// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Non-Lag Moving Average (NLMA)", "NLMA", overlay=true)

//@function Calculates NLMA using damped cosine (fading sinusoid) FIR kernel
//@param source Series to calculate NLMA from
//@param period Lookback period - defines the cycle length of the cosine kernel
//@returns NLMA value, calculates from first bar using available data
//@description NonLagMA by Igorad (TrendLaboratory). Uses a damped cosine kernel
//  (fading sinusoid) derived from FATL/SATL digital filter coefficient analysis.
//  The cosine creates negative weights that subtract lagged price components,
//  reducing lag while maintaining smoothness. Weight formula:
//    w[i] = cos(2*PI*i / cycle) * (1 - i/cycle)
//  where cycle = period, creating one full cosine oscillation with linear decay.
//  Negative weights in the mid-section cancel lag (analogous to DEMA's 2*EMA-EMA2).
//  Normalization by signed weight sum preserves DC gain = 1.
nlma(series float source, simple int period) =>
    if period <= 0
        runtime.error("Period must be greater than 0")
    int p = math.min(bar_index + 1, period)
    var int prev_p = 0
    var array<float> cos_weights = array.new_float(period, 0.0)
    // Recompute weights when effective period changes (warmup)
    if p != prev_p
        cos_weights := array.new_float(p, 0.0)
        for j = 0 to p - 1
            // Damped cosine: cosine oscillation × linear decay envelope
            float angle = 2.0 * math.pi * j / p
            float decay = 1.0 - float(j) / float(p)
            array.set(cos_weights, j, math.cos(angle) * decay)
        prev_p := p
    float sum_wv = 0.0
    float sum_w = 0.0
    for i = 0 to p - 1
        float price = source[i]
        if not na(price)
            float w = array.get(cos_weights, i)
            sum_wv += price * w
            sum_w += w
    nz(sum_wv / sum_w, source)

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

// Inputs
i_period = input.int(14, "Period", minval=1)
i_source = input.source(close, "Source")

// Calculation
nlma_value = nlma(i_source, i_period)

// Plot
plot(nlma_value, "NLMA", color=color.yellow, linewidth=2)