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
AnalysisInterpolationLoess
This Pine Script v5 library provides a LOESS local weighted smoothing routine for paired x and y sample arrays.
GitHub stars261on the repository
Pine versionv5runs as is
Lines of code217
Settings4inputs
LicenceNone statedfile: MPL-2.0
Last update4 years ago13 Nov 2021
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Source Code
217 lines of Pine Script v5 from beta/libs/AnalysisInterpolationLoess.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 LOESS, local weighted Smoothing function.
library(title='AnalysisInterpolationLoess')
// reference:
// https://commons.apache.org/proper/commons-math/javadocs/api-3.3/org/apache/commons/math3/analysis/interpolation/LoessInterpolator.html
// @function Helper function for the loess library
// @param value float, value.
// @returns float
tricubic (float value) => //{
if value > 1.0
0.0
else
math.pow(1 - math.pow(value, 3), 3)
//}
// @function Helper function for the loess library
// @param value float, value.
// @param exponent float, exponent.
// @returns float
polyweight (float value, float exponent) => //{
if value > 1.0
0.0
else
math.pow(1 - math.pow(value, exponent), exponent)
//{ credit to @midtownSk8rguy
//}}
// @function LOESS, local weighted Smoothing function.
// @param sample_x int array, x values.
// @param sample_y float array, y values.
// @param point_span int, local point interval span.
export loess (int[] sample_x, float[] sample_y, int point_span=2) => //{
int _size_x = array.size(id=sample_x)-1
int _size_y = array.size(id=sample_y)-1
// to improve performance there is:
// no monotonic sequence check, no null checks.
if _size_x < 1 or _size_y < 1
runtime.error('AnalysisInterpolationLoess -> loess(): samples x and y must have at the least 1 element.')
float[] _A = na
else if _size_x != _size_y
runtime.error('AnalysisInterpolationLoess -> loess(): samples x and y must have the same number of elements.')
float[] _A = na
else if point_span < 1
runtime.error('AnalysisInterpolationLoess -> loess(): point_span must be positive integer number over 0.')
float[] _A = na
else if 2 * point_span > _size_x
runtime.error('AnalysisInterpolationLoess -> loess(): point_span must be smaller than sample size.')
float[] _A = na
else
float[] _yloess = array.new_float(size=1 + _size_x)
for _i = 0 to _size_x
int _xi = array.get(id=sample_x, index=_i)
// define the index interval to pool the values
int _start = 0
int _end = _size_x
if _i < 1 + point_span
_start := math.max(0, _i - point_span)
_end := _i + point_span
else
_start := _i - point_span
_end := math.min(_i + point_span, _size_x)
// grab the values for the interval span
int[] _span_x = array.slice(id=sample_x, index_from=_start, index_to=_end)
float[] _span_y = array.slice(id=sample_y, index_from=_start, index_to=_end)
// calculate the distance, weights then perform local regression
int _size_s = array.size(id=_span_x)-1
float _sum_w = 0.0
float _sum_x = 0.0
float _sum_x2 = 0.0
float _sum_y = 0.0
float _sum_xy = 0.0
for _s = 0 to _size_s
int _xs = array.get(id=_span_x, index=_s)
float _ys = array.get(id=_span_y, index=_s)
int _ds = math.abs(_xs-_xi)
float _ws = tricubic(_ds / point_span)
float _wxs = _ws * _xs
_sum_w += _ws
_sum_x += _wxs
_sum_x2 += _wxs * _xs
_sum_y += _ws * _ys
_sum_xy += _wxs * _ys
float _mean_x = _sum_x / _sum_w
float _mean_y = _sum_y / _sum_w
float _mean_xy = _sum_xy / _sum_w
float _mean_x2 = _sum_x2 / _sum_w
float _mx2xx = _mean_x2 - math.pow(_mean_x, 2)
float _beta = 0.0
if math.sqrt(math.abs(_mx2xx)) < 1.0e-15
_beta := (_mean_xy - _mean_x * _mean_y) / _mx2xx
float _alpha = _mean_y - _beta * _mean_x
//update current y loess value at _i index
array.set(id=_yloess, index=_i, value=_beta * _xi + _alpha)
_yloess
//{ usage:
// length = input.int(50)
// npoints= input.int(7)
// f_l1(_x1, _y1, _x2, _y2) => line.new(_x1, _y1, _x2, _y2, color=#DDDD00, style=line.style_solid, width=1)
// import RicardoSantos/ArrayExtension/2 as ae
// a = bar_index < length ? array.from(0) : ae.to_int(ae.sequence_from_series(bar_index, length, 0, true), 'floor')
// b = bar_index < length ? array.from(0.0) : ae.sequence_from_series(close, length, 0, true)
// if barstate.islastconfirmedhistory
// c = loess(a, b, npoints)
// label.new(bar_index, 0.0, str.tostring(c, '#.###'))
// for _i = 1 to array.size(a)-1
// _x1 = array.get(a, _i-1)
// _x2 = array.get(a, _i )
// _by1 = array.get(c, _i-1)
// _by2 = array.get(c, _i)
// f_l1(_x1, _by1, _x2, _by2)
// plot(close)
//}}
// @function aLOESS, adaptive local weighted Smoothing function.
// @param sample_x int array, x values.
// @param sample_y float array, y values.
// @param point_span int, local point interval span.
export aloess (int[] sample_x, float[] sample_y, int point_span=2, float span_exponent=3.0) => //{
int _size_x = array.size(id=sample_x)-1
int _size_y = array.size(id=sample_y)-1
// to improve performance there is:
// no monotonic sequence check, no null checks.
if _size_x < 1 or _size_y < 1
runtime.error('AnalysisInterpolationLoess -> aloess(): samples x and y must have at the least 1 element.')
float[] _A = na
else if _size_x != _size_y
runtime.error('AnalysisInterpolationLoess -> aloess(): samples x and y must have the same number of elements.')
float[] _A = na
else if point_span < 1
runtime.error('AnalysisInterpolationLoess -> aloess(): point_span must be positive integer number over 0.')
float[] _A = na
else if 2 * point_span > _size_x
runtime.error('AnalysisInterpolationLoess -> aloess(): point_span must be smaller than sample size.')
float[] _A = na
else
float[] _yloess = array.new_float(size=1 + _size_x)
for _i = 0 to _size_x
int _xi = array.get(id=sample_x, index=_i)
// define the index interval to pool the values
int _start = 0
int _end = _size_x
if _i < 1 + point_span
_start := math.max(0, _i - point_span)
_end := _i + point_span
else
_start := _i - point_span
_end := math.min(_i + point_span, _size_x)
// grab the values for the interval span
int[] _span_x = array.slice(id=sample_x, index_from=_start, index_to=_end)
float[] _span_y = array.slice(id=sample_y, index_from=_start, index_to=_end)
// calculate the distance, weights then perform local regression
int _size_s = array.size(id=_span_x)-1
float _sum_w = 0.0
float _sum_x = 0.0
float _sum_x2 = 0.0
float _sum_y = 0.0
float _sum_xy = 0.0
for _s = 0 to _size_s
int _xs = array.get(id=_span_x, index=_s)
float _ys = array.get(id=_span_y, index=_s)
int _ds = math.abs(_xs-_xi)
float _ws = polyweight(_ds / point_span, span_exponent)
float _wxs = _ws * _xs
_sum_w += _ws
_sum_x += _wxs
_sum_x2 += _wxs * _xs
_sum_y += _ws * _ys
_sum_xy += _wxs * _ys
float _mean_x = _sum_x / _sum_w
float _mean_y = _sum_y / _sum_w
float _mean_xy = _sum_xy / _sum_w
float _mean_x2 = _sum_x2 / _sum_w
float _mx2xx = _mean_x2 - math.pow(_mean_x, 2)
float _beta = 0.0
if math.sqrt(math.abs(_mx2xx)) < 1.0e-15
_beta := (_mean_xy - _mean_x * _mean_y) / _mx2xx
float _alpha = _mean_y - _beta * _mean_x
//update current y loess value at _i index
array.set(id=_yloess, index=_i, value=_beta * _xi + _alpha)
_yloess
//{ usage:
adaptive = input.bool(false)
length = input.int(50)
npoints = input.int(7)
exp = input.float(3.0)
f_l1(_x1, _y1, _x2, _y2) => line.new(_x1, _y1, _x2, _y2, color=#DDDD00, style=line.style_solid, width=1)
import RicardoSantos/ArrayGenerate/1 as ag
import RicardoSantos/ArrayExtension/1 as ae
a = bar_index <= length ? array.from(0) : ae.to_int(ag.sequence_from_series(bar_index, length, 0, true), 'floor')
b = bar_index <= length ? array.from(0.0) : ag.sequence_from_series(close, length, 0, true)
if barstate.islastconfirmedhistory
c = adaptive ? aloess(a, b, npoints, exp) : loess(a, b, npoints)
// label.new(bar_index, 0.0, str.tostring(c, '#.###'))
for _i = 1 to array.size(a)-1
_x1 = array.get(a, _i-1)
_x2 = array.get(a, _i )
_by1 = array.get(c, _i-1)
_by2 = array.get(c, _i)
f_l1(_x1, _by1, _x2, _by2)
plot(close)
//}}
Overview
AnalysisInterpolationLoess builds a local neighborhood around each sample, applies a tricubic distance weight, and fits a weighted local regression. A separate polynomial weight helper uses a configurable exponent. Callers pass the point span that sets the neighborhood width. The library draws nothing and performs no trading signals, entries, or exits. It rejects mismatched, empty, or oversized spans with runtime errors and skips monotonic and null checks for speed.
- LOESS local weighted smoothing
- Tricubic distance weighting
- Polynomial weight helper
- Configurable point span
- Runtime sample validation
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.
Settings
The inputs you can change from the gear icon on the chart. Defaults are the author's.
| Setting | Type | Default | Variable |
|---|---|---|---|
| adaptive | bool | false | adaptive |
| length | int | 50 | length |
| npoints | int | 7 | npoints |
| exp | float | 3.0 | exp |
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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