Moment-Based Adaptive DetectionMBAD (Moment-Based Adaptive Detection) : a method applicable to a wide range of purposes, like outlier or novelty detection, that requires building a sensible interval/set of thresholds. Unlike other methods that are static and rely on optimizations that inevitably lead to underfitting/overfitting, it dynamically adapts to your data distribution without any optimizations, MLE, or stuff, and provides a set of data-driven adaptive thresholds, based on closed-form solution with O(n) algo complexity.
1.5 years ago, when I was still living in Versailles at my friend's house not knowing what was gonna happen in my life tomorrow, I made a damn right decision not to give up on one idea and to actually R&D it and see what’s up. It allowed me to create this one.
The Method Explained
I’ve been wandering about z-values, why exactly 6 sigmas, why 95%? Who decided that? Why would you supersede your opinion on data? Based on what? Your ego?
Then I consciously noticed a couple of things:
1) In control theory & anomaly detection, the popular threshold is 3 sigmas (yet nobody can firmly say why xD). If your data is Laplace, 3 sigmas is not enough; you’re gonna catch too many values, so it needs a higher sigma.
2) Yet strangely, the normal distribution has kurtosis of 3, and 6 for Laplace.
3) Kurtosis is a standardized moment, a moment scaled by stdev, so it means "X amount of something measured in stdevs."
4) You generate synthetic data, you check on real data (market data in my case, I am a quant after all), and you see on both that:
lower extension = mean - standard deviation * kurtosis ≈ data minimum
upper extension = mean + standard deviation * kurtosis ≈ data maximum
Why not simply use max/min?
- Lower info gain: We're not using all info available in all data points to estimate max/min; we just pick the current higher and lower values. Lol, it’s the same as dropping exponential smoothing with alpha = 0 on stationary data & calling it a day.
You can’t update the estimates of min and max when new data arrives containing info about the matter. All you can do is just extend min and max horizontally, so you're not using new info arriving inside new data.
- Mixing order and non-order statistics is a bad idea; we're losing integrity and coherence. That's why I don't like the Hurst exponent btw (and yes, I came up with better metrics of my own).
- Max & min are not even true order statistics, unlike a percentile (finding which requires sorting, which requires multiple passes over your data). To find min or max, you just need to do one traversal over your data. Then with or without any weighting, 100th percentile will equal max. So unlike a weighted percentile, you can’t do weighted max. Then while you can always check max and min of a geometric shape, now try to calculate the 56th percentile of a pentagram hehe.
TL;DR max & min are rather topological characteristics of data, just as the difference between starting and ending points. Not much to do with statistics.
Now the second part of the ballet is to work with data asymmetry:
1) Skewness is also scaled by stdev -> so it must represent a shift from the data midrange measured in stdevs -> given asymmetric data, we can include this info in our models. Unlike kurtosis, skewness has a sign, so we add it to both thresholds:
lower extension = mean - standard deviation * kurtosis + standard deviation * skewness
upper extension = mean + standard deviation * kurtosis + standard deviation * skewness
2) Now our method will work with skewed data as well, omg, ain’t it cool?
3) Hold up, but what about 5th and 6th moments (hyperskewness & hyperkurtosis)? They should represent something meaningful as well.
4) Perhaps if extensions represent current estimated extremums, what goes beyond? Limits, beyond which we expect data not to be able to pass given the current underlying process generating the data?
When you extend this logic to higher-order moments, i.e., hyperskewness & hyperkurtosis (5th and 6th moments), they measure asymmetry and shape of distribution tails, not its core as previous moments -> makes no sense to mix 4th and 3rd moments (skewness and kurtosis) with 5th & 6th, so we get:
lower limit = mean - standard deviation * hyperkurtosis + standard deviation * hyperskewness
upper limit = mean + standard deviation * hyperkurtosis + standard deviation * hyperskewness
While extensions model your data’s natural extremums based on current info residing in the data without relying on order statistics, limits model your data's maximum possible and minimum possible values based on current info residing in your data. If a new data point trespasses limits, it means that a significant change in the data-generating process has happened, for sure, not probably—a confirmed structural break.
And finally we use time and volume weighting to include order & process intensity information in our model.
I can't stress it enough: despite the popularity of these non-weighted methods applied in mainstream open-access time series modeling, it doesn’t make ANY sense to use non-weighted calculations on time series data . Time = sequence, it matters. If you reverse your time series horizontally, your means, percentiles, whatever, will stay the same. Basically, your calculations will give the same results on different data. When you do it, you disregard the order of data that does have order naturally. Does it make any sense to you? It also concerns regressions applied on time series as well, because even despite the slope being opposite on your reversed data, the centroid (through which your regression line always comes through) will be the same. It also might concern Fourier (yes, you can do weighted Fourier) and even MA and AR models—might, because I ain’t researched it extensively yet.
I still can’t believe it’s nowhere online in open access. No chance I’m the first one who got it. It’s literally in front of everyone’s eyes for centuries—why no one tells about it?
How to use
That’s easy: can be applied to any, even non-stationary and/or heteroscedastic time series to automatically detect novelties, outliers, anomalies, structural breaks, etc. In terms of quant trading, you can try using extensions for mean reversion trades and limits for emergency exits, for example. The market-making application is kinda obvious as well.
The only parameter the model has is length, and it should NOT be optimized but picked consciously based on the process/system you’re applying it to and based on the task. However, this part is not about sharing info & an open-access instrument with the world. This is about using dem instruments to do actual business, and we can’t talk about it.
∞
Method
CandlesGroup_TypesLibrary "CandlesGroup_Types"
CandlesGroup Type allows you to efficiently store and access properties of all the candles in your chart.
You can easily manipulate large datasets, work with multiple timeframes, or analyze multiple symbols simultaneously. By encapsulating the properties of each candle within a CandlesGroup object, you gain a convenient and organized way to handle complex candlestick patterns and data.
For usage instructions and detailed examples, please refer to the comments and examples provided in the source code.
method init(_self)
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup)
method init(_self, propertyNames)
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup)
propertyNames (string )
method get(_self, key)
get values array from a given property name
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
key (string) : : key name of selected property. Default is "index"
Returns: values array
method size(_self)
get size of values array. By default it equals to current bar_index
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
Returns: size of values array
method push(_self, key, value)
push single value to specific property
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
key (string) : : key name of selected property
value (float) : : property value
Returns: CandlesGroup object
method push(_self, arr)
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup)
arr (float )
method populate(_self, ohlc)
populate ohlc to CandlesGroup
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
ohlc (float ) : : array of ohlc
Returns: CandlesGroup object
method populate(_self, values, propertiesNames)
populate values base on given properties Names
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
values (float ) : : array of property values
propertiesNames (string ) : : an array stores property names. Use as keys to get values
Returns: CandlesGroup object
method populate(_self)
populate values (default setup)
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
Returns: CandlesGroup object
method lookback(arr, bars_lookback)
get property value on previous candles. For current candle, use *.lookback()
Namespace types: float
Parameters:
arr (float ) : : array of selected property values
bars_lookback (int) : : number of candles lookback. 0 = current candle. Default is 0
Returns: single property value
method highest_within_bars(_self, hiSource, start, end, useIndex)
get the highest property value between specific candles
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
hiSource (string) : : key name of selected property
start (int) : : start bar for calculation. Default is candles lookback value from current candle. 'index' value is used if 'useIndex' = true
end (int) : : end bar for calculation. Default is candles lookback value from current candle. 'index' value is used if 'useIndex' = true. Default is 0
useIndex (bool) : : use index instead of lookback value. Default = false
Returns: the highest value within candles
method highest_within_bars(_self, returnWithIndex, hiSource, start, end, useIndex)
get the highest property value and bar index between specific candles
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
returnWithIndex (bool) : : the function only applicable when it is true
hiSource (string) : : key name of selected property
start (int) : : start bar for calculation. Default is candles lookback value from current candle. 'index' value is used if 'useIndex' = true
end (int) : : end bar for calculation. Default is candles lookback value from current candle. 'index' value is used if 'useIndex' = true. Default is 0
useIndex (bool) : : use index instead of lookback value. Default = false
Returns:
method highest_point_within_bars(_self, hiSource, start, end, useIndex)
get a Point object which contains highest property value between specific candles
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
hiSource (string) : : key name of selected property
start (int) : : start bar for calculation. Default is candles lookback value from current candle. 'index' value is used if 'useIndex' = true
end (int) : : end bar for calculation. Default is candles lookback value from current candle. 'index' value is used if 'useIndex' = true. Default is 0
useIndex (bool) : : use index instead of lookback value. Default = false
Returns: Point object contains highest property value
method lowest_within_bars(_self, loSource, start, end, useIndex)
get the lowest property value between specific candles
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
loSource (string) : : key name of selected property
start (int) : : start bar for calculation. Default is candles lookback value from current candle. 'index' value is used if 'useIndex' = true
end (int) : : end bar for calculation. Default is candles lookback value from current candle. 'index' value is used if 'useIndex' = true. Default is 0
useIndex (bool) : : use index instead of lookback value. Default = false
Returns: the lowest value within candles
method lowest_within_bars(_self, returnWithIndex, loSource, start, end, useIndex)
get the lowest property value and bar index between specific candles
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
returnWithIndex (bool) : : the function only applicable when it is true
loSource (string) : : key name of selected property
start (int) : : start bar for calculation. Default is candles lookback value from current candle. 'index' value is used if 'useIndex' = true
end (int) : : end bar for calculation. Default is candles lookback value from current candle. 'index' value is used if 'useIndex' = true. Default is 0
useIndex (bool) : : use index instead of lookback value. Default = false
Returns:
method lowest_point_within_bars(_self, loSource, start, end, useIndex)
get a Point object which contains lowest property value between specific candles
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
loSource (string) : : key name of selected property
start (int) : : start bar for calculation. Default is candles lookback value from current candle. 'index' value is used if 'useIndex' = true
end (int) : : end bar for calculation. Default is candles lookback value from current candle. 'index' value is used if 'useIndex' = true. Default is 0
useIndex (bool) : : use index instead of lookback value. Default = false
Returns: Point object contains lowest property value
method time2bar(_self, t)
Convert UNIX time to bar index of active chart
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
t (int) : : UNIX time
Returns: bar index
method time2bar(_self, timezone, YYYY, MMM, DD, hh, mm, ss)
Convert timestamp to bar index of active chart. User defined timezone required
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
timezone (string) : : User defined timezone
YYYY (int) : : Year
MMM (int) : : Month
DD (int) : : Day
hh (int) : : Hour. Default is 0
mm (int) : : Minute. Default is 0
ss (int) : : Second. Default is 0
Returns: bar index
method time2bar(_self, YYYY, MMM, DD, hh, mm, ss)
Convert timestamp to bar index of active chart
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
YYYY (int) : : Year
MMM (int) : : Month
DD (int) : : Day
hh (int) : : Hour. Default is 0
mm (int) : : Minute. Default is 0
ss (int) : : Second. Default is 0
Returns: bar index
method get_prop_from_time(_self, key, t)
get single property value from UNIX time
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
key (string) : : key name of selected property
t (int) : : UNIX time
Returns: single property value
method get_prop_from_time(_self, key, timezone, YYYY, MMM, DD, hh, mm, ss)
get single property value from timestamp. User defined timezone required
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
key (string) : : key name of selected property
timezone (string) : : User defined timezone
YYYY (int) : : Year
MMM (int) : : Month
DD (int) : : Day
hh (int) : : Hour. Default is 0
mm (int) : : Minute. Default is 0
ss (int) : : Second. Default is 0
Returns: single property value
method get_prop_from_time(_self, key, YYYY, MMM, DD, hh, mm, ss)
get single property value from timestamp
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
key (string) : : key name of selected property
YYYY (int) : : Year
MMM (int) : : Month
DD (int) : : Day
hh (int) : : Hour. Default is 0
mm (int) : : Minute. Default is 0
ss (int) : : Second. Default is 0
Returns: single property value
method bar2time(_self, index)
Convert bar index of active chart to UNIX time
Namespace types: CandlesGroup
Parameters:
_self (CandlesGroup) : : CandlesGroup object
index (int) : : bar index
Returns: UNIX time
Point
A point on chart
Fields:
price (series float) : : price value
bar (series int) : : bar index
bartime (series int) : : time in UNIX format of bar
Property
Property object which contains values of all candles
Fields:
name (series string) : : name of property
values (float ) : : an array stores values of all candles. Size of array = bar_index
CandlesGroup
Candles Group object which contains properties of all candles
Fields:
propertyNames (string ) : : an array stores property names. Use as keys to get values
properties (Property ) : : array of Property objects
RGB Color Codes Chart█ OVERVIEW
This indicator is an educational indicator to make pine coders easier to input color code.
Color code displayed either in hex or rgb code or both.
█ INSPIRATIONS
RGB Color Codes Chart
Table Color For Pairing Black And White
█ FEATURES
Hover table cell to see all properties of color such as Hex code and RGB code via tooltip.
Cell can be show either Full, HEX, RGB, R, G, B or na.
█ LIMITATION
This code does not consider usage of color.new()
█ CONSIDERATION
Code consideration to be used such as color.r(), color.g(), color.b() and color.rgb()
█ EXAMPLE OF USAGE / EXPLAINATION
Regression Channel Alternative MTF V2█ OVERVIEW
This indicator is a predecessor to Regression Channel Alternative MTF , which is coded based on latest update of type, object and method.
█ IMPORTANT NOTES
This indicator is NOT true Multi Timeframe (MTF) but considered as Alternative MTF which calculate 100 bars for Primary MTF, can be refer from provided line helper.
The timeframe scenarios are defined based on Position, Swing and Intraday Trader.
Suppported Timeframe : W, D, 60, 15, 5 and 1.
Channel drawn based on regression calculation.
Angle channel is NOT supported.
█ INSPIRATIONS
These timeframe scenarios are defined based on Harmonic Trading : Volume Three written by Scott M Carney.
By applying channel on each timeframe, MW or ABCD patterns can be easily identified manually.
This can also be applied on other chart patterns.
█ CREDITS
Scott M Carney, Harmonic Trading : Volume Three (Reaction vs. Reversal)
█ TIMEFRAME EXPLAINED
Higher / Distal : The (next) longer or larger comparative timeframe after primary pattern has been identified.
Primary / Clear : Timeframe that possess the clearest pattern structure.
Lower / Proximate : The (next) shorter timeframe after primary pattern has been identified.
Lowest : Check primary timeframe as main reference.
█ FEATURES
Color is determined by trend or timeframe.
Some color is depends on chart contrast color.
Color is determined by trend or timeframe.
█ EXAMPLE OF USAGE / EXPLAINATION
Zigzag Array ExperimentalThis is experimental script for zigzag which uses type, method and array. Not recommend for actual usage, for pine script study maybe useful.
In this experiment, I use type as coded below. It seems have limitation as specially when push as array. As Trading View recommendation, pushing float and int into array especially for type not guarantee to work. I agree with that. Preferred to push array as line or label especially for types.
// @type Used for point especially for array
// @field x int value for bar_index
// @field y float value for price
// @field sty label style
// @field col color for text label
// @field str high or low string
type point
int x = na
float y = na
string sty = na
color col = na
string str = na
I simulate the arrays as below.
var dirLine = array.new()
var dirLabel = array.new()
var dirPoint = array.new()
....
dirPoint.unshift(zigzag.createPoint(0))
dirLabel.unshift(zigzag.createLabel(fontSize, 0, true))
dirLine.unshift(zigzag.createLine(width, switchLine, 0, true))
Here are some results.
RSI Divergence Method█ OVERVIEW
This is a divergence indicator based on Relative Strength Index (RSI).
My attempt to make this indicator updated based on latest pine script features such as type, object and method.
█ FEATURES
1. Color of plot and label is based on contrast color of chart background. Able to customize color from style menu.
2. Big divergence (Regular Divergence) is based on lime / red color.
3. Small divergence (Hidden Divergence) is based on contrast color of chart background.
█ EXAMPLES / USAGES
Vector2FunctionClipLibrary "Vector2FunctionClip"
Sutherland-Hodgman polygon clipping algorithm.
reference:
.
rosettacode.org
.
clip(source, reference)
Perform Clip operation on a vector with another.
Parameters:
source : array . Source polygon to be clipped.
reference : array . Reference polygon to clip source.
Returns: array.
Vector2ArrayLibrary "Vector2Array"
functions to handle vector2 Array operations.
.
references:
docs.unity3d.com
gist.github.com
github.com
gist.github.com
gist.github.com
gist.github.com
.
from(source, prop_sep, vect_sep)
Generate array of vector2 from string.
Parameters:
source : string Source string of the vectors.
prop_sep : string Separator character of the vector properties (x`,`y).
vect_sep : string Separator character of the vectors ((x,y)`;`(x,y)).
Returns: array.
max(vectors)
Combination of the highest elements in column of a array of vectors.
Parameters:
vectors : array, Array of Vector2 objects.
Returns: Vector2.Vector2, Vector2 object.
-> usage:
`a = Vector2.from(1.0) , b = Vector2.from(2.0), c = Vector2.from(3.0), d = max(array.from(a, b, c)) , plot(d.x)`
min(vectors)
Combination of the lowest elements in column of a array of vectors.
Parameters:
vectors : array, Array of Vector2 objects.
Returns: Vector2.Vector2, Vector2 object.
-> usage:
`a = Vector2.from(1.0) , b = Vector2.from(2.0), c = Vector2.from(3.0), d = min(array.from(a, b, c)) , plot(d.x)`
sum(vectors)
Total sum of all vectors.
Parameters:
vectors : array, ID of the vector2 array.
Returns: Vector2.Vector2, vector2 object.
-> usage:
`a = Vector2.from(1.0) , b = Vector2.from(2.0), c = Vector2.from(3.0), d = sum(array.from(a, b, c)) , plot(d.x)`
center(vectors)
Finds the vector center of the array.
Parameters:
vectors : array, ID of the vector2 array.
Returns: Vector2.Vector2, vector2 object.
-> usage:
`a = Vector2.from(1.0) , b = Vector2.from(2.0), c = Vector2.from(3.0), d = center(array.from(a, b, c)) , plot(d.x)`
rotate(vectors, center, degree)
Rotate Array vectors around origin vector by a angle.
Parameters:
vectors : array, ID of the vector2 array.
center : Vector2.Vector2 , Vector2 object. Center of the rotation.
degree : float , Angle value.
Returns: rotated points array.
-> usage:
`a = Vector2.from(1.0) , b = Vector2.from(2.0), c = Vector2.from(3.0), d = rotate(array.from(a, b, c), b, 45.0)`
scale(vectors, center, rate)
Scale Array vectors based on a origin vector perspective.
Parameters:
vectors : array, ID of the vector2 array.
center : Vector2.Vector2 , Vector2 object. Origin center of the transformation.
rate : float , Rate to apply transformation.
Returns: rotated points array.
-> usage:
`a = Vector2.from(1.0) , b = Vector2.from(2.0), c = Vector2.from(3.0), d = scale(array.from(a, b, c), b, 1.25)`
move(vectors, center, rate)
Move Array vectors by a rate of the distance to center position (LERP).
Parameters:
vectors : array, ID of the vector2 array.
center
rate
Returns: Moved points array.
-> usage:
`a = Vector2.from(1.0) , b = Vector2.from(2.0), c = Vector2.from(3.0), d = move(array.from(a, b, c), b, 1.25)`
to_string(id, separator)
Reads a array of vectors into a string, of the form ` `.
Parameters:
id : array, ID of the vector2 array.
separator : string separator for cell splitting.
Returns: string Translated complex array into string.
-> usage:
`a = Vector2.from(1.0) , b = Vector2.from(2.0), c = Vector2.from(3.0), d = to_string(array.from(a, b, c))`
to_string(id, format, separator)
Reads a array of vectors into a string, of the form ` `.
Parameters:
id : array, ID of the vector2 array.
format : string , Format to apply transformation.
separator : string , Separator for cell splitting.
Returns: string Translated complex array into string.
-> usage:
`a = Vector2.from(1.234) , b = Vector2.from(2.23), c = Vector2.from(3.1234), d = to_string(array.from(a, b, c), "#.##")`
Segment2Library "Segment2"
Structure representation of a directed straight line in two dimensions from origin to target vectors.
.
reference:
graphics.stanford.edu
.
new(origin, target)
Generate a new segment.
Parameters:
origin : Vector2 . Origin of the segment.
target : Vector2 . Target of the segment.
Returns: Segment2.
new(origin_x, origin_y, target_x, target_y)
Generate a new segment.
Parameters:
origin_x : float . Origin of the segment x coordinate.
origin_y : float . Origin of the segment y coordinate.
target_x : float . Target of the segment x coordinate.
target_y : float . Target of the segment y coordinate.
Returns: Segment2.
copy(this)
Copy a segment.
Parameters:
this : Vector2 . Segment to copy.
Returns: Segment2.
length_squared(this)
Squared length of the normalized segment vector. For comparing vectors this is computationaly lighter.
Parameters:
this : Segment2 . Sorce segment.
Returns: float.
length(this)
Length of the normalized segment vector.
Parameters:
this : Segment2 . Sorce segment.
Returns: float.
opposite(this)
Reverse the direction of the segment.
Parameters:
this : Segment2 . Source segment.
Returns: Segment2.
is_degenerate(this)
Segment is degenerate when origin and target are equal.
Parameters:
this : Segment2 . Source segment.
Returns: bool.
is_horizontal(this)
Segment is horizontal?.
Parameters:
this : Segment2 . Source segment.
Returns: bool.
is_horizontal(this, precision)
Segment is horizontal?.
Parameters:
this : Segment2 . Source segment.
precision : float . Limit of precision.
Returns: bool.
is_vertical(this)
Segment is vertical?.
Parameters:
this : Segment2 . Source segment.
Returns: bool.
is_vertical(this, precision)
Segment is vertical?.
Parameters:
this : Segment2 . Source segment.
precision : float . Limit of precision.
Returns: bool.
equals(this, other)
Tests two segments for equality (share same origin and target).
Parameters:
this : Segment2 . Source segment.
other : Segment2 . Target segment.
Returns: bool.
nearest_to_point(this, point)
Find the nearest point in a segment to another point.
Parameters:
this : Segment2 . Source segment.
point : Vector2 . Point to aproximate.
Returns: Vector2.
intersection(this, other)
Find the intersection vector of 2 lines.
Parameters:
this : Segment2 . Segment A.
other : Segment2 . Segment B.
Returns: Vector2.Vector2 Object.
extend(this, at_origin, at_target)
Extend a segment by the percent ratio provided.
Parameters:
this : Segment2 . Source segment.
at_origin : float . Percent ratio to extend at origin vector.
at_target : float . Percent ratio to extend at target vector.
Returns: Segment2.
to_string(this)
Translate segment to string format `( (x,y), (x,y) )`.
Parameters:
this : Segment2 . Source segment.
Returns: string.
to_string(this, format)
Translate segment to string format `((x,y), (x,y))`.
Parameters:
this : Segment2 . Source segment.
format : string . Format string to apply.
Returns: string.
to_array(this)
Translate segment to array format.
Parameters:
this : Segment2 . Source segment.
Returns: array.
Vector2DrawQuadLibrary "Vector2DrawQuad"
functions to handle vector2 Quad drawing operations.
new(a, b, c, d, xloc, bg_color, line_color, line_style, line_width)
Draws a quadrilateral with background fill.
Parameters:
a : v2 . Vector2 object, in the form `(x, y)`.
b : v2 . Vector2 object, in the form `(x, y)`.
c : v2 . Vector2 object, in the form `(x, y)`.
d : v2 . Vector2 object, in the form `(x, y)`.
xloc : string . Type of axis unit, bar_index or time.
bg_color : color . Color of the background.
line_color : color . Color of the line.
line_style : string . Style of the line.
line_width : int . Width of the line.
Returns: Quad object.
copy(this)
Copy a existing quad object.
Parameters:
this : Quad . Source quad.
Returns: Quad.
set_position_a(this, x, y)
Set the position of corner `a` (modifies source quad).
Parameters:
this : Quad . Source quad.
x : int . Value at the x axis.
y : float . Value at the y axis.
Returns: Source Quad.
set_position_a(this, position)
Set the position of corner `a` (modifies source quad).
Parameters:
this : Quad . Source quad.
position : Vector2 . New position.
Returns: Source Quad.
set_position_b(this, x, y)
Set the position of corner `b` (modifies source quad).
Parameters:
this : Quad . Source quad.
x : int . Value at the x axis.
y : float . Value at the y axis.
Returns: Source Quad.
set_position_b(this, position)
Set the position of corner `b` (modifies source quad).
Parameters:
this : Quad . Source quad.
position : Vector2 . New position.
Returns: Source Quad.
set_position_c(this, x, y)
Set the position of corner `c` (modifies source quad).
Parameters:
this : Quad . Source quad.
x : int . Value at the x axis.
y : float . Value at the y axis.
Returns: Source Quad.
set_position_c(this, position)
Set the position of corner `c` (modifies source quad).
Parameters:
this : Quad . Source quad.
position : Vector2 . New position.
Returns: Source Quad.
set_position_d(this, x, y)
Set the position of corner `d` (modifies source quad).
Parameters:
this : Quad . Source quad.
x : int . Value at the x axis.
y : float . Value at the y axis.
Returns: Source Quad.
set_position_d(this, position)
Set the position of corner `d` (modifies source quad).
Parameters:
this : Quad . Source quad.
position : Vector2 . New position.
Returns: Source Quad.
set_style(this, bg_color, line_color, line_style, line_width)
Update quad style options (modifies Source quad).
Parameters:
this : Quad . Source quad.
bg_color : color . Color of the background.
line_color : color . Color of the line.
line_style : string . Style of the line.
line_width : int . Width of the line.
Returns: Source Quad.
set_bg_color(this, bg_color)
Update quad style options (modifies Source quad).
Parameters:
this : Quad . Source quad.
bg_color : color . Color of the background.
Returns: Source Quad.
set_line_color(this, line_color)
Update quad style options (modifies Source quad).
Parameters:
this : Quad . Source quad.
line_color : color . Color of the line.
Returns: Source Quad.
set_line_style(this, line_style)
Update quad style options (modifies Source quad).
Parameters:
this : Quad . Source quad.
line_style : string . Style of the line.
Returns: Source Quad.
set_line_width(this, line_width)
Update quad style options (modifies Source quad).
Parameters:
this : Quad . Source quad.
line_width : int . Width of the line.
Returns: Source Quad.
move(this, x, y)
Move quad by provided amount (modifies source quad).
Parameters:
this : Quad . Source quad.
x : float . Amount to move the vertices of the quad in the x axis.
y : float . Amount to move the vertices of the quad in the y axis.
Returns: Source Quad.
move(this, amount)
Move quad by provided amount (modifies source quad).
Parameters:
this : Quad . Source quad.
amount : Vector2 . Amount to move the vertices of the quad in the x and y axis.
Returns: Source Quad.
rotate_around(this, center, angle)
Rotate source quad around a center (modifies source quad).
Parameters:
this : Quad . Source quad.
center : Vector2 . Center coordinates of the rotation.
angle : float . Value of angle in degrees.
Returns: Source Quad.
rotate_around(this, center_x, center_y, angle)
Rotate source quad around a center (modifies source quad).
Parameters:
this : Quad . Source quad.
center_x : int . Center coordinates of the rotation.
center_y : float . Center coordinates of the rotation.
angle : float . Value of angle in degrees.
Returns: Source Quad.
Vector2DrawTriangleLibrary "Vector2DrawTriangle"
Functions to draw a triangle and manipulate its properties.
new(a, b, c, xloc, bg_color, line_color, line_style, line_width)
Draws a triangle with background fill using line prototype.
Parameters:
a : v2 . Vector2 object, in the form `(x, y)`.
b : v2 . Vector2 object, in the form `(x, y)`.
c : v2 . Vector2 object, in the form `(x, y)`.
xloc : string . Type of axis unit, bar_index or time.
bg_color : color . Color of the background.
line_color : color . Color of the line.
line_style : string . Style of the line.
line_width : int . Width of the line.
Returns: Triangle object.
copy(this)
Copy a existing triangle object.
Parameters:
this : Triangle . Source triangle.
Returns: Triangle.
set_position_a(this, x, y)
Set the position of corner `a` (modifies source triangle).
Parameters:
this : Triangle . Source triangle.
x : int . Value at the x axis.
y : float . Value at the y axis.
Returns: Source Triangle.
set_position_a(this, position)
Set the position of corner `a` (modifies source triangle).
Parameters:
this : Triangle . Source triangle.
position : Vector2 . New position.
Returns: Source Triangle.
set_position_b(this, x, y)
Set the position of corner `b` (modifies source triangle).
Parameters:
this : Triangle . Source triangle.
x : int . Value at the x axis.
y : float . Value at the y axis.
Returns: Source Triangle.
set_position_b(this, position)
Set the position of corner `b` (modifies source triangle).
Parameters:
this : Triangle . Source triangle.
position : Vector2 . New position.
Returns: Source Triangle.
set_position_c(this, x, y)
Set the position of corner `c` (modifies source triangle).
Parameters:
this : Triangle . Source triangle.
x : int . Value at the x axis.
y : float . Value at the y axis.
Returns: Source Triangle.
set_position_c(this, position)
Set the position of corner `c` (modifies source triangle).
Parameters:
this : Triangle . Source triangle.
position : Vector2 . New position.
Returns: Source Triangle.
set_style(this, bg_color, line_color, line_style, line_width)
Update triangle style options (modifies Source triangle).
Parameters:
this : Triangle . Source triangle.
bg_color : color . Color of the background.
line_color : color . Color of the line.
line_style : string . Style of the line.
line_width : int . Width of the line.
Returns: Source Triangle.
set_bg_color(this, bg_color)
Update triangle style options (modifies Source triangle).
Parameters:
this : Triangle . Source triangle.
bg_color : color . Color of the background.
Returns: Source Triangle.
set_line_color(this, line_color)
Update triangle style options (modifies Source triangle).
Parameters:
this : Triangle . Source triangle.
line_color : color . Color of the line.
Returns: Source Triangle.
set_line_style(this, line_style)
Update triangle style options (modifies Source triangle).
Parameters:
this : Triangle . Source triangle.
line_style : string . Style of the line.
Returns: Source Triangle.
set_line_width(this, line_width)
Update triangle style options (modifies Source triangle).
Parameters:
this : Triangle . Source triangle.
line_width : int . Width of the line.
Returns: Source Triangle.
move(this, x, y)
Move triangle by provided amount (modifies source triangle).
Parameters:
this : Triangle . Source triangle.
x : float . Amount to move the vertices of the triangle in the x axis.
y : float . Amount to move the vertices of the triangle in the y axis.
Returns: Source Triangle.
move(this, amount)
Move triangle by provided amount (modifies source triangle).
Parameters:
this : Triangle . Source triangle.
amount : Vector2 . Amount to move the vertices of the triangle in the x and y axis.
Returns: Source Triangle.
rotate_around(this, center, angle)
Rotate source triangle around a center (modifies source triangle).
Parameters:
this : Triangle . Source triangle.
center : Vector2 . Center coordinates of the rotation.
angle : float . Value of angle in degrees.
Returns: Source Triangle.
rotate_around(this, center_x, center_y, angle)
Rotate source triangle around a center (modifies source triangle).
Parameters:
this : Triangle . Source triangle.
center_x : int . Center coordinates of the rotation.
center_y : float . Center coordinates of the rotation.
angle : float . Value of angle in degrees.
Returns: Source Triangle.
Vector2Library "Vector2"
Representation of two dimensional vectors or points.
This structure is used to represent positions in two dimensional space or vectors,
for example in spacial coordinates in 2D space.
~~~
references:
docs.unity3d.com
gist.github.com
github.com
gist.github.com
gist.github.com
gist.github.com
~~~
new(x, y)
Create a new Vector2 object.
Parameters:
x : float . The x value of the vector, default=0.
y : float . The y value of the vector, default=0.
Returns: Vector2. Vector2 object.
-> usage:
`unitx = Vector2.new(1.0) , plot(unitx.x)`
from(value)
Assigns value to a new vector `x,y` elements.
Parameters:
value : float, x and y value of the vector.
Returns: Vector2. Vector2 object.
-> usage:
`one = Vector2.from(1.0), plot(one.x)`
from(value, element_sep, open_par, close_par)
Assigns value to a new vector `x,y` elements.
Parameters:
value : string . The `x` and `y` value of the vector in a `x,y` or `(x,y)` format, spaces and parentesis will be removed automatically.
element_sep : string . Element separator character, default=`,`.
open_par : string . Open parentesis character, default=`(`.
close_par : string . Close parentesis character, default=`)`.
Returns: Vector2. Vector2 object.
-> usage:
`one = Vector2.from("1.0,2"), plot(one.x)`
copy(this)
Creates a deep copy of a vector.
Parameters:
this : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = Vector2.new(1.0) , b = a.copy() , plot(b.x)`
down()
Vector in the form `(0, -1)`.
Returns: Vector2. Vector2 object.
left()
Vector in the form `(-1, 0)`.
Returns: Vector2. Vector2 object.
right()
Vector in the form `(1, 0)`.
Returns: Vector2. Vector2 object.
up()
Vector in the form `(0, 1)`.
Returns: Vector2. Vector2 object.
one()
Vector in the form `(1, 1)`.
Returns: Vector2. Vector2 object.
zero()
Vector in the form `(0, 0)`.
Returns: Vector2. Vector2 object.
minus_one()
Vector in the form `(-1, -1)`.
Returns: Vector2. Vector2 object.
unit_x()
Vector in the form `(1, 0)`.
Returns: Vector2. Vector2 object.
unit_y()
Vector in the form `(0, 1)`.
Returns: Vector2. Vector2 object.
nan()
Vector in the form `(float(na), float(na))`.
Returns: Vector2. Vector2 object.
xy(this)
Return the values of `x` and `y` as a tuple.
Parameters:
this : Vector2 . Vector2 object.
Returns: .
-> usage:
`a = Vector2.new(1.0, 1.0) , = a.xy() , plot(ax)`
length_squared(this)
Length of vector `a` in the form. `a.x^2 + a.y^2`, for comparing vectors this is computationaly lighter.
Parameters:
this : Vector2 . Vector2 object.
Returns: float. Squared length of vector.
-> usage:
`a = Vector2.new(1.0, 1.0) , plot(a.length_squared())`
length(this)
Magnitude of vector `a` in the form. `sqrt(a.x^2 + a.y^2)`
Parameters:
this : Vector2 . Vector2 object.
Returns: float. Length of vector.
-> usage:
`a = Vector2.new(1.0, 1.0) , plot(a.length())`
normalize(a)
Vector normalized with a magnitude of 1, in the form. `a / length(a)`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = normalize(Vector2.new(3.0, 2.0)) , plot(a.y)`
isNA(this)
Checks if any of the components is `na`.
Parameters:
this : Vector2 . Vector2 object.
Returns: bool.
usage:
p = Vector2.new(1.0, na) , plot(isNA(p)?1:0)
add(a, b)
Adds vector `b` to `a`, in the form `(a.x + b.x, a.y + b.y)`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = one() , b = one() , c = add(a, b) , plot(c.x)`
add(a, b)
Adds vector `b` to `a`, in the form `(a.x + b, a.y + b)`.
Parameters:
a : Vector2 . Vector2 object.
b : float . Value.
Returns: Vector2. Vector2 object.
-> usage:
`a = one() , b = 1.0 , c = add(a, b) , plot(c.x)`
add(a, b)
Adds vector `b` to `a`, in the form `(a + b.x, a + b.y)`.
Parameters:
a : float . Value.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = 1.0 , b = one() , c = add(a, b) , plot(c.x)`
subtract(a, b)
Subtract vector `b` from `a`, in the form `(a.x - b.x, a.y - b.y)`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = one() , b = one() , c = subtract(a, b) , plot(c.x)`
subtract(a, b)
Subtract vector `b` from `a`, in the form `(a.x - b, a.y - b)`.
Parameters:
a : Vector2 . vector2 object.
b : float . Value.
Returns: Vector2. Vector2 object.
-> usage:
`a = one() , b = 1.0 , c = subtract(a, b) , plot(c.x)`
subtract(a, b)
Subtract vector `b` from `a`, in the form `(a - b.x, a - b.y)`.
Parameters:
a : float . value.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = 1.0 , b = one() , c = subtract(a, b) , plot(c.x)`
multiply(a, b)
Multiply vector `a` with `b`, in the form `(a.x * b.x, a.y * b.y)`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = one() , b = one() , c = multiply(a, b) , plot(c.x)`
multiply(a, b)
Multiply vector `a` with `b`, in the form `(a.x * b, a.y * b)`.
Parameters:
a : Vector2 . Vector2 object.
b : float . Value.
Returns: Vector2. Vector2 object.
-> usage:
`a = one() , b = 1.0 , c = multiply(a, b) , plot(c.x)`
multiply(a, b)
Multiply vector `a` with `b`, in the form `(a * b.x, a * b.y)`.
Parameters:
a : float . Value.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = 1.0 , b = one() , c = multiply(a, b) , plot(c.x)`
divide(a, b)
Divide vector `a` with `b`, in the form `(a.x / b.x, a.y / b.y)`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(3.0) , b = from(2.0) , c = divide(a, b) , plot(c.x)`
divide(a, b)
Divide vector `a` with value `b`, in the form `(a.x / b, a.y / b)`.
Parameters:
a : Vector2 . Vector2 object.
b : float . Value.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(3.0) , b = 2.0 , c = divide(a, b) , plot(c.x)`
divide(a, b)
Divide value `a` with vector `b`, in the form `(a / b.x, a / b.y)`.
Parameters:
a : float . Value.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = 3.0 , b = from(2.0) , c = divide(a, b) , plot(c.x)`
negate(a)
Negative of vector `a`, in the form `(-a.x, -a.y)`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(3.0) , b = a.negate , plot(b.x)`
pow(a, b)
Raise vector `a` with exponent vector `b`, in the form `(a.x ^ b.x, a.y ^ b.y)`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(3.0) , b = from(2.0) , c = pow(a, b) , plot(c.x)`
pow(a, b)
Raise vector `a` with value `b`, in the form `(a.x ^ b, a.y ^ b)`.
Parameters:
a : Vector2 . Vector2 object.
b : float . Value.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(3.0) , b = 2.0 , c = pow(a, b) , plot(c.x)`
pow(a, b)
Raise value `a` with vector `b`, in the form `(a ^ b.x, a ^ b.y)`.
Parameters:
a : float . Value.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = 3.0 , b = from(2.0) , c = pow(a, b) , plot(c.x)`
sqrt(a)
Square root of the elements in a vector.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(3.0) , b = sqrt(a) , plot(b.x)`
abs(a)
Absolute properties of the vector.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(-3.0) , b = abs(a) , plot(b.x)`
min(a)
Lowest element of a vector.
Parameters:
a : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = min(a) , plot(b)`
max(a)
Highest element of a vector.
Parameters:
a : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = max(a) , plot(b)`
vmax(a, b)
Highest elements of two vectors.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 2.0) , b = new(2.0, 3.0) , c = vmax(a, b) , plot(c.x)`
vmax(a, b, c)
Highest elements of three vectors.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
c : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 2.0) , b = new(2.0, 3.0) , c = new(1.5, 4.5) , d = vmax(a, b, c) , plot(d.x)`
vmin(a, b)
Lowest elements of two vectors.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 2.0) , b = new(2.0, 3.0) , c = vmin(a, b) , plot(c.x)`
vmin(a, b, c)
Lowest elements of three vectors.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
c : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 2.0) , b = new(2.0, 3.0) , c = new(1.5, 4.5) , d = vmin(a, b, c) , plot(d.x)`
perp(a)
Perpendicular Vector of `a`, in the form `(a.y, -a.x)`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = perp(a) , plot(b.x)`
floor(a)
Compute the floor of vector `a`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = floor(a) , plot(b.x)`
ceil(a)
Ceils vector `a`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = ceil(a) , plot(b.x)`
ceil(a, digits)
Ceils vector `a`.
Parameters:
a : Vector2 . Vector2 object.
digits : int . Digits to use as ceiling.
Returns: Vector2. Vector2 object.
round(a)
Round of vector elements.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = round(a) , plot(b.x)`
round(a, precision)
Round of vector elements.
Parameters:
a : Vector2 . Vector2 object.
precision : int . Number of digits to round vector "a" elements.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(0.123456, 1.234567) , b = round(a, 2) , plot(b.x)`
fractional(a)
Compute the fractional part of the elements from vector `a`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.123456, 1.23456) , b = fractional(a) , plot(b.x)`
dot_product(a, b)
dot_product product of 2 vectors, in the form `a.x * b.x + a.y * b.y.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = dot_product(a, b) , plot(c)`
cross_product(a, b)
cross product of 2 vectors, in the form `a.x * b.y - a.y * b.x`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = cross_product(a, b) , plot(c)`
equals(a, b)
Compares two vectors
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: bool. Representing the equality.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = equals(a, b) ? 1 : 0 , plot(c)`
sin(a)
Compute the sine of argument vector `a`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = sin(a) , plot(b.x)`
cos(a)
Compute the cosine of argument vector `a`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = cos(a) , plot(b.x)`
tan(a)
Compute the tangent of argument vector `a`.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = tan(a) , plot(b.x)`
atan2(x, y)
Approximation to atan2 calculation, arc tangent of `y/x` in the range (-pi,pi) radians.
Parameters:
x : float . The x value of the vector.
y : float . The y value of the vector.
Returns: float. Value with angle in radians. (negative if quadrante 3 or 4)
-> usage:
`a = new(3.0, 1.5) , b = atan2(a.x, a.y) , plot(b)`
atan2(a)
Approximation to atan2 calculation, arc tangent of `y/x` in the range (-pi,pi) radians.
Parameters:
a : Vector2 . Vector2 object.
Returns: float, value with angle in radians. (negative if quadrante 3 or 4)
-> usage:
`a = new(3.0, 1.5) , b = atan2(a) , plot(b)`
distance(a, b)
Distance between vector `a` and `b`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = distance(a, b) , plot(c)`
rescale(a, length)
Rescale a vector to a new magnitude.
Parameters:
a : Vector2 . Vector2 object.
length : float . Magnitude.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = 2.0 , c = rescale(a, b) , plot(c.x)`
rotate(a, radians)
Rotates vector by a angle.
Parameters:
a : Vector2 . Vector2 object.
radians : float . Angle value in radians.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = 2.0 , c = rotate(a, b) , plot(c.x)`
rotate_degree(a, degree)
Rotates vector by a angle.
Parameters:
a : Vector2 . Vector2 object.
degree : float . Angle value in degrees.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = 45.0 , c = rotate_degree(a, b) , plot(c.x)`
rotate_around(this, center, angle)
Rotates vector `target` around `origin` by angle value.
Parameters:
this
center : Vector2 . Vector2 object.
angle : float . Angle value in degrees.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = rotate_around(a, b, 45.0) , plot(c.x)`
perpendicular_distance(a, b, c)
Distance from point `a` to line between `b` and `c`.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
c : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(1.5, 2.6) , b = from(1.0) , c = from(3.0) , d = perpendicular_distance(a, b, c) , plot(d.x)`
project(a, axis)
Project a vector onto another.
Parameters:
a : Vector2 . Vector2 object.
axis : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = project(a, b) , plot(c.x)`
projectN(a, axis)
Project a vector onto a vector of unit length.
Parameters:
a : Vector2 . Vector2 object.
axis : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = projectN(a, b) , plot(c.x)`
reflect(a, axis)
Reflect a vector on another.
Parameters:
a : Vector2 . Vector2 object.
axis
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = reflect(a, b) , plot(c.x)`
reflectN(a, axis)
Reflect a vector to a arbitrary axis.
Parameters:
a : Vector2 . Vector2 object.
axis
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = reflectN(a, b) , plot(c.x)`
angle(a)
Angle in radians of a vector.
Parameters:
a : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = angle(a) , plot(b)`
angle_unsigned(a, b)
unsigned degree angle between 0 and +180 by given two vectors.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = angle_unsigned(a, b) , plot(c)`
angle_signed(a, b)
Signed degree angle between -180 and +180 by given two vectors.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = angle_signed(a, b) , plot(c)`
angle_360(a, b)
Degree angle between 0 and 360 by given two vectors
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = angle_360(a, b) , plot(c)`
clamp(a, min, max)
Restricts a vector between a min and max value.
Parameters:
a : Vector2 . Vector2 object.
min
max
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = from(2.5) , d = clamp(a, b, c) , plot(d.x)`
clamp(a, min, max)
Restricts a vector between a min and max value.
Parameters:
a : Vector2 . Vector2 object.
min : float . Lower boundary value.
max : float . Higher boundary value.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = clamp(a, 2.0, 2.5) , plot(b.x)`
lerp(a, b, rate)
Linearly interpolates between vectors a and b by rate.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
rate : float . Value between (a:-infinity -> b:1.0), negative values will move away from b.
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = lerp(a, b, 0.5) , plot(c.x)`
herp(a, b, rate)
Hermite curve interpolation between vectors a and b by rate.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
rate : Vector2 . Vector2 object. Value between (a:0 > 1:b).
Returns: Vector2. Vector2 object.
-> usage:
`a = new(3.0, 1.5) , b = from(2.0) , c = from(2.5) , d = herp(a, b, c) , plot(d.x)`
transform(position, mat)
Transform a vector by the given matrix.
Parameters:
position : Vector2 . Source vector.
mat : M32 . Transformation matrix
Returns: Vector2. Transformed vector.
transform(position, mat)
Transform a vector by the given matrix.
Parameters:
position : Vector2 . Source vector.
mat : M44 . Transformation matrix
Returns: Vector2. Transformed vector.
transform(position, mat)
Transform a vector by the given matrix.
Parameters:
position : Vector2 . Source vector.
mat : matrix . Transformation matrix, requires a 3x2 or a 4x4 matrix.
Returns: Vector2. Transformed vector.
transform(this, rotation)
Transform a vector by the given quaternion rotation value.
Parameters:
this : Vector2 . Source vector.
rotation : Quaternion . Rotation to apply.
Returns: Vector2. Transformed vector.
area_triangle(a, b, c)
Find the area in a triangle of vectors.
Parameters:
a : Vector2 . Vector2 object.
b : Vector2 . Vector2 object.
c : Vector2 . Vector2 object.
Returns: float.
-> usage:
`a = new(1.0, 2.0) , b = from(2.0) , c = from(1.0) , d = area_triangle(a, b, c) , plot(d.x)`
random(max)
2D random value.
Parameters:
max : Vector2 . Vector2 object. Vector upper boundary.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(2.0) , b = random(a) , plot(b.x)`
random(max)
2D random value.
Parameters:
max : float, Vector upper boundary.
Returns: Vector2. Vector2 object.
-> usage:
`a = random(2.0) , plot(a.x)`
random(min, max)
2D random value.
Parameters:
min : Vector2 . Vector2 object. Vector lower boundary.
max : Vector2 . Vector2 object. Vector upper boundary.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(1.0) , b = from(2.0) , c = random(a, b) , plot(c.x)`
random(min, max)
2D random value.
Parameters:
min : Vector2 . Vector2 object. Vector lower boundary.
max : Vector2 . Vector2 object. Vector upper boundary.
Returns: Vector2. Vector2 object.
-> usage:
`a = random(1.0, 2.0) , plot(a.x)`
noise(a)
2D Noise based on Morgan McGuire @morgan3d.
Parameters:
a : Vector2 . Vector2 object.
Returns: Vector2. Vector2 object.
-> usage:
`a = from(2.0) , b = noise(a) , plot(b.x)`
to_string(a)
Converts vector `a` to a string format, in the form `"(x, y)"`.
Parameters:
a : Vector2 . Vector2 object.
Returns: string. In `"(x, y)"` format.
-> usage:
`a = from(2.0) , l = barstate.islast ? label.new(bar_index, 0.0, to_string(a)) : label(na)`
to_string(a, format)
Converts vector `a` to a string format, in the form `"(x, y)"`.
Parameters:
a : Vector2 . Vector2 object.
format : string . Format to apply transformation.
Returns: string. In `"(x, y)"` format.
-> usage:
`a = from(2.123456) , l = barstate.islast ? label.new(bar_index, 0.0, to_string(a, "#.##")) : label(na)`
to_array(a)
Converts vector to a array format.
Parameters:
a : Vector2 . Vector2 object.
Returns: array.
-> usage:
`a = from(2.0) , b = to_array(a) , plot(array.get(b, 0))`
to_barycentric(this, a, b, c)
Captures the barycentric coordinate of a cartesian position in the triangle plane.
Parameters:
this : Vector2 . Source cartesian coordinate position.
a : Vector2 . Triangle corner `a` vertice.
b : Vector2 . Triangle corner `b` vertice.
c : Vector2 . Triangle corner `c` vertice.
Returns: bool.
from_barycentric(this, a, b, c)
Captures the cartesian coordinate of a barycentric position in the triangle plane.
Parameters:
this : Vector2 . Source barycentric coordinate position.
a : Vector2 . Triangle corner `a` vertice.
b : Vector2 . Triangle corner `b` vertice.
c : Vector2 . Triangle corner `c` vertice.
Returns: bool.
to_complex(this)
Translate a Vector2 structure to complex.
Parameters:
this : Vector2 . Source vector.
Returns: Complex.
to_polar(this)
Translate a Vector2 cartesian coordinate into polar coordinates.
Parameters:
this : Vector2 . Source vector.
Returns: Pole. The returned angle is in radians.
Forecasting - Seasonal Naive MethodFor completeness here is a naive method with seasonality. The idea behind naive method with seasonality is to take last value from same season and treat it as a forecast. Its counterpart, naive method without seasonality, involves taking last mean value, i.e forecast = sma(x, p) .
Forecasting - Simple Mean MethodThis is a continuation of my series on forecasting techniques. The idea behind the Simple Mean method is to somehow extend historical mean to the future. In this case a forecast equals to last value plus average change.
Forecasting - Holt’s Linear Trend ForecastingHolt's Forecasting method
Holt (1957) extended simple exponential smoothing to allow the forecasting of data with a trend. This method involves a forecast equation and two smoothing equations (one for the level and one for the trend):
Forecast equation: ŷ = l + h * b
Level equation: l = alpha * y + (1 - alpha) * (l + b)
Trend equation: b = beta * (l - l) + (1 - beta) * b
where:
l (or l) denotes an estimate of the level of the series at time t,
b (or b) denotes an estimate of the trend (slope) of the series at time t,
alpha is the smoothing parameter for the level, 0 ≤ alpha ≤ 1, and
beta is the smoothing parameter for the trend, 0 ≤ beta ≤ 1.
As with simple exponential smoothing, the level equation here shows that l is a weighted average of observation y and the one-step-ahead training forecast for time t, here given by l+b. The trend equation shows that b is a weighted average of the estimated trend at time t based on l-l and b, the previous estimate of the trend.
The forecast function is not flat but trending. The h-step-ahead forecast is equal to the last estimated level plus h times the last estimated trend value. Hence the forecasts are a linear function of h.
B3 HL2 Method Candle PainterThis script is similar to the "Hi-Lo" or "Clear" methods of painting bars. Instead of using the tips/edges of the candles like those two, the "(H+L)/2" method uses the change in (high+low)/2 to paint the bars. This gives you some similar results if you were to be binary with the candle coloring. However, my coloring scheme is not entirely binary. There are 5 possible colors:
HL2>LastHigh = Bright Green
HL2LastHL2 = Dull Green
HL2<LastHL2 = Dull Red
Bar Change (close - open) is going against the indicator = Gray
Free to share and enjoy!
~B3
666 & BKThis method uses common numbers which rule the word, 666, so ma 6,12,18,66,180 and the boss method whose ma 7, 14, 21, 77, 231.
