
            if ratio < 0.0
                ratio := 0.0
            float d = math.pow(ratio, _P_EXP)
            d := math.min(math.max(d, 1.0), _LOG_PARAM)

            // 5) Update upperBand / lowerBand via sqrtDivider ^ sqrt(d)
            float adapt = math.pow(_SQRT_DIV, math.sqrt(d))
            if source > upperBand
                upperBand := source
            else
                upperBand := source - (source - upperBand) * adapt
            if source < lowerBand
                lowerBand := source
            else
                lowerBand := source - (source - lowerBand) * adapt

            current_volty := d

    current_volty

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

// Inputs
i_period = input.int(10, "Period", minval=1, tooltip="Number of bars used in the calculation")
i_source = input.source(close, "Source")

// Calculation
jvolty_value = jvolty(i_source, i_period)

// Plot
plot(jvolty_value, "Jvolty", color=color.orange, linewidth=2)
hline(1.0, "Min Volatility", color=color.gray, linestyle=hline.style_dotted)