// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Recursive Gaussian Moving Average (RGMA)", "RGMA", overlay=true)

//@function Calculates RGMA using cascaded recursive filters to approximate Gaussian smoothing
//@param source Series to calculate RGMA from
//@param period Effective smoothing period
//@param passes Number of recursive passes (higher = more Gaussian-like)
//@returns RGMA value with gaussian-like smoothing properties using recursive calculation
//@optimized Uses cascaded exponential filters for O(1) complexity per bar
rgma(series float source, simple int period, simple int passes=3) =>
    simple float alpha = 2.0 / (period / math.sqrt(passes) + 1.0)
    var array<float> filters = array.new_float(passes, na)
    float result = na
    if not na(source)
        if na(array.get(filters, 0))
            array.fill(filters, source)
            result := source
        else
            array.set(filters, 0, alpha * (source - array.get(filters, 0)) + array.get(filters, 0))
            if passes > 1
                for i = 1 to passes - 1
                    array.set(filters, i, alpha * (array.get(filters, i - 1) - array.get(filters, i)) + array.get(filters, i))
            result := array.get(filters, passes - 1)
    result

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

// Inputs
i_period = input.int(10, "Period", minval=1)
i_passes = input.int(3, "Passes", minval=1, maxval=10, tooltip="More passes create more Gaussian-like smoothing")
i_source = input.source(close, "Source")

// Calculation
rgma_value = rgma(i_source, i_period, i_passes)

// Plot
plot(rgma_value, "RGMA", color=color.yellow, linewidth=2)