KernelFunctions is a Pine Script v5 library that exports kernel weight functions for Nadaraya-Watson style estimation. It calculates a Rational Quadratic kernel, a Gaussian kernel based on a radial basis function, and a periodic kernel that models repeating be
Library · Pine Script v5 · Library
CorrelationExtendsStatistics
This Pine Script v5 library exposes numerical helpers for correlation and special-function work and draws nothing on a chart.
GitHub stars261on the repository
Pine versionv5runs as is
Lines of code392
Settings0inputs
LicenceNone statedfile: MPL-2.0
Last update4 years ago13 Nov 2021
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- 3Paste over the templateCreate a new library, select all of the template text and paste. Press Save and give it a name.
- 4Publish or import itA library draws nothing. Publish it from the editor, then import its functions in your own scripts.
Source Code
392 lines of Pine Script v5 from beta/libs/others/CorrelationExtendsStatistics.pinescript, published under MPL-2.0 (file header). Keep the author's credit and licence lines when you reuse it.
// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © RicardoSantos
//@version=5
// @description TODO: add library description here
library(title='CorrelationExtendsStatistics')
// reference:
// https://people.sc.fsu.edu/~jburkardt/f_src/correlation/correlation.html
// https://people.sc.fsu.edu/~jburkardt/f_src/correlation/correlation.f90
// @function real machine-dependent constants.
// @param _i int, input value (1 > _i > 5).
f_r8_mach (int _i) => //{
if _i < 1
0.0
else if _i == 1
4.450147717014403e-308
else if _i == 2
8.988465674311579e+307
else if _i == 3
1.110223024625157e-016
else if _i == 4
2.220446049250313e-016
else if _i == 5
0.301029995663981
else if 5 < _i
0.0
// reference:
// https://people.sc.fsu.edu/~jburkardt/f_src/fn/fn.f90 line: 25905
//{
// ! Discussion:
// !
// ! R8_MACH can be used to obtain machine-dependent parameters
// ! for the local machine environment. It is a function
// ! with one input argument, and can be called as follows:
// !
// ! D = R8_MACH ( I )
// !
// ! where I=1,...,5. The output value of D above is
// ! determined by the input value of I:.
// !
// ! R8_MACH ( 1) = B^(EMIN-1), the smallest positive magnitude.
// ! R8_MACH ( 2) = B^EMAX*(1 - B^(-T)), the largest magnitude.
// ! R8_MACH ( 3) = B^(-T), the smallest relative spacing.
// ! R8_MACH ( 4) = B^(1-T), the largest relative spacing.
// ! R8_MACH ( 5) = LOG10(B)
//}//}
// @function initializes a Chebyshev series.
// @param DOS float array, the Chebyshev coefficients.
// @param NOS int, the number of coefficients.
// @param ETA float, the desired accuracy.
f_r8_inits (float[] dos, int nos, float eta) =>//{
int _value = 0
if nos < 1
// number of coefficients < 1
int(na)
else if eta < array.get(id=dos, index=nos)
// ETA may be too small
_value := nos
else
float _err = 0.0
for _i = 0 to 999999
_value += 1
_err += math.abs(array.get(id=dos, index=_i))
if eta < _err
break
_value
// reference:
// https://people.sc.fsu.edu/~jburkardt/f_src/fn/fn.f90 line:24371
//}
// @function evaluates a Chebyshev series.
// @param eval_point float, evaluation point, -1.1 < x < +1.1 .
// @param a float array, the Chebyshev coefficients.
// @param c_index int, the index of Chebyshev coefficient. 0 < c_index < 20
f_r8_csevl (float eval_point, float[] cseries, int c_index) => //{
if c_index < 1
// number of terms <= 0
float(na)
else if 20 < c_index
// 20 < bumber of terms
float(na)
else if eval_point < -1.1 or 1.1 < eval_point
// eval_point outside input range
float(na)
else
float _twox = 2.0 * eval_point
float _b2 = 0.0
float _b1 = 0.0
float _b0 = 0.0
for _i = c_index to 1
_b2 := _b1
_b1 := _b0
_b0 := _twox * _b1 - _b2 + array.get(id=cseries, index=_i)
5.0 * (_b0 - _b2)
// usage:
// float[] tt = array.from(+0.00000000000000000000000000000000e+00,
// +0.10025416196893913701073127264074e+00,
// -0.66522300776440513177678757831124e+00,
// +0.24898370349828131370460468726680e+00,
// -0.33252723170035769653884341503854e-01,
// +0.23114179304694015462904924117729e-02,
// -0.99112774199508092339048519336549e-04,
// +0.28916708643998808884733903747078e-05,
// -0.61210858663032635057818407481516e-07,
// +0.98386507938567841324768748636415e-09,
// -0.12423551597301765145515897006836e-10,
// +0.12654336302559045797915827210363e-12,
// -0.10619456495287244546914817512959e-14,
// +0.74706210758024567437098915584000e-17,
// -0.44697032274412780547627007999999e-19,
// +0.23024281584337436200523093333333e-21,
// -0.10319144794166698148522666666666e-23,
// +0.40608178274873322700800000000000e-26,
// -0.14143836005240913919999999999999e-28,
// +0.43910905496698880000000000000000e-31 )
// plot(f_r8_csevl(1.1, tt, 15))
//
// reference:
// https://people.sc.fsu.edu/~jburkardt/f_src/fn/fn.f90 line: 21643
//}
// @function evaluates the modulus and phase for the Bessel J0 and Y0 functions.
// @param x float, the argument. 4.0 > x > +inf
// @returns
// ampl
// theta
f_r8_b0mp (float x) => //{
//{
float[] _bm0cs = array.from( 0.0,
+0.9211656246827742712573767730182e-01,
-0.1050590997271905102480716371755e-02,
+0.1470159840768759754056392850952e-04,
-0.5058557606038554223347929327702e-06,
+0.2787254538632444176630356137881e-07,
-0.2062363611780914802618841018973e-08,
+0.1870214313138879675138172596261e-09,
-0.1969330971135636200241730777825e-10,
+0.2325973793999275444012508818052e-11,
-0.3009520344938250272851224734482e-12,
+0.4194521333850669181471206768646e-13,
-0.6219449312188445825973267429564e-14,
+0.9718260411336068469601765885269e-15,
-0.1588478585701075207366635966937e-15,
+0.2700072193671308890086217324458e-16,
-0.4750092365234008992477504786773e-17,
+0.8615128162604370873191703746560e-18,
-0.1605608686956144815745602703359e-18,
+0.3066513987314482975188539801599e-19,
-0.5987764223193956430696505617066e-20,
+0.1192971253748248306489069841066e-20,
-0.2420969142044805489484682581333e-21,
+0.4996751760510616453371002879999e-22,
-0.1047493639351158510095040511999e-22,
+0.2227786843797468101048183466666e-23,
-0.4801813239398162862370542933333e-24,
+0.1047962723470959956476996266666e-24,
-0.2313858165678615325101260800000e-25,
+0.5164823088462674211635199999999e-26,
-0.1164691191850065389525401599999e-26,
+0.2651788486043319282958336000000e-27,
-0.6092559503825728497691306666666e-28,
+0.1411804686144259308038826666666e-28,
-0.3298094961231737245750613333333e-29,
+0.7763931143074065031714133333333e-30,
-0.1841031343661458478421333333333e-30,
+0.4395880138594310737100799999999e-31)
float[] _bth0cs = array.from( 0.0,
-0.24901780862128936717709793789967e+00,
+0.48550299609623749241048615535485e-03,
-0.54511837345017204950656273563505e-05,
+0.13558673059405964054377445929903e-06,
-0.55691398902227626227583218414920e-08,
+0.32609031824994335304004205719468e-09,
-0.24918807862461341125237903877993e-10,
+0.23449377420882520554352413564891e-11,
-0.26096534444310387762177574766136e-12,
+0.33353140420097395105869955014923e-13,
-0.47890000440572684646750770557409e-14,
+0.75956178436192215972642568545248e-15,
-0.13131556016891440382773397487633e-15,
+0.24483618345240857495426820738355e-16,
-0.48805729810618777683256761918331e-17,
+0.10327285029786316149223756361204e-17,
-0.23057633815057217157004744527025e-18,
+0.54044443001892693993017108483765e-19,
-0.13240695194366572724155032882385e-19,
+0.33780795621371970203424792124722e-20,
-0.89457629157111779003026926292299e-21,
+0.24519906889219317090899908651405e-21,
-0.69388422876866318680139933157657e-22,
+0.20228278714890138392946303337791e-22,
-0.60628500002335483105794195371764e-23,
+0.18649748964037635381823788396270e-23,
-0.58783732384849894560245036530867e-24,
+0.18958591447999563485531179503513e-24,
-0.62481979372258858959291620728565e-25,
+0.21017901684551024686638633529074e-25,
-0.72084300935209253690813933992446e-26,
+0.25181363892474240867156405976746e-26,
-0.89518042258785778806143945953643e-27,
+0.32357237479762298533256235868587e-27,
-0.11883010519855353657047144113796e-27,
+0.44306286907358104820579231941731e-28,
-0.16761009648834829495792010135681e-28,
+0.64292946921207466972532393966088e-29,
-0.24992261166978652421207213682763e-29,
+0.98399794299521955672828260355318e-30,
-0.39220375242408016397989131626158e-30,
+0.15818107030056522138590618845692e-30,
-0.64525506144890715944344098365426e-31,
+0.26611111369199356137177018346367e-31)
float[] _bm02cs = array.from( 0.0,
+0.9500415145228381369330861335560e-01,
-0.3801864682365670991748081566851e-03,
+0.2258339301031481192951829927224e-05,
-0.3895725802372228764730621412605e-07,
+0.1246886416512081697930990529725e-08,
-0.6065949022102503779803835058387e-10,
+0.4008461651421746991015275971045e-11,
-0.3350998183398094218467298794574e-12,
+0.3377119716517417367063264341996e-13,
-0.3964585901635012700569356295823e-14,
+0.5286111503883857217387939744735e-15,
-0.7852519083450852313654640243493e-16,
+0.1280300573386682201011634073449e-16,
-0.2263996296391429776287099244884e-17,
+0.4300496929656790388646410290477e-18,
-0.8705749805132587079747535451455e-19,
+0.1865862713962095141181442772050e-19,
-0.4210482486093065457345086972301e-20,
+0.9956676964228400991581627417842e-21,
-0.2457357442805313359605921478547e-21,
+0.6307692160762031568087353707059e-22,
-0.1678773691440740142693331172388e-22,
+0.4620259064673904433770878136087e-23,
-0.1311782266860308732237693402496e-23,
+0.3834087564116302827747922440276e-24,
-0.1151459324077741271072613293576e-24,
+0.3547210007523338523076971345213e-25,
-0.1119218385815004646264355942176e-25,
+0.3611879427629837831698404994257e-26,
-0.1190687765913333150092641762463e-26,
+0.4005094059403968131802476449536e-27,
-0.1373169422452212390595193916017e-27,
+0.4794199088742531585996491526437e-28,
-0.1702965627624109584006994476452e-28,
+0.6149512428936330071503575161324e-29,
-0.2255766896581828349944300237242e-29,
+0.8399707509294299486061658353200e-30,
-0.3172997595562602355567423936152e-30,
+0.1215205298881298554583333026514e-30,
-0.4715852749754438693013210568045e-31)
float[] _bt02cs = array.from( 0.0,
-0.24548295213424597462050467249324e+00,
+0.12544121039084615780785331778299e-02,
-0.31253950414871522854973446709571e-04,
+0.14709778249940831164453426969314e-05,
-0.99543488937950033643468850351158e-07,
+0.85493166733203041247578711397751e-08,
-0.86989759526554334557985512179192e-09,
+0.10052099533559791084540101082153e-09,
-0.12828230601708892903483623685544e-10,
+0.17731700781805131705655750451023e-11,
-0.26174574569485577488636284180925e-12,
+0.40828351389972059621966481221103e-13,
-0.66751668239742720054606749554261e-14,
+0.11365761393071629448392469549951e-14,
-0.20051189620647160250559266412117e-15,
+0.36497978794766269635720591464106e-16,
-0.68309637564582303169355843788800e-17,
+0.13107583145670756620057104267946e-17,
-0.25723363101850607778757130649599e-18,
+0.51521657441863959925267780949333e-19,
-0.10513017563758802637940741461333e-19,
+0.21820381991194813847301084501333e-20,
-0.46004701210362160577225905493333e-21,
+0.98407006925466818520953651199999e-22,
-0.21334038035728375844735986346666e-22,
+0.46831036423973365296066286933333e-23,
-0.10400213691985747236513382399999e-23,
+0.23349105677301510051777740800000e-24,
-0.52956825323318615788049749333333e-25,
+0.12126341952959756829196287999999e-25,
-0.28018897082289428760275626666666e-26,
+0.65292678987012873342593706666666e-27,
-0.15337980061873346427835733333333e-27,
+0.36305884306364536682359466666666e-28,
-0.86560755713629122479172266666666e-29,
+0.20779909972536284571238399999999e-29,
-0.50211170221417221674325333333333e-30,
+0.12208360279441714184191999999999e-30,
-0.29860056267039913454250666666666e-31)
//}
float _pi4 = 0.785398163397448309615660845819876
float _eta = 0.1 * f_r8_mach(3)
int _nbm0 = f_r8_inits(_bm0cs, 37, _eta)
int _nbt02 = f_r8_inits(_bt02cs, 39, _eta)
int _nbm02 = f_r8_inits(_bm02cs, 40, _eta)
int _nbth0 = f_r8_inits(_bth0cs, 44, _eta)
float _xmax = 1.0 / f_r8_mach(4)
if x < 4.0
// x under limit
[float(na), float(na)]
else
if x <= 8.0
float _z = (128.0 / x / x - 5.0) / 3.0
_ampl = (0.75 + f_r8_csevl(_z, _bm0cs, _nbm0)) / math.sqrt(x)
_theta = x - _pi4 + f_r8_csevl(_z, _bt02cs, _nbt02) / x
[_ampl, _theta]
else
float _z = 128.0 / x / x - 1.0
_ampl = (0.75 + f_r8_csevl(_z, _bm02cs, _nbm02)) / math.sqrt(x)
_theta = x - _pi4 + f_r8_csevl(_z, _bth0cs, _nbth0) / x
[_ampl, _theta]
// usage:
// [aa, bb] = f_r8_b0mp(math.pi*2)
// plot(aa), plot(bb)
//}
// @function a
f_r8_besj0 (float _x) => //{
//{
float[] _bj0cs = array.from(
+0.00000000000000000000000000000000e+00,
+0.10025416196893913701073127264074e+00,
-0.66522300776440513177678757831124e+00,
+0.24898370349828131370460468726680e+00,
-0.33252723170035769653884341503854e-01,
+0.23114179304694015462904924117729e-02,
-0.99112774199508092339048519336549e-04,
+0.28916708643998808884733903747078e-05,
-0.61210858663032635057818407481516e-07,
+0.98386507938567841324768748636415e-09,
-0.12423551597301765145515897006836e-10,
+0.12654336302559045797915827210363e-12,
-0.10619456495287244546914817512959e-14,
+0.74706210758024567437098915584000e-17,
-0.44697032274412780547627007999999e-19,
+0.23024281584337436200523093333333e-21,
-0.10319144794166698148522666666666e-23,
+0.40608178274873322700800000000000e-26,
-0.14143836005240913919999999999999e-28,
+0.43910905496698880000000000000000e-31 )
//}
int _ntj0 = 0
_xsml = 0.0
if ( _ntj0 == 0 )
_ntj0 := f_r8_inits(_bj0cs, 19, 0.1 * f_r8_mach(3))
_xsml := math.sqrt(4.0 * f_r8_mach(3))
_y = math.abs(_x)
if _y <= _xsml
1.0
else if _y <= 4.0
f_r8_csevl(0.125 * _y * _y - 1.0, _bj0cs, _ntj0)
else
[_ampl, _theta] = f_r8_b0mp(_y)
_ampl * math.cos(_theta)
// usage:
// plot(f_r8_besj0(0.2))
// reference:
// https://people.sc.fsu.edu/~jburkardt/f_src/fn/fn.f90 line: 17498
//}
// @function Evaluates the Bessel J. correlation method.
// @param sample_a float array, sample data.
// @param correlation_length int, correlation length.
// @returns float array with correlations.
export correlation_bessel_j(float[] sample_a, int correlation_length) => //{
int _size_a = array.size(id=sample_a)
if _size_a > 0
float[] _corr = array.new_float(size=_size_a)
for _i = 0 to _size_a-1
float _y = math.abs(array.get(id=sample_a, index=_i)) / correlation_length
array.set(id=_corr, index=_i, value=f_r8_besj0(_y))
_corr
if barstate.islast
_arr = array.from(0.2, 0.5, 0.0, 0.23, 0.56, 0.70, 0.3, 0.8, 0.3, 0.9)
_t = correlation_bessel_j(_arr, 2)
label.new(bar_index, 0.0, str.format('{0}', _t))
//}
Overview
CorrelationExtendsStatistics returns machine-dependent floating-point constants, truncates a Chebyshev coefficient array to a requested accuracy, and evaluates a Chebyshev series at a point inside a narrow valid range. There are no inputs, signals, entries, exits, or position rules. The library header still lacks a description, and the published excerpt ends mid-example.
- Machine-dependent floating-point constants
- Chebyshev series initialization by accuracy
- Chebyshev series evaluation
- Exported functions for other scripts
Details
Published by
ricardosantos79 on GitHub
Code credit
RicardoSantos, as written in the script's header
Type
Library, Pine Script v5
Draws
Library (no plots)
Markets
Any symbol
Timeframes
Any timeframe
Risk Notes
No repainting, lookahead or stacked entries were found in its code or README. That says nothing about how well it works: test it first.
Third-party code. ForexR did not write, test or endorse this script, and the summary above was generated automatically from its code and README. Indicators describe the past, and a strategy's backtest can look better than live trading, especially when a script repaints. Check it in the Strategy Tester and on a demo account before you rely on it.
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