True Strength Index (TSI)

// Licensed under the Apache License, Version 2.0
// © mihakralj
//@version=6
indicator("True Strength Index (TSI)", "TSI", overlay=false)

//@function Calculates the True Strength Index and its signal line.
//@param src series float The source series.
//@param longLen simple int The lookback period for the first EMA smoothing (typically 25).
//@param shortLen simple int The lookback period for the second EMA smoothing (typically 13).
//@param signalLen simple int The lookback period for the signal line EMA (typically 13).
//@returns tuple [float, float] A tuple containing the TSI value and its signal line.
//@optimized for performance and dirty data
tsi(series float src, simple int longLen, simple int shortLen, simple int signalLen) =>
    if longLen <= 0 or shortLen <= 0 or signalLen <= 0
        runtime.error("Lengths must be greater than 0")
    float mom = src - nz(src[1])
    float absMom = math.abs(mom)
    var float emaMomLong = na, var float emaMomLong_e = 1.0, var bool emaMomLong_warmup = true
    var float emaMomShort = na, var float emaMomShort_e = 1.0, var bool emaMomShort_warmup = true
    var float emaAbsMomLong = na, var float emaAbsMomLong_e = 1.0, var bool emaAbsMomLong_warmup = true
    var float emaAbsMomShort = na, var float emaAbsMomShort_e = 1.0, var bool emaAbsMomShort_warmup = true
    var float emaSignal = na, var float emaSignal_e = 1.0, var bool emaSignal_warmup = true
    float alphaLong = 2.0 / math.max(longLen, 1)
    float alphaShort = 2.0 / math.max(shortLen, 1)
    float alphaSignal = 2.0 / math.max(signalLen, 1)
    float smoothedMomLong = 0.0
    float smoothedAbsMomLong = 0.0
    float doubleSmoothedMom = 0.0
    float doubleSmoothedAbsMom = 0.0
    float tsiValue = 0.0
    float signalLineValue = 0.0
    if not na(mom)
        if na(emaMomLong)
            emaMomLong := 0.0
            smoothedMomLong := mom
        else
            emaMomLong := alphaLong * (mom - emaMomLong) + emaMomLong
            if emaMomLong_warmup
                emaMomLong_e *= (1 - alphaLong)
                smoothedMomLong := (1.0 / (1.0 - emaMomLong_e)) * emaMomLong
                if emaMomLong_e <= 1e-10
                    emaMomLong_warmup := false
            else
                smoothedMomLong := emaMomLong
        if na(emaMomShort)
            emaMomShort := 0.0
            doubleSmoothedMom := smoothedMomLong
        else
            emaMomShort := alphaShort * (smoothedMomLong - emaMomShort) + emaMomShort
            if emaMomShort_warmup
                emaMomShort_e *= (1 - alphaShort)
                doubleSmoothedMom := (1.0 / (1.0 - emaMomShort_e)) * emaMomShort
                if emaMomShort_e <= 1e-10
                    emaMomShort_warmup := false
            else
                doubleSmoothedMom := emaMomShort
        if na(emaAbsMomLong)
            emaAbsMomLong := 0.0
            smoothedAbsMomLong := absMom
        else
            emaAbsMomLong := alphaLong * (absMom - emaAbsMomLong) + emaAbsMomLong
            if emaAbsMomLong_warmup
                emaAbsMomLong_e *= (1 - alphaLong)
                smoothedAbsMomLong := (1.0 / (1.0 - emaAbsMomLong_e)) * emaAbsMomLong
                if emaAbsMomLong_e <= 1e-10
                    emaAbsMomLong_warmup := false
            else
                smoothedAbsMomLong := emaAbsMomLong
        if na(emaAbsMomShort)
            emaAbsMomShort := 0.0
            doubleSmoothedAbsMom := smoothedAbsMomLong
        else
            emaAbsMomShort := alphaShort * (smoothedAbsMomLong - emaAbsMomShort) + emaAbsMomShort
            if emaAbsMomShort_warmup
                emaAbsMomShort_e *= (1 - alphaShort)
                doubleSmoothedAbsMom := (1.0 / (1.0 - emaAbsMomShort_e)) * emaAbsMomShort
                if emaAbsMomShort_e <= 1e-10
                    emaAbsMomShort_warmup := false
            else
                doubleSmoothedAbsMom := emaAbsMomShort
        if doubleSmoothedAbsMom != 0
            tsiValue := 100 * (doubleSmoothedMom / doubleSmoothedAbsMom)
        else
            tsiValue := 0
        if na(emaSignal)
            emaSignal := 0.0
            signalLineValue := tsiValue
        else
            emaSignal := alphaSignal * (tsiValue - emaSignal) + emaSignal
            if emaSignal_warmup
                emaSignal_e *= (1 - alphaSignal)
                signalLineValue := (1.0 / (1.0 - emaSignal_e)) * emaSignal
                if emaSignal_e <= 1e-10
                    emaSignal_warmup := false
            else
                signalLineValue := emaSignal
    else
        tsiValue := nz(tsiValue[1], 50.0)
        signalLineValue := nz(signalLineValue[1], 50.0)
    [tsiValue, signalLineValue]
// ---------- Main loop ----------
// Inputs
i_source = input.source(close, "Source")
i_longLen = input.int(25, "Long Length", minval=1)
i_shortLen = input.int(13, "Short Length", minval=1)
i_signalLen = input.int(13, "Signal Length", minval=1)

// Calculation
[tsi_value, signal_line] = tsi(i_source, i_longLen, i_shortLen, i_signalLen)

// Plot
plot(tsi_value, "TSI", color=color.blue, linewidth=2)
plot(signal_line, "Signal Line", color=color.red, linewidth=2)