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

//@function Calculates SGMA using Savitzky-Golay filter with polynomial fitting
//@param source Series to calculate SGMA from
//@param period Lookback period - FIR window size (must be odd)
//@param deg Polynomial degree (default: 2)
//@returns SGMA value, calculates from first bar using available data
//@optimized Uses Savitzky-Golay coefficients with O(n) complexity per bar due to lookback loop
sgma(series float source, simple int period, simple int deg=2) =>
    if period <= 0
        runtime.error("Period must be greater than 0")
    int use_period = period % 2 == 0 ? period + 1 : period
    int use_deg = deg < 0 or deg >= use_period ? 2 : math.min(deg, 4)
    int p = math.min(bar_index + 1, use_period)
    var array<float> weights = array.new_float(1, 1.0)
    var int last_p = 1
    var int last_deg = use_deg
    if last_p != p or last_deg != use_deg
        weights := array.new_float(p, 0.0)
        if use_deg == 2
            if p == 5
                array.set(weights, 0, -0.0857)
                array.set(weights, 1, 0.3429)
                array.set(weights, 2, 0.4857)
                array.set(weights, 3, 0.3429)
                array.set(weights, 4, -0.0857)
            else if p == 7
                array.set(weights, 0, -0.0476)
                array.set(weights, 1, 0.0952)
                array.set(weights, 2, 0.2857)
                array.set(weights, 3, 0.3333)
                array.set(weights, 4, 0.2857)
                array.set(weights, 5, 0.0952)
                array.set(weights, 6, -0.0476)
            else if p == 9
                array.set(weights, 0, -0.0281)
                array.set(weights, 1, 0.0337)
                array.set(weights, 2, 0.1236)
                array.set(weights, 3, 0.2247)
                array.set(weights, 4, 0.2921)
                array.set(weights, 5, 0.2247)
                array.set(weights, 6, 0.1236)
                array.set(weights, 7, 0.0337)
                array.set(weights, 8, -0.0281)
            else
                float half_window = (p - 1) / 2.0
                float total_weight = 0.0
                for i = 0 to p - 1
                    float x = i - half_window
                    float norm_x = x / half_window
                    float w = 1.0 - norm_x * norm_x
                    array.set(weights, i, w)
                    total_weight += w
                float inv_total = 1.0 / total_weight
                for i = 0 to p - 1
                    array.set(weights, i, array.get(weights, i) * inv_total)
        else
            float half_window = (p - 1) / 2.0
            float total_weight = 0.0
            for i = 0 to p - 1
                float x = i - half_window
                float norm_x = x / half_window
                float w = 0.0
                if use_deg == 0
                    w := 1.0
                else if use_deg == 1
                    w := 1.0 - math.abs(norm_x)
                else if use_deg == 3
                    w := 1.0 - math.abs(math.pow(norm_x, 3.0))
                else if use_deg == 4
                    w := 1.0 - math.pow(norm_x, 4.0)
                else
                    w := 1.0 - norm_x * norm_x
                array.set(weights, i, w)
                total_weight += w
            if total_weight > 0.0
                float inv_total = 1.0 / total_weight
                for i = 0 to p - 1
                    array.set(weights, i, array.get(weights, i) * inv_total)
        last_p := p
        last_deg := use_deg
    float sum = 0.0
    float weight_sum = 0.0
    for i = 0 to p - 1
        float price = source[i]
        if not na(price)
            float w = array.get(weights, i)
            sum += price * w
            weight_sum += w
    nz(sum / weight_sum, source)

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

// Inputs
i_period = input.int(9, "Period", minval=3, step=2, tooltip="Must be odd number (will be adjusted if even)")
i_degree = input.int(2, "Polynomial Degree", minval=0, maxval=4, tooltip="Higher degrees fit more complex shapes but risk overfitting")
i_source = input.source(close, "Source")

// Calculation
sgma_value = sgma(i_source, i_period, i_degree)

// Plot
plot(sgma_value, "SGMA", color=color.yellow, linewidth=2)