Savitzky-Golay Filter (SGF)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Savitzky-Golay Filter (SGF)", "SGF", overlay=true)

//@function Applies Savitzky-Golay filter to input series
//@param src Input series to filter
//@param window_size Window size (rounded down to nearest odd number)
//@param poly_order Polynomial order (2 or 4 recommended)
//@returns Filtered series
//@optimized Uses polynomial convolution with O(n) complexity per bar
sgf(series float src, simple int window_size, simple int poly_order) =>
    int adj_size = math.max(1, window_size % 2 == 0 ? window_size - 1 : window_size)
    if poly_order >= adj_size
        runtime.error("Polynomial order must be less than window size")
    var array<float> coeffs = array.new_float(0)
    array.clear(coeffs)
    int half_window = int(adj_size / 2)
    float sum_denom = 0.0
    if poly_order == 2
        for i = -half_window to half_window
            float weight = 3.0 * (3.0 * adj_size * adj_size - 7.0 - 20.0 * i * i)
            array.push(coeffs, weight)
            sum_denom += weight
    else if poly_order == 4
        for i = -half_window to half_window
            float i2 = i * i
            float weight = 15.0 + i2 * (-20.0 + i2 * 6.0)
            array.push(coeffs, weight)
            sum_denom += weight
    else
        for i = -half_window to half_window
            float weight = 1.0 - math.abs(float(i)) / float(half_window)
            array.push(coeffs, weight)
            sum_denom += weight
    if sum_denom != 0.0
        for i = 0 to adj_size - 1
            array.set(coeffs, i, array.get(coeffs, i) / sum_denom)
    float sum = 0.0
    float weight_sum = 0.0
    for i = 0 to adj_size - 1
        float price = src[i]
        if not na(price)
            float w = array.get(coeffs, i)
            sum += price * w
            weight_sum += w
    nz(sum / weight_sum, src)

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

// Inputs
i_window = input.int(21, "Window Size", minval=1, step=2)
i_order = input.int(2, "Polynomial Order", minval=2, maxval=4, step=2)
i_source = input.source(close, "Source")

// Calculation
sgf_val = sgf(i_source, i_window, i_order)

// Plot
plot(sgf_val, "SGF", color=color.yellow, linewidth=2)