PINE LIBRARY
업데이트됨 Isotropic Coordinate System (ICS)
Library "ICS"
Isotropic Coordinate System (ICS): a dimensionless price-time space
for scale-invariant chart geometry.
Vertical axis: y = ln(price) / sigma, where sigma is the Yang-Zhang (2000)
minimum-variance, drift-independent, gap-consistent OHLC volatility estimator.
Horizontal axis: two scalings via the XScale enum.
legacy : x = bars / lookback. Linear window fraction. Backward compatible.
isotropic : x = sqrt(bars / lookback), with y additionally divided by
sqrt(lookback). Diffusion-consistent (sqrt-time scaling), so that
tan(theta) equals the z-score of the move and 45 degrees
corresponds to a move of exactly one standard deviation
of the n-bar log-return distribution. Assumes approximately
iid returns within the sigma window (the standard assumption
behind sqrt-time scaling; see Danielsson & Zigrand, 2006, for
its known limits under vol clustering and jumps).
Every output (angle, length, area, centroid) is a pure dimensionless number,
comparable across symbols, currencies, and timeframes.
Reference: Yang, D. & Zhang, Q. (2000), "Drift-Independent Volatility
Estimation Based on High, Low, Open, and Close Prices",
The Journal of Business, 73(3), 477-492.
yangZhangSigma(length)
Yang-Zhang volatility estimator. Minimum-variance, unbiased,
drift-independent, and consistent with opening gaps
(Yang & Zhang, 2000). Uses the unbiased sample variance
(biased = false) for both the overnight and open-to-close
components, matching the estimator's unbiasedness claim.
Parameters:
length (simple int): (simple int) Rolling window length. Must be >= 2.
Returns: (series float) Per-bar sigma, floored at 1e-10.
toX(bars, lookback, mode)
Dimensionless horizontal coordinate.
Parameters:
bars (int): (series int) Signed bar distance from the anchor.
lookback (int): (series int) Window length acting as the horizontal unit.
mode (series XScale): (series XScale) Scaling mode.
Returns: (series float) Signed dimensionless x.
toY(price, sigma, lookback, mode)
Dimensionless vertical coordinate.
Parameters:
price (float): (series float) Price. Must be > 0.
sigma (float): (series float) Yang-Zhang sigma. Must be > 1e-10.
lookback (int): (series int) Window length (used by isotropic mode only).
mode (series XScale): (series XScale) Scaling mode.
Returns: (series float) Dimensionless y, or na when inputs are invalid.
moveZScore(dLogPrice, sigma, bars)
Z-score of a log-price move over n bars: dLog / (sigma * sqrt(n)).
In isotropic mode this equals tan(theta) of the same move.
Parameters:
dLogPrice (float): (series float) ln(target) - ln(anchor).
sigma (float): (series float) Per-bar Yang-Zhang sigma. Must be > 1e-10.
bars (int): (series int) Number of bars in the move. Must be > 0.
Returns: (series float) The z-score, or na when inputs are invalid.
triangle(td, anchorPrice, anchorBar, targetPrice, targetBar, sig, lookback, mode)
Right triangle between an anchor and a target, computed entirely
in ICS space. Writes results in place into `td` and returns it.
On invalid inputs every field is set to na, so world X never
receives contaminated numbers.
Parameters:
td (TriangleData): (TriangleData) Output object, updated in place.
anchorPrice (float): (series float) Anchor price (world A). Must be > 0.
anchorBar (int): (series int) Anchor bar_index.
targetPrice (float): (series float) Target price (world A). Must be > 0.
targetBar (int): (series int) Target bar_index. Must differ from anchorBar.
sig (float): (series float) Yang-Zhang sigma. Must be > 1e-10.
lookback (int): (series int) Horizontal unit window.
mode (series XScale): (series XScale) Scaling mode.
Returns: (TriangleData) The same `td`, for chaining.
pinTriangle(td, anchorPrice, anchorBar, extremePrice, bodyPrice, curBar, sig, lookback, mode)
Pin (wick) triangle with three vertices in ICS space:
A = anchor, B = candle extreme, C = candle body edge.
Side BC is the wick. theta = signed angle at A between AB and AC.
Since xB = xC, the shoelace area reduces exactly to
0.5 * |yB - yC| * |dx|.
Parameters:
td (TriangleData): (TriangleData) Output object, updated in place.
anchorPrice (float): (series float) Anchor price (hh or ll). Must be > 0.
anchorBar (int): (series int) Anchor bar_index.
extremePrice (float): (series float) Candle extreme (high or low). Must be > 0.
bodyPrice (float): (series float) Candle body edge. Must be > 0.
curBar (int): (series int) Current bar_index. Must differ from anchorBar.
sig (float): (series float) Yang-Zhang sigma. Must be > 1e-10.
lookback (int): (series int) Horizontal unit window.
mode (series XScale): (series XScale) Scaling mode.
Returns: (TriangleData) The same `td`, for chaining.
zeroTri(td)
Resets a TriangleData to na. Use when the structure is inactive,
so inactive periods never enter moving averages or normalization
as fake zero values.
Parameters:
td (TriangleData): (TriangleData) Object to reset, updated in place.
Returns: (TriangleData) The same `td`, for chaining.
TriangleData
One triangle's measurements in ICS space. All fields dimensionless.
Fields:
theta (series float): Signed hypotenuse angle in degrees; in isotropic mode tan(theta) is the z-score of the move.
dy (series float): Signed Euclidean magnitude of the hypotenuse.
area (series float): Triangle area (>= 0).
centroidY (series float): Vertical centroid of the triangle.
FrozenAnchors
Anchors frozen at a reference bar, plus activity state.
Fields:
hh (series float): Highest high at the freeze bar (world-A price units).
ll (series float): Lowest low at the freeze bar (world-A price units).
mid (series float): Geometric mean sqrt(hh * ll) at the freeze bar.
bar_x (series int): bar_index of the freeze bar.
time_x (series int): time of the freeze bar.
is_active (series bool): Whether the frozen structure is currently active.
Isotropic Coordinate System (ICS): a dimensionless price-time space
for scale-invariant chart geometry.
Vertical axis: y = ln(price) / sigma, where sigma is the Yang-Zhang (2000)
minimum-variance, drift-independent, gap-consistent OHLC volatility estimator.
Horizontal axis: two scalings via the XScale enum.
legacy : x = bars / lookback. Linear window fraction. Backward compatible.
isotropic : x = sqrt(bars / lookback), with y additionally divided by
sqrt(lookback). Diffusion-consistent (sqrt-time scaling), so that
tan(theta) equals the z-score of the move and 45 degrees
corresponds to a move of exactly one standard deviation
of the n-bar log-return distribution. Assumes approximately
iid returns within the sigma window (the standard assumption
behind sqrt-time scaling; see Danielsson & Zigrand, 2006, for
its known limits under vol clustering and jumps).
Every output (angle, length, area, centroid) is a pure dimensionless number,
comparable across symbols, currencies, and timeframes.
Reference: Yang, D. & Zhang, Q. (2000), "Drift-Independent Volatility
Estimation Based on High, Low, Open, and Close Prices",
The Journal of Business, 73(3), 477-492.
yangZhangSigma(length)
Yang-Zhang volatility estimator. Minimum-variance, unbiased,
drift-independent, and consistent with opening gaps
(Yang & Zhang, 2000). Uses the unbiased sample variance
(biased = false) for both the overnight and open-to-close
components, matching the estimator's unbiasedness claim.
Parameters:
length (simple int): (simple int) Rolling window length. Must be >= 2.
Returns: (series float) Per-bar sigma, floored at 1e-10.
toX(bars, lookback, mode)
Dimensionless horizontal coordinate.
Parameters:
bars (int): (series int) Signed bar distance from the anchor.
lookback (int): (series int) Window length acting as the horizontal unit.
mode (series XScale): (series XScale) Scaling mode.
Returns: (series float) Signed dimensionless x.
toY(price, sigma, lookback, mode)
Dimensionless vertical coordinate.
Parameters:
price (float): (series float) Price. Must be > 0.
sigma (float): (series float) Yang-Zhang sigma. Must be > 1e-10.
lookback (int): (series int) Window length (used by isotropic mode only).
mode (series XScale): (series XScale) Scaling mode.
Returns: (series float) Dimensionless y, or na when inputs are invalid.
moveZScore(dLogPrice, sigma, bars)
Z-score of a log-price move over n bars: dLog / (sigma * sqrt(n)).
In isotropic mode this equals tan(theta) of the same move.
Parameters:
dLogPrice (float): (series float) ln(target) - ln(anchor).
sigma (float): (series float) Per-bar Yang-Zhang sigma. Must be > 1e-10.
bars (int): (series int) Number of bars in the move. Must be > 0.
Returns: (series float) The z-score, or na when inputs are invalid.
triangle(td, anchorPrice, anchorBar, targetPrice, targetBar, sig, lookback, mode)
Right triangle between an anchor and a target, computed entirely
in ICS space. Writes results in place into `td` and returns it.
On invalid inputs every field is set to na, so world X never
receives contaminated numbers.
Parameters:
td (TriangleData): (TriangleData) Output object, updated in place.
anchorPrice (float): (series float) Anchor price (world A). Must be > 0.
anchorBar (int): (series int) Anchor bar_index.
targetPrice (float): (series float) Target price (world A). Must be > 0.
targetBar (int): (series int) Target bar_index. Must differ from anchorBar.
sig (float): (series float) Yang-Zhang sigma. Must be > 1e-10.
lookback (int): (series int) Horizontal unit window.
mode (series XScale): (series XScale) Scaling mode.
Returns: (TriangleData) The same `td`, for chaining.
pinTriangle(td, anchorPrice, anchorBar, extremePrice, bodyPrice, curBar, sig, lookback, mode)
Pin (wick) triangle with three vertices in ICS space:
A = anchor, B = candle extreme, C = candle body edge.
Side BC is the wick. theta = signed angle at A between AB and AC.
Since xB = xC, the shoelace area reduces exactly to
0.5 * |yB - yC| * |dx|.
Parameters:
td (TriangleData): (TriangleData) Output object, updated in place.
anchorPrice (float): (series float) Anchor price (hh or ll). Must be > 0.
anchorBar (int): (series int) Anchor bar_index.
extremePrice (float): (series float) Candle extreme (high or low). Must be > 0.
bodyPrice (float): (series float) Candle body edge. Must be > 0.
curBar (int): (series int) Current bar_index. Must differ from anchorBar.
sig (float): (series float) Yang-Zhang sigma. Must be > 1e-10.
lookback (int): (series int) Horizontal unit window.
mode (series XScale): (series XScale) Scaling mode.
Returns: (TriangleData) The same `td`, for chaining.
zeroTri(td)
Resets a TriangleData to na. Use when the structure is inactive,
so inactive periods never enter moving averages or normalization
as fake zero values.
Parameters:
td (TriangleData): (TriangleData) Object to reset, updated in place.
Returns: (TriangleData) The same `td`, for chaining.
TriangleData
One triangle's measurements in ICS space. All fields dimensionless.
Fields:
theta (series float): Signed hypotenuse angle in degrees; in isotropic mode tan(theta) is the z-score of the move.
dy (series float): Signed Euclidean magnitude of the hypotenuse.
area (series float): Triangle area (>= 0).
centroidY (series float): Vertical centroid of the triangle.
FrozenAnchors
Anchors frozen at a reference bar, plus activity state.
Fields:
hh (series float): Highest high at the freeze bar (world-A price units).
ll (series float): Lowest low at the freeze bar (world-A price units).
mid (series float): Geometric mean sqrt(hh * ll) at the freeze bar.
bar_x (series int): bar_index of the freeze bar.
time_x (series int): time of the freeze bar.
is_active (series bool): Whether the frozen structure is currently active.
릴리즈 노트
v2Updated:
toX(bars, lookback)
Dimensionless horizontal coordinate, sqrt-time scaled.
Parameters:
bars (int): (series int) Signed bar distance from the anchor.
lookback (simple int): (simple int) Window length acting as the horizontal unit.
Returns: (series float) Signed dimensionless x.
toY(price, sigma, lookback)
Dimensionless vertical coordinate.
Parameters:
price (float): (series float) Price. Must be > 0.
sigma (float): (series float) Yang-Zhang sigma. Must be > 1e-10.
lookback (simple int): (simple int) Window length (vertical sqrt normalizer).
Returns: (series float) Dimensionless y, or na when inputs are invalid.
moveZScore(dLogPrice, sigma, bars)
Z-score of a log-price move over n bars: dLog / (sigma * sqrt(n)).
This equals tan(theta) of the same move in ICS space.
Parameters:
dLogPrice (float): (series float) ln(target) - ln(anchor).
sigma (float): (series float) Per-bar Yang-Zhang sigma. Must be > 1e-10.
bars (int): (series int) Number of bars in the move. Must be > 0.
Returns: (series float) The z-score, or na when inputs are invalid.
triangle(td, anchorPrice, anchorBar, targetPrice, targetBar, sig, lookback)
Right triangle between an anchor and a target, computed entirely
in ICS space. Writes results in place into `td` and returns it.
On invalid inputs every field is set to na, so world X never
receives contaminated numbers.
Parameters:
td (TriangleData): (TriangleData) Output object, updated in place.
anchorPrice (float): (series float) Anchor price (world A). Must be > 0.
anchorBar (int): (series int) Anchor bar_index.
targetPrice (float): (series float) Target price (world A). Must be > 0.
targetBar (int): (series int) Target bar_index. Must differ from anchorBar.
sig (float): (series float) Yang-Zhang sigma. Must be > 1e-10.
lookback (simple int): (simple int) Horizontal unit window.
Returns: (TriangleData) The same `td`, for chaining.
pinTriangle(td, anchorPrice, anchorBar, extremePrice, bodyPrice, curBar, sig, lookback)
Pin (wick) triangle with three vertices in ICS space:
A = anchor, B = candle extreme, C = candle body edge.
Side BC is the wick. theta = signed angle at A between AB and AC.
Since xB = xC, the shoelace area reduces exactly to
0.5 * |yB - yC| * |dx|.
Parameters:
td (TriangleData): (TriangleData) Output object, updated in place.
anchorPrice (float): (series float) Anchor price (hh or ll). Must be > 0.
anchorBar (int): (series int) Anchor bar_index.
extremePrice (float): (series float) Candle extreme (high or low). Must be > 0.
bodyPrice (float): (series float) Candle body edge. Must be > 0.
curBar (int): (series int) Current bar_index. Must differ from anchorBar.
sig (float): (series float) Yang-Zhang sigma. Must be > 1e-10.
lookback (simple int): (simple int) Horizontal unit window.
Returns: (TriangleData) The same `td`, for chaining.
TriangleData
One triangle's measurements in ICS space. All fields dimensionless.
Fields:
theta (series float): Signed hypotenuse angle in degrees; tan(theta) is the z-score of the move.
dy (series float): Signed Euclidean magnitude of the hypotenuse.
area (series float): Triangle area (>= 0).
centroidY (series float): Vertical centroid of the triangle.
파인 라이브러리
트레이딩뷰의 진정한 정신에 따라, 작성자는 이 파인 코드를 오픈소스 라이브러리로 게시하여 커뮤니티의 다른 파인 프로그래머들이 재사용할 수 있도록 했습니다. 작성자에게 경의를 표합니다! 이 라이브러리는 개인적으로 사용하거나 다른 오픈소스 게시물에서 사용할 수 있지만, 이 코드의 게시물 내 재사용은 하우스 룰에 따라 규제됩니다.
Measuring markets through Volume Dynamics & Geometric Frameworks.
For invite-only script access, DM on TradingView or via x.com/sabanci_ata
For invite-only script access, DM on TradingView or via x.com/sabanci_ata
면책사항
해당 정보와 게시물은 금융, 투자, 트레이딩 또는 기타 유형의 조언이나 권장 사항으로 간주되지 않으며, 트레이딩뷰에서 제공하거나 보증하는 것이 아닙니다. 자세한 내용은 이용 약관을 참조하세요.
파인 라이브러리
트레이딩뷰의 진정한 정신에 따라, 작성자는 이 파인 코드를 오픈소스 라이브러리로 게시하여 커뮤니티의 다른 파인 프로그래머들이 재사용할 수 있도록 했습니다. 작성자에게 경의를 표합니다! 이 라이브러리는 개인적으로 사용하거나 다른 오픈소스 게시물에서 사용할 수 있지만, 이 코드의 게시물 내 재사용은 하우스 룰에 따라 규제됩니다.
Measuring markets through Volume Dynamics & Geometric Frameworks.
For invite-only script access, DM on TradingView or via x.com/sabanci_ata
For invite-only script access, DM on TradingView or via x.com/sabanci_ata
면책사항
해당 정보와 게시물은 금융, 투자, 트레이딩 또는 기타 유형의 조언이나 권장 사항으로 간주되지 않으며, 트레이딩뷰에서 제공하거나 보증하는 것이 아닙니다. 자세한 내용은 이용 약관을 참조하세요.