// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Relative Volatility Index (RVI)", shorttitle="RVI", overlay=false)

//@function Calculates the Relative Volatility Index (RVI).
//@param src The source series to calculate RVI from. Default is `close`.
//@param stdevLength The lookback period for calculating the standard deviation of source prices. Default is 10.
//@param rmaLength The lookback period for Wilder's smoothing (RMA) of the upward and downward standard deviations. Default is 14.
//@returns float The Relative Volatility Index value.
rvi(series float src = close, simple int stdevLength = 10, simple int rmaLength = 14) =>
    float currentStdDev = 0.0
    var array<float> buffer_stddev = array.new_float(stdevLength, na) // p_stddev simplified
    var int head_stddev = 0, var int count_stddev = 0
    var float sum_stddev = 0.0, var float sumSq_stddev = 0.0
    float oldest_stddev = array.get(buffer_stddev, head_stddev)
    if not na(oldest_stddev)
        sum_stddev -= oldest_stddev
        sumSq_stddev -= oldest_stddev * oldest_stddev
        count_stddev -= 1
    float val_stddev = nz(src) 
    sum_stddev += val_stddev
    sumSq_stddev += val_stddev * val_stddev
    count_stddev += 1
    array.set(buffer_stddev, head_stddev, val_stddev)
    head_stddev := (head_stddev + 1) % stdevLength // p_stddev simplified
    if count_stddev > 1
        currentStdDev := math.sqrt(math.max(0.0, (sumSq_stddev / count_stddev) - math.pow(sum_stddev / count_stddev, 2)))
    else
        currentStdDev := 0.0 
    float priceChange = src - src[1]
    float upStd_val = 0.0, float downStd_val = 0.0
    if priceChange > 0
        upStd_val := currentStdDev
    else if priceChange < 0
        downStd_val := currentStdDev
    var float raw_rma_up = 0.0, var float e_up = 1.0
    var float avgUpStd = 0.0 , var float EPSILON_rma = 1e-10 
    if not na(upStd_val) 
        float alpha_up = 1.0 / float(rmaLength)
        raw_rma_up := (raw_rma_up * (rmaLength - 1) + upStd_val) / rmaLength
        e_up := (1 - alpha_up) * e_up
    avgUpStd := e_up > EPSILON_rma ? raw_rma_up / (1.0 - e_up) : raw_rma_up
    if rmaLength == 0 
        avgUpStd := upStd_val
    var float raw_rma_down = 0.0, var float e_down = 1.0
    var float avgDownStd = 0.0
    if not na(downStd_val) 
        float alpha_down = 1.0 / float(rmaLength)
        raw_rma_down := (raw_rma_down * (rmaLength - 1) + downStd_val) / rmaLength
        e_down := (1 - alpha_down) * e_down
    avgDownStd := e_down > EPSILON_rma ? raw_rma_down / (1.0 - e_down) : raw_rma_down
    if rmaLength == 0
        avgDownStd := downStd_val
    float rviValue = 50.0 
    float sumAvgStd = nz(avgUpStd) + nz(avgDownStd) 
    if sumAvgStd != 0
        rviValue := 100 * nz(avgUpStd) / sumAvgStd 
    rviValue

// ---------- Main loop ----------
// Inputs
i_src_rvi = input.source(close, "Source")
i_stdevLength_rvi = input.int(10, "StdDev Length", minval=2, tooltip="Lookback period for calculating the Standard Deviation of source prices.")
i_rmaLength_rvi = input.int(14, "RMA Length (Wilder's Smoothing)", minval=1, tooltip="Lookback period for smoothing Upward and Downward Standard Deviations.")

// Calculation
rviValue = rvi(i_src_rvi, i_stdevLength_rvi, i_rmaLength_rvi)

// Plot
plot(rviValue, "RVI", color=color.yellow, linewidth=2)