// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("Least Squares Moving Average (LSMA)", "LSMA", overlay=true)

//@function Calculates LSMA by fitting a linear regression line to price data
//@param source Series to calculate LSMA from
//@param period Lookback period for the linear regression
//@returns LSMA value, calculates from first bar using available data
//@optimized Uses circular buffer with linear regression for O(n) complexity per bar
lsma(series float source, simple int period) =>
    if period <= 1
        runtime.error("Period must be greater than 1")
        source
    else
        int p = math.min(bar_index + 1, period)
        if p <= 1
            source
        else
            var array<float> buffer = array.new_float(period, na)
            var int head = 0
            array.set(buffer, head, source)
            head := (head + 1) % period
            float sum_y = 0.0
            float sum_xy = 0.0
            float sum_x = 0.0
            float sum_x2 = 0.0
            float count = 0.0
            int idx = (head - 1 + period) % period
            for i = 0 to p - 1
                float val = array.get(buffer, idx)
                if not na(val)
                    sum_x += i
                    sum_y += val
                    sum_xy += i * val
                    sum_x2 += i * i
                    count += 1.0
                idx := (idx - 1 + period) % period
            if count <= 1.0
                source
            else
                float denom = count * sum_x2 - sum_x * sum_x
                if denom == 0.0
                    source
                else
                    float slope = (count * sum_xy - sum_x * sum_y) / denom
                    float intercept = (sum_y - slope * sum_x) / count
                    intercept

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

// Inputs
i_period = input.int(10, "Period", minval=1)
i_source = input.source(close, "Source")

// Calculation
lsma_value = lsma(i_source, i_period)

// Plot
plot(lsma_value, "LSMA", color=color.yellow, linewidth=2)