MathProbabilityDistributionLibrary "MathProbabilityDistribution"
Probability Distribution Functions.
name(idx) Indexed names helper function.
Parameters:
idx : int, position in the range (0, 6).
Returns: string, distribution name.
usage:
.name(1)
Notes:
(0) => 'StdNormal'
(1) => 'Normal'
(2) => 'Skew Normal'
(3) => 'Student T'
(4) => 'Skew Student T'
(5) => 'GED'
(6) => 'Skew GED'
zscore(position, mean, deviation) Z-score helper function for x calculation.
Parameters:
position : float, position.
mean : float, mean.
deviation : float, standard deviation.
Returns: float, z-score.
usage:
.zscore(1.5, 2.0, 1.0)
std_normal(position) Standard Normal Distribution.
Parameters:
position : float, position.
Returns: float, probability density.
usage:
.std_normal(0.6)
normal(position, mean, scale) Normal Distribution.
Parameters:
position : float, position in the distribution.
mean : float, mean of the distribution, default=0.0 for standard distribution.
scale : float, scale of the distribution, default=1.0 for standard distribution.
Returns: float, probability density.
usage:
.normal(0.6)
skew_normal(position, skew, mean, scale) Skew Normal Distribution.
Parameters:
position : float, position in the distribution.
skew : float, skewness of the distribution.
mean : float, mean of the distribution, default=0.0 for standard distribution.
scale : float, scale of the distribution, default=1.0 for standard distribution.
Returns: float, probability density.
usage:
.skew_normal(0.8, -2.0)
ged(position, shape, mean, scale) Generalized Error Distribution.
Parameters:
position : float, position.
shape : float, shape.
mean : float, mean, default=0.0 for standard distribution.
scale : float, scale, default=1.0 for standard distribution.
Returns: float, probability.
usage:
.ged(0.8, -2.0)
skew_ged(position, shape, skew, mean, scale) Skew Generalized Error Distribution.
Parameters:
position : float, position.
shape : float, shape.
skew : float, skew.
mean : float, mean, default=0.0 for standard distribution.
scale : float, scale, default=1.0 for standard distribution.
Returns: float, probability.
usage:
.skew_ged(0.8, 2.0, 1.0)
student_t(position, shape, mean, scale) Student-T Distribution.
Parameters:
position : float, position.
shape : float, shape.
mean : float, mean, default=0.0 for standard distribution.
scale : float, scale, default=1.0 for standard distribution.
Returns: float, probability.
usage:
.student_t(0.8, 2.0, 1.0)
skew_student_t(position, shape, skew, mean, scale) Skew Student-T Distribution.
Parameters:
position : float, position.
shape : float, shape.
skew : float, skew.
mean : float, mean, default=0.0 for standard distribution.
scale : float, scale, default=1.0 for standard distribution.
Returns: float, probability.
usage:
.skew_student_t(0.8, 2.0, 1.0)
select(distribution, position, mean, scale, shape, skew, log) Conditional Distribution.
Parameters:
distribution : string, distribution name.
position : float, position.
mean : float, mean, default=0.0 for standard distribution.
scale : float, scale, default=1.0 for standard distribution.
shape : float, shape.
skew : float, skew.
log : bool, if true apply log() to the result.
Returns: float, probability.
usage:
.select('StdNormal', __CYCLE4F__, log=true)
MATH
historicalrangeLibrary "historicalrange"
Library provices a method to calculate historical percentile range of series.
hpercentrank(source) calculates historical percentrank of the source
Parameters:
source : Source for which historical percentrank needs to be calculated. Source should be ranging between 0-100. If using a source which can beyond 0-100, use short term percentrank to baseline them.
Returns: pArray - percentrank array which contains how many instances of source occurred at different levels.
upperPercentile - percentile based on higher value
lowerPercentile - percentile based on lower value
median - median value of the source
max - max value of the source
distancefromath(source) returns stats on historical distance from ath in terms of percentage
Parameters:
source : for which stats are calculated
Returns: percentile and related historical stats regarding distance from ath
distancefromma(maType, length, source) returns stats on historical distance from moving average in terms of percentage
Parameters:
maType : Moving Average Type : Can be sma, ema, hma, rma, wma, vwma, swma, highlow, linreg, median
length : Moving Average Length
source : for which stats are calculated
Returns: percentile and related historical stats regarding distance from ath
bpercentb(source, maType, length, multiplier, sticky) returns percentrank and stats on historical bpercentb levels
Parameters:
source : Moving Average Source
maType : Moving Average Type : Can be sma, ema, hma, rma, wma, vwma, swma, highlow, linreg, median
length : Moving Average Length
multiplier : Standard Deviation multiplier
sticky : - sticky boundaries which will only change when value is outside boundary.
Returns: percentile and related historical stats regarding Bollinger Percent B
kpercentk(source, maType, length, multiplier, useTrueRange, sticky) returns percentrank and stats on historical kpercentk levels
Parameters:
source : Moving Average Source
maType : Moving Average Type : Can be sma, ema, hma, rma, wma, vwma, swma, highlow, linreg, median
length : Moving Average Length
multiplier : Standard Deviation multiplier
useTrueRange : - if set to false, uses high-low.
sticky : - sticky boundaries which will only change when value is outside boundary.
Returns: percentile and related historical stats regarding Keltener Percent K
dpercentd(useAlternateSource, alternateSource, length, sticky) returns percentrank and stats on historical dpercentd levels
Parameters:
useAlternateSource : - Custom source is used only if useAlternateSource is set to true
alternateSource : - Custom source
length : - donchian channel length
sticky : - sticky boundaries which will only change when value is outside boundary.
Returns: percentile and related historical stats regarding Donchian Percent D
oscillator(type, length, shortLength, longLength, source, highSource, lowSource, method, highlowLength, sticky) oscillator - returns Choice of oscillator with custom overbought/oversold range
Parameters:
type : - oscillator type. Valid values : cci, cmo, cog, mfi, roc, rsi, stoch, tsi, wpr
length : - Oscillator length - not used for TSI
shortLength : - shortLength only used for TSI
longLength : - longLength only used for TSI
source : - custom source if required
highSource : - custom high source for stochastic oscillator
lowSource : - custom low source for stochastic oscillator
method : - Valid values for method are : sma, ema, hma, rma, wma, vwma, swma, highlow, linreg, median
highlowLength : - length on which highlow of the oscillator is calculated
sticky : - overbought, oversold levels won't change unless crossed
Returns: percentile and related historical stats regarding oscillator
ArrayOperationsLibrary "ArrayOperations"
Array element wise basic operations.
add(sample_a, sample_b) Adds sample_b to sample_a and returns a new array.
Parameters:
sample_a : values to be added to.
sample_b : values to add.
Returns: array with added results.
- sample_a provides type format for output.
- arrays do not need to be symmetric.
- sample_a must have same or more elements than sample_b
subtract(sample_a, sample_b) Subtracts sample_b from sample_a and returns a new array.
sample_a : values to be subtracted from.
sample_b : values to subtract.
Returns: array with subtracted results.
- sample_a provides type format for output.
- arrays do not need to be symmetric.
- sample_a must have same or more elements than sample_b
multiply(sample_a, sample_b) multiply sample_a by sample_b and returns a new array.
sample_a : values to multiply.
sample_b : values to multiply with.
Returns: array with multiplied results.
- sample_a provides type format for output.
- arrays do not need to be symmetric.
- sample_a must have same or more elements than sample_b
divide(sample_a, sample_b) Divide sample_a by sample_b and returns a new array.
sample_a : values to divide.
sample_b : values to divide with.
Returns: array with divided results.
- sample_a provides type format for output.
- arrays do not need to be symmetric.
- sample_a must have same or more elements than sample_b
power(sample_a, sample_b) power sample_a by sample_b and returns a new array.
sample_a : values to power.
sample_b : values to power with.
Returns: float array with power results.
- sample_a provides type format for output.
- arrays do not need to be symmetric.
- sample_a must have same or more elements than sample_b
remainder(sample_a, sample_b) Remainder sample_a by sample_b and returns a new array.
sample_a : values to remainder.
sample_b : values to remainder with.
Returns: array with remainder results.
- sample_a provides type format for output.
- arrays do not need to be symmetric.
- sample_a must have same or more elements than sample_b
equal(sample_a, sample_b) Check element wise sample_a equals sample_b and returns a new array.
sample_a : values to check.
sample_b : values to check.
Returns: int array with results.
- sample_a provides type format for output.
- arrays do not need to be symmetric.
- sample_a must have same or more elements than sample_b
not_equal(sample_a, sample_b) Check element wise sample_a not equals sample_b and returns a new array.
sample_a : values to check.
sample_b : values to check.
Returns: int array with results.
- sample_a provides type format for output.
- arrays do not need to be symmetric.
- sample_a must have same or more elements than sample_b
over_or_equal(sample_a, sample_b) Check element wise sample_a over or equals sample_b and returns a new array.
sample_a : values to check.
sample_b : values to check.
Returns: int array with results.
- sample_a provides type format for output.
- arrays do not need to be symmetric.
- sample_a must have same or more elements than sample_b
under_or_equal(sample_a, sample_b) Check element wise sample_a under or equals sample_b and returns a new array.
sample_a : values to check.
sample_b : values to check.
Returns: int array with results.
- sample_a provides type format for output.
- arrays do not need to be symmetric.
- sample_a must have same or more elements than sample_b
over(sample_a, sample_b) Check element wise sample_a over sample_b and returns a new array.
sample_a : values to check.
sample_b : values to check.
Returns: int array with results.
- sample_a provides type format for output.
- arrays do not need to be symmetric.
- sample_a must have same or more elements than sample_b
under(sample_a, sample_b) Check element wise sample_a under sample_b and returns a new array.
sample_a : values to check.
sample_b : values to check.
Returns: int array with results.
- sample_a provides type format for output.
- arrays do not need to be symmetric.
- sample_a must have same or more elements than sample_b
and_(sample_a, sample_b) Check element wise sample_a and sample_b and returns a new array.
sample_a : values to check.
sample_b : values to check.
Returns: int array with results.
- sample_a provides type format for output.
- arrays do not need to be symmetric.
- sample_a must have same or more elements than sample_b
or_(sample_a, sample_b) Check element wise sample_a or sample_b and returns a new array.
sample_a : values to check.
sample_b : values to check.
Returns: int array with results.
- sample_a provides type format for output.
- arrays do not need to be symmetric.
- sample_a must have same or more elements than sample_b
all(sample) Check element wise if all numeric samples are true (!= 0).
sample : values to check.
Returns: int.
any(sample) Check element wise if any numeric samples are true (!= 0).
sample : values to check.
Returns: int.
FunctionWeekofmonthLibrary "FunctionWeekofmonth"
Week of Month function.
weekofmonth(utime) Week of month for provided unix time.
Parameters:
utime : int, unix timestamp.
Returns: int
WIPNNetworkLibrary "WIPNNetwork"
this is a work in progress (WIP) and prone to have some errors, so use at your own risk...
let me know if you find any issues..
Method for a generalized Neural Network.
network(x) Generalized Neural Network Method.
Parameters:
x : TODO: add parameter x description here
Returns: TODO: add what function returns
FunctionBlackScholesLibrary "FunctionBlackScholes"
Some methods for the Black Scholes Options Model, which demonstrates several approaches to the valuation of a European call.
// reference:
// people.math.sc.edu
// people.math.sc.edu
asset_path(s0, mu, sigma, t1, n) Simulates the behavior of an asset price over time.
Parameters:
s0 : float, asset price at time 0.
mu : float, growth rate.
sigma : float, volatility.
t1 : float, time to expiry date.
n : int, time steps to expiry date.
Returns: option values at each equal timed step (0 -> t1)
binomial(s0, e, r, sigma, t1, m) Uses the binomial method for a European call.
Parameters:
s0 : float, asset price at time 0.
e : float, exercise price.
r : float, interest rate.
sigma : float, volatility.
t1 : float, time to expiry date.
m : int, time steps to expiry date.
Returns: option value at time 0.
bsf(s0, t0, e, r, sigma, t1) Evaluates the Black-Scholes formula for a European call.
Parameters:
s0 : float, asset price at time 0.
t0 : float, time at which the price is known.
e : float, exercise price.
r : float, interest rate.
sigma : float, volatility.
t1 : float, time to expiry date.
Returns: option value at time 0.
forward(e, r, sigma, t1, nx, nt, smax) Forward difference method to value a European call option.
Parameters:
e : float, exercise price.
r : float, interest rate.
sigma : float, volatility.
t1 : float, time to expiry date.
nx : int, number of space steps in interval (0, L).
nt : int, number of time steps.
smax : float, maximum value of S to consider.
Returns: option values for the european call, float array of size ((nx-1) * (nt+1)).
mc(s0, e, r, sigma, t1, m) Uses Monte Carlo valuation on a European call.
Parameters:
s0 : float, asset price at time 0.
e : float, exercise price.
r : float, interest rate.
sigma : float, volatility.
t1 : float, time to expiry date.
m : int, time steps to expiry date.
Returns: confidence interval for the estimated range of valuation.
FunctionMinkowskiDistanceLibrary "FunctionMinkowskiDistance"
Method for Minkowski Distance,
The Minkowski distance or Minkowski metric is a metric in a normed vector space
which can be considered as a generalization of both the Euclidean distance and
the Manhattan distance.
It is named after the German mathematician Hermann Minkowski.
reference: en.wikipedia.org
double(point_ax, point_ay, point_bx, point_by, p_value) Minkowsky Distance for single points.
Parameters:
point_ax : float, x value of point a.
point_ay : float, y value of point a.
point_bx : float, x value of point b.
point_by : float, y value of point b.
p_value : float, p value, default=1.0(1: manhatan, 2: euclidean), does not support chebychev.
Returns: float
ndim(point_x, point_y, p_value) Minkowsky Distance for N dimensions.
Parameters:
point_x : float array, point x dimension attributes.
point_y : float array, point y dimension attributes.
p_value : float, p value, default=1.0(1: manhatan, 2: euclidean), does not support chebychev.
Returns: float
TimeLockedMALibrary "TimeLockedMA"
Library & function(s) which generates a moving average that stays locked to users desired time preference.
TODO - Add functionality for more moving average types. IE: smooth, weighted etc...
Example:
time_locked_ma(close, length=1, timeframe='days', type='ema')
Will generate a 1 day exponential moving average that will stay consistent across all chart intervals.
Error Handling
On small time frames with large moving averages (IE: 1min chart with a 50 week moving average), you'll get a study error that says "(function "sma") references too many candles in history" .
To fix this, make sure you have timeframe="" as an indicator() header. Next, in the indicator settings, increase the timeframe from to a higher interval until the error goes away.
By default, it's set to "Chart". Bringing the interval up to 1hr will usually solve the issue.
Furthermore, adding timeframe_gaps=false to your indicator() header will give you an approximation of real-time values.
Misc Info
For time_lock_ma() setting type='na' will return the relative length value that adjusts dynamically to user's chart time interval.
This is good for plugging into other functions where a lookback or length is required. (IE: Bollinger Bands)
time_locked_ma(source, length, timeframe, type) Creates a moving average that is locked to a desired timeframe
Parameters:
source : float, Moving average source
length : int, Moving average length
timeframe : string, Desired timeframe. Use: "minutes", "hours", "days", "weeks", "months", "chart"
type : string, string Moving average type. Use "SMA" (default) or "EMA". Value of "NA" will return relative lookback length.
Returns: moving average that is locked to desired timeframe.
timeframe_convert(t, a, b) Converts timeframe to desired timeframe. From a --> b
Parameters:
t : int, Time interval
a : string, Time period
b : string, Time period to convert to
Returns: Converted timeframe value
chart_time(timeframe_period, timeframe_multiplier) Separates timeframe.period function and returns chart interval and period
Parameters:
timeframe_period : string, timeframe.period
timeframe_multiplier : int, timeframe.multiplier
Enjoy :)
FunctionGenerateRandomPointsInShapeLibrary "FunctionGenerateRandomPointsInShape"
Generate random vector points in geometric shape (parallelogram, triangle)
random_parallelogram(vector_a, vector_b) Generate random vector point in a parallelogram shape.
Parameters:
vector_a : float array, vector of (x, y) shape.
vector_b : float array, vector of (x, y) shape.
Returns: float array, vector of (x, y) shape.
random_triangle(vector_a, vector_b) Generate random vector point in a triangle shape.
Parameters:
vector_a : float array, vector of (x, y) shape.
vector_b : float array, vector of (x, y) shape.
Returns: float array, vector of (x, y) shape.
Punchline_LibLibrary "Punchline_Lib"
roundSmart(float) Truncates decimal points of a float value based on the amount of digits before the decimal point
Parameters:
float : _value any number
Returns: float
tostring_smart(float) converts a float to a string, intelligently cutting off decimal points
Parameters:
float : _value any number
Returns: string
FunctionNNLayerLibrary "FunctionNNLayer"
Generalized Neural Network Layer method.
function(inputs, weights, n_nodes, activation_function, bias, alpha, scale) Generalized Layer.
Parameters:
inputs : float array, input values.
weights : float array, weight values.
n_nodes : int, number of nodes in layer.
activation_function : string, default='sigmoid', name of the activation function used.
bias : float, default=1.0, bias to pass into activation function.
alpha : float, default=na, if required to pass into activation function.
scale : float, default=na, if required to pass into activation function.
Returns: float
FunctionNNPerceptronLibrary "FunctionNNPerceptron"
Perceptron Function for Neural networks.
function(inputs, weights, bias, activation_function, alpha, scale) generalized perceptron node for Neural Networks.
Parameters:
inputs : float array, the inputs of the perceptron.
weights : float array, the weights for inputs.
bias : float, default=1.0, the default bias of the perceptron.
activation_function : string, default='sigmoid', activation function applied to the output.
alpha : float, default=na, if required for activation.
scale : float, default=na, if required for activation.
@outputs float
InterpolationLibrary "Interpolation"
Functions for interpolating values. Can be useful in signal processing or applied as a sigmoid function.
linear(k, delta, offset, unbound) Returns the linear adjusted value.
Parameters:
k : A number (float) from 0 to 1 representing where the on the line the value is.
delta : The amount the value should change as k reaches 1.
offset : The start value.
unbound : When true, k values less than 0 or greater than 1 are still calculated. When false (default), k values less than 0 will return the offset value and values greater than 1 will return (offset + delta).
quadIn(k, delta, offset, unbound) Returns the quadratic (easing-in) adjusted value.
Parameters:
k : A number (float) from 0 to 1 representing where the on the curve the value is.
delta : The amount the value should change as k reaches 1.
offset : The start value.
unbound : When true, k values less than 0 or greater than 1 are still calculated. When false (default), k values less than 0 will return the offset value and values greater than 1 will return (offset + delta).
quadOut(k, delta, offset, unbound) Returns the quadratic (easing-out) adjusted value.
Parameters:
k : A number (float) from 0 to 1 representing where the on the curve the value is.
delta : The amount the value should change as k reaches 1.
offset : The start value.
unbound : When true, k values less than 0 or greater than 1 are still calculated. When false (default), k values less than 0 will return the offset value and values greater than 1 will return (offset + delta).
quadInOut(k, delta, offset, unbound) Returns the quadratic (easing-in-out) adjusted value.
Parameters:
k : A number (float) from 0 to 1 representing where the on the curve the value is.
delta : The amount the value should change as k reaches 1.
offset : The start value.
unbound : When true, k values less than 0 or greater than 1 are still calculated. When false (default), k values less than 0 will return the offset value and values greater than 1 will return (offset + delta).
cubicIn(k, delta, offset, unbound) Returns the cubic (easing-in) adjusted value.
Parameters:
k : A number (float) from 0 to 1 representing where the on the curve the value is.
delta : The amount the value should change as k reaches 1.
offset : The start value.
unbound : When true, k values less than 0 or greater than 1 are still calculated. When false (default), k values less than 0 will return the offset value and values greater than 1 will return (offset + delta).
cubicOut(k, delta, offset, unbound) Returns the cubic (easing-out) adjusted value.
Parameters:
k : A number (float) from 0 to 1 representing where the on the curve the value is.
delta : The amount the value should change as k reaches 1.
offset : The start value.
unbound : When true, k values less than 0 or greater than 1 are still calculated. When false (default), k values less than 0 will return the offset value and values greater than 1 will return (offset + delta).
cubicInOut(k, delta, offset, unbound) Returns the cubic (easing-in-out) adjusted value.
Parameters:
k : A number (float) from 0 to 1 representing where the on the curve the value is.
delta : The amount the value should change as k reaches 1.
offset : The start value.
unbound : When true, k values less than 0 or greater than 1 are still calculated. When false (default), k values less than 0 will return the offset value and values greater than 1 will return (offset + delta).
expoIn(k, delta, offset, unbound) Returns the exponential (easing-in) adjusted value.
Parameters:
k : A number (float) from 0 to 1 representing where the on the curve the value is.
delta : The amount the value should change as k reaches 1.
offset : The start value.
unbound : When true, k values less than 0 or greater than 1 are still calculated. When false (default), k values less than 0 will return the offset value and values greater than 1 will return (offset + delta).
expoOut(k, delta, offset, unbound) Returns the exponential (easing-out) adjusted value.
Parameters:
k : A number (float) from 0 to 1 representing where the on the curve the value is.
delta : The amount the value should change as k reaches 1.
offset : The start value.
unbound : When true, k values less than 0 or greater than 1 are still calculated. When false (default), k values less than 0 will return the offset value and values greater than 1 will return (offset + delta).
expoInOut(k, delta, offset, unbound) Returns the exponential (easing-in-out) adjusted value.
Parameters:
k : A number (float) from 0 to 1 representing where the on the curve the value is.
delta : The amount the value should change as k reaches 1.
offset : The start value.
unbound : When true, k values less than 0 or greater than 1 are still calculated. When false (default), k values less than 0 will return the offset value and values greater than 1 will return (offset + delta).
using(fn, k, delta, offset, unbound) Returns the adjusted value by function name.
Parameters:
fn : The name of the function. Allowed values: linear, quadIn, quadOut, quadInOut, cubicIn, cubicOut, cubicInOut, expoIn, expoOut, expoInOut.
k : A number (float) from 0 to 1 representing where the on the curve the value is.
delta : The amount the value should change as k reaches 1.
offset : The start value.
unbound : When true, k values less than 0 or greater than 1 are still calculated. When false (default), k values less than 0 will return the offset value and values greater than 1 will return (offset + delta).
CRC.lib Log FunctionsLibrary "CRCLog"
default_params() Returns default high/low intercept/slope parameter values for Bitcoin that can be adjusted and used to calculate new Regression Log lines
log_regression() Returns set of (fib) spaced lines representing log regression (default values attempt fitted to INDEX:BTCUSD genesis-2021)
CRC.lib Bars - Bar FunctionsLibrary "CRCBars"
min_max(open, open) Get bar min (low) and max (high) price points
Parameters:
open : Open price data
open : Close price data
Returns:
is_bullish_bearish(open, open) Get bar bullish/bearish boolean signals
Parameters:
open : Open price data
open : Close price data
Returns:
sizes(open, open, open, open) Get bar sizes based on open/high/low/close data
Parameters:
open : Open price data
open : High price data
open : Low price data
open : Close price data
Returns:
options_expiration_and_strike_price_calculatorLibrary "options_expiration_and_strike_price_calculator"
TODO: add library description here
fun()
this is a library to help calculate options strike price and expiration that you can add to a script i use it mainly for symbol calulation to place orders to buy options on TD ameritrade so it will be set up to order options on TD ameritrade using json order placer and webhook it fills in the area in the json under symbol i suggest manually adding the year it should look like this is an example of an order to buy 10 call options using json through td ameritrade api
"complexOrderStrategyType": "NONE",
"orderType": "LIMIT",
"session": "NORMAL",
"price": "6.45",
"duration": "DAY",
"orderStrategyType": "SINGLE",
"orderLegCollection":
}
GenericTALibrary "GenericTA"
What is it?
The real generic library. Which means it is just covering most built-in indicators / functions, but with more parameters, so the user don't have to write more few lines to achieve something simple and replicative.
Development process?
Will tidy it up, and setting up in later stage.
Welcome to inbox me to improve the library ------
If you are finding a similar thing. That's a good news. Because I am making it.
FFTLibraryLibrary "FFTLibrary" contains a function for performing Fast Fourier Transform (FFT) along with a few helper functions. In general, FFT is defined for complex inputs and outputs. The real and imaginary parts of formally complex data are treated as separate arrays (denoted as x and y). For real-valued data, the array of imaginary parts should be filled with zeros.
FFT function
fft(x, y, dir) : Computes the one-dimensional discrete Fourier transform using an in-place complex-to-complex FFT algorithm . Note: The transform also produces a mirror copy of the frequency components, which correspond to the signal's negative frequencies.
Parameters:
x : float array, real part of the data, array size must be a power of 2
y : float array, imaginary part of the data, array size must be the same as x ; for real-valued input, y must be an array of zeros
dir : string, options = , defines the direction of the transform: forward" (time-to-frequency) or inverse (frequency-to-time)
Returns: x, y : tuple (float array, float array), real and imaginary parts of the transformed data (original x and y are changed on output)
Helper functions
fftPower(x, y) : Helper function that computes the power of each frequency component (in other words, Fourier amplitudes squared).
Parameters:
x : float array, real part of the Fourier amplitudes
y : float array, imaginary part of the Fourier amplitudes
Returns: power : float array of the same length as x and y , Fourier amplitudes squared
fftFreq(N) : Helper function that returns the FFT sample frequencies defined in cycles per timeframe unit. For example, if the timeframe is 5m, the frequencies are in cycles/(5 minutes).
Parameters:
N : int, window length (number of points in the transformed dataset)
Returns: freq : float array of N, contains the sample frequencies (with zero at the start).
FunctionArrayReduceLibrary "FunctionArrayReduce"
A limited method to reduce a array using a mathematical formula.
float_(formula, samples, arguments, initial_value) Method to reduce a array using a mathematical formula.
Parameters:
formula : string, the mathematical formula, accepts some default name codes (index, output, previous, current, integer index of arguments array).
samples : float array, the data to process.
arguments : float array, the extra arguments of the formula.
initial_value : float, default=0, a initial base value for the process.
Returns: float.
Notes:
** if initial value is specified as "na" it will default to the first element of samples.
FunctionProbabilityDistributionSamplingLibrary "FunctionProbabilityDistributionSampling"
Methods for probability distribution sampling selection.
sample(probabilities) Computes a random selected index from a probability distribution.
Parameters:
probabilities : float array, probabilities of sample.
Returns: int.
FunctionElementsInArrayLibrary "FunctionElementsInArray"
Methods to count number of elements in arrays
count_float(sample, value) Counts the number of elements equal to provided value in array.
Parameters:
sample : float array, sample data to process.
value : float value to check for equality.
Returns: int.
count_int(sample, value) Counts the number of elements equal to provided value in array.
Parameters:
sample : int array, sample data to process.
value : int value to check for equality.
Returns: int.
count_string(sample, value) Counts the number of elements equal to provided value in array.
Parameters:
sample : string array, sample data to process.
value : string value to check for equality.
Returns: int.
count_bool(sample, value) Counts the number of elements equal to provided value in array.
Parameters:
sample : bool array, sample data to process.
value : bool value to check for equality.
Returns: int.
count_color(sample, value) Counts the number of elements equal to provided value in array.
Parameters:
sample : color array, sample data to process.
value : color value to check for equality.
Returns: int.
extract_indices_float(sample, value) Counts the number of elements equal to provided value in array, and returns its indices.
Parameters:
sample : float array, sample data to process.
value : float value to check for equality.
Returns: int.
extract_indices_int(sample, value) Counts the number of elements equal to provided value in array, and returns its indices.
Parameters:
sample : int array, sample data to process.
value : int value to check for equality.
Returns: int.
extract_indices_string(sample, value) Counts the number of elements equal to provided value in array, and returns its indices.
Parameters:
sample : string array, sample data to process.
value : string value to check for equality.
Returns: int.
extract_indices_bool(sample, value) Counts the number of elements equal to provided value in array, and returns its indices.
Parameters:
sample : bool array, sample data to process.
value : bool value to check for equality.
Returns: int.
extract_indices_color(sample, value) Counts the number of elements equal to provided value in array, and returns its indices.
Parameters:
sample : color array, sample data to process.
value : color value to check for equality.
Returns: int.
LinearRegressionLibraryLibrary "LinearRegressionLibrary" contains functions for fitting a regression line to the time series by means of different models, as well as functions for estimating the accuracy of the fit.
Linear regression algorithms:
RepeatedMedian(y, n, lastBar) applies repeated median regression (robust linear regression algorithm) to the input time series within the selected interval.
Parameters:
y :: float series, source time series (e.g. close)
n :: integer, the length of the selected time interval
lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval)
Output:
mSlope :: float, slope of the regression line
mInter :: float, intercept of the regression line
TheilSen(y, n, lastBar) applies the Theil-Sen estimator (robust linear regression algorithm) to the input time series within the selected interval.
Parameters:
y :: float series, source time series
n :: integer, the length of the selected time interval
lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval)
Output:
tsSlope :: float, slope of the regression line
tsInter :: float, intercept of the regression line
OrdinaryLeastSquares(y, n, lastBar) applies the ordinary least squares regression (non-robust) to the input time series within the selected interval.
Parameters:
y :: float series, source time series
n :: integer, the length of the selected time interval
lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval)
Output:
olsSlope :: float, slope of the regression line
olsInter :: float, intercept of the regression line
Model performance metrics:
metricRMSE(y, n, lastBar, slope, intercept) returns the Root-Mean-Square Error (RMSE) of the regression. The better the model, the lower the RMSE.
Parameters:
y :: float series, source time series (e.g. close)
n :: integer, the length of the selected time interval
lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval)
slope :: float, slope of the evaluated linear regression line
intercept :: float, intercept of the evaluated linear regression line
Output:
rmse :: float, RMSE value
metricMAE(y, n, lastBar, slope, intercept) returns the Mean Absolute Error (MAE) of the regression. MAE is is similar to RMSE but is less sensitive to outliers. The better the model, the lower the MAE.
Parameters:
y :: float series, source time series
n :: integer, the length of the selected time interval
lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval)
slope :: float, slope of the evaluated linear regression line
intercept :: float, intercept of the evaluated linear regression line
Output:
mae :: float, MAE value
metricR2(y, n, lastBar, slope, intercept) returns the coefficient of determination (R squared) of the regression. The better the linear regression fits the data (compared to the sample mean), the closer the value of the R squared is to 1.
Parameters:
y :: float series, source time series
n :: integer, the length of the selected time interval
lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval)
slope :: float, slope of the evaluated linear regression line
intercept :: float, intercept of the evaluated linear regression line
Output:
Rsq :: float, R-sqared score
Usage example:
//@version=5
indicator('ExampleLinReg', overlay=true)
// import the library
import tbiktag/LinearRegressionLibrary/1 as linreg
// define the studied interval: last 100 bars
int Npoints = 100
int lastBar = bar_index
int firstBar = bar_index - Npoints
// apply repeated median regression to the closing price time series within the specified interval
{square bracket}slope, intercept{square bracket} = linreg.RepeatedMedian(close, Npoints, lastBar)
// calculate the root-mean-square error of the obtained linear fit
rmse = linreg.metricRMSE(close, Npoints, lastBar, slope, intercept)
// plot the line and print the RMSE value
float y1 = intercept
float y2 = intercept + slope * (Npoints - 1)
if barstate.islast
{indent} line.new(firstBar,y1, lastBar,y2)
{indent} label.new(lastBar,y2,text='RMSE = '+str.format("{0,number,#.#}", rmse))
FunctionCompoundInterestLibrary "FunctionCompoundInterest"
Method for compound interest.
simple_compound(principal, rate, duration) Computes compound interest for given duration.
Parameters:
principal : float, the principal or starting value.
rate : float, the rate of interest.
duration : float, the period of growth.
Returns: float.
variable_compound(principal, rates, duration) Computes variable compound interest for given duration.
Parameters:
principal : float, the principal or starting value.
rates : float array, the rates of interest.
duration : int, the period of growth.
Returns: float array.
simple_compound_array(principal, rates, duration) Computes variable compound interest for given duration.
Parameters:
principal : float, the principal or starting value.
rates : float array, the rates of interest.
duration : int, the period of growth.
Returns: float array.
variable_compound_array(principal, rates, duration) Computes variable compound interest for given duration.
Parameters:
principal : float, the principal or starting value.
rates : float array, the rates of interest.
duration : int, the period of growth.
Returns: float array.