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MATH

HighClassCalculationsLibrary "HighClassCalculations" Advanced Pine Script v6 calculation library for statistical, normalization, trend, and risk metrics. safeDiv(numerator, denominator, fallback)   Safe division helper that prevents division-by-zero errors.   Parameters:      numerator (float) : Value on the top of the fraction.      denominator (float) : Value on the bottom of the fraction.      fallback (float) : Value returned when denominator is zero.   Returns: Result of the division or fallback. clamp(value, minValue, maxValue)   Clamps a value into a fixed range.   Parameters:      value (float) : Source value.      minValue (float) : Minimum allowed value.      maxValue (float) : Maximum allowed value.   Returns: Clamped value. rescale(value, oldMin, oldMax, newMin, newMax)   Rescales a value from one range into another range.   Parameters:      value (float) : Source value.      oldMin (float) : Source range minimum.      oldMax (float) : Source range maximum.      newMin (float) : Target range minimum.      newMax (float) : Target range maximum.   Returns: Rescaled value. normalize(src, len)   Returns the min-max normalized position of a series within a rolling window.   Parameters:      src (float) : Source series.      len (int) : Rolling lookback window.   Returns: Value between 0 and 1 when the range is valid. rangePercent(src, len)   Returns the source position inside its rolling range as a percentage.   Parameters:      src (float) : Source series.      len (int) : Rolling lookback window.   Returns: Value between 0 and 100 when the range is valid. zScore(src, len)   Calculates the z-score of a series.   Parameters:      src (float) : Source series.      len (int) : Rolling lookback window.   Returns: Standardized z-score. robustZScore(src, len)   Calculates a robust z-score using median absolute deviation.   Parameters:      src (float) : Source series.      len (int) : Rolling lookback window.   Returns: Robust z-score less sensitive to outliers. percentileRank(src, len)   Calculates percentile rank for the latest value inside a rolling window.   Parameters:      src (float) : Source series.      len (int) : Rolling lookback window.   Returns: Percentile rank from 0 to 100. percentileValue(src, len, percentile)   Calculates the value at a requested percentile inside a rolling window.   Parameters:      src (float) : Source series.      len (int) : Rolling lookback window.      percentile (float) : Requested percentile from 0 to 100.   Returns: Percentile value. simpleReturn(src)   Calculates simple arithmetic return versus the previous bar.   Parameters:      src (float) : Price or equity series.   Returns: One-bar simple return. logReturn(src)   Calculates log return versus the previous bar.   Parameters:      src (float) : Price or equity series.   Returns: One-bar log return. compoundedReturn(src, len)   Calculates cumulative return over a fixed lookback.   Parameters:      src (float) : Price or equity series.      len (int) : Lookback window.   Returns: Return from src to current src. realizedVolatility(src, len, annualization)   Calculates realized volatility from log returns and annualizes it.   Parameters:      src (float) : Price or equity series.      len (int) : Rolling lookback window.      annualization (float) : Number of bars used for annualization.   Returns: Annualized volatility. downsideDeviation(returnSeries, len, mar, annualization)   Calculates downside deviation from a return series.   Parameters:      returnSeries (float) : Series of returns, not raw price.      len (int) : Rolling lookback window.      mar (float) : Minimum acceptable return.      annualization (float) : Number of bars used for annualization.   Returns: Annualized downside deviation. rollingSharpe(returnSeries, len, riskFreeRate, annualization)   Calculates a rolling Sharpe ratio from a return series.   Parameters:      returnSeries (float) : Series of returns, not raw price.      len (int) : Rolling lookback window.      riskFreeRate (float) : Per-bar risk free rate.      annualization (float) : Number of bars used for annualization.   Returns: Annualized Sharpe ratio. rollingSortino(returnSeries, len, mar, annualization)   Calculates a rolling Sortino ratio from a return series.   Parameters:      returnSeries (float) : Series of returns, not raw price.      len (int) : Rolling lookback window.      mar (float) : Minimum acceptable return.      annualization (float) : Number of bars used for annualization.   Returns: Annualized Sortino ratio. efficiencyRatio(src, len)   Calculates Kaufman's efficiency ratio.   Parameters:      src (float) : Source series.      len (int) : Rolling lookback window.   Returns: Efficiency ratio from 0 to 1. regressionSlope(src, len)   Calculates rolling linear regression slope.   Parameters:      src (float) : Source series.      len (int) : Rolling lookback window.   Returns: Slope per bar. regressionAngle(src, len)   Converts rolling regression slope into an angle.   Parameters:      src (float) : Source series.      len (int) : Rolling lookback window.   Returns: Slope angle in degrees. beta(asset, benchmark, len)   Calculates rolling beta versus a benchmark series.   Parameters:      asset (float) : Asset series.      benchmark (float) : Benchmark series.      len (int) : Rolling lookback window.   Returns: Beta coefficient. alpha(asset, benchmark, len, riskFreeRate)   Calculates Jensen-style alpha versus a benchmark series.   Parameters:      asset (float) : Asset return series.      benchmark (float) : Benchmark return series.      len (int) : Rolling lookback window.      riskFreeRate (float) : Per-bar risk free rate.   Returns: Alpha over the rolling window. ulcerIndex(src, len)   Calculates the Ulcer Index for a series.   Parameters:      src (float) : Price or equity series.      len (int) : Rolling lookback window.   Returns: Ulcer Index value. maxDrawdown(src, len)   Calculates the maximum drawdown over a rolling window.   Parameters:      src (float) : Price or equity series.      len (int) : Rolling lookback window.   Returns: Maximum drawdown as a negative decimal. atrPercent(len, src)   Calculates ATR as a percentage of price.   Parameters:      len (simple int) : ATR lookback window.      src (float) : Reference price used for the percentage denominator.   Returns: ATR percent. relativeVolume(len)   Calculates relative volume versus its rolling average.   Parameters:      len (simple int) : Rolling lookback window.   Returns: Volume divided by average volume. getAllFunctions()   Returns a comma-separated list of all exported calculation helpers.   Returns: Function catalog for quick reference.
ไลบรารี Pine Script®
โดย TheTradingSpiderMan
EMALibrary "EMA" TODO: A library that allows you to draw a variety of EMA lines over on your chart. A(length, src)   Parameters:      length (simple int)      src (float) B(length, src)   Parameters:      length (simple int)      src (float) C(length, src)   Parameters:      length (simple int)      src (float) D(length, src)   Parameters:      length (simple int)      src (float) E(length, src)   Parameters:      length (simple int)      src (float) F(length, src)   Parameters:      length (simple int)      src (float)
ไลบรารี Pine Script®
โดย terencepek
Vantage_LO1_Sizing**Overview** Position-sizing library for the LO1 breakout box day-trading strategy. Provides a unified recoup (opposite-add) sizing pipeline and dollar-risk/profit helpers. Extracting these functions into a library avoids Pine Script's function inlining, reducing compiled token count in the main strategy. **Exported Type: RecoupSizingResult** Holds the output of the 8-step sizing pipeline: • Micro-level quantities (raw, DLL-capped, final) • YM-level quantities (pre/post min-1-YM policy, proxy-capped) • Risk gate values (projected loss, worst-case drawdown, pass/fail) • Recoup scenario P&L (net outcome if T1 stops and recoup wins) **Exported Functions** `f_calcTradeRiskDollars(entry, stop, qty)` → float Projected risk in dollars. Converts price distance to ticks via syminfo.mintick, then to dollars via syminfo.pointvalue. `f_calcTradeProfitDollars(entry, tp, qty)` → float Projected profit in dollars. Same tick-to-dollar conversion applied to the take-profit distance. `f_computeRecoupSizing(...)` → RecoupSizingResult 8-step recoup sizing pipeline: 1. Raw micro qty from risk multiplier (CEILING) 2. Daily loss limit cap at micro level 3. Micro-to-YM conversion (FLOOR) 4. Minimum-1-YM policy 5. Proxy capacity cap 6. Micro-equivalent for risk gating 7. Worst-case projection (base stop + opposing flatten + recoup stop) 8. Risk gate pass/fail Plus scenario P&L: net recoup outcome and T1-win profit. **Usage** import Vantage-Stack/Vantage_LO1_Sizing/1 as sz float risk = sz.f_calcTradeRiskDollars(entry, stop, qty) sz.RecoupSizingResult r = sz.f_computeRecoupSizing(baseQty, baseEntry, baseStop, recoupEntry, recoupStop, recoupTP, multiplier, proxyMul, minOneYM, curLoss, maxLoss, maxProxy, t1TP, oppTP, oppFrac, oppRemoval) ====================== Library "Vantage_LO1_Sizing" Position sizing library for LO1 breakout box strategy. Extracts pure-computation functions to reduce compiled token count in the main script. f_calcTradeRiskDollars(_entry, _stop, _qty)   Calculates projected risk in dollars for a position (qty × |entry−stop| in ticks × pointvalue).   Parameters:      _entry (float) : Entry price      _stop (float) : Stop-loss price      _qty (float) : Position quantity (contracts)   Returns: Risk in dollars f_calcTradeProfitDollars(_entry, _tp, _qty)   Calculates projected profit in dollars for a position (qty × |tp−entry| in ticks × pointvalue).   Parameters:      _entry (float) : Entry price      _tp (float) : Take-profit price      _qty (float) : Position quantity (contracts)   Returns: Profit in dollars f_computeRecoupSizing(baseQtyMicro, baseEntry, baseStop, recoupEntry, recoupStop, recoupTP, oppositeMultiplier, proxyQtyMul, minOneYMEnabled, currentLossDollars, maxDailyLossLimit, maxProxyCap, t1TPPrice, oppTPPrice, oppAddStopFrac, opposingRemovalEnabled)   Computes recoup (opposite-add) position sizing through an 8-step pipeline: raw micro qty, DLL cap, micro-to-YM conversion, min-1-YM policy, proxy cap, risk gating, worst-case projection, and recoup scenario P&L.   Parameters:      baseQtyMicro (int) : T1 micro-contract quantity      baseEntry (float) : T1 entry price      baseStop (float) : T1 stop-loss price      recoupEntry (float) : Recoup entry price      recoupStop (float) : Recoup stop-loss price      recoupTP (float) : Recoup take-profit price      oppositeMultiplier (float) : Target risk multiplier for recoup vs T1 (e.g., 4.0)      proxyQtyMul (float) : Micro-to-YM conversion factor (0 = no proxy)      minOneYMEnabled (bool) : Force minimum 1 YM contract when proxy is active      currentLossDollars (float) : Running session loss in dollars (0 for estimate mode)      maxDailyLossLimit (float) : Daily loss limit in dollars (-1 = disabled)      maxProxyCap (int) : Maximum proxy contracts cap (0 = unlimited)      t1TPPrice (float) : T1 take-profit price (for scenario P&L calculation)      oppTPPrice (float) : Opposing MYM TP price when T1 stops (for scenario profit calc)      oppAddStopFrac (float) : Fraction of base risk for opposite MYM emergency flatten      opposingRemovalEnabled (bool) : Whether opposing removal entry mode is active   Returns: RecoupSizingResult with quantities, risk values, and scenario P&L RecoupSizingResult   Holds the complete output of the 8-step recoup sizing pipeline: micro/YM quantities, risk gate results, worst-case projections, and recoup-scenario P&L.   Fields:      microQtyRaw (series int)      microCapByDLL (series int)      microQtyCapped (series int)      ymQtyPre (series int)      ymQtyFinal (series int)      microEqForGate (series int)      projectedLossRecoup (series float)      dllRemaining (series float)      totalWorstCase (series float)      riskOK (series bool)      oppMYMLoss (series float)      didMinOneOverride (series bool)      dllForcedZero (series bool)      recoupScenarioNet (series float)      t1WinProfit (series float)
ไลบรารี Pine Script®
โดย Vantage-Stack
biasHelperbiasHelpers: Core Engine for Bias Analytics against a set of Benchmarks Overview The ` biasHelper ` library is a highly optimized backend engine designed specifically for evaluating, tracking, and aggregating bias analytics across timeframes. Built on strict Model-View-Controller (MVC) software architecture principles, this library encapsulates all complex mathematical processing, state caching, and string formatting. By offloading these responsibilities, it allows front-end indicators to remain exceptionally lightweight, mathematically pure, and dedicated entirely to UI visualization. This library features built-in anti-repainting guardrails, deterministic pseudo-random evaluations, and dynamic memory allocation through User-Defined Types (UDTs). --- Core Architecture & Design Philosophy This library operates using two primary User-Defined Types (UDTs) that track the lifecycle of a trading session: 1. ` SessionInfo `: The primary memory matrix. It tracks OHLC data, prevailing directional bias, Heikin-Ashi extensions, and cumulative hit/close counts. 2. ` SessionLines `: The visual array tracker. It orchestrates the projection of structural support/resistance levels and evaluates live price touches against them. By maintaining state inside these objects rather than utilizing global arrays, the library ensures O(1) time complexity during bar evaluation, resulting in lightning-fast execution even on dense chart histories. --- Exported Types (UDTs) `SessionInfo` The core data structure for tracking session metrics and bias execution. * **Price Tracking**: `prevHigh`, `prevLow`, `currentHigh`, `currentLow`, `currentOpen`. * **Heikin-Ashi Anchors**: `prevHaOpen`, `prevHaClose`. * **State Trackers**: `pushedUp` (bool), `currentBias` (int: 1 = Bullish, -1 = Bearish, 0 = Neutral). * **Metric Accumulators**: `bullishCount`, `bearishCount`, `hitHighCount`, `hitLowCount`, `closeHighCount`, `closeLowCount`. `SessionLines` The spatial data structure for tracking visual levels and live touches. * Lines : `highLine`, `lowLine`. * Touch Booleans : `hitHighLine`, `hitLowLine`. --- Data & State Management `updateData(infoObj, isNew, pClose, cOpen, cHigh, cLow)` The standard market structure logic handler. It evaluates historical structural breaks against the previous close to determine the prevailing directional bias without repainting. * Parameters : Evaluates state using standard OHLC inputs and strictly anchors to `close ` (`pClose`) to guarantee real-time parity with historical states. `updateBenchmarkData(infoObj, isNew, pClose, cOpen, cHigh, cLow, bType, tfSeconds)` A dynamic routing matrix for alternative bias benchmarks. * Supported `bType` Routing : * `"MOM"`: Pure Candlestick Momentum (Close vs. Open). * `"HA"`: Synthetic Heikin-Ashi Momentum evaluated securely within standard chart data. * `"ABULL"` / `"ABEAR"`: Static directional evaluations (Always Bullish / Always Bearish). * `"COIN"`: Deterministic pseudo-random generation. Generates a perfect 50/50 randomized output anchored mathematically to the timestamp and previous close, guaranteeing it never repaints or flickers on live ticks. * `"DTD"`: Day-to-Day alternating parity based on absolute time intervals. `processLines(linesObj, infoObj, isNew, tRight, lStyle, currHigh, currLow)` Draws historical support/resistance barriers and evaluates current price action (`currHigh`, `currLow`) to register touches and successful close-throughs. --- Math & Aggregation `calcTrueRate(biasCount, hitCount, closeCount)` Calculates the *True Close-Through Rate* (Success Rate × Close-Through Rate) while safely handling zero-division scenarios. Returns a standardized float coefficient. `getTotals(infoObj)` Extracts aggregated cross-directional totals for condensed dashboard views. * Returns : A tuple ` `. --- UI Formatting Utilities `getTablePos(pos)` & `getTableSize(size)` Translates string-based user inputs (e.g., `"Top Right"`, `"Normal"`) into native Pine Script structural variables (`position.top_right`, `size.normal`). `formatResult(hit, biasCount)` Converts raw integers into a cleanly formatted fractional percentage string (e.g., `"45.2%"`). `formatPercent(value)` Converts a raw floating-point coefficient into a polished percentage string. --- Implementation Example To utilize this library in your indicator, instantiate the UDTs and pass them through the update loops securely: import TRSTNGLRD/biasHelpers/4 as lib // 1. Initialize Objects var lib.SessionInfo sessionData = lib.SessionInfo.new() var lib.SessionLines sessionLines = lib.SessionLines.new() // 2. Evaluate State if isEligibleTimeframe sessionData.updateData(isNewSession, close , open, high, low) = sessionLines.processLines(sessionData, isNewSession, rightTime, lineStyle, high, low) // 3. Extract Formatted Data = sessionData.getTotals() string trueRate = lib.formatPercent(lib.calcTrueRate(tBias, tHit, tClose)) Note to Developers This library adheres strictly to TradingView's anti-repainting guidelines. When feeding inputs into `updateData` or `updateBenchmarkData`, always utilize the previous bar's close (`close `) for the `pClose` parameter. Live data (`high`, `low`) should exclusively be passed into the `processLines` method to allow real-time touch detection.
ไลบรารี Pine Script®
โดย TRSTNGLRD
lib_murrey Murrey Math level calculation and overbought/oversold zone detection. Computes the 8 Murrey Math levels (0/8 through 8/8) plus extended levels (+1/8, -1/8). Returns the current zone (-2 to +2) indicating oversold, neutral, or overbought conditions. Configurable frame size and multiplier. Ported from Murrey Math Lines by Nanda86: **Exports:** `get_murrey_levels()` — returns key Murrey levels (0/8, 4/8, 8/8, +1/8, -1/8), zone value, and increment. Used by: TCD - Trade Consistent & Disciplined (indicator)
ไลบรารี Pine Script®
โดย TradeCandD
backtestLibrary "backtest" curve(disp_ind)   Call function to get a certain curve of your strategy.   Parameters:      disp_ind (string)   Returns: Returns type of curve plot. cleaner(disp_ind, plot)   Call function to filter out your Strategy plots   Parameters:      disp_ind (string)      plot (float) backtestTable(option, position)   Assign this function to a random variable to get the "Performance Table"   Parameters:      option (simple string)      position (simple string)
ไลบรารี Pine Script®
โดย TheTradingSpiderMan
blueprint_ephemeris_lib🔭 Library blueprint_ephemeris_lib Consolidated planetary ephemeris library with improved accuracy. Supersedes previous individual planet libraries (lib_vsop_core, lib_vsop_mercury, lib_vsop_venus, etc.). One import gives you geocentric/heliocentric positions for all 10 solar system bodies. █ ACCURACY — VALIDATED AGAINST JPL DE440 Every planetary body was validated against NASA's DE440 ephemeris (via Skyfield). Using only 1.6% of the full VSOP87D theory (511 of 31,577 terms), this library achieves sub-arcminute accuracy for all planets: Sun 0.004° (14 arcseconds) Mercury 0.005° (18") Venus 0.006° (22") Mars 0.010° (36") Jupiter 0.007° (25") Saturn 0.009° (32") Uranus 0.013° (47") Neptune 0.017° (61") Moon 0.062° (3.7') Pluto 0.059° (3.5') All bodies under 0.1° RMS — more than sufficient for aspect calculations, ingress timing, and planetary line work. The Sun is accurate to 14 arcseconds using a truncated series that fits entirely inside Pine Script's token limits. █ WHAT'S NEW (V2) The original ephemeris required 11 chained library imports. A full validation audit uncovered critical coefficient errors and motivated this rewrite: • L1 Precession Fix — All 8 VSOP87 planets had incorrect longitude rate coefficients (VSOP87B values instead of VSOP87D). Each was missing +0.24382 rad/millennium of general precession. This single correction reduced error from ~0.75° to < 0.1° across the board. • 28% Smaller — 4,300 lines across 11 files → ~3,100 lines in 1 file. • Single Import — No dependency chain. Faster execution. • Moon Improvements — Functions accept raw `time` directly. Node functions renamed with explicit north/south designation. █ THEORIES VSOP87D (Bretagnon & Francou, 1988) — Mercury through Neptune 511 truncated terms out of 31,577 total (1.6%). Heliocentric spherical coordinates in the ecliptic of date. ELP2000-82 (Chapront-Touzé & Chapront, 1983) — Moon 91 terms (48 longitude + 43 latitude) from Meeus Chapter 47. Meeus Series (Meeus, 1998) — Pluto Analytical series from "Astronomical Algorithms" Ch. 37. Valid ±1 century from J2000. █ HOW TO USE Import the library: import BlueprintResearch/blueprint_ephemeris_lib/1 as eph Basic — plot a planet's geocentric longitude and declination: float jupiter_lon = eph.get_longitude(eph.Planet.Jupiter, time, true) float jupiter_decl = eph.get_declination(eph.Planet.Jupiter, time) plot(jupiter_lon, "Jupiter Geo Lon", color.yellow) plot(jupiter_decl, "Jupiter Decl", color.red) Retrograde detection: bool mercury_retro = eph.is_retrograde(eph.Planet.Mercury, time) bgcolor(mercury_retro ? color.new(color.red, 90) : na) Moon nodes and declination: float north_node = eph.get_mean_north_node_lon(time) float south_node = eph.get_mean_south_node_lon(time) float moon_decl = eph.get_declination(time) plot(north_node, "North Node", color.green) plot(south_node, "South Node", color.purple) plot(moon_decl, "Moon Declination", color.orange) Dynamic planet selection from input: string planet_str = input.string("Sun", "Planet", options= ) eph.Planet p = eph.string_to_planet(planet_str) float geo = eph.get_longitude(p, time, true) float helio = eph.get_longitude(p, time, false) float speed = eph.get_speed(p, time) plot(geo, "Geocentric", color.yellow) plot(helio, "Heliocentric", color.blue) plot(speed * 100, "Speed x100", color.white) All functions accept TradingView's `time` variable directly. █ FUNCTIONS Unified API (all planets): `get_longitude(Planet, time, preferGeo)` — geo or heliocentric longitude `get_declination(Planet, time)` — equatorial declination `get_speed(Planet, time)` — longitude speed (°/day) `is_retrograde(Planet, time)` — true when retrograde `string_to_planet(string)` — name to enum Averages : `get_avg6_geo_lon` / `get_avg6_helio_lon` — Mercury–Saturn `get_avg8_geo_lon` / `get_avg8_helio_lon` — Mercury–Neptune Moon (direct access): `get_geo_ecl_lon(time)` · `get_geo_ecl_lat(time)` · `get_declination(time)` `get_mean_north_node_lon(time)` · `get_mean_south_node_lon(time)` `get_true_north_node_lon(time)` · `get_true_south_node_lon(time)` `get_north_node_declination(time)` · `get_south_node_declination(time)` █ LIMITATIONS • Truncated series — sub-degree accuracy, not sub-arcsecond. More than sufficient for ingress timing and aspect work. • Validated against DE440 across 250 years (1850–2100). Over this full span, the worst-case VSOP87 planet (Uranus) is 0.017° RMS / 0.043° max error. Ingress dates manually verified back to the late 1800s with consistent accuracy. • Pluto uses Meeus series, limited to ±1 century from J2000. • Moon has no speed function. █ ACKNOWLEDGMENTS Coefficient validation was made possible by Greg Miller's VSOP87 multi-language project, which provides the complete VSOP87D coefficient tables in accessible formats. His work converting the original Fortran data files into CSV/JSON for multiple languages was essential for identifying the L1 precession errors in the original libraries. Miller released this work into the public domain. github.com/gmiller123456/vsop87-multilang References : • Meeus, Jean. Astronomical Algorithms (2nd Ed., 1998) • Bretagnon & Francou. VSOP87 Solutions (Astronomy & Astrophysics, 1988) • Chapront-Touzé & Chapront. ELP2000-82 (1983) █ OPEN SOURCE MIT License — part of the Blueprint Research open-source toolkit. Source code on GitHub get_geo_ecl_lon(time_)   Returns geocentric ecliptic longitude of the Moon.   Parameters:      time_ (float)   Returns: (float) Longitude in degrees, range [0, 360). get_geo_ecl_lat(time_)   Returns geocentric ecliptic latitude of the Moon.   Parameters:      time_ (float)   Returns: (float) Latitude in degrees. get_obliquity_j(time_)   Returns mean obliquity of the ecliptic.   Parameters:      time_ (float)   Returns: (float) Obliquity in degrees. get_declination(time_)   Returns geocentric equatorial declination of the Moon.   Parameters:      time_ (float)   Returns: (float) Declination in degrees, range where positive is north. get_declination(p, t)   Returns planetary geocentric equatorial declination.   Parameters:      p (series Planet) : (Planet) Planet to query.      t (float) : (float) Unix timestamp in milliseconds (use built-in 'time' variable).   Returns: (float) Geocentric declination in degrees, range where positive is north. @note Declination is always geocentric (no heliocentric equivalent in library). get_mean_north_node_lon(time_)   Returns mean longitude of the Moon's North Node (ascending node).   Parameters:      time_ (float)   Returns: (float) Longitude in degrees, range [0, 360). @note Mean node is a simple averaged calculation, reducing computational error. Used for declination calculations. get_mean_south_node_lon(time_)   Returns mean longitude of the Moon's South Node (descending node).   Parameters:      time_ (float)   Returns: (float) Longitude in degrees, range [0, 360). Equals North Node + 180°. get_true_north_node_lon(time_)   Returns true longitude of the Moon's North Node with perturbation corrections.   Parameters:      time_ (float)   Returns: (float) Longitude in degrees, range [0, 360). @note True node includes periodic perturbations but formula is low precision. Consider using mean node for consistency. get_true_south_node_lon(time_)   Returns true longitude of the Moon's South Node with perturbation corrections.   Parameters:      time_ (float)   Returns: (float) Longitude in degrees, range [0, 360). Equals True North Node + 180°. get_north_node_declination(time_)   Returns declination of the Moon's North Node.   Parameters:      time_ (float)   Returns: (float) Declination in degrees, range (bounded by obliquity). @note Uses mean node for calculation (more consistent than true node). get_south_node_declination(time_)   Returns declination of the Moon's South Node.   Parameters:      time_ (float)   Returns: (float) Declination in degrees. Inverse of North Node declination. normalizeLongitude(lon)   Normalizes any longitude value to the range [0, 360) degrees.   Parameters:      lon (float) : (float) Longitude in degrees (can be any value, including negative or >360).   Returns: (float) Normalized longitude in range [0, 360). string_to_planet(planetStr)   Converts a planet string identifier to Planet enum value.   Parameters:      planetStr (string) : (string) Planet name (case-insensitive). Supports formats: "Sun", "☉︎ Sun", "sun", "SUN"   Returns: (Planet) Corresponding Planet enum. Returns Planet.Sun if string not recognized. @note Supported planet strings: Sun, Moon, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto get_longitude(p, t, preferGeo)   Returns planetary longitude with automatic coordinate system selection.   Parameters:      p (series Planet) : (Planet) Planet to query.      t (float) : (float) Unix timestamp in milliseconds (use built-in 'time' variable).      preferGeo (bool) : (bool) If true, return geocentric; if false, return heliocentric.   Returns: (float) Longitude in degrees, normalized to range [0, 360). @note Sun and Moon always return geocentric regardless of preference (heliocentric not applicable). get_speed(p, t)   Returns planetary geocentric longitude speed (rate of change).   Parameters:      p (series Planet) : (Planet) Planet to query.      t (float) : (float) Unix timestamp in milliseconds (use built-in 'time' variable).   Returns: (float) Geocentric longitude speed in degrees per day. Negative values indicate retrograde motion. Returns na for Moon. @note Speed is always geocentric (no heliocentric equivalent in library). Moon speed calculation not implemented. get_avg6_geo_lon(t)   get_avg6_geo_lon @description Returns the arithmetic average of the geocentric longitudes for the six outer planets: Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto.   Parameters:      t (float) : (float) Time in Unix timestamp (milliseconds).   Returns: (float) Average geocentric longitude of the six outer planets in degrees, range [0, 360). get_avg6_helio_lon(t)   get_avg6_helio_lon @description Returns the arithmetic average of the heliocentric longitudes for the six outer planets: Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto.   Parameters:      t (float) : (float) Time in Unix timestamp (milliseconds).   Returns: (float) Average heliocentric longitude of the six outer planets in degrees, range [0, 360). get_avg8_geo_lon(t)   get_avg8_geo_lon @description Returns the arithmetic average of the geocentric longitudes for all eight classical planets: Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto.   Parameters:      t (float) : (float) Time in Unix timestamp (milliseconds).   Returns: (float) Average geocentric longitude of all eight classical planets in degrees, range [0, 360). get_avg8_helio_lon(t)   get_avg8_helio_lon @description Returns the arithmetic average of the heliocentric longitudes for all eight classical planets: Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto.   Parameters:      t (float) : (float) Time in Unix timestamp (milliseconds).   Returns: (float) Average heliocentric longitude of all eight classical planets in degrees, range [0, 360). is_retrograde(p, t)   Returns true if the planet is currently in retrograde motion (geocentric speed < 0) == 0 = stationary.   Parameters:      p (series Planet) : The planet to check.      t (float) : Time in Unix timestamp (milliseconds).   Returns: true if the planet is in retrograde, false otherwise.
ไลบรารี Pine Script®
โดย BlueprintResearch
6
StolenKernelFunctionsLibrary "StolenKernelFunctions" This library provides non-repainting kernel functions for Nadaraya-Watson estimator implementations. This allows for easy substition/comparison of different kernel functions for one another in indicators. Furthermore, kernels can easily be combined with other kernels to create newer, more customized kernels. rationalQuadratic(_src, _lookback, _relativeWeight, startAtBar)   Rational Quadratic Kernel - An infinite sum of Gaussian Kernels of different length scales.   Parameters:      _src (float) : The source series.      _lookback (simple int) : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.      _relativeWeight (simple float) : Relative weighting of time frames. Smaller values resut in a more stretched out curve and larger values will result in a more wiggly curve. As this value approaches zero, the longer time frames will exert more influence on the estimation. As this value approaches infinity, the behavior of the Rational Quadratic Kernel will become identical to the Gaussian kernel.      startAtBar (simple int)   Returns: yhat The estimated values according to the Rational Quadratic Kernel. gaussian(_src, _lookback, startAtBar)   Gaussian Kernel - A weighted average of the source series. The weights are determined by the Radial Basis Function (RBF).   Parameters:      _src (float) : The source series.      _lookback (simple int) : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.      startAtBar (simple int)   Returns: yhat The estimated values according to the Gaussian Kernel. periodic(_src, _lookback, _period, startAtBar)   Periodic Kernel - The periodic kernel (derived by David Mackay) allows one to model functions which repeat themselves exactly.   Parameters:      _src (float) : The source series.      _lookback (simple int) : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.      _period (simple int) : The distance between repititions of the function.      startAtBar (simple int)   Returns: yhat The estimated values according to the Periodic Kernel. locallyPeriodic(_src, _lookback, _period, startAtBar)   Locally Periodic Kernel - The locally periodic kernel is a periodic function that slowly varies with time. It is the product of the Periodic Kernel and the Gaussian Kernel.   Parameters:      _src (float) : The source series.      _lookback (simple int) : The number of bars used for the estimation. This is a sliding value that represents the most recent historical bars.      _period (simple int) : The distance between repititions of the function.      startAtBar (simple int)   Returns: yhat The estimated values according to the Locally Periodic Kernel.
ไลบรารี Pine Script®
โดย chris_dempsey
ma_libraryTitle: Library: Advanced Moving Average Collection Description: This library provides a comprehensive set of Moving Average algorithms, ranging from standard filters (SMA, EMA) to adaptive trendlines (KAMA, FRAMA) and experimental smoothers (ALMA, JMA). It has been fully optimized for Pine Script v6, ensuring efficient execution and strict robustness against na (missing) values. Unlike standard implementations that propagate na values, these functions dynamically recalculate weights to maintain continuity in disjointed datasets. 🧩 Library Features Robustness: Non-recursive filters ignore na values within the lookback window. Recursive filters maintain state to prevent calculation breaks. Optimization: Logic updated to v6 standards, utilizing efficient loops and var persistence. Standardization: All functions utilize a consistent f_ prefix and standardized parameters for easy integration. Scope: Contains over 35 different smoothing algorithms. 📊 Input Requirements Source (src): The data series to smooth (usually close, hl2, etc.). Length (length): The lookback period (must be a simple int). Specifics: Some adaptive MAs (like f_evwma) require volume data, while others (like f_alma) require offset/sigma settings. 🛠️ Integration Example You can import the library and call functions directly, or use the built-in f_selector to create dynamic inputs for your users. code Pine download content_copy expand_less //@version=6 indicator("MA Library Demo", overlay=true) // Import the library import YourUsername/ma_/1 as ma // --- Example 1: Direct Function Call --- // calculating Jurik Moving Average (JMA) float jma_val = ma.f_jma(close, 14) plot(jma_val, "JMA", color=color.yellow, linewidth=2) // --- Example 2: User Selector --- // Allowing the user to choose the MA type via settings string selected_type = input.string("ALMA", "MA Type", options= ) int length = input.int(20, "Length") // Using the generic selector function float dynamic_ma = ma.f_selector(close, length, selected_type) plot(dynamic_ma, "Dynamic MA", color=color.aqua) 📋 Included Algorithms The following methods are available (prefixed with f_): Standard: SMA, EMA, WMA, VWMA, RMA Adaptive: KAMA (Kaufman), FRAMA (Fractal), VIDYA (Chande/VARMA), VAMA (Vol. Adjusted) Low Lag: ZLEMA (Zero Lag), HMA (Hull), JMA (Jurik), DEMA, TEMA Statistical/Math: LSMA (Least Squares), GMMA (Geometric Mean), FLSMA (Fisher Least Squares) Advanced/Exotic: ALMA (Arnaud Legoux) EIT (Ehlers Instantaneous Trend) ESD (Ehlers Simple Decycler) AHMA (Ahrens) BMF (Blackman Filter) CMA (Corrective) DSWF (Damped Sine Wave) EVWMA (Elastic Vol. Weighted) HCF (Hybrid Convolution) LMA (Leo) MD (McGinley Dynamic) MF (Modular Filter) MM (Moving Median) QMA (Quick) RPMA (Repulsion) RSRMA (Right Sided Ricker) SMMA (Smoothed) SSMA (Shapeshifting) SWMA (Sine Weighted) TMA (Triangular) TSF (True Strength Force) VBMA (Variable Band)
ไลบรารี Pine Script®
โดย Nodial
NodialTreesLows2: ML Random Forest / Pivot Lows (Part 2 of 2)Title: `Library: ML Random Forest / Pivot Lows (Part 2 of 2)` Description: This library contains the second half (Trees 6-11) of the Random Forest Classifier designed to validate Pivot Lows (Long setups). It is a direct extension of NodialTreesL1 and cannot be used alone. Due to Pine Script's compilation limits on complexity and file size, the 12-tree ensemble model has been split into two separate libraries. ### 🧩 Library Contents This module exports the following methods representing the specific decision paths of the trained AI model: - `tree_6(array f)` - `tree_7(array f)` - `tree_8(array f)` - `tree_9(array f)` - `tree_10(array f)` - `tree_11(array f)` ### ⚠️ Implementation Guide To use this library, you must combine it with Part 1. Please refer to the NodialTreesLows1 library description for: 1. The full Integration Code Example (how to average the votes). 2. The exact Input Feature List (the 27 required metrics). 3. Detailed explanation of the Machine Learning logic. How to finish the integration: Import this library alongside Part 1 and add the results of `tree_6` through `tree_11` to your voting sum, as shown in the Part 1 documentation.
ไลบรารี Pine Script®
โดย Nodial
NodialTreesLows1: ML Random Forest / Pivot Lows (Part 1 of 2)Title: `Library: ML Random Forest / Pivot Lows (Part 1 of 2)` Description: This library contains the first half (Trees 0-5) of a Random Forest Classifier designed to validate Pivot Lows (Long setups). Due to Pine Script size constraints, the model is split into two libraries. You must use this library in conjunction with NodialTreesL2 to run the full ensemble. ### 🧩 System Architecture - Model: Random Forest (12 Trees total). - This Library: Contains `tree_0` to `tree_5`. - Logic: Each tree analyzes a feature array and outputs a probability score. - Target: Validating Swing Lows / Support Bounces. ### 📊 Input Requirements The methods expect an `array` of size 27 containing market features (Price Action, Momentum, Volatility, Volume, Structure). The exact order of features is critical for the model's accuracy. ### 🛠️ Integration Example Since this is a modular library, you need to import both parts and average their results to get the final prediction. ### 📋 Feature Mapping (Array Indexing) To get accurate predictions, the input array must contain exactly 27 floats in this specific order: 0. Timeframe (in seconds) 1. RSI (Raw Value) 2. MACD Histogram 3. Relative Volume 4. EMA Distance (%) 5. EMA Slope 6. ATR Ratio 7. ADX 8. Buying/Selling Pressure 9. Wick Ratio 10-16. Divergences & Pattern Flags (Boolean 0.0/1.0) 17-22. Proprietary Momentum Metrics ("Onion" Structure) 23-26. Derived Volatility/Volume Features *Note: For the advanced proprietary metrics (Indices 17-26), users must implement their own calculations or use compatible indicators.* //@version=6 indicator("My ML Long Strategy", overlay=true) // Import BOTH libraries import YourUsername/NodialTreesL1/1 as rf_part1 import YourUsername/NodialTreesL2/1 as rf_part2 // ... (Calculate your 27 features and fill the array) ... // var features = array.from(timeframe, rsi, macd, ...) // Calculate Ensemble Probability (Average of 12 Trees) float vote_sum = 0.0 // Trees from Part 1 vote_sum += rf_part1.tree_0(features) vote_sum += rf_part1.tree_1(features) vote_sum += rf_part1.tree_2(features) vote_sum += rf_part1.tree_3(features) vote_sum += rf_part1.tree_4(features) vote_sum += rf_part1.tree_5(features) // Trees from Part 2 (Trees 6-11) vote_sum += rf_part2.tree_6(features) vote_sum += rf_part2.tree_7(features) vote_sum += rf_part2.tree_8(features) vote_sum += rf_part2.tree_9(features) vote_sum += rf_part2.tree_10(features) vote_sum += rf_part2.tree_11(features) // Final Probability (0.0 to 1.0) float final_prob = vote_sum / 12.0 if final_prob > 0.60 label.new(bar_index, low, "Valid Low", color=color.green)
ไลบรารี Pine Script®
โดย Nodial
NodialTreesHighs2: ML Random Forest / Pivot Highs (Part 2 of 2)Title: `Library: ML Random Forest / Pivot Highs (Part 2 of 2)` Description: This library contains the second half (Trees 6-11) of the Random Forest Classifier designed to validate Pivot Highs (Short setups). It is a direct extension of NodialTreesH1 and cannot be used alone. Due to Pine Script's compilation limits on complexity and file size, the 12-tree ensemble model has been split into two separate libraries. ### 🧩 Library Contents This module exports the following methods representing the specific decision paths of the trained AI model: - `tree_6(array f)` - `tree_7(array f)` - `tree_8(array f)` - `tree_9(array f)` - `tree_10(array f)` - `tree_11(array f)` ### ⚠️ Implementation Guide To use this library, you must combine it with Part 1. Please refer to the NodialTreesH1 library description for: 1. The full Integration Code Example (how to average the votes). 2. The exact Input Feature List (the 27 required metrics). 3. Detailed explanation of the Machine Learning logic. How to finish the integration: Import this library alongside Part 1 and add the results of `tree_6` through `tree_11` to your voting sum, as shown in the Part 1 documentation.
ไลบรารี Pine Script®
โดย Nodial
NodialTreesHighs1: ML Random Forest / Pivot Highs (Part 1 of 2)Title: `Library: ML Random Forest / Pivot Highs (Part 1 of 2)` Description: This library contains the first half (Trees 0-5) of a Random Forest Classifier designed to validate Pivot Highs (Short setups). Due to Pine Script size constraints, the model is split into two libraries. You must use this library in conjunction with NodialTreesH2 to run the full ensemble. ### 🧩 System Architecture - Model: Random Forest (12 Trees total). - This Library: Contains `tree_0` to `tree_5`. - Logic: Each tree analyzes a feature array and outputs a probability score. - Target: Validating Swing Highs / Resistance Rejections. ### 📊 Input Requirements The methods expect an `array` of size 27 containing market features (Price Action, Momentum, Volatility, Volume, Structure). The exact order of features is critical for the model's accuracy. ### 🛠️ Integration Example Since this is a modular library, you need to import both parts and average their results to get the final prediction. ### 📋 Feature Mapping (Array Indexing) To get accurate predictions, the input array must contain exactly 27 floats in this specific order: 0. Timeframe (in seconds) 1. RSI (Raw Value) 2. MACD Histogram 3. Relative Volume 4. EMA Distance (%) 5. EMA Slope 6. ATR Ratio 7. ADX 8. Buying/Selling Pressure 9. Wick Ratio 10-16. Divergences & Pattern Flags (Boolean 0.0/1.0) 17-22. Proprietary Momentum Metrics ("Onion" Structure) 23-26. Derived Volatility/Volume Features *Note: For the advanced proprietary metrics (Indices 17-26), users must implement their own calculations or use compatible indicators.* //@version=6 indicator("My ML Short Strategy", overlay=true) // Import BOTH libraries import YourUsername/NodialTreesH1/1 as rf_part1 import YourUsername/NodialTreesH2/1 as rf_part2 // ... (Calculate your 27 features and fill the array) ... // var features = array.from(timeframe, rsi, macd, ...) // Calculate Ensemble Probability (Average of 12 Trees) float vote_sum = 0.0 // Trees from Part 1 vote_sum += rf_part1.tree_0(features) vote_sum += rf_part1.tree_1(features) vote_sum += rf_part1.tree_2(features) vote_sum += rf_part1.tree_3(features) vote_sum += rf_part1.tree_4(features) vote_sum += rf_part1.tree_5(features) // Trees from Part 2 (Trees 6-11) vote_sum += rf_part2.tree_6(features) vote_sum += rf_part2.tree_7(features) vote_sum += rf_part2.tree_8(features) vote_sum += rf_part2.tree_9(features) vote_sum += rf_part2.tree_10(features) vote_sum += rf_part2.tree_11(features) // Final Probability (0.0 to 1.0) float final_prob = vote_sum / 12.0 if final_prob > 0.60 label.new(bar_index, high, "Valid Short", color=color.red)
ไลบรารี Pine Script®
โดย Nodial
PineStats█ OVERVIEW PineStats is a comprehensive statistical analysis library for Pine Script v6, providing 104 functions across 6 modules. Built for quantitative traders, researchers, and indicator developers who need professional-grade statistics without reinventing the wheel. For building mean-reversion strategies, analyzing return distributions, measuring correlations, or testing for market regimes. █ MODULES CORE STATISTICS (20 functions) • Central tendency: mean, median, WMA, EMA • Dispersion: variance, stdev, MAD, range • Standardization: z-score, robust z-score, normalize, percentile • Distribution shape: skewness, kurtosis PROBABILITY DISTRIBUTIONS (17 functions) • Normal: PDF, CDF, inverse CDF (quantile function) • Power-law: Hill estimator, MLE alpha, survival function • Exponential: PDF, CDF, rate estimation • Normality testing: Jarque-Bera test ENTROPY (9 functions) • Shannon entropy (information theory) • Tsallis entropy (non-extensive, fat-tail sensitive) • Permutation entropy (ordinal patterns) • Approximate entropy (regularity measure) • Entropy-based regime detection PROBABILITY (21 functions) • Win rates and expected value • First passage time estimation • TP/SL probability analysis • Conditional probability and Bayes updates • Streak and drawdown probabilities REGRESSION (19 functions) • Linear regression: slope, intercept, forecast • Goodness of fit: R², adjusted R², standard error • Statistical tests: t-statistic, p-value, significance • Trend analysis: strength, angle, acceleration • Quadratic regression CORRELATION (18 functions) • Pearson, Spearman, Kendall correlation • Covariance, beta, alpha (Jensen's) • Rolling correlation analysis • Autocorrelation and cross-correlation • Information ratio, tracking error █ QUICK START import HenriqueCentieiro/PineStats/1 as stats // Z-score for mean reversion z = stats.zscore(close, 20) // Test if returns are normally distributed returns = (close - close ) / close isGaussian = stats.is_normal(returns, 100, 0.05) // Regression channel = stats.linreg_channel(close, 50, 2.0) // Correlation with benchmark spyReturns = request.security("SPY", timeframe.period, close/close - 1) beta = stats.beta(returns, spyReturns, 60) █ USE CASES ✓ Mean Reversion — z-scores, percentiles, Bollinger-style analysis ✓ Regime Detection — entropy measures, correlation regimes ✓ Risk Analysis — drawdown probability, VaR via quantiles ✓ Strategy Evaluation — expected value, win rates, R:R analysis ✓ Distribution Analysis — normality tests, fat-tail detection ✓ Multi-Asset — beta, alpha, correlation, relative strength █ NOTES • All functions return `na` on invalid inputs • Designed for Pine Script v6 • Fully documented in the library header • Part of the Pine ecosystem: PineStats, PineQuant, PineCriticality, PineWavelet █ REFERENCES • Abramowitz & Stegun — Normal CDF approximation • Acklam's algorithm — Inverse normal CDF • Hill estimator — Power-law tail estimation • Tsallis statistics — Non-extensive entropy Full documentation in the library header. mean(src, length)   Calculates the arithmetic mean (simple moving average) over a lookback period   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 1)   Returns: Arithmetic mean of the last `length` values, or `na` if inputs invalid wma_custom(src, length)   Calculates weighted moving average with linearly decreasing weights   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 1)   Returns: Weighted moving average, or `na` if inputs invalid ema_custom(src, length)   Calculates exponential moving average   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 1)   Returns: Exponential moving average, or `na` if inputs invalid median(src, length)   Calculates the median value over a lookback period   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 1)   Returns: Median value, or `na` if inputs invalid variance(src, length)   Calculates population variance over a lookback period   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 1)   Returns: Population variance, or `na` if inputs invalid stdev(src, length)   Calculates population standard deviation over a lookback period   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 1)   Returns: Population standard deviation, or `na` if inputs invalid mad(src, length)   Calculates Median Absolute Deviation (MAD) - robust dispersion measure   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 1)   Returns: MAD value, or `na` if inputs invalid data_range(src, length)   Calculates the range (highest - lowest) over a lookback period   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 1)   Returns: Range value, or `na` if inputs invalid zscore(src, length)   Calculates z-score (number of standard deviations from mean)   Parameters:      src (float) : Source series      length (simple int) : Lookback period for mean and stdev calculation (must be >= 2)   Returns: Z-score, or `na` if inputs invalid or stdev is zero zscore_robust(src, length)   Calculates robust z-score using median and MAD (resistant to outliers)   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 2)   Returns: Robust z-score, or `na` if inputs invalid or MAD is zero normalize(src, length)   Normalizes value to range using min-max scaling   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 1)   Returns: Normalized value in , or `na` if inputs invalid or range is zero percentile(src, length)   Calculates percentile rank of current value within lookback window   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 1)   Returns: Percentile rank (0 to 100), or `na` if inputs invalid winsorize(src, length, lower_pct, upper_pct)   Winsorizes values by clamping to percentile bounds (reduces outlier impact)   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 1)      lower_pct (simple float) : Lower percentile bound (0-100, e.g., 5 for 5th percentile)      upper_pct (simple float) : Upper percentile bound (0-100, e.g., 95 for 95th percentile)   Returns: Winsorized value clamped to bounds skewness(src, length)   Calculates sample skewness (measure of distribution asymmetry)   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 3)   Returns: Skewness value (negative = left tail, positive = right tail), or `na` if invalid kurtosis(src, length)   Calculates excess kurtosis (measure of distribution tail heaviness)   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 4)   Returns: Excess kurtosis (>0 = heavy tails, <0 = light tails), or `na` if invalid count_valid(src, length)   Counts non-na values in lookback window (useful for data quality checks)   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 1)   Returns: Count of valid (non-na) values sum(src, length)   Calculates sum over lookback period   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 1)   Returns: Sum of values, or `na` if inputs invalid cumsum(src)   Calculates cumulative sum (running total from first bar)   Parameters:      src (float) : Source series   Returns: Cumulative sum change(src, length)   Returns the change (difference) from n bars ago   Parameters:      src (float) : Source series      length (simple int) : Number of bars to look back (must be >= 1)   Returns: Current value minus value from `length` bars ago roc(src, length)   Calculates Rate of Change (percentage change from n bars ago)   Parameters:      src (float) : Source series      length (simple int) : Number of bars to look back (must be >= 1)   Returns: Percentage change as decimal (0.05 = 5%), or `na` if invalid normal_pdf_standard(x)   Calculates the standard normal probability density function (PDF)   Parameters:      x (float) : The value to evaluate   Returns: PDF value at x for standard normal N(0,1) normal_pdf(x, mu, sigma)   Calculates the normal probability density function (PDF)   Parameters:      x (float) : The value to evaluate      mu (float) : Mean of the distribution (default: 0)      sigma (float) : Standard deviation (default: 1, must be > 0)   Returns: PDF value at x for normal N(mu, sigma²) normal_cdf_standard(x)   Calculates the standard normal cumulative distribution function (CDF)   Parameters:      x (float) : The value to evaluate   Returns: Probability P(X <= x) for standard normal N(0,1) @description Uses Abramowitz & Stegun approximation (formula 7.1.26), accurate to ~1.5e-7 normal_cdf(x, mu, sigma)   Calculates the normal cumulative distribution function (CDF)   Parameters:      x (float) : The value to evaluate      mu (float) : Mean of the distribution (default: 0)      sigma (float) : Standard deviation (default: 1, must be > 0)   Returns: Probability P(X <= x) for normal N(mu, sigma²) normal_inv_standard(p)   Calculates the inverse standard normal CDF (quantile function)   Parameters:      p (float) : Probability value (must be in (0, 1))   Returns: x such that P(X <= x) = p for standard normal N(0,1) @description Uses Acklam's algorithm, accurate to ~1.15e-9 normal_inv(p, mu, sigma)   Calculates the inverse normal CDF (quantile function)   Parameters:      p (float) : Probability value (must be in (0, 1))      mu (float) : Mean of the distribution      sigma (float) : Standard deviation (must be > 0)   Returns: x such that P(X <= x) = p for normal N(mu, sigma²) power_law_alpha(src, length, tail_pct)   Estimates power-law exponent (alpha) using Hill estimator   Parameters:      src (float) : Source series (typically absolute returns or drawdowns)      length (simple int) : Lookback period (must be >= 10 for reliable estimates)      tail_pct (simple float) : Percentage of data to use for tail estimation (default: 0.1 = top 10%)   Returns: Estimated alpha (tail index), typically 2-4 for financial data @description Alpha < 2 indicates infinite variance (very heavy tails) @description Alpha < 3 indicates infinite kurtosis @description Alpha > 4 suggests near-Gaussian behavior power_law_alpha_mle(src, length, x_min)   Estimates power-law alpha using maximum likelihood (Clauset method)   Parameters:      src (float) : Source series (positive values expected)      length (simple int) : Lookback period (must be >= 20)      x_min (float) : Minimum threshold for power-law behavior   Returns: Estimated alpha using MLE power_law_pdf(x, alpha, x_min)   Calculates power-law probability density (Pareto Type I)   Parameters:      x (float) : Value to evaluate (must be >= x_min)      alpha (float) : Power-law exponent (must be > 1)      x_min (float) : Minimum value / scale parameter (must be > 0)   Returns: PDF value power_law_survival(x, alpha, x_min)   Calculates power-law survival function P(X > x)   Parameters:      x (float) : Value to evaluate (must be >= x_min)      alpha (float) : Power-law exponent (must be > 1)      x_min (float) : Minimum value / scale parameter (must be > 0)   Returns: Probability of exceeding x power_law_ks(src, length, alpha, x_min)   Tests if data follows power-law using simplified Kolmogorov-Smirnov   Parameters:      src (float) : Source series      length (simple int) : Lookback period      alpha (float) : Estimated alpha from power_law_alpha()      x_min (float) : Threshold value   Returns: KS statistic (lower = better fit, typically < 0.1 for good fit) is_power_law(src, length, tail_pct, ks_threshold)   Simple test if distribution appears to follow power-law   Parameters:      src (float) : Source series      length (simple int) : Lookback period      tail_pct (simple float) : Tail percentage for alpha estimation      ks_threshold (simple float) : Maximum KS statistic for acceptance (default: 0.1)   Returns: true if KS test suggests power-law fit exp_pdf(x, lambda)   Calculates exponential probability density function   Parameters:      x (float) : Value to evaluate (must be >= 0)      lambda (float) : Rate parameter (must be > 0)   Returns: PDF value exp_cdf(x, lambda)   Calculates exponential cumulative distribution function   Parameters:      x (float) : Value to evaluate (must be >= 0)      lambda (float) : Rate parameter (must be > 0)   Returns: Probability P(X <= x) exp_lambda(src, length)   Estimates exponential rate parameter (lambda) using MLE   Parameters:      src (float) : Source series (positive values)      length (simple int) : Lookback period   Returns: Estimated lambda (1/mean) jarque_bera(src, length)   Calculates Jarque-Bera test statistic for normality   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 10)   Returns: JB statistic (higher = more deviation from normality) @description Under normality, JB ~ chi-squared(2). JB > 6 suggests non-normality at 5% level is_normal(src, length, significance)   Tests if distribution is approximately normal   Parameters:      src (float) : Source series      length (simple int) : Lookback period      significance (simple float) : Significance level (default: 0.05)   Returns: true if Jarque-Bera test does not reject normality shannon_entropy(src, length, n_bins)   Calculates Shannon entropy from a probability distribution   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 10)      n_bins (simple int) : Number of histogram bins for discretization (default: 10)   Returns: Shannon entropy in bits (log base 2) @description Higher entropy = more randomness/uncertainty, lower = more predictability shannon_entropy_norm(src, length, n_bins)   Calculates normalized Shannon entropy   Parameters:      src (float) : Source series      length (simple int) : Lookback period      n_bins (simple int) : Number of histogram bins   Returns: Normalized entropy where 0 = perfectly predictable, 1 = maximum randomness tsallis_entropy(src, length, q, n_bins)   Calculates Tsallis entropy with q-parameter   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 10)      q (float) : Entropic index (q=1 recovers Shannon entropy)      n_bins (simple int) : Number of histogram bins   Returns: Tsallis entropy value @description q < 1: emphasizes rare events (fat tails) @description q = 1: equivalent to Shannon entropy @description q > 1: emphasizes common events optimal_q(src, length)   Estimates optimal q parameter from kurtosis   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: Estimated q value that best captures the distribution's tail behavior @description Uses relationship: q ≈ (5 + kurtosis) / (3 + kurtosis) for kurtosis > 0 tsallis_q_gaussian(x, q, beta)   Calculates Tsallis q-Gaussian probability density   Parameters:      x (float) : Value to evaluate      q (float) : Tsallis q parameter (must be < 3)      beta (float) : Width parameter (inverse temperature, must be > 0)   Returns: q-Gaussian PDF value @description q=1 recovers standard Gaussian permutation_entropy(src, length, order)   Calculates permutation entropy (ordinal pattern complexity)   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 20)      order (simple int) : Embedding dimension / pattern length (2-5, default: 3)   Returns: Normalized permutation entropy @description Measures complexity of temporal ordering patterns @description 0 = perfectly predictable sequence, 1 = random approx_entropy(src, length, m, r)   Calculates Approximate Entropy (ApEn) - regularity measure   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 50)      m (simple int) : Embedding dimension (default: 2)      r (simple float) : Tolerance as fraction of stdev (default: 0.2)   Returns: Approximate entropy value (higher = more irregular/complex) @description Lower ApEn indicates more self-similarity and predictability entropy_regime(src, length, q, n_bins)   Detects market regime based on entropy level   Parameters:      src (float) : Source series (typically returns)      length (simple int) : Lookback period      q (float) : Tsallis q parameter (use optimal_q() or default 1.5)      n_bins (simple int) : Number of histogram bins   Returns: Regime indicator: -1 = trending (low entropy), 0 = transition, 1 = ranging (high entropy) entropy_risk(src, length)   Calculates entropy-based risk indicator   Parameters:      src (float) : Source series (typically returns)      length (simple int) : Lookback period   Returns: Risk score where 1 = maximum divergence from Gaussian 1 hit_rate(src, length)   Calculates hit rate (probability of positive outcome) over lookback   Parameters:      src (float) : Source series (positive values count as hits)      length (simple int) : Lookback period   Returns: Hit rate as decimal hit_rate_cond(condition, length)   Calculates hit rate for custom condition over lookback   Parameters:      condition (bool) : Boolean series (true = hit)      length (simple int) : Lookback period   Returns: Hit rate as decimal expected_value(src, length)   Calculates expected value of a series   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: Expected value (mean) expected_value_trade(win_prob, take_profit, stop_loss)   Calculates expected value for a trade with TP and SL levels   Parameters:      win_prob (float) : Probability of hitting TP (0-1)      take_profit (float) : Take profit in price units or %      stop_loss (float) : Stop loss in price units or % (positive value)   Returns: Expected value per trade @description EV = (win_prob * TP) - ((1 - win_prob) * SL) breakeven_winrate(take_profit, stop_loss)   Calculates breakeven win rate for given TP/SL ratio   Parameters:      take_profit (float) : Take profit distance      stop_loss (float) : Stop loss distance   Returns: Required win rate for breakeven (EV = 0) reward_risk_ratio(take_profit, stop_loss)   Calculates the reward-to-risk ratio   Parameters:      take_profit (float) : Take profit distance      stop_loss (float) : Stop loss distance   Returns: R:R ratio fpt_probability(src, length, target, max_bars)   Estimates probability of price reaching target within N bars   Parameters:      src (float) : Source series (typically returns)      length (simple int) : Lookback for volatility estimation      target (float) : Target move (in same units as src, e.g., % return)      max_bars (simple int) : Maximum bars to consider   Returns: Probability of reaching target within max_bars @description Based on random walk with drift approximation fpt_mean(src, length, target)   Estimates mean first passage time to target level   Parameters:      src (float) : Source series (typically returns)      length (simple int) : Lookback for volatility estimation      target (float) : Target move   Returns: Expected number of bars to reach target (can be infinite) fpt_historical(src, length, target)   Counts historical bars to reach target from each point   Parameters:      src (float) : Source series (typically price or returns)      length (simple int) : Lookback period      target (float) : Target move from each starting point   Returns: Array of first passage times (na if target not reached within lookback) tp_probability(src, length, tp_distance, sl_distance)   Estimates probability of hitting TP before SL   Parameters:      src (float) : Source series (typically returns)      length (simple int) : Lookback for estimation      tp_distance (float) : Take profit distance (positive)      sl_distance (float) : Stop loss distance (positive)   Returns: Probability of TP being hit first trade_probability(src, length, tp_pct, sl_pct)   Calculates complete trade probability and EV analysis   Parameters:      src (float) : Source series (typically returns)      length (simple int) : Lookback period      tp_pct (float) : Take profit percentage      sl_pct (float) : Stop loss percentage   Returns: Tuple: cond_prob(condition_a, condition_b, length)   Calculates conditional probability P(B|A) from historical data   Parameters:      condition_a (bool) : Condition A (the given condition)      condition_b (bool) : Condition B (the outcome)      length (simple int) : Lookback period   Returns: P(B|A) = P(A and B) / P(A) bayes_update(prior, likelihood, false_positive)   Updates probability using Bayes' theorem   Parameters:      prior (float) : Prior probability P(H)      likelihood (float) : P(E|H) - probability of evidence given hypothesis      false_positive (float) : P(E|~H) - probability of evidence given hypothesis is false   Returns: Posterior probability P(H|E) streak_prob(win_rate, streak_length)   Calculates probability of N consecutive wins given win rate   Parameters:      win_rate (float) : Single-trade win probability      streak_length (simple int) : Number of consecutive wins   Returns: Probability of streak losing_streak_prob(win_rate, streak_length)   Calculates probability of experiencing N consecutive losses   Parameters:      win_rate (float) : Single-trade win probability      streak_length (simple int) : Number of consecutive losses   Returns: Probability of losing streak drawdown_prob(src, length, dd_threshold)   Estimates probability of drawdown exceeding threshold   Parameters:      src (float) : Source series (returns)      length (simple int) : Lookback period      dd_threshold (float) : Drawdown threshold (as positive decimal, e.g., 0.10 = 10%)   Returns: Historical probability of exceeding drawdown threshold prob_to_odds(prob)   Calculates odds from probability   Parameters:      prob (float) : Probability (0-1)   Returns: Odds (prob / (1 - prob)) odds_to_prob(odds)   Calculates probability from odds   Parameters:      odds (float) : Odds ratio   Returns: Probability (0-1) implied_prob(decimal_odds)   Calculates implied probability from decimal odds (betting)   Parameters:      decimal_odds (float) : Decimal odds (e.g., 2.5 means $2.50 return per $1 bet)   Returns: Implied probability logit(prob)   Calculates log-odds (logit) from probability   Parameters:      prob (float) : Probability (must be in (0, 1))   Returns: Log-odds inv_logit(log_odds)   Calculates probability from log-odds (inverse logit / sigmoid)   Parameters:      log_odds (float) : Log-odds value   Returns: Probability (0-1) linreg_slope(src, length)   Calculates linear regression slope   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 2)   Returns: Slope coefficient (change per bar) linreg_intercept(src, length)   Calculates linear regression intercept   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 2)   Returns: Intercept (predicted value at oldest bar in window) linreg_value(src, length)   Calculates predicted value at current bar using linear regression   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: Predicted value at current bar (end of regression line) linreg_forecast(src, length, offset)   Forecasts value N bars ahead using linear regression   Parameters:      src (float) : Source series      length (simple int) : Lookback period for regression      offset (simple int) : Bars ahead to forecast (positive = future)   Returns: Forecasted value linreg_channel(src, length, mult)   Calculates linear regression channel with bands   Parameters:      src (float) : Source series      length (simple int) : Lookback period      mult (simple float) : Standard deviation multiplier for bands   Returns: Tuple: r_squared(src, length)   Calculates R-squared (coefficient of determination)   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: R² value where 1 = perfect linear fit adj_r_squared(src, length)   Calculates adjusted R-squared (accounts for sample size)   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: Adjusted R² value std_error(src, length)   Calculates standard error of estimate (residual standard deviation)   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: Standard error residual(src, length)   Calculates residual at current bar   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: Residual (actual - predicted) residuals(src, length)   Returns array of all residuals in lookback window   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: Array of residuals t_statistic(src, length)   Calculates t-statistic for slope coefficient   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: T-statistic (slope / standard error of slope) slope_pvalue(src, length)   Approximates p-value for slope t-test (two-tailed)   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: Approximate p-value is_significant(src, length, alpha)   Tests if regression slope is statistically significant   Parameters:      src (float) : Source series      length (simple int) : Lookback period      alpha (simple float) : Significance level (default: 0.05)   Returns: true if slope is significant at alpha level trend_strength(src, length)   Calculates normalized trend strength based on R² and slope   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: Trend strength where sign indicates direction trend_angle(src, length)   Calculates trend angle in degrees   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: Angle in degrees (positive = uptrend, negative = downtrend) linreg_acceleration(src, length)   Calculates trend acceleration (second derivative)   Parameters:      src (float) : Source series      length (simple int) : Lookback period for each regression   Returns: Acceleration (change in slope) linreg_deviation(src, length)   Calculates deviation from regression line in standard error units   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: Deviation in standard error units (like z-score) quadreg_coefficients(src, length)   Fits quadratic regression and returns coefficients   Parameters:      src (float) : Source series      length (simple int) : Lookback period (must be >= 4)   Returns: Tuple: for y = a*x² + b*x + c quadreg_value(src, length)   Calculates quadratic regression value at current bar   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: Predicted value from quadratic fit correlation(x, y, length)   Calculates Pearson correlation coefficient between two series   Parameters:      x (float) : First series      y (float) : Second series      length (simple int) : Lookback period (must be >= 3)   Returns: Correlation coefficient covariance(x, y, length)   Calculates sample covariance between two series   Parameters:      x (float) : First series      y (float) : Second series      length (simple int) : Lookback period (must be >= 2)   Returns: Covariance value beta(asset, benchmark, length)   Calculates beta coefficient (slope of regression of y on x)   Parameters:      asset (float) : Asset returns series      benchmark (float) : Benchmark returns series      length (simple int) : Lookback period   Returns: Beta coefficient @description Beta = Cov(asset, benchmark) / Var(benchmark) alpha(asset, benchmark, length, risk_free)   Calculates alpha (Jensen's alpha / intercept)   Parameters:      asset (float) : Asset returns series      benchmark (float) : Benchmark returns series      length (simple int) : Lookback period      risk_free (float) : Risk-free rate (default: 0)   Returns: Alpha value (excess return not explained by beta) spearman(x, y, length)   Calculates Spearman rank correlation coefficient   Parameters:      x (float) : First series      y (float) : Second series      length (simple int) : Lookback period (must be >= 3)   Returns: Spearman correlation @description More robust to outliers than Pearson correlation kendall_tau(x, y, length)   Calculates Kendall's tau rank correlation (simplified)   Parameters:      x (float) : First series      y (float) : Second series      length (simple int) : Lookback period (must be >= 3)   Returns: Kendall's tau correlation_change(x, y, length, change_period)   Calculates change in correlation over time   Parameters:      x (float) : First series      y (float) : Second series      length (simple int) : Lookback period for correlation      change_period (simple int) : Period over which to measure change   Returns: Change in correlation correlation_regime(x, y, length, ma_length)   Detects correlation regime based on level and stability   Parameters:      x (float) : First series      y (float) : Second series      length (simple int) : Lookback period for correlation      ma_length (simple int) : Moving average length for smoothing   Returns: Regime: -1 = negative, 0 = uncorrelated, 1 = positive correlation_stability(x, y, length, stability_length)   Calculates correlation stability (inverse of volatility)   Parameters:      x (float) : First series      y (float) : Second series      length (simple int) : Lookback for correlation      stability_length (simple int) : Lookback for stability calculation   Returns: Stability score where 1 = perfectly stable relative_strength(asset, benchmark, length)   Calculates relative strength of asset vs benchmark   Parameters:      asset (float) : Asset price series      benchmark (float) : Benchmark price series      length (simple int) : Smoothing period   Returns: Relative strength ratio (normalized) tracking_error(asset, benchmark, length)   Calculates tracking error (standard deviation of excess returns)   Parameters:      asset (float) : Asset returns      benchmark (float) : Benchmark returns      length (simple int) : Lookback period   Returns: Tracking error (annualize by multiplying by sqrt(252) for daily data) information_ratio(asset, benchmark, length)   Calculates information ratio (risk-adjusted excess return)   Parameters:      asset (float) : Asset returns      benchmark (float) : Benchmark returns      length (simple int) : Lookback period   Returns: Information ratio capture_ratio(asset, benchmark, length, up_capture)   Calculates up/down capture ratio   Parameters:      asset (float) : Asset returns      benchmark (float) : Benchmark returns      length (simple int) : Lookback period      up_capture (simple bool) : If true, calculate up capture; if false, down capture   Returns: Capture ratio autocorrelation(src, length, lag)   Calculates autocorrelation at specified lag   Parameters:      src (float) : Source series      length (simple int) : Lookback period      lag (simple int) : Lag for autocorrelation (default: 1)   Returns: Autocorrelation at specified lag partial_autocorr(src, length)   Calculates partial autocorrelation at lag 1   Parameters:      src (float) : Source series      length (simple int) : Lookback period   Returns: PACF at lag 1 (equals ACF at lag 1) autocorr_test(src, length, max_lag)   Tests for significant autocorrelation (Ljung-Box inspired)   Parameters:      src (float) : Source series      length (simple int) : Lookback period      max_lag (simple int) : Maximum lag to test   Returns: Sum of squared autocorrelations (higher = more autocorrelation) cross_correlation(x, y, length, lag)   Calculates cross-correlation at specified lag   Parameters:      x (float) : First series      y (float) : Second series (lagged)      length (simple int) : Lookback period      lag (simple int) : Lag to apply to y (positive = y leads x)   Returns: Cross-correlation at specified lag cross_correlation_peak(x, y, length, max_lag)   Finds lag with maximum cross-correlation   Parameters:      x (float) : First series      y (float) : Second series      length (simple int) : Lookback period      max_lag (simple int) : Maximum lag to search (both directions)   Returns: Tuple:
ไลบรารี Pine Script®
โดย HenriqueCentieiro
1
moving_averages# MovingAverages Library - PineScript v6 A comprehensive PineScript v6 library containing **50+ Moving Average calculations** for TradingView. --- ## 📦 Installation ```pinescript import TheTradingSpiderMan/moving_averages/1 as MA ``` --- ## 📊 All Available Moving Averages (50+) ### Basic Moving Averages | Function | Selector Key | Description | | -------- | ------------ | ------------------------------------------ | | `sma()` | `SMA` | Simple Moving Average - arithmetic mean | | `ema()` | `EMA` | Exponential Moving Average | | `wma()` | `WMA` | Weighted Moving Average | | `vwma()` | `VWMA` | Volume Weighted Moving Average | | `rma()` | `RMA` | Relative/Smoothed Moving Average | | `smma()` | `SMMA` | Smoothed Moving Average (alias for RMA) | | `swma()` | - | Symmetrically Weighted MA (4-period fixed) | ### Hull Family | Function | Selector Key | Description | | -------- | ------------ | ------------------------------- | | `hma()` | `HMA` | Hull Moving Average | | `ehma()` | `EHMA` | Exponential Hull Moving Average | ### Double/Triple Smoothed | Function | Selector Key | Description | | -------------- | ------------ | --------------------------------- | | `dema()` | `DEMA` | Double Exponential Moving Average | | `tema()` | `TEMA` | Triple Exponential Moving Average | | `tma()` | `TMA` | Triangular Moving Average | | `t3()` | `T3` | Tillson T3 Moving Average | | `twma()` | `TWMA` | Triple Weighted Moving Average | | `swwma()` | `SWWMA` | Smoothed Weighted Moving Average | | `trixSmooth()` | `TRIXSMOOTH` | Triple EMA Smoothed | ### Zero/Low Lag | Function | Selector Key | Description | | --------- | ------------ | ----------------------------------- | | `zlema()` | `ZLEMA` | Zero Lag Exponential MA | | `lsma()` | `LSMA` | Least Squares Moving Average | | `epma()` | `EPMA` | Endpoint Moving Average | | `ilrs()` | `ILRS` | Integral of Linear Regression Slope | ### Adaptive Moving Averages | Function | Selector Key | Description | | ---------- | ------------ | ------------------------------- | | `kama()` | `KAMA` | Kaufman Adaptive Moving Average | | `frama()` | `FRAMA` | Fractal Adaptive Moving Average | | `vidya()` | `VIDYA` | Variable Index Dynamic Average | | `vma()` | `VMA` | Variable Moving Average | | `vama()` | `VAMA` | Volume Adjusted Moving Average | | `rvma()` | `RVMA` | Rolling VMA | | `apexMA()` | `APEXMA` | Apex Moving Average | ### Ehlers Filters | Function | Selector Key | Description | | ----------------- | --------------- | --------------------------------- | | `superSmoother()` | `SUPERSMOOTHER` | Ehlers Super Smoother | | `butterworth2()` | `BUTTERWORTH2` | 2-Pole Butterworth Filter | | `butterworth3()` | `BUTTERWORTH3` | 3-Pole Butterworth Filter | | `instantTrend()` | `INSTANTTREND` | Ehlers Instantaneous Trendline | | `edsma()` | `EDSMA` | Deviation Scaled Moving Average | | `mama()` | `MAMA` | Mesa Adaptive Moving Average | | `fama()` | `FAMAVAL` | Following Adaptive Moving Average | ### Laguerre Family | Function | Selector Key | Description | | -------------------- | ------------------ | ------------------------ | | `laguerreFilter()` | `LAGUERRE` | Laguerre Filter | | `adaptiveLaguerre()` | `ADAPTIVELAGUERRE` | Adaptive Laguerre Filter | ### Special Weighted | Function | Selector Key | Description | | ---------- | ------------ | -------------------------------- | | `alma()` | `ALMA` | Arnaud Legoux Moving Average | | `sinwma()` | `SINWMA` | Sine Weighted Moving Average | | `gwma()` | `GWMA` | Gaussian Weighted Moving Average | | `nma()` | `NMA` | Natural Moving Average | ### Jurik/McGinley/Coral | Function | Selector Key | Description | | ------------ | ------------ | --------------------- | | `jma()` | `JMA` | Jurik Moving Average | | `mcginley()` | `MCGINLEY` | McGinley Dynamic | | `coral()` | `CORAL` | Coral Trend Indicator | ### Mean Types | Function | Selector Key | Description | | -------------- | ------------ | ------------------------- | | `medianMA()` | `MEDIANMA` | Median Moving Average | | `gma()` | `GMA` | Geometric Moving Average | | `harmonicMA()` | `HARMONICMA` | Harmonic Moving Average | | `trimmedMA()` | `TRIMMEDMA` | Trimmed Moving Average | | `cma()` | `CMA` | Cumulative Moving Average | ### Volume-Based | Function | Selector Key | Description | | --------- | ------------ | -------------------------- | | `evwma()` | `EVWMA` | Elastic Volume Weighted MA | ### Other Specialized | Function | Selector Key | Description | | ----------------- | --------------- | --------------------------- | | `hwma()` | `HWMA` | Holt-Winters Moving Average | | `gdema()` | `GDEMA` | Generalized DEMA | | `rema()` | `REMA` | Regularized EMA | | `modularFilter()` | `MODULARFILTER` | Modular Filter | | `rmt()` | `RMT` | Recursive Moving Trendline | | `qrma()` | `QRMA` | Quadratic Regression MA | | `wilderSmooth()` | `WILDERSMOOTH` | Welles Wilder Smoothing | | `leoMA()` | `LEOMA` | Leo Moving Average | | `ahrensMA()` | `AHRENSMA` | Ahrens Moving Average | | `runningMA()` | `RUNNINGMA` | Running Moving Average | | `ppoMA()` | `PPOMA` | PPO-based Moving Average | | `fisherMA()` | `FISHERMA` | Fisher Transform MA | --- ## 🎯 Helper Functions | Function | Description | | ---------------- | ------------------------------------------------------------- | | `wcp()` | Weighted Close Price: (H+L+2\*C)/4 | | `typicalPrice()` | Typical Price: (H+L+C)/3 | | `medianPrice()` | Median Price: (H+L)/2 | | `selector()` | **Master selector** - choose any MA by string name | | `getAllTypes()` | Returns all supported MA type names as comma-separated string | --- ## 🔧 Usage Examples ### Basic Usage ```pinescript //@version=6 indicator("MA Example") import quantablex/moving_averages/1 as MA // Simple calls plot(MA.sma(close, 20), "SMA 20", color.blue) plot(MA.ema(close, 20), "EMA 20", color.red) plot(MA.hma(close, 20), "HMA 20", color.green) ``` ### Using the Selector Function (50+ MA Types) ```pinescript //@version=6 indicator("MA Selector") import quantablex/moving_averages/1 as MA // Full list of all supported types: // SMA,EMA,WMA,VWMA,RMA,SMMA,HMA,EHMA,DEMA,TEMA,TMA,T3,TWMA,SWWMA,TRIXSMOOTH, // ZLEMA,LSMA,EPMA,ILRS,KAMA,FRAMA,VIDYA,VMA,VAMA,RVMA,APEXMA,SUPERSMOOTHER, // BUTTERWORTH2,BUTTERWORTH3,INSTANTTREND,EDSMA,LAGUERRE,ADAPTIVELAGUERRE, // ALMA,SINWMA,GWMA,NMA,JMA,MCGINLEY,CORAL,MEDIANMA,GMA,HARMONICMA,TRIMMEDMA, // EVWMA,HWMA,GDEMA,REMA,MODULARFILTER,RMT,QRMA,WILDERSMOOTH,LEOMA,AHRENSMA, // RUNNINGMA,PPOMA,MAMA,FAMAVAL,FISHERMA,CMA maType = input.string("EMA", "MA Type", options= ) length = input.int(20, "Length") plot(MA.selector(close, length, maType), "Selected MA", color.orange) ``` ### Advanced Moving Averages ```pinescript //@version=6 indicator("Advanced MAs") import quantablex/moving_averages/1 as MA // ALMA with custom offset and sigma plot(MA.alma(close, 20, 0.85, 6), "ALMA", color.purple) // KAMA with custom fast/slow periods plot(MA.kama(close, 10, 2, 30), "KAMA", color.teal) // T3 with custom volume factor plot(MA.t3(close, 20, 0.7), "T3", color.yellow) // Laguerre Filter with custom gamma plot(MA.laguerreFilter(close, 0.8), "Laguerre", color.lime) ``` --- ## 📈 MA Selection Guide | Use Case | Recommended MAs | | ---------------------- | ------------------------------------------- | | **Trend Following** | EMA, DEMA, TEMA, HMA, CORAL | | **Low Lag Required** | ZLEMA, HMA, EHMA, JMA, LSMA | | **Volatile Markets** | KAMA, VIDYA, FRAMA, VMA, ADAPTIVELAGUERRE | | **Smooth Signals** | T3, LAGUERRE, SUPERSMOOTHER, BUTTERWORTH2/3 | | **Support/Resistance** | SMA, WMA, TMA, MEDIANMA | | **Scalping** | MCGINLEY, ZLEMA, HMA, INSTANTTREND | | **Noise Reduction** | MAMA, EDSMA, GWMA, TRIMMEDMA | | **Volume-Based** | VWMA, EVWMA, VAMA | --- ## ⚙️ Parameters Reference ### Common Parameters - `src` - Source series (close, open, hl2, hlc3, etc.) - `len` - Period length (integer) ### Special Parameters - `alma()`: `offset` (0-1), `sigma` (curve shape) - `kama()`: `fastLen`, `slowLen` - `t3()`: `vFactor` (volume factor) - `jma()`: `phase` (-100 to 100) - `laguerreFilter()`: `gamma` (0-1 damping) - `rema()`: `lambda` (regularization) - `modularFilter()`: `beta` (sensitivity) - `gdema()`: `mult` (multiplier, 2 = standard DEMA) - `trimmedMA()`: `trimPct` (0-0.5, percentage to trim) - `mama()/fama()`: `fastLimit`, `slowLimit` - `adaptiveLaguerre()`: Uses `len` for adaptation period --- ## 📝 Notes - All 50+ functions are exported for use in any PineScript v6 indicator/strategy - The `selector()` function supports **all MA types** via string key - Use `getAllTypes()` to get a comma-separated list of all supported MA names - Some MAs (CMA, INSTANTTREND, LAGUERRE, MAMA) don't use `len` parameter - Use `nz()` wrapper if handling potential NA values in your calculations --- **Author:** thetradingspiderman **Version:** 1.0 **PineScript Version:** 6 **Total MA Types:** 50+
ไลบรารี Pine Script®
โดย TheTradingSpiderMan
SpatialIndexYou can start using this now by inserthing this at the top of your indicator/strategy/library. import ArunaReborn/SpatialIndex/1 as SI Overview SpatialIndex is a high-performance Pine Script library that implements price-bucketed spatial indexing for efficient proximity queries on large datasets. Instead of scanning through hundreds or thousands of items linearly (O(n)), this library provides O(k) bucket lookup where k is typically just a handful of buckets, dramatically improving performance for price-based filtering operations. This library works with any data type through index-based references, making it universally applicable for support/resistance levels, pivot points, order zones, pattern detection points, Fair Value Gaps, and any other price-based data that needs frequent proximity queries. Why This Library Exists The Problem When building advanced technical indicators that track large numbers of price levels (support/resistance zones, pivot points, order blocks, etc.), you often need to answer questions like: - *"Which levels are within 5% of the current price?"* - *"What zones overlap with this price range?"* - *"Are there any significant levels near my entry point?"* The naive approach is to loop through every single item and check its price. For 500 levels across multiple timeframes, this means 500 comparisons every bar . On instruments with thousands of historical bars, this quickly becomes a performance bottleneck that can cause scripts to time out or lag. The Solution SpatialIndex solves this by organizing items into price buckets —like filing cabinets organized by price range. When you query for items near $50,000, the library only looks in the relevant buckets (e.g., $49,000-$51,000 range), ignoring all other price regions entirely. Performance Example: - Linear scan: Check 500 items = 500 comparisons per query - Spatial index: Check 3-5 buckets with ~10 items each = 30-50 comparisons per query - Result: 10-16x faster queries Key Features Core Capabilities - ✅ Generic Design : Works with any data type via index references - ✅ Multiple Index Strategies : Fixed bucket size or ATR-based dynamic sizing - ✅ Range Support : Index items that span price ranges (zones, gaps, channels) - ✅ Efficient Queries : O(k) bucket lookup instead of O(n) linear scan - ✅ Multiple Query Types : Proximity percentage, fixed range, exact price with tolerance - ✅ Dynamic Updates : Add, remove, update items in O(1) time - ✅ Batch Operations : Efficient bulk removal and reindexing - ✅ Query Caching : Optional caching for repeated queries within same bar - ✅ Statistics & Debugging : Built-in stats and diagnostic functions ### Advanced Features - ATR-Based Bucketing : Automatically adjusts bucket sizes based on volatility - Multi-Bucket Spanning : Items that span ranges are indexed in all overlapping buckets - Reindexing Support : Handles array removals with automatic index shifting - Cache Management : Configurable query caching with automatic invalidation - Empty Bucket Cleanup : Automatically removes empty buckets to minimize memory How It Works The Bucketing Concept Think of price space as divided into discrete buckets, like a histogram: ``` Price Range: $98-$100 $100-$102 $102-$104 $104-$106 $106-$108 Bucket Key: 49 50 51 52 53 Items: ``` When you query for items near $103: 1. Calculate which buckets overlap the $101.50-$104.50 range (keys 50, 51, 52) 2. Return items from only those buckets: 3. Never check items in buckets 49 or 53 Bucket Size Selection Fixed Size Mode: ```pine var SI.SpatialBucket index = SI.newSpatialBucket(2.0) // $2 per bucket ``` - Good for: Instruments with stable price ranges - Example: For stocks trading at $100, 2.0 = 2% increments ATR-Based Mode: ```pine float atr = ta.atr(14) var SI.SpatialBucket index = SI.newSpatialBucketATR(1.0, atr) // 1x ATR per bucket SI.updateATR(index, atr) // Update each bar ``` - Good for: Instruments with varying volatility - Adapts automatically to market conditions - 1.0 multiplier = one bucket spans one ATR unit Optimal Bucket Size: The library includes a helper function to calculate optimal size: ```pine float optimalSize = SI.calculateOptimalBucketSize(close, 5.0) // For 5% proximity queries ``` This ensures queries span approximately 3 buckets for optimal performance. Index-Based Architecture The library doesn't store your actual data—it only stores indices that point to your external arrays: ```pine // Your data var array levels = array.new() var array types = array.new() var array ages = array.new() // Your index var SI.SpatialBucket index = SI.newSpatialBucket(2.0) // Add a level array.push(levels, 50000.0) array.push(types, "support") array.push(ages, 0) SI.add(index, array.size(levels) - 1, 50000.0) // Store index 0 // Query near current price SI.QueryResult result = SI.queryProximity(index, close, 5.0) for idx in result.indices float level = array.get(levels, idx) string type = array.get(types, idx) // Work with your actual data ``` This design means: - ✅ Works with any data structure you define - ✅ No data duplication - ✅ Minimal memory footprint - ✅ Full control over your data --- Usage Guide Basic Setup ```pine // Import library import username/SpatialIndex/1 as SI // Create index var SI.SpatialBucket index = SI.newSpatialBucket(2.0) // Your data arrays var array supportLevels = array.new() var array touchCounts = array.new() ``` Adding Items Single Price Point: ```pine // Add a support level at $50,000 array.push(supportLevels, 50000.0) array.push(touchCounts, 1) int levelIdx = array.size(supportLevels) - 1 SI.add(index, levelIdx, 50000.0) ``` Price Range (Zones/Gaps): ```pine // Add a resistance zone from $51,000 to $52,000 array.push(zoneBottoms, 51000.0) array.push(zoneTops, 52000.0) int zoneIdx = array.size(zoneBottoms) - 1 SI.addRange(index, zoneIdx, 51000.0, 52000.0) // Indexed in all overlapping buckets ``` Querying Items Proximity Query (Percentage): ```pine // Find all levels within 5% of current price SI.QueryResult result = SI.queryProximity(index, close, 5.0) if array.size(result.indices) > 0 for idx in result.indices float level = array.get(supportLevels, idx) // Process nearby level ``` Fixed Range Query: ```pine // Find all items between $49,000 and $51,000 SI.QueryResult result = SI.queryRange(index, 49000.0, 51000.0) ``` Exact Price with Tolerance: ```pine // Find items at exactly $50,000 +/- $100 SI.QueryResult result = SI.queryAt(index, 50000.0, 100.0) ``` Removing Items Safe Removal Pattern: ```pine SI.QueryResult result = SI.queryProximity(index, close, 5.0) if array.size(result.indices) > 0 // IMPORTANT: Sort descending to safely remove from arrays array sorted = SI.sortIndicesDescending(result) for idx in sorted // Remove from index SI.remove(index, idx) // Remove from your data arrays array.remove(supportLevels, idx) array.remove(touchCounts, idx) // Reindex to maintain consistency SI.reindexAfterRemoval(index, idx) ``` Batch Removal (More Efficient): ```pine // Collect indices to remove array toRemove = array.new() for i = 0 to array.size(supportLevels) - 1 if array.get(touchCounts, i) > 10 // Remove old levels array.push(toRemove, i) // Remove in descending order from data arrays array sorted = array.copy(toRemove) array.sort(sorted, order.descending) for idx in sorted SI.remove(index, idx) array.remove(supportLevels, idx) array.remove(touchCounts, idx) // Batch reindex (much faster than individual reindexing) SI.reindexAfterBatchRemoval(index, toRemove) ``` Updating Items ```pine // Update a level's price (e.g., after refinement) float newPrice = 50100.0 SI.update(index, levelIdx, newPrice) array.set(supportLevels, levelIdx, newPrice) // Update a zone's range SI.updateRange(index, zoneIdx, 51000.0, 52500.0) array.set(zoneBottoms, zoneIdx, 51000.0) array.set(zoneTops, zoneIdx, 52500.0) ``` Query Caching For repeated queries within the same bar: ```pine // Create cache (persistent) var SI.CachedQuery cache = SI.newCachedQuery() // Cached query (returns cached result if parameters match) SI.QueryResult result = SI.queryProximityCached( index, cache, close, 5.0, // proximity% 1 // cache duration in bars ) // Invalidate cache when index changes significantly if bigChangeDetected SI.invalidateCache(cache) ``` --- Practical Examples Example 1: Support/Resistance Finder ```pine //@version=6 indicator("S/R with Spatial Index", overlay=true) import username/SpatialIndex/1 as SI // Data storage var array levels = array.new() var array types = array.new() // "support" or "resistance" var array touches = array.new() var array ages = array.new() // Spatial index var SI.SpatialBucket index = SI.newSpatialBucket(close * 0.02) // 2% buckets // Detect pivots bool isPivotHigh = ta.pivothigh(high, 5, 5) bool isPivotLow = ta.pivotlow(low, 5, 5) // Add new levels if isPivotHigh array.push(levels, high ) array.push(types, "resistance") array.push(touches, 1) array.push(ages, 0) SI.add(index, array.size(levels) - 1, high ) if isPivotLow array.push(levels, low ) array.push(types, "support") array.push(touches, 1) array.push(ages, 0) SI.add(index, array.size(levels) - 1, low ) // Find nearby levels (fast!) SI.QueryResult nearby = SI.queryProximity(index, close, 3.0) // Within 3% // Process nearby levels for idx in nearby.indices float level = array.get(levels, idx) string type = array.get(types, idx) // Check for touch if type == "support" and low <= level and low > level array.set(touches, idx, array.get(touches, idx) + 1) else if type == "resistance" and high >= level and high < level array.set(touches, idx, array.get(touches, idx) + 1) // Age and cleanup old levels for i = array.size(ages) - 1 to 0 array.set(ages, i, array.get(ages, i) + 1) // Remove levels older than 500 bars or with 5+ touches if array.get(ages, i) > 500 or array.get(touches, i) >= 5 SI.remove(index, i) array.remove(levels, i) array.remove(types, i) array.remove(touches, i) array.remove(ages, i) SI.reindexAfterRemoval(index, i) // Visualization for idx in nearby.indices line.new(bar_index, array.get(levels, idx), bar_index + 10, array.get(levels, idx), color=array.get(types, idx) == "support" ? color.green : color.red) ``` Example 2: Multi-Timeframe Zone Detector ```pine //@version=6 indicator("MTF Zones", overlay=true) import username/SpatialIndex/1 as SI // Store zones from multiple timeframes var array zoneBottoms = array.new() var array zoneTops = array.new() var array zoneTimeframes = array.new() // ATR-based spatial index for adaptive bucketing var SI.SpatialBucket index = SI.newSpatialBucketATR(1.0, ta.atr(14)) SI.updateATR(index, ta.atr(14)) // Update bucket size with volatility // Request higher timeframe data = request.security(syminfo.tickerid, "240", ) // Detect HTF zones if not na(htf_high) and not na(htf_low) float zoneTop = htf_high float zoneBottom = htf_low * 0.995 // 0.5% zone thickness // Check if zone already exists nearby SI.QueryResult existing = SI.queryRange(index, zoneBottom, zoneTop) if array.size(existing.indices) == 0 // No overlapping zones // Add new zone array.push(zoneBottoms, zoneBottom) array.push(zoneTops, zoneTop) array.push(zoneTimeframes, "4H") int idx = array.size(zoneBottoms) - 1 SI.addRange(index, idx, zoneBottom, zoneTop) // Query zones near current price SI.QueryResult nearbyZones = SI.queryProximity(index, close, 2.0) // Within 2% // Highlight nearby zones for idx in nearbyZones.indices box.new(bar_index - 50, array.get(zoneBottoms, idx), bar_index, array.get(zoneTops, idx), bgcolor=color.new(color.blue, 90)) ``` ### Example 3: Performance Comparison ```pine //@version=6 indicator("Spatial Index Performance Test") import username/SpatialIndex/1 as SI // Generate 500 random levels var array levels = array.new() var SI.SpatialBucket index = SI.newSpatialBucket(close * 0.02) if bar_index == 0 for i = 0 to 499 float randomLevel = close * (0.9 + math.random() * 0.2) // +/- 10% array.push(levels, randomLevel) SI.add(index, i, randomLevel) // Method 1: Linear scan (naive approach) int linearCount = 0 float proximityPct = 5.0 float lowBand = close * (1 - proximityPct/100) float highBand = close * (1 + proximityPct/100) for i = 0 to array.size(levels) - 1 float level = array.get(levels, i) if level >= lowBand and level <= highBand linearCount += 1 // Method 2: Spatial index query SI.QueryResult result = SI.queryProximity(index, close, proximityPct) int spatialCount = array.size(result.indices) // Compare performance plot(result.queryCount, "Items Examined (Spatial)", color=color.green) plot(linearCount, "Items Examined (Linear)", color=color.red) plot(spatialCount, "Results Found", color=color.blue) // Spatial index typically examines 10-50 items vs 500 for linear scan! ``` API Reference Summary Initialization - `newSpatialBucket(bucketSize)` - Fixed bucket size - `newSpatialBucketATR(atrMultiplier, atrValue)` - ATR-based buckets - `updateATR(sb, newATR)` - Update ATR for dynamic sizing Adding Items - `add(sb, itemIndex, price)` - Add item at single price point - `addRange(sb, itemIndex, priceBottom, priceTop)` - Add item spanning range Querying - `queryProximity(sb, refPrice, proximityPercent)` - Query by percentage - `queryRange(sb, priceBottom, priceTop)` - Query fixed range - `queryAt(sb, price, tolerance)` - Query exact price with tolerance - `queryProximityCached(sb, cache, refPrice, pct, duration)` - Cached query Removing & Updating - `remove(sb, itemIndex)` - Remove item - `update(sb, itemIndex, newPrice)` - Update item price - `updateRange(sb, itemIndex, newBottom, newTop)` - Update item range - `reindexAfterRemoval(sb, removedIndex)` - Reindex after single removal - `reindexAfterBatchRemoval(sb, removedIndices)` - Batch reindex - `clear(sb)` - Remove all items Utilities - `size(sb)` - Get item count - `isEmpty(sb)` - Check if empty - `contains(sb, itemIndex)` - Check if item exists - `getStats(sb)` - Get debug statistics string - `calculateOptimalBucketSize(price, pct)` - Calculate optimal bucket size - `sortIndicesDescending(result)` - Sort for safe removal - `sortIndicesAscending(result)` - Sort ascending Performance Characteristics Time Complexity - Add : O(1) for single point, O(m) for range spanning m buckets - Remove : O(1) lookup + O(b) bucket cleanup where b = buckets item spans - Query : O(k) where k = buckets in range (typically 3-5) vs O(n) linear scan - Update : O(1) removal + O(1) addition = O(1) total Space Complexity - Memory per item : ~8 bytes for index reference + map overhead - Bucket overhead : Proportional to price range coverage - Typical usage : For 500 items with 50 active buckets ≈ 4-8KB total Scalability - ✅ 100 items : ~5-10x faster than linear scan - ✅ 500 items : ~10-15x faster - ✅ 1000+ items : ~15-20x faster - ⚠️ Performance degrades if bucket size is too small (too many buckets) - ⚠️ Performance degrades if bucket size is too large (too many items per bucket) Best Practices Bucket Size Selection 1. Start with 2-5% of asset price for percentage-based queries 2. Use ATR-based mode for volatile assets or multi-symbol scripts 3. Test bucket size using `calculateOptimalBucketSize()` function 4. Monitor with `getStats()` to ensure reasonable bucket count Memory Management 1. Clear old items regularly to prevent unbounded growth 2. Use age tracking to remove stale data 3. Set maximum item limits based on your needs 4. Batch removals are more efficient than individual removals Query Optimization 1. Use caching for repeated queries within same bar 2. Invalidate cache when index changes significantly 3. Sort results descending before removal iteration 4. Batch operations when possible (reindexing, removal) Data Consistency 1. Always reindex after removal to maintain index alignment 2. Remove from arrays in descending order to avoid index shifting issues 3. Use batch reindex for multiple simultaneous removals 4. Keep external arrays and index in sync at all times Limitations & Caveats Known Limitations - Not suitable for exact price matching : Use tolerance with `queryAt()` - Bucket size affects performance : Too small = many buckets, too large = many items per bucket - Memory usage : Scales with price range coverage and item count - Reindexing overhead : Removing items mid-array requires index shifting When NOT to Use - ❌ Datasets with < 50 items (linear scan is simpler) - ❌ Items that change price every bar (constant reindexing overhead) - ❌ When you need ALL items every time (no benefit over arrays) - ❌ Exact price level matching without tolerance (use maps instead) When TO Use - ✅ Large datasets (100+ items) with occasional queries - ✅ Proximity-based filtering (% of price, ATR-based ranges) - ✅ Multi-timeframe level tracking - ✅ Zone/range overlap detection - ✅ Price-based spatial filtering --- Technical Details Bucketing Algorithm Items are assigned to buckets using integer division: ``` bucketKey = floor((price - basePrice) / bucketSize) ``` For ATR-based mode: ``` effectiveBucketSize = atrValue × atrMultiplier bucketKey = floor((price - basePrice) / effectiveBucketSize) ``` Range Indexing Items spanning price ranges are indexed in all overlapping buckets to ensure accurate range queries. The midpoint bucket is designated as the "primary bucket" for removal operations. Index Consistency The library maintains two maps: 1. `buckets`: Maps bucket keys → IntArray wrappers containing item indices 2. `itemToBucket`: Maps item indices → primary bucket key (for O(1) removal) This dual-mapping ensures both fast queries and fast removal while maintaining consistency. Implementation Note: Pine Script doesn't allow nested collections (map containing arrays directly), so the library uses an `IntArray` wrapper type to hold arrays within the map structure. This is an internal implementation detail that doesn't affect usage. --- Version History Version 1.0 - Initial release Credits & License License : Mozilla Public License 2.0 (TradingView default) Library Type : Open-source educational resource This library is designed as a public domain utility for the Pine Script community. As per TradingView library rules, this code can be freely reused by other authors. If you use this library in your scripts, please provide appropriate credit as required by House Rules. Summary SpatialIndex is a specialized library that solves a specific problem: fast proximity queries on large price-based datasets . If you're building indicators that track hundreds of levels, zones, or price points and need to frequently filter by proximity to current price, this library can provide 10-20x performance improvements over naive linear scanning. The index-based architecture makes it universally applicable to any data type, and the ATR-based bucketing ensures it adapts to market conditions automatically. Combined with query caching and batch operations, it provides a complete solution for spatial data management in Pine Script. Use this library when speed matters and your dataset is large.
ไลบรารี Pine Script®
โดย ArunaReborn
MLMatrixLibOverview MLMatrixLib is a comprehensive Pine Script v6 library implementing machine learning algorithms using native matrix operations. This library provides traders and developers with a toolkit of statistical and ML methods for building quantitative trading systems, performing data analysis, and creating adaptive indicators. How It Works The library leverages Pine Script's native matrix type to perform efficient linear algebra operations. Each algorithm is implemented from first principles, using matrix decomposition, iterative optimization, and statistical estimation techniques. All functions are designed for numerical stability with careful handling of edge cases. --- Library Contents (34 Sections) Section 1: Utility Functions & Matrix Operations Core building blocks including: • identity(n) - Creates n×n identity matrix • diagonal(values) - Creates diagonal matrix from array • ones(rows, cols) / zeros(rows, cols) - Matrix constructors • frobeniusNorm(m) / l1Norm(m) - Matrix norm calculations • hadamard(m1, m2) - Element-wise multiplication • columnMeans(m) / rowMeans(m) - Statistical aggregations • standardize(m) - Z-score normalization (zero mean, unit variance) • minMaxNormalize(m) - Scale values to range • fitStandardScaler(m) / fitMinMaxScaler(m) - Reusable scaler parameters • addBiasColumn(m) - Prepend column of ones for regression • arrayMedian(arr) / arrayPercentile(arr, p) - Array statistics Section 2: Activation Functions Numerically stable implementations: • sigmoid(x) / sigmoidMatrix(m) - Logistic function with overflow protection • tanhActivation(x) / tanhMatrix(m) - Hyperbolic tangent • relu(x) / reluMatrix(m) - Rectified Linear Unit • leakyRelu(x, alpha) - Leaky ReLU with configurable slope • elu(x, alpha) - Exponential Linear Unit • Derivatives for backpropagation: sigmoidDerivative, tanhDerivative, reluDerivative Section 3: Linear Regression (OLS) Ordinary Least Squares implementation using the normal equation (X'X)⁻¹X'y: • fitLinearRegression(X, y) - Fits model, returns coefficients, R², standard error • fitSimpleLinearRegression(x, y) - Single-variable regression • predictLinear(model, X) - Generate predictions • predictionInterval(model, X, confidence) - Confidence intervals using t-distribution • Model type stores: coefficients, R-squared, residuals, standard error Section 4: Weighted Linear Regression Generalized least squares with observation weights: • fitWeightedLinearRegression(X, y, weights) - Solves (X'WX)⁻¹X'Wy • Useful for downweighting outliers or emphasizing recent data Section 5: Polynomial Regression Fits polynomials of arbitrary degree: • fitPolynomialRegression(x, y, degree) - Constructs Vandermonde matrix • predictPolynomial(model, x) - Evaluate polynomial at points Section 6: Ridge Regression (L2 Regularization) Adds penalty term λ||β||² to prevent overfitting: • fitRidgeRegression(X, y, lambda) - Solves (X'X + λI)⁻¹X'y • Lambda parameter controls regularization strength Section 7: LASSO Regression (L1 Regularization) Coordinate descent algorithm for sparse solutions: • fitLassoRegression(X, y, lambda, maxIter, tolerance) - Iterative soft-thresholding • Produces sparse coefficients by driving some to exactly zero • softThreshold(x, lambda) - Core shrinkage operator Section 8: Elastic Net (L1 + L2 Regularization) Combines LASSO and Ridge penalties: • fitElasticNet(X, y, lambda, alpha, maxIter, tolerance) • Alpha balances L1 vs L2: alpha=1 is LASSO, alpha=0 is Ridge Section 9: Huber Robust Regression Iteratively Reweighted Least Squares (IRLS) for outlier resistance: • fitHuberRegression(X, y, delta, maxIter, tolerance) • Delta parameter defines transition between L1 and L2 loss • Downweights observations with large residuals Section 10: Quantile Regression Estimates conditional quantiles using linear programming approximation: • fitQuantileRegression(X, y, tau, maxIter, tolerance) • Tau specifies quantile (0.5 = median, 0.25 = lower quartile, etc.) Section 11: Logistic Regression (Binary Classification) Gradient descent optimization of cross-entropy loss: • fitLogisticRegression(X, y, learningRate, maxIter, tolerance) • predictProbability(model, X) - Returns probabilities • predictClass(model, X, threshold) - Returns binary predictions Section 12: Linear SVM (Support Vector Machine) Sub-gradient descent with hinge loss: • fitLinearSVM(X, y, C, learningRate, maxIter) • C parameter controls regularization (higher = harder margin) • predictSVM(model, X) - Returns class predictions Section 13: Recursive Least Squares (RLS) Online learning with exponential forgetting: • createRLSState(nFeatures, lambda, delta) - Initialize state • updateRLS(state, x, y) - Update with new observation • Lambda is forgetting factor (0.95-0.99 typical) • Useful for adaptive indicators that update incrementally Section 14: Covariance and Correlation Matrix statistics: • covarianceMatrix(m) - Sample covariance • correlationMatrix(m) - Pearson correlations • pearsonCorrelation(x, y) - Single correlation coefficient • spearmanCorrelation(x, y) - Rank-based correlation Section 15: Principal Component Analysis (PCA) Dimensionality reduction via eigendecomposition: • fitPCA(X, nComponents) - Power iteration method • transformPCA(X, model) - Project data onto principal components • Returns components, explained variance, and mean Section 16: K-Means Clustering Lloyd's algorithm with k-means++ initialization: • fitKMeans(X, k, maxIter, tolerance) - Cluster data points • predictCluster(model, X) - Assign new points to clusters • withinClusterVariance(model) - Measure cluster compactness Section 17: Gaussian Mixture Model (GMM) Expectation-Maximization algorithm: • fitGMM(X, k, maxIter, tolerance) - Soft clustering with probabilities • predictProbaGMM(model, X) - Returns membership probabilities • Models data as mixture of Gaussian distributions Section 18: Kalman Filter Linear state estimation: • createKalman1D(processNoise, measurementNoise, ...) - 1D filter • createKalman2D(processNoise, measurementNoise) - Position + velocity tracking • kalmanStep(state, measurement) - Predict-update cycle • Optimal filtering for noisy measurements Section 19: K-Nearest Neighbors (KNN) Instance-based learning: • fitKNN(X, y) - Store training data • predictKNN(model, X, k) - Classify by majority vote • predictKNNRegression(model, X, k) - Average of k neighbors • predictKNNWeighted(model, X, k) - Distance-weighted voting Section 20: Neural Network (Feedforward) Multi-layer perceptron: • createNeuralNetwork(architecture) - Define layer sizes • trainNeuralNetwork(nn, X, y, learningRate, epochs) - Backpropagation • predictNN(nn, X) - Forward pass • Supports configurable hidden layers Section 21: Naive Bayes Classifier Gaussian Naive Bayes: • fitNaiveBayes(X, y) - Estimate class-conditional distributions • predictNaiveBayes(model, X) - Maximum a posteriori classification • Assumes feature independence given class Section 22: Anomaly Detection Statistical outlier detection: • fitAnomalyDetector(X, contamination) - Mahalanobis distance-based • detectAnomalies(model, X) - Returns anomaly scores • isAnomaly(model, X, threshold) - Binary classification Section 23: Dynamic Time Warping (DTW) Time series similarity: • dtw(series1, series2) - Compute DTW distance • Handles sequences of different lengths • Useful for pattern matching Section 24: Markov Chain / Regime Detection Discrete state transitions: • fitMarkovChain(states, nStates) - Estimate transition matrix • predictNextState(transitionMatrix, currentState) - Most likely next state • stationaryDistribution(transitionMatrix) - Long-run probabilities Section 25: Hidden Markov Model (Simple) Baum-Welch algorithm: • fitHMM(observations, nStates, maxIter) - EM training • viterbi(model, observations) - Most likely state sequence • Useful for regime detection Section 26: Exponential Smoothing & Holt-Winters Time series smoothing: • exponentialSmooth(data, alpha) - Simple exponential smoothing • holtWinters(data, alpha, beta, gamma, seasonLength) - Triple smoothing • Captures trend and seasonality Section 27: Entropy and Information Theory Information measures: • entropy(probabilities) - Shannon entropy in bits • conditionalEntropy(jointProbs, marginalProbs) - H(X|Y) • mutualInformation(probsX, probsY, jointProbs) - I(X;Y) • kldivergence(p, q) - Kullback-Leibler divergence Section 28: Hurst Exponent Long-range dependence measure: • hurstExponent(data) - R/S analysis • H < 0.5: mean-reverting, H = 0.5: random walk, H > 0.5: trending Section 29: Change Detection (CUSUM) Cumulative sum control chart: • cusumChangeDetection(data, threshold, drift) - Detect regime changes • cusumOnline(value, prevCusumPos, prevCusumNeg, target, drift) - Streaming version Section 30: Autocorrelation Serial dependence analysis: • autocorrelation(data, maxLag) - ACF for all lags • partialAutocorrelation(data, maxLag) - PACF via Durbin-Levinson • Useful for time series model identification Section 31: Ensemble Methods Model combination: • baggingPredict(models, X) - Average predictions • votingClassify(models, X) - Majority vote • Improves robustness through aggregation Section 32: Model Evaluation Metrics Performance assessment: • mse(actual, predicted) / rmse / mae / mape - Regression metrics • accuracy(actual, predicted) - Classification accuracy • precision / recall / f1Score - Binary classification metrics • confusionMatrix(actual, predicted, nClasses) - Multi-class evaluation • rSquared(actual, predicted) / adjustedRSquared - Goodness of fit Section 33: Cross-Validation Model validation: • trainTestSplit(X, y, trainRatio) - Random split • Foundation for walk-forward validation Section 34: Trading Convenience Functions Trading-specific utilities: • priceMatrix(length) - OHLC data as matrix • logReturns(length) - Log return series • rollingSlope(src, length) - Linear trend strength • kalmanFilter(src, processNoise, measurementNoise) - Filtered price • kalmanFilter2D(src, ...) - Price with velocity estimate • adaptiveMA(src, sensitivity) - Kalman-based adaptive moving average • volAdjMomentum(src, length) - Volatility-normalized momentum • detectSRLevels(length, nLevels) - K-means based S/R detection • buildFeatures(src, lengths) - Multi-timeframe feature construction • technicalFeatures(length) - Standard indicator feature set (RSI, MACD, BB, ATR, etc.) • lagFeatures(src, lags) - Time-lagged features • sharpeRatio(returns) - Risk-adjusted return measure • sortinoRatio(returns) - Downside risk-adjusted return • maxDrawdown(equity) - Maximum peak-to-trough decline • calmarRatio(returns, equity) - Return/drawdown ratio • kellyCriterion(winRate, avgWin, avgLoss) - Optimal position sizing • fractionalKelly(...) - Conservative Kelly sizing • rollingBeta(assetReturns, benchmarkReturns) - Market exposure • fractalDimension(data) - Market complexity measure --- Usage Example ``` import YourUsername/MLMatrixLib/1 as ml // Create feature matrix matrix X = ml.priceMatrix(50) X := ml.standardize(X) // Fit linear regression ml.LinearRegressionModel model = ml.fitLinearRegression(X, y) float prediction = ml.predictLinear(model, X_new) // Kalman filter for smoothing float smoothedPrice = ml.kalmanFilter(close, 0.01, 1.0) // Detect support/resistance levels array levels = ml.detectSRLevels(100, 3) // K-means clustering for regime detection ml.KMeansModel km = ml.fitKMeans(features, 3) int cluster = ml.predictCluster(km, newFeature) ``` --- Technical Notes • All matrix operations use Pine Script's native matrix type • Numerical stability ensured through: - Clamping exponential arguments to prevent overflow - Division by zero protection with epsilon thresholds - Iterative algorithms with convergence tolerance • Designed for bar-by-bar execution in Pine Script's event-driven model • Compatible with Pine Script v6 --- Disclaimer This library provides mathematical tools for quantitative analysis. It does not constitute financial advice. Past performance of any algorithm does not guarantee future results. Users are responsible for validating models on their specific use cases and understanding the limitations of each method.
ไลบรารี Pine Script®
โดย ArunaReborn
BarCoreLibrary "BarCore" BarCore is a foundational library for technical analysis, providing essential functions for evaluating the structural properties of candlesticks and inter-bar relationships. It prioritizes ratio-based metrics (0.0 to 1.0) over absolute prices, making it asset-agnostic and ideal for robust pattern recognition, momentum analysis, and volume-weighted pressure evaluation. Key modules: - Structure & Range: High-precision bar and body metrics with relative positioning. - Wick Dynamics: Absolute and relative wick analysis for identifying price rejection. - Inter-bar Logic: Containment, coverage, and quantitative price overlap (Ratio-based). - Gap Intelligence: Real body and price gaps with customizable significance thresholds. - Flow & Pressure: Volume-weighted buying/selling pressure and Money Flow metrics. isBuyingBar()   Checks if the bar is a bullish (up) bar, where close is greater than open.   Returns: bool True if the bar closed higher than it opened. isSellingBar()   Checks if the bar is a bearish (down) bar, where close is less than open.   Returns: bool True if the bar closed lower than it opened. barMidpoint()   Calculates the absolute midpoint of the bar's total range (High + Low) / 2.   Returns: float The midpoint price of the bar. barRange()   Calculates the absolute size of the bar's total range (High to Low).   Returns: float The absolute difference between high and low. barRangeMidpoint()   Calculates half of the bar's total range size.   Returns: float Half the bar's range size. realBodyHigh()   Returns the higher price between the open and close.   Returns: float The top of the real body. realBodyLow()   Returns the lower price between the open and close.   Returns: float The bottom of the real body. realBodyMidpoint()   Calculates the absolute midpoint of the bar's real body.   Returns: float The midpoint price of the real body. realBodyRange()   Calculates the absolute size of the bar's real body.   Returns: float The absolute difference between open and close. realBodyRangeMidpoint()   Calculates half of the bar's real body size.   Returns: float Half the real body size. upperWickRange()   Calculates the absolute size of the upper wick.   Returns: float The range from high to the real body high. lowerWickRange()   Calculates the absolute size of the lower wick.   Returns: float The range from the real body low to low. openRatio()   Returns the location of the open price relative to the bar's total range (0.0 at low to 1.0 at high).   Returns: float The ratio of the distance from low to open, divided by the total range. closeRatio()   Returns the location of the close price relative to the bar's total range (0.0 at low to 1.0 at high).   Returns: float The ratio of the distance from low to close, divided by the total range. realBodyRatio()   Calculates the ratio of the real body size to the total bar range.   Returns: float The real body size divided by the bar range. Returns 0 if barRange is 0. upperWickRatio()   Calculates the ratio of the upper wick size to the total bar range.   Returns: float The upper wick size divided by the bar range. Returns 0 if barRange is 0. lowerWickRatio()   Calculates the ratio of the lower wick size to the total bar range.   Returns: float The lower wick size divided by the bar range. Returns 0 if barRange is 0. upperWickToBodyRatio()   Calculates the ratio of the upper wick size to the real body size.   Returns: float The upper wick size divided by the real body size. Returns 0 if realBodyRange is 0. lowerWickToBodyRatio()   Calculates the ratio of the lower wick size to the real body size.   Returns: float The lower wick size divided by the real body size. Returns 0 if realBodyRange is 0. totalWickRatio()   Calculates the ratio of the total wick range (Upper Wick + Lower Wick) to the total bar range.   Returns: float The total wick range expressed as a ratio of the bar's total range. Returns 0 if barRange is 0. isBodyExpansion()   Checks if the current bar's real body range is larger than the previous bar's real body range (body expansion).   Returns: bool True if realBodyRange() > realBodyRange() . isBodyContraction()   Checks if the current bar's real body range is smaller than the previous bar's real body range (body contraction).   Returns: bool True if realBodyRange() < realBodyRange() . isWithinPrevBar(inclusive)   Checks if the current bar's range is entirely within the previous bar's range.   Parameters:      inclusive (bool) : If true, allows equality (<=, >=). Default is false.   Returns: bool True if High < High AND Low > Low . isCoveringPrevBar(inclusive)   Checks if the current bar's range fully covers the entire previous bar's range.   Parameters:      inclusive (bool) : If true, allows equality (<=, >=). Default is false.   Returns: bool True if High > High AND Low < Low . isWithinPrevBody(inclusive)   Checks if the current bar's real body is entirely inside the previous bar's real body.   Parameters:      inclusive (bool) : If true, allows equality (<=, >=). Default is false.   Returns: bool True if the current body is contained inside the previous body. isCoveringPrevBody(inclusive)   Checks if the current bar's real body fully covers the previous bar's real body.   Parameters:      inclusive (bool) : If true, allows equality (<=, >=). Default is false.   Returns: bool True if the current body fully covers the previous body. isOpenWithinPrevBody(inclusive)   Checks if the current bar's open price falls within the real body range of the previous bar.   Parameters:      inclusive (bool) : If true, includes the boundary prices. Default is false.   Returns: bool True if the open price is between the previous bar's real body high and real body low. isCloseWithinPrevBody(inclusive)   Checks if the current bar's close price falls within the real body range of the previous bar.   Parameters:      inclusive (bool) : If true, includes the boundary prices. Default is false.   Returns: bool True if the close price is between the previous bar's real body high and real body low. isPrevOpenWithinBody(inclusive)   Checks if the previous bar's open price falls within the current bar's real body range.   Parameters:      inclusive (bool) : If true, includes the boundary prices. Default is false.   Returns: bool True if open is between the current bar's real body high and real body low. isPrevCloseWithinBody(inclusive)   Checks if the previous bar's closing price falls within the current bar's real body range.   Parameters:      inclusive (bool) : If true, includes the boundary prices. Default is false.   Returns: bool True if close is between the current bar's real body high and real body low. isOverlappingPrevBar()   Checks if there is any price overlap between the current bar's range and the previous bar's range.   Returns: bool True if the current bar's range has any intersection with the previous bar's range. bodyOverlapRatio()   Calculates the percentage of the current real body that overlaps with the previous real body.   Returns: float The overlap ratio (0.0 to 1.0). 1.0 means the current body is entirely within the previous body's price range. isCompletePriceGapUp()   Checks for a complete price gap up where the current bar's low is strictly above the previous bar's high, meaning there is zero price overlap between the two bars.   Returns: bool True if the current low is greater than the previous high. isCompletePriceGapDown()   Checks for a complete price gap down where the current bar's high is strictly below the previous bar's low, meaning there is zero price overlap between the two bars.   Returns: bool True if the current high is less than the previous low. isRealBodyGapUp()   Checks for a gap between the current and previous real bodies.   Returns: bool True if the current body is completely above the previous body. isRealBodyGapDown()   Checks for a gap between the current and previous real bodies.   Returns: bool True if the current body is completely below the previous body. gapRatio()   Calculates the percentage difference between the current open and the previous close, expressed as a decimal ratio.   Returns: float The gap ratio (positive for gap up, negative for gap down). Returns 0 if the previous close is 0. gapPercentage()   Calculates the percentage difference between the current open and the previous close.   Returns: float The gap percentage (positive for gap up, negative for gap down). Returns 0 if previous close is 0. isGapUp()   Checks for a basic gap up, where the current bar's open is strictly higher than the previous bar's close. This is the minimum condition for a gap up.   Returns: bool True if the current open is greater than the previous close (i.e., gapRatio is positive). isGapDown()   Checks for a basic gap down, where the current bar's open is strictly lower than the previous bar's close. This is the minimum condition for a gap down.   Returns: bool True if the current open is less than the previous close (i.e., gapRatio is negative). isSignificantGapUp(minRatio)   Checks if the current bar opened significantly higher than the previous close, as defined by a minimum percentage ratio.   Parameters:      minRatio (float) : The minimum required gap percentage ratio. Default is 0.03 (3%).   Returns: bool True if the gap ratio (open vs. previous close) is greater than or equal to the minimum ratio. isSignificantGapDown(minRatio)   Checks if the current bar opened significantly lower than the previous close, as defined by a minimum percentage ratio.   Parameters:      minRatio (float) : The minimum required gap percentage ratio. Default is 0.03 (3%).   Returns: bool True if the absolute value of the gap ratio (open vs. previous close) is greater than or equal to the minimum ratio. trueRangeComponentHigh()   Calculates the absolute distance from the current bar's High to the previous bar's Close, representing one of the components of the True Range.   Returns: float The absolute difference: |High - Close |. trueRangeComponentLow()   Calculates the absolute distance from the current bar's Low to the previous bar's Close, representing one of the components of the True Range.   Returns: float The absolute difference: |Low - Close |. isUpperWickDominant(minRatio)   Checks if the upper wick is significantly long relative to the total range.   Parameters:      minRatio (float) : Minimum ratio of the wick to the total bar range. Default is 0.7 (70%).   Returns: bool True if the upper wick dominates the bar's range. isUpperWickNegligible(maxRatio)   Checks if the upper wick is very small relative to the total range.   Parameters:      maxRatio (float) : Maximum ratio of the wick to the total bar range. Default is 0.05 (5%).   Returns: bool True if the upper wick is negligible. isLowerWickDominant(minRatio)   Checks if the lower wick is significantly long relative to the total range.   Parameters:      minRatio (float) : Minimum ratio of the wick to the total bar range. Default is 0.7 (70%).   Returns: bool True if the lower wick dominates the bar's range. isLowerWickNegligible(maxRatio)   Checks if the lower wick is very small relative to the total range.   Parameters:      maxRatio (float) : Maximum ratio of the wick to the total bar range. Default is 0.05 (5%).   Returns: bool True if the lower wick is negligible. isSymmetric(maxTolerance)   Checks if the upper and lower wicks are roughly equal in length.   Parameters:      maxTolerance (float) : Maximum allowable percentage difference between the two wicks. Default is 0.15 (15%).   Returns: bool True if wicks are symmetric within the tolerance level. isMarubozuBody(minRatio)   Candle with a very large body relative to the total range (minimal wicks).   Parameters:      minRatio (float) : Minimum body size ratio. Default is 0.9 (90%).   Returns: bool True if the bar has minimal wicks (Marubozu body). isLargeBody(minRatio)   Candle with a large body relative to the total range.   Parameters:      minRatio (float) : Minimum body size ratio. Default is 0.6 (60%).   Returns: bool True if the bar has a large body. isSmallBody(maxRatio)   Candle with a small body relative to the total range.   Parameters:      maxRatio (float) : Maximum body size ratio. Default is 0.4 (40%).   Returns: bool True if the bar has small body. isDojiBody(maxRatio)   Candle with a very small body relative to the total range (indecision).   Parameters:      maxRatio (float) : Maximum body size ratio. Default is 0.1 (10%).   Returns: bool True if the bar has a very small body. isLowerWickExtended(minRatio)   Checks if the lower wick is significantly extended relative to the real body size.   Parameters:      minRatio (float) : Minimum required ratio of the lower wick length to the real body size. Default is 2.0 (Lower wick must be at least twice the body's size).   Returns: bool True if the lower wick's length is at least `minRatio` times the size of the real body. isUpperWickExtended(minRatio)   Checks if the upper wick is significantly extended relative to the real body size.   Parameters:      minRatio (float) : Minimum required ratio of the upper wick length to the real body size. Default is 2.0 (Upper wick must be at least twice the body's size).   Returns: bool True if the upper wick's length is at least `minRatio` times the size of the real body. isStrongBuyingBar(minCloseRatio, maxOpenRatio)   Checks for a bar with strong bullish momentum (open near low, close near high), indicating high conviction.   Parameters:      minCloseRatio (float) : Minimum required ratio for the close location (relative to range, e.g., 0.7 means close must be in the top 30%). Default is 0.7 (70%).      maxOpenRatio (float) : Maximum allowed ratio for the open location (relative to range, e.g., 0.3 means open must be in the bottom 30%). Default is 0.3 (30%).   Returns: bool True if the bar is bullish, opened in the low extreme, and closed in the high extreme. isStrongSellingBar(maxCloseRatio, minOpenRatio)   Checks for a bar with strong bearish momentum (open near high, close near low), indicating high conviction.   Parameters:      maxCloseRatio (float) : Maximum allowed ratio for the close location (relative to range, e.g., 0.3 means close must be in the bottom 30%). Default is 0.3 (30%).      minOpenRatio (float) : Minimum required ratio for the open location (relative to range, e.g., 0.7 means open must be in the top 30%). Default is 0.7 (70%).   Returns: bool True if the bar is bearish, opened in the high extreme, and closed in the low extreme. isWeakBuyingBar(maxCloseRatio, maxBodyRatio)   Identifies a bar that is technically bullish but shows significant weakness, characterized by a failure to close near the high and a small body size.   Parameters:      maxCloseRatio (float) : Maximum allowed ratio for the close location relative to the range (e.g., 0.6 means the close must be in the bottom 60% of the bar's range). Default is 0.6 (60%).      maxBodyRatio (float) : Maximum allowed ratio for the real body size relative to the bar's range (e.g., 0.4 means the body is small). Default is 0.4 (40%).   Returns: bool True if the bar is bullish, but its close is weak and its body is small. isWeakSellingBar(minCloseRatio, maxBodyRatio)   Identifies a bar that is technically bearish but shows significant weakness, characterized by a failure to close near the low and a small body size.   Parameters:      minCloseRatio (float) : Minimum required ratio for the close location relative to the range (e.g., 0.4 means the close must be in the top 60% of the bar's range). Default is 0.4 (40%).      maxBodyRatio (float) : Maximum allowed ratio for the real body size relative to the bar's range (e.g., 0.4 means the body is small). Default is 0.4 (40%).   Returns: bool True if the bar is bearish, but its close is weak and its body is small. balanceOfPower()   Measures the net pressure of buyers vs. sellers within the bar, normalized to the bar's range.   Returns: float A value between -1.0 (strong selling) and +1.0 (strong buying), representing the strength and direction of the close relative to the open. buyingPressure()   Measures the net buying volume pressure based on the close location and volume.   Returns: float A numerical value representing the volume weighted buying pressure. sellingPressure()   Measures the net selling volume pressure based on the close location and volume.   Returns: float A numerical value representing the volume weighted selling pressure. moneyFlowMultiplier()   Calculates the Money Flow Multiplier (MFM), which is the price component of Money Flow and CMF.   Returns: float A normalized value from -1.0 (strong selling) to +1.0 (strong buying), representing the net directional pressure. moneyFlowVolume()   Calculates the Money Flow Volume (MFV), which is the Money Flow Multiplier weighted by the bar's volume.   Returns: float A numerical value representing the volume-weighted money flow. Positive = buying dominance; negative = selling dominance. isAccumulationBar()   Checks for basic accumulation on the current bar, requiring both positive Money Flow Volume and a buying bar (closing higher than opening).   Returns: bool True if the bar exhibits buying dominance through its internal range location and is a buying bar. isDistributionBar()   Checks for basic distribution on the current bar, requiring both negative Money Flow Volume and a selling bar (closing lower than opening).   Returns: bool True if the bar exhibits selling dominance through its internal range location and is a selling bar.
ไลบรารี Pine Script®
โดย sgbpulse
CausalityLib - granger casuality and transfer entropy helpersLibrary "CausalityLib" Causality Analysis Library - Transfer Entropy, Granger Causality, and Causality Filtering f_shannon_entropy(data, num_bins)   Calculate Shannon entropy of data distribution   Parameters:      data (array) : Array of continuous values      num_bins (int) : Number of bins for discretization   Returns: Entropy value (higher = more randomness) f_calculate_te_score(primary_arr, ticker_arr, window, bins, lag)   Calculate Transfer Entropy from source to target   Parameters:      primary_arr (array) : Target series (e.g., primary ticker returns)      ticker_arr (array) : Source series (e.g., basket ticker returns)      window (int) : Window size for TE calculation      bins (int) : Number of bins for discretization      lag (int) : Lag for source series   Returns: - TE score and direction (-1 or 1) f_correlation_at_lag(primary_arr, ticker_arr, lag, window, correlation_method)   Calculate Pearson correlation at specific lag   Parameters:      primary_arr (array) : Primary series      ticker_arr (array) : Ticker series      lag (int) : Lag value (positive = ticker lags primary)      window (int) : Window size for correlation      correlation_method (string) : Correlation method to use ("Pearson", "Spearman", "Kendall")   Returns: Correlation coefficient f_calculate_granger_score(primary_arr, ticker_arr, window, max_lag, correlation_method)   Calculate Granger causality score with lag testing   Parameters:      primary_arr (array) : Primary series      ticker_arr (array) : Ticker series      window (int) : Window size for correlation      max_lag (int) : Maximum lag to test      correlation_method (string) : Correlation method to use   Returns: - Granger score and directional beta f_partial_correlation(x_arr, y_arr, z_arr, window)   Calculate partial correlation between X and Y controlling for Z   Parameters:      x_arr (array) : First series      y_arr (array) : Second series      z_arr (array) : Mediator series      window (int) : Window size for correlation   Returns: Partial correlation coefficient f_pcmci_filter_score(raw_score, primary_arr, ticker_arr, mediator1, mediator2, mediator3, mediator4, window)   PCMCI Filter: Adjust Granger score by checking for mediating tickers   Parameters:      raw_score (float) : Original Granger score      primary_arr (array) : Primary series      ticker_arr (array) : Ticker series      mediator1 (array) : First potential mediator series      mediator2 (array) : Second potential mediator series      mediator3 (array) : Third potential mediator series      mediator4 (array) : Fourth potential mediator series      window (int) : Window size for correlation   Returns: Filtered score (reduced if causality is indirect/spurious)
ไลบรารี Pine Script®
โดย cybermediaboy
demark_utilsLibrary "demark_utils" f_grade(score)   Parameters:      score (float) f_clampScore(score)   Parameters:      score (float) f_px(v)   Parameters:      v (float) f_pxOrDash(v)   Parameters:      v (float) f_sum(src, length)   Parameters:      src (float)      length (int) f_hasAnyBits(bus, mask)   Parameters:      bus (int)      mask (int) f_busSetMask(bus, mask)   Parameters:      bus (int)      mask (int) f_evSet(bus, flag)   Parameters:      bus (int)      flag (int) f_evSet2(bus, flag)   Parameters:      bus (int)      flag (int)
ไลบรารี Pine Script®
โดย Anchoritezzz