// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Linear Transformation (LINEAR)", "Lineartrans", overlay=false)

//@function Applies a linear transformation (y = a*(x - sma) + sma + b) relative to the source's SMA, calculated internally.
//@param source series float The input series to transform.
//@param period simple int The lookback period for the internal SMA calculation.
//@param a float The scaling factor (slope).
//@param b float The offset (intercept).
//@returns series float The linearly transformed series relative to its internally calculated SMA.
//@optimized for performance and dirty data
linear(series float source, float a, float b) =>
    if na(source) or na(a) or na(b)
        runtime.error("Parameters 'source', 'a', 'b' cannot be na and 'period' must be > 0.")
    var int p = 200
    var array<float> buffer = array.new_float(p, na)
    var int head = 0
    var float sum = 0.0
    var int valid_count = 0
    float oldest = array.get(buffer, head)
    if not na(oldest)
        sum -= oldest
        valid_count -= 1
    if not na(source)
        sum += source
        valid_count += 1
    array.set(buffer, head, source)
    head := (head + 1) % p
    smaValue = nz(sum / valid_count, source)
    a * (source - smaValue) + smaValue + b


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

// Inputs
i_source = input(close, "Source")
i_smaPeriod = input.int(200, "SMA Period", minval=1)
i_a = input.float(2.0, "Scale (a)")
i_b = input.float(20.0, "Offset (b)")

// Calculation
transformedSource = linear(i_source, i_a, i_b)

// Plot
plot(transformedSource, "Linear Transformation", color=color.yellow, linewidth=2)