Relative Vigor Index (RVGI)

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

//@function Calculates RVGI — momentum oscillator comparing close-open vs high-low
//@param period SMA smoothing period for the SWMA-weighted numerator/denominator
//@returns [rvgi, signal] RVGI value and its 4-bar SWMA signal line
//@description RVGI measures the conviction of a price move by comparing closing
//  strength to the full range:
//    Step 1: SWMA(close-open, 4 bars) with weights [1/6, 2/6, 2/6, 1/6]
//    Step 2: SWMA(high-low, 4 bars) with same weights
//    Step 3: SMA(step1, period) / SMA(step2, period) → RVGI
//    Step 4: SWMA(RVGI, 4 bars) → Signal line
//  The SWMA (Symmetrically Weighted Moving Average) uses fixed 4-bar kernel:
//    swma(x) = (x[3] + 2*x[2] + 2*x[1] + x[0]) / 6
//  SMA sums use O(1) circular buffers with §3 count-based warmup.
//  Defensive division: denominator == 0 returns 0.
//  Crossovers of RVGI and Signal indicate momentum shifts.
//  In uptrends, closes tend near highs → positive RVGI; downtrends → negative.
rvgi(simple int period) =>
    if period <= 0
        runtime.error("Period must be greater than 0")

    // --- SWMA of (close - open): weights [1,2,2,1]/6 over 4 bars ---
    float co0 = close - open
    float co1 = nz(close[1]) - nz(open[1])
    float co2 = nz(close[2]) - nz(open[2])
    float co3 = nz(close[3]) - nz(open[3])
    float swmaNum = (co3 + 2.0 * co2 + 2.0 * co1 + co0) / 6.0

    // --- SWMA of (high - low): weights [1,2,2,1]/6 over 4 bars ---
    float hl0 = high - low
    float hl1 = nz(high[1]) - nz(low[1])
    float hl2 = nz(high[2]) - nz(low[2])
    float hl3 = nz(high[3]) - nz(low[3])
    float swmaDen = (hl3 + 2.0 * hl2 + 2.0 * hl1 + hl0) / 6.0

    // --- SMA of swmaNum over period (circular buffer, §3 warmup) ---
    var array<float> numBuf  = array.new_float(period, na)
    var int numHead          = 0
    var float numSum         = 0.0
    var int numCount         = 0

    float oldNum = array.get(numBuf, numHead)
    if not na(oldNum)
        numSum -= oldNum
    else
        numCount += 1
    numSum += nz(swmaNum)
    array.set(numBuf, numHead, nz(swmaNum))
    numHead := (numHead + 1) % period

    float smaNum = numSum / math.max(1, numCount)

    // --- SMA of swmaDen over period (circular buffer, §3 warmup) ---
    var array<float> denBuf  = array.new_float(period, na)
    var int denHead          = 0
    var float denSum         = 0.0
    var int denCount         = 0

    float oldDen = array.get(denBuf, denHead)
    if not na(oldDen)
        denSum -= oldDen
    else
        denCount += 1
    denSum += nz(swmaDen)
    array.set(denBuf, denHead, nz(swmaDen))
    denHead := (denHead + 1) % period

    float smaDen = denSum / math.max(1, denCount)

    // --- RVGI = numSMA / denSMA ---
    float rvgiVal = smaDen == 0.0 ? 0.0 : smaNum / smaDen

    // --- Signal: SWMA of RVGI over 4 bars ---
    var float rv1 = 0.0
    var float rv2 = 0.0
    var float rv3 = 0.0
    float sig = (rv3 + 2.0 * rv2 + 2.0 * rv1 + rvgiVal) / 6.0
    rv3 := rv2
    rv2 := rv1
    rv1 := rvgiVal

    [rvgiVal, sig]

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

// Inputs
i_period = input.int(10, "Period", minval=1)

// Calculation
[rvgiLine, sigLine] = rvgi(i_period)

// Plot
plot(rvgiLine, "RVGI", color=color.yellow, linewidth=2)
plot(sigLine, "Signal", color=color.aqua, linewidth=1)
hline(0, "Zero", color=color.gray, linestyle=hline.style_dotted)