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//@version=5
indicator("Machine Learning Supertrend", overlay = true, timeframe = "", timeframe_gaps = true)

// Parameters
atrPeriod = input.int(25, "ATR Length", minval = 1)
factor = input.float(2.2, "Factor", minval = 0.01, step = 0.01)
sigma = 0.03
forecast = input.int(3, "Forecast Period", minval = 0)  // Number of bars to forecast

// Source
src = input.source(close, 'Source')

// Kernel Function (Gaussian Process Regression)
rbf(x1, x2, l) => math.exp(-math.pow(x1 - x2, 2) / (2.0 * math.pow(l, 2)))

kernel_matrix(X1, X2, l) =>
    km = matrix.new<float>(X1.size(), X2.size())
    for i = 0 to X1.size() - 1
        for j = 0 to X2.size() - 1
            km.set(i, j, rbf(X1.get(i), X2.get(j), l))
    km

// Initialize Gaussian Process Regression
var identity = matrix.new<int>(atrPeriod, atrPeriod, 0)
var array<float> K_row = na

if barstate.isfirst
    xtrain = array.new<int>(0)
    xtest = array.new<int>(0)

    // Training data setup
    for i = 0 to atrPeriod-1
        for j = 0 to atrPeriod-1
            identity.set(i, j, i == j ? 1 : 0)
        xtrain.push(i)

    // Test data (future prediction)
    for i = 0 to atrPeriod-1 + forecast
        xtest.push(i)

    // Compute kernel matrices
    s = identity.mult(sigma * sigma)
    Ktrain = kernel_matrix(xtrain, xtrain, atrPeriod).sum(s)
    K_inv = Ktrain.pinv()
    K_star = kernel_matrix(xtrain, xtest, atrPeriod)
    K_row := K_star.transpose().mult(K_inv).row(atrPeriod-1 + forecast)

// Machine Learning Moving Average
var float prev_supertrend = na
mean = ta.sma(src, atrPeriod)

// ML Prediction with Forecast
float out = na
if bar_index > atrPeriod
    dotprod = 0.
    for i = 0 to atrPeriod-1
        dotprod += K_row.get(i) * (src[atrPeriod-1 - i] - mean)
    out := dotprod + mean

// Use forecasted value
predicted_value = out[forecast]

// ML-based ATR estimation
mae = ta.sma(math.abs(src - predicted_value), atrPeriod) * factor
upper = predicted_value + mae
lower = predicted_value - mae

// Supertrend Calculation
float supertrend = na

if prev_supertrend == na
    supertrend := close > lower ? lower : upper
else
    supertrend := close > prev_supertrend ? lower : upper

// Ensure the trend follows the previous one if not broken
supertrend := na(supertrend) ? prev_supertrend : supertrend
prev_supertrend := supertrend

// Detect trend direction (1 = bullish, 0 = bearish)
trend_direction = supertrend == lower ? 1 : 0

// Plot Up & Down Trend Lines
upTrend = plot(trend_direction == 1 ? supertrend : na, "Up Trend", color = color.green, style = plot.style_linebr)
downTrend = plot(trend_direction == 0 ? supertrend : na, "Down Trend", color = color.red, style = plot.style_linebr)

// Middle of the candle (used for filling)
bodyMiddle = plot(barstate.isfirst ? na : (open + close) / 2, "Body Middle", display = display.none)

// Fill areas
fill(bodyMiddle, upTrend, color.new(color.green, 90), fillgaps = false)
fill(bodyMiddle, downTrend, color.new(color.red, 90), fillgaps = false)

// Alerts for trend change
alertcondition(trend_direction != trend_direction[1], title='Trend Change', message='Supertrend ML changed direction')