Median Cascade Trend

// This Pine Script® code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © BackQuant

//@version=6
indicator("Median Cascade Trend [BackQuant]", "Median Cascade [BackQuant]", overlay = true)

// Inputs
const string g1 = "Median Cascade"
const string g2 = "Low-Pass Filter"
const string g3 = "Chop Filter"
const string g4 = "UI Settings"

float src = input.source(close, "Source", group = g1)
int stages = input.int(3, "Cascade Stages", minval = 1, maxval = 3, group = g1, tooltip = "Number of causal median filters applied before the low-pass stage.")
int medianLen1 = input.int(3, "Median Stage 1", minval = 2, maxval = 50, group = g1, tooltip = "Removes isolated one-bar spikes.")
int medianLen2 = input.int(5, "Median Stage 2", minval = 2, maxval = 50, group = g1, tooltip = "Removes remaining short-duration noise.")
int medianLen3 = input.int(7, "Median Stage 3", minval = 2, maxval = 50, group = g1, tooltip = "Final median stage before low-pass smoothing.")

int smoothLen = input.int(10, "Low-Pass Length", minval = 2, maxval = 100, group = g2, tooltip = "Two-pole Super Smoother applied after the median cascade.")
int directionLen = input.int(2, "Direction Lookback", minval = 1, maxval = 20, group = g2, tooltip = "Bars used to determine the direction of the final trend line.")

bool useGate = input.bool(true, "Chop Filter", group = g3, tooltip = "Blocks trend changes when movement lacks directional efficiency or sufficient slope.")
string gateMode = input.string("Both", "Gate Mode", options = ["Efficiency Ratio", "ATR-Normalized Slope", "Both", "Either"], group = g3, tooltip = "Both requires efficiency and slope to pass. Either allows a trend when one condition passes.")
int efficiencyLen = input.int(20, "Efficiency Length", minval = 5, maxval = 100, group = g3)
float efficiencyMin = input.float(0.25, "Minimum Efficiency", minval = 0.0, maxval = 1.0, step = 0.05, group = g3)
int slopeLen = input.int(2, "Slope Length", minval = 1, maxval = 20, group = g3)
int slopeAtrLen = input.int(14, "Slope ATR Length", minval = 1, maxval = 100, group = g3)
float slopeMin = input.float(0.08, "Minimum ATR-Normalized Slope", minval = 0.0, maxval = 5.0, step = 0.01, group = g3)

bool showLine = input.bool(true, "Show Trend Line", group = g4)
bool showFill = input.bool(true, "Gradient Fill", group = g4)
bool showGlow = input.bool(true, "Trend Glow", group = g4)
bool showSig = input.bool(true, "Show Signals", group = g4)
bool showBlocked = input.bool(false, "Show Blocked Flips", group = g4)
bool showGate = input.bool(true, "Show Gate Status", group = g4)
string gateDisplay = input.string("Dim", "Closed Gate Display", options = ["Dim", "Neutral", "Hide"], group = g4)
bool paintBar = input.bool(true, "Color Candles", group = g4)
int lineW = input.int(3, "Line Width", minval = 1, maxval = 6, group = g4)
color longCol = input.color(#00ff00, "Bullish", inline = "c", group = g4)
color shortCol = input.color(#ff0000, "Bearish", inline = "c", group = g4)
color gateCol = input.color(#555555, "Gated", inline = "c", group = g4)

// Two-Pole Super Smoother
superSmoother(float source, simple int length) =>
    float a1 = math.exp(-1.414 * math.pi / length)
    float b1 = 2.0 * a1 * math.cos(1.414 * math.pi / length)
    float c2 = b1
    float c3 = -a1 * a1
    float c1 = 1.0 - c2 - c3
    float filt = na
    filt := c1 * (source + nz(source[1], source)) * 0.5 + c2 * nz(filt[1], source) + c3 * nz(filt[2], source)
    filt

// Median Cascade
float median1 = ta.median(src, medianLen1)
float median2 = ta.median(median1, medianLen2)
float median3 = ta.median(median2, medianLen3)
float medianOut = stages == 1 ? median1 : stages == 2 ? median2 : median3

// Low-Pass Stage
float trendLine = superSmoother(medianOut, smoothLen)

// Chop Filter
float netMovement = math.abs(trendLine - trendLine[efficiencyLen])
float totalMovement = math.sum(math.abs(ta.change(trendLine)), efficiencyLen)
float efficiency = totalMovement > 0.0 ? netMovement / totalMovement : 0.0

float slopeAtr = ta.atr(slopeAtrLen)
float normalizedSlope = slopeAtr > 0.0 ? math.abs(trendLine - trendLine[slopeLen]) / slopeAtr : 0.0

bool efficiencyPass = efficiency >= efficiencyMin
bool slopePass = normalizedSlope >= slopeMin
bool gatePass = gateMode == "Efficiency Ratio" ? efficiencyPass : gateMode == "ATR-Normalized Slope" ? slopePass : gateMode == "Either" ? efficiencyPass or slopePass : efficiencyPass and slopePass
bool gateOpen = not useGate or gatePass

// Trend
int rawTrend = trendLine > trendLine[directionLen] ? 1 : trendLine < trendLine[directionLen] ? -1 : 0

var int trend = 0
if gateOpen and rawTrend != 0 and rawTrend != trend
    trend := rawTrend

bool bullFlip = trend == 1 and trend[1] == -1
bool bearFlip = trend == -1 and trend[1] == 1
bool blocked = not gateOpen and rawTrend != 0 and rawTrend != trend and rawTrend != rawTrend[1]

// Plot Colors
color baseTrendCol = trend == 1 ? longCol : trend == -1 ? shortCol : color.gray
color trendCol = not gateOpen and showGate and gateDisplay == "Neutral" ? gateCol : baseTrendCol
int lineAlpha = not gateOpen and showGate and gateDisplay == "Dim" ? 65 : 0
float plottedTrend = not gateOpen and showGate and gateDisplay == "Hide" ? na : trendLine

color candleCol = baseTrendCol
if not gateOpen and showGate
    candleCol := gateDisplay == "Neutral" ? gateCol : gateDisplay == "Hide" ? na : color.new(baseTrendCol, 65)
else
    candleCol := color.new(baseTrendCol, 10)

// Plots
pLine = plot(showLine ? plottedTrend : na, "Median Cascade Trend", color = color.new(trendCol, lineAlpha), linewidth = lineW)
pPrice = plot(close, "Price Ref", display = display.none, editable = false)

// Gradient Fill
fill(pPrice, pLine, close > trendLine ? close : trendLine, close > trendLine ? trendLine : close, showFill and close > trendLine and not na(plottedTrend) ? color.new(trendCol, 20 + lineAlpha) : na, showFill and close > trendLine and not na(plottedTrend) ? color.new(trendCol, 92) : na, title = "Bull Fill")
fill(pPrice, pLine, close < trendLine ? trendLine : close, close < trendLine ? close : trendLine, showFill and close < trendLine and not na(plottedTrend) ? color.new(trendCol, 20 + lineAlpha) : na, showFill and close < trendLine and not na(plottedTrend) ? color.new(trendCol, 92) : na, title = "Bear Fill")

// Trend Glow
float glow = ta.atr(14) * 0.06
pGlowLower = plot(not na(plottedTrend) ? trendLine - glow : na, "Glow Lower Ref", display = display.none, editable = false)
pGlowUpper = plot(not na(plottedTrend) ? trendLine + glow : na, "Glow Upper Ref", display = display.none, editable = false)
fill(pLine, pGlowLower, showGlow and not na(plottedTrend) ? color.new(trendCol, 55 + int(lineAlpha * 0.5)) : na, title = "Glow Lower")
fill(pLine, pGlowUpper, showGlow and not na(plottedTrend) ? color.new(trendCol, 55 + int(lineAlpha * 0.5)) : na, title = "Glow Upper")

// Candles
barcolor(paintBar ? candleCol : na, title = "Trend Candles")

// Signals
plotshape(showSig and bullFlip ? trendLine : na, "Bull Flip", shape.labelup, location.absolute, longCol, text = "▲", textcolor = chart.bg_color, size = size.small)
plotshape(showSig and bearFlip ? trendLine : na, "Bear Flip", shape.labeldown, location.absolute, shortCol, text = "▼", textcolor = chart.bg_color, size = size.small)
plotshape(showBlocked and blocked ? trendLine : na, "Blocked Flip", shape.xcross, location.absolute, gateCol, size = size.tiny)

// Alerts
alertcondition(bullFlip, "Median Cascade Bullish", "Median Cascade Trend turned bullish on {{ticker}}")
alertcondition(bearFlip, "Median Cascade Bearish", "Median Cascade Trend turned bearish on {{ticker}}")
alertcondition(blocked, "Median Cascade Flip Blocked", "Median Cascade trend change blocked by the chop filter on {{ticker}}")