// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Regularized EMA (REMA)", "REMA", overlay=true)

//@function Calculates REMA using exponential smoothing with regularization term
//@param source Series to calculate REMA from
//@param period Lookback period used to determine alpha value
//@param lambda Regularization parameter (0-1) controlling smoothness
//@returns REMA value, calculates from first bar using available data
//@optimized Uses regularization term to reduce noise for O(1) complexity
rema(series float source, simple int period, simple float lambda=0.5) =>
    float alpha = 2.0 / (period + 1.0)
    var float rema_val = na
    var float prev_rema = na
    float result = na
    if not na(source)
        if na(rema_val)
            rema_val := source
            prev_rema := source
            result := rema_val
        else
            prev_rema := rema_val
            float ema_component = alpha * (source - rema_val) + rema_val
            float reg_component = rema_val + (rema_val - prev_rema)
            rema_val := lambda * (ema_component - reg_component) + reg_component
            result := rema_val
    else
        result := rema_val
    result

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

// Inputs
i_period = input.int(10, "Period", minval=1)
i_lambda = input.float(0.5, "Lambda", minval=0.0, maxval=1.0, step=0.1, tooltip="Regularization parameter: 0 = maximum regularization, 1 = standard EMA")
i_source = input.source(close, "Source")

// Calculation
rema_value = rema(i_source, i_period, i_lambda)

// Plot
plot(rema_value, "REMA", color=color.yellow, linewidth=2)