PINE LIBRARY
Telah dikemas kini 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.
Nota Keluaran
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.
Perpustakaan Pine
Dalam semangat TradingView sebenar, penulis telah menerbitkan kod Pine ini sebagai perpustakaan sumber terbuka supaya pengaturcara Pine lain dari komuniti kami boleh menggunakannya semula. Sorakan kepada penulis! Anda boleh menggunakan perpustakaan ini secara peribadi atau dalam penerbitan sumber terbuka lain, tetapi penggunaan semula kod ini dalam penerbitan adalah dikawal selia oleh Peraturan Dalaman.
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
Penafian
Maklumat dan penerbitan adalah tidak bertujuan, dan tidak membentuk, nasihat atau cadangan kewangan, pelaburan, dagangan atau jenis lain yang diberikan atau disahkan oleh TradingView. Baca lebih dalam Terma Penggunaan.
Perpustakaan Pine
Dalam semangat TradingView sebenar, penulis telah menerbitkan kod Pine ini sebagai perpustakaan sumber terbuka supaya pengaturcara Pine lain dari komuniti kami boleh menggunakannya semula. Sorakan kepada penulis! Anda boleh menggunakan perpustakaan ini secara peribadi atau dalam penerbitan sumber terbuka lain, tetapi penggunaan semula kod ini dalam penerbitan adalah dikawal selia oleh Peraturan Dalaman.
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
Penafian
Maklumat dan penerbitan adalah tidak bertujuan, dan tidak membentuk, nasihat atau cadangan kewangan, pelaburan, dagangan atau jenis lain yang diberikan atau disahkan oleh TradingView. Baca lebih dalam Terma Penggunaan.