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
MathSpecialFunctionsTestFunctions
This library provides implementations of standard mathematical test functions used for optimization algorithm evaluation.
GitHub stars261on the repository
Pine versionv5runs as is
Lines of code187
Settings0inputs
LicenceNone statedfile: MPL-2.0
Last update4 years ago13 Nov 2021
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Source Code
187 lines of Pine Script v5 from beta/libs/Math/MathSpecialFunctionsTestFunctions.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 Methods for test functions.
library(title='MathSpecialFunctionsTestFunctions')
// reference:
// https://github.com/mathnet/mathnet-numerics/blob/a50d68d52def605a53d129cc60ea3371a2e97548/src/Numerics/SpecialFunctions/TestFunctions.cs
// imports:
import RicardoSantos/DebugConsole/1 as console
[__T, __C] = console.init(25)
import RicardoSantos/MathConstants/1 as constants
// constants.Pi2() -> ackley()
// @function Valley-shaped Rosenbrock function for 2 dimensions: (x,y) -> (1-x)^2 + 100*(y-x^2)^2.
// @param input_x float, common range within (-5.0, 10.0) or (-2.048, 2.048).
// @param input_y float, common range within (-5.0, 10.0) or (-2.048, 2.048).
// @returns float
export rosenbrock (float input_x, float input_y) => //{
float _a = 1.0 - input_x
float _b = input_y - math.pow(input_x, 2.0)
math.pow(_a, 2.0) + 100 * math.pow(_b, 2.0)
//{ usage:
console.queue_one(__C, str.format('rosenbrock(2, 1): {0}', rosenbrock(2.0, 1.0)))
//{ remarks:
// This function has a global minimum at (1,1) with f(1,1) = 0.
// Common range: [-5,10] or [-2.048,2.048].
// https://en.wikipedia.org/wiki/Rosenbrock_function
// http://www.sfu.ca/~ssurjano/rosen.html
// test: https://www.wolframalpha.com/input/?i=rosenbrock+function+%282%2C1%29
//}}}
// @function Valley-shaped Rosenbrock function for 2 or more dimensions.
// @param samples float array, common range within (-5.0, 10.0) or (-2.048, 2.048).
// @returns float
export rosenbrock_mdim (float[] samples) => //{
int _size = array.size(samples)
if _size < 2
runtime.error('MathSpecialFunctionsTestFunctions -> ackley(): "samples" has wrong size.')
float(na)
else
float _sum = 0.0
for _i = 1 to _size-1
float _xi = array.get(samples, _i)
_sum += rosenbrock(array.get(samples, _i - 1), array.get(samples, _i))
_sum
//{ usage:
console.queue_one(__C, str.format('rosenbrock_mdim([2, 1, ,-1, -2]): {0}', rosenbrock_mdim(array.from(2.0, 1.0, -1.0, -2.0))))
//{ remarks:
// This function have a global minimum of all ones and, for 8 > N > 3, a local minimum at (-1,1,...,1).
// https://en.wikipedia.org/wiki/Rosenbrock_function
// http://www.sfu.ca/~ssurjano/rosen.html
//}}}
// @function Himmelblau, a multi-modal function: (x,y) -> (x^2+y-11)^2 + (x+y^2-7)^2
// @param input_x float, common range within (-6.0, 6.0 ).
// @param input_y float, common range within (-6.0, 6.0 ).
// @returns float
export himmelblau (float input_x, float input_y) => //{
float _a = math.pow(input_x, 2.0) + input_y - 11.0
float _b = input_x + math.pow(input_y, 2.0) - 7.0
math.pow(_a, 2.0) + math.pow(_b, 2.0)
//{ usage:
console.queue_one(__C, str.format('himmelblau(2, 1): {0}', himmelblau(2.0, 1.0)))
//{ remarks:
// This function has 4 global minima with f(x,y) = 0.
// Common range: [-6,6].
// Named after David Mautner Himmelblau
// https://en.wikipedia.org/wiki/Himmelblau%27s_function
//}}}
// @function Rastrigin, a highly multi-modal function with many local minima.
// @param samples float array, common range within (-5.12, 5.12 ).
// @returns float
export rastrigin (float[] samples) => //{
int _size = array.size(samples)
if _size < 1
runtime.error('MathSpecialFunctionsTestFunctions -> ackley(): "samples" has wrong size.')
float(na)
else
float _pi2 = constants.Pi2()
float _sx2 = 0.0
for _i = 0 to _size-1
float _xi = array.get(samples, _i)
_sx2 += math.pow(_xi, 2.0) - 10.0 * math.cos(_pi2 * _xi)
_sx2 += 10.0 * _size
//{ usage:
console.queue_one(__C, str.format('rastrigin([2, 1, ,-1, -2]): {0}', rastrigin(array.from(2.0, 1.0, -1.0, -2.0))))
//{ remarks:
// Global minimum of all zeros with f(0) = 0.
// Common range: [-5.12,5.12].
// https://en.wikipedia.org/wiki/Rastrigin_function
// http://www.sfu.ca/~ssurjano/rastr.html
//}}}
// @function Drop-Wave, a multi-modal and highly complex function with many local minima.
// @param input_x float, common range within (-5.12, 5.12 ).
// @param input_y float, common range within (-5.12, 5.12 ).
// @returns float
export drop_wave (float input_x, float input_y) => //{
float _t = math.pow(input_x, 2.0) + math.pow(input_y, 2.0)
-(1.0 + math.cos(12.0 * math.sqrt(_t))) / (0.5 * _t + 2.0)
//{ usage:
console.queue_one(__C, str.format('drop_wave(2, 1): {0}', drop_wave(2.0, 1.0)))
//{ remarks:
// Global minimum of all zeros with f(0) = -1.
// Common range: [-5.12,5.12].
// http://www.sfu.ca/~ssurjano/drop.html
//}}}
// @function Ackley, a function with many local minima. It is nearly flat in outer regions but has a large hole at the center.
// @param input_x float array, common range within (-32.768, 32.768 ).
// @returns float
export ackley (float[] samples) => //{
int _size = array.size(samples)
if _size < 1
runtime.error('MathSpecialFunctionsTestFunctions -> ackley(): "samples" has wrong size.')
float(na)
else
float _pi2 = constants.Pi2()
float _u = 0.0
float _v = 0.0
for _i = 0 to _size-1
float _xi = array.get(samples, _i)
_u += math.pow(_xi, 2.0)
_v += math.cos(_pi2 * _xi)
_u /= _size
_v /= _size
-20.0 * math.exp(-0.2 * math.sqrt(_u)) - math.exp(_v) + 20.0 + math.e
//{ usage:
console.queue_one(__C, str.format('ackley([2, 1, ,-1, -2]): {0}', ackley(array.from(2.0, 1.0, -1.0, -2.0))))
//{ remarks:
// Global minimum of all zeros with f(0) = 0.
// Common range: [-32.768, 32.768].
// http://www.sfu.ca/~ssurjano/ackley.html
//}}}
// @function Bowl-shaped first Bohachevsky function.
// @param input_x float, common range within (-100.0, 100.0 ).
// @param input_y float, common range within (-100.0, 100.0 ).
// @returns float
export bohachevsky1 (float input_x, float input_y) => //{
math.pow(input_x, 2.0) + 2.0 * math.pow(input_y, 2.0) - 0.3 * math.cos(3.0 * math.pi * input_x) - 0.4 * math.cos(4.0 * math.pi * input_y)
//{ usage:
console.queue_one(__C, str.format('bohachevsky1(2, 1): {0}', bohachevsky1(2.0, 1.0)))
//{ remarks:
// Global minimum of all zeros with f(0,0) = 0.
// Common range: [-100, 100]
// http://www.sfu.ca/~ssurjano/boha.html
//}}}
// @function Plate-shaped Matyas function.
// @param input_x float, common range within (-10.0, 10.0 ).
// @param input_y float, common range within (-10.0, 10.0 ).
// @returns float
export matyas (float input_x, float input_y) => //{
0.26 * (math.pow(input_x, 2.0) + math.pow(input_y, 2.0)) - 0.48 * input_x * input_y
//{ usage:
console.queue_one(__C, str.format('matyas(2, 1): {0}', matyas(2.0, 1.0)))
//{ remarks:
// Global minimum of all zeros with f(0,0) = 0.
// Common range: [-10, 10].
// http://www.sfu.ca/~ssurjano/matya.html
//}}}
// @function Valley-shaped six-hump camel back function.
// @param input_x float, common range within (-3.0, 3.0 ).
// @param input_y float, common range within (-2.0, 2.0 ).
// @returns float
export six_hump_camel (float input_x, float input_y) => //{
float _x2 = math.pow(input_x, 2)
float _y2 = math.pow(input_y, 2)
(4.0 - 2.1 * _x2 + math.pow(_x2, 2.0) / 3.0) * _x2 + input_x * input_y + (-4.0 + 4.0 * _y2) * _y2
//{ usage:
console.queue_one(__C, str.format('six_hump_camel(2, 1): {0}', six_hump_camel(2.0, 1.0)))
//{ remarks:
// Two global minima and four local minima. Global minima with f(x) ) -1.0316 at (0.0898,-0.7126) and (-0.0898,0.7126).
// Common range: x in [-3,3], y in [-2,2].
// http://www.sfu.ca/~ssurjano/camel6.html
//}}}
//##############################################################################
console.update(__T, __C)
Overview
The Rosenbrock function creates a valley-shaped problem with a global minimum at (1,1), while its multi-dimensional version accepts array inputs for higher dimensions. The Himmelblau function offers a multi-modal surface with four global minima, and the Rastrigin function introduces many local minima for testing robustness. These functions calculate values based on input parameters or sample arrays without plotting on charts or generating trading signals. They serve as benchmarks and can be called from other scripts via the exported functions. The library draws nothing on the price chart and has no inputs or settings.
- Rosenbrock function
- Himmelblau function
- Rastrigin function
- Multi-dimensional arrays
- Optimization benchmarks
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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