Ehlers Trendflex (TRENDFLEX)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
// Indicator algorithm (C) 2013 John F. Ehlers
indicator("Ehlers Trendflex (TRENDFLEX)", "TRENDFLEX", overlay=false)

//@function Calculates Ehlers Trendflex using SuperSmoother pre-filtering and cumulative slope with RMS normalization
//@param source Series to calculate Trendflex from
//@param period Lookback period for trend measurement (>= 1)
//@returns Normalized Trendflex value centered around zero
//@optimized Uses O(1) running sum for cumulative slope instead of O(N) loop, with RMS normalization
trendflex(series float source, simple int period) =>
    if period <= 0
        runtime.error("Period must be positive")

    float src = nz(source)

    // SuperSmoother (2-pole Butterworth lowpass) coefficients
    float halfPeriod = period * 0.5
    float a1 = math.exp(-1.414 * math.pi / halfPeriod)
    float b1 = 2.0 * a1 * math.cos(1.414 * math.pi / halfPeriod)
    float c2 = b1
    float c3 = -(a1 * a1)
    float c1 = 1.0 - c2 - c3

    // SuperSmoother filter state
    var float filt = 0.0
    var float filt1 = 0.0
    float new_filt = bar_index < 2 ? src : c1 * (src + nz(src[1])) * 0.5 + c2 * filt + c3 * filt1
    filt1 := filt
    filt := new_filt

    // O(1) cumulative slope via circular buffer and running sum
    // Sum = Σ(Filt - Filt[i]) for i=1..N = N × Filt - Σ(Filt[i])
    var array<float> buf = array.new_float(period, 0.0)
    var int head = 0
    var float running_sum = 0.0
    var int count = 0

    int n = math.min(count, period)
    float slope_sum = n > 0 ? (n * new_filt - running_sum) / period : 0.0

    float oldest = array.get(buf, head)
    running_sum -= oldest
    running_sum += new_filt
    array.set(buf, head, new_filt)
    head := (head + 1) % period
    if count < period
        count += 1

    // RMS normalization via exponential mean-square
    var float ms = 0.0
    ms := 0.04 * slope_sum * slope_sum + 0.96 * ms

    float result = ms > 0 ? slope_sum / math.sqrt(ms) : 0.0
    na(source) ? na : result

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

// Inputs
i_period = input.int(20, "Period", minval=1, tooltip="Lookback period for trend measurement")
i_source = input.source(close, "Source")

// Calculation
trendflex_value = trendflex(i_source, i_period)

// Plot
plot(trendflex_value, "TRENDFLEX", color=color.yellow, linewidth=2)
hline(0, "Zero", color=color.gray, linestyle=hline.style_dotted)