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
MathComplexExtension
This Pine Script v5 library extends complex-number handling for other scripts.
GitHub stars261on the repository
Pine versionv5runs as is
Lines of code300
Settings0inputs
LicenceNone statedfile: MPL-2.0
Last update4 years ago13 Nov 2021
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Source Code
300 lines of Pine Script v5 from beta/libs/MathComplex/MathComplexExtension.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 A set of utility functions to handle complex numbers.
library(title='MathComplexExtension')
// references:
// https://en.wikipedia.org/wiki/Complex_number
// js: https://rosettacode.org/wiki/Fast_Fourier_transform
// https://github.com/trekhleb/javascript-algorithms/blob/477f30b0bdac6024874d2976de1eca7afe0176dd/src/algorithms/math/complex-number/ComplexNumber.js#L3
// https://github.com/infusion/Complex.js/
// https://github.com/mathnet/mathnet-numerics/blob/a50d68d52def605a53d129cc60ea3371a2e97548/src/Numerics/Complex32.cs
// imports:
import RicardoSantos/DebugConsole/2 as console
// console.init(), console.queue(), console.update()
[__T, __C] = console.init(20) //initiate console configuration variables.
//
import RicardoSantos/MathConstants/1 as mc
// mc.Pi2() -> cubic_roots()
import RicardoSantos/MathComplexCore/3 as complex
//
import RicardoSantos/MathComplexOperator/2 as complex_op
//
// @function The phase value of complex number complex_number.
// @param complex_number float array, pseudo complex number in the form of a array [real, imaginary].
// @param in_radians boolean, value for the type of angle value, default=true, options=(true: radians, false: degrees)
// @returns float value with phase.
export get_phase (float[] complex_number, bool in_radians=true) => //{
float _re = complex.get_real(complex_number)
float _im = complex.get_imaginary(complex_number)
float _phase = math.atan(math.abs(_im) / math.abs(_re))
if not in_radians
_phase := _phase * (180 / math.pi) // radian to degrees
else
if _re < 0 and _im > 0
_phase := math.pi - nz(_phase)
else if _re < 0 and _im < 0
_phase := -(math.pi - nz(_phase))
else if _re > 0 and _im < 0
_phase := -nz(_phase)
else if _re == 0 and _im > 0
_phase := math.pi / 2.0
else if _re == 0 and _im < 0
_phase := -math.pi / 2.0
else if _re < 0 and _im == 0
_phase := math.pi
else if _re > 0 and _im == 0
_phase := 0.0
else if _re == 0 and _im == 0
// More correctly would be to set 'indeterminate'.
// But just for simplicity reasons let's set zero.
_phase := 0.0
else
na
_phase
//{ usage:
// console.queue_one(__C, str.format('phase of complex number "5.2+3.0i" = in radeans: {0, number, #.##}, in degrees: {1, number, #.##}', get_phase(new(5.2, 3.0), true), get_phase(new(5.2, 3.0), false) )) // 36.0
//}}
// @function Natural logarithm of complex number (base E).
// @param complex_number float array, pseudo complex number in the form of a array [real, imaginary].
// @returns float array, complex number.
export natural_logarithm (float[] complex_number) => //{
if not complex.is_complex(complex_number)
runtime.error('MathComplex -> natural_logarithm(): "complex_number" has the wrong size.')
array.new_float(na)
else if complex.is_real_non_negative(complex_number)
complex.new(math.log(complex.get_real(complex_number)), 0.0)
else
float _re = math.pow(complex.get_real(complex_number), 2)
float _im = math.pow(complex.get_imaginary(complex_number), 2)
complex.new(0.5 * math.log(complex_op.magnitude_squared(complex_number)), get_phase(complex_number, true))
//{ usage:
// console.queue_one(__C, str.format('natural logarithm of complex number "-1.0+0i" = {0} // iπ', to_string(natural_logarithm(new(-1.0, 0.0)), '#.##'))) // "0.0+3.1416i", "iπ"
//{ remarks:
// https://github.com/mathnet/mathnet-numerics/blob/a50d68d52def605a53d129cc60ea3371a2e97548/src/Numerics/Complex32.cs#L350
// https://www.mathworks.com/help/matlab/ref/log.html
//}}}
// @function Common logarithm of complex number (base 10).
// @param complex_number float array, pseudo complex number in the form of a array [real, imaginary].
// @returns float array, complex number.
export common_logarithm (float[] complex_number) => //{
if not complex.is_complex(complex_number)
runtime.error('MathComplex -> common_logarithm(): "complex_number" has the wrong size.')
array.new_float(na)
else
complex_op.divide(natural_logarithm(complex_number), complex.new(mc.Ln10(), 0.0))
//{ usage:
// console.queue_one(__C, str.format('common logarithm of complex number "0-2i" = {0} ', to_string(common_logarithm(new(0.0, -2.0)), '#.##'))) // "0.301-0.6822i"
//{ remarks:
// https://github.com/mathnet/mathnet-numerics/blob/a50d68d52def605a53d129cc60ea3371a2e97548/src/Numerics/Complex32.cs#L350
// https://www.mathworks.com/help/matlab/ref/log10.html
//}}}
// @function Common logarithm of complex number (custom base).
// @param complex_number float array, pseudo complex number in the form of a array [real, imaginary].
// @param base float, base value.
// @returns float array, complex number.
export logarithm (float[] complex_number, float base) => //{
if not complex.is_complex(complex_number)
runtime.error('MathComplex -> common_logarithm(): "complex_number" has the wrong size.')
array.new_float(na)
else
complex_op.divide(natural_logarithm(complex_number), complex.new(math.log(base), 0.0))
//{ usage:
// console.queue_one(__C, str.format('logarithm of complex number "0-2i" = {0} ', to_string(logarithm(new(0.0, -2.0), 10.0), '#.##'))) // "0.301-0.6822i"
//{ remarks:
// https://github.com/mathnet/mathnet-numerics/blob/a50d68d52def605a53d129cc60ea3371a2e97548/src/Numerics/Complex32.cs#L350
// https://www.mathworks.com/help/matlab/ref/log10.html
//}}}
// @function Raise complex_number with complex_exponent.
// @param complex_number float array, pseudo complex number in the form of a array [real, imaginary].
// @param complex_exponent float array, pseudo complex number in the form of a array [real, imaginary].
// @returns float array, pseudo complex number in the form of a array [real, imaginary]
export power (float[] complex_number, float[] complex_exponent) => //{
if not complex.is_complex(complex_number)
runtime.error('MathComplex -> power(): "complex_number" has the wrong size.')
array.new_float(na)
else
float _a_re = complex.get_real(complex_number)
float _a_im = complex.get_imaginary(complex_number)
float _b_re = complex.get_real(complex_exponent)
float _b_im = complex.get_imaginary(complex_exponent)
if complex.is_zero(complex_number)
if complex.is_zero(complex_exponent)
complex.one()
else if _b_re > 0.0
complex.zero()
else if _b_re < 0.0
if _b_im == 0
complex.new(float(na), 0.0) // "+∞+0i"
else
complex.nan() // "+∞+∞i"
complex.nan()
else
// (exponent * natural_logarithm()).exponential()
complex_op.exponential(complex_op.multiply(complex_exponent, natural_logarithm(complex_number)))
//{ usage:
// console.queue_one(__C, str.format('power of complex number "2+1i" ^ "4+0i" = {0} ', to_string(power(new(2.0, 1.0), new(4.0, 0.0)), '#.##'))) // "-7+24i"
//{ remarks:
// https://www.superprof.co.uk/resources/academic/maths/arithmetic/complex-numbers/power-of-a-complex-number.html
//}}}
// @function Raise complex_number with inverse of complex_exponent.
// @param complex_number float array, pseudo complex number in the form of a array [real, imaginary].
// @param complex_exponent float array, pseudo complex number in the form of a array [real, imaginary].
// @returns float array, pseudo complex number in the form of a array [real, imaginary]
export root (float[] complex_number, float[] complex_exponent) => //{
if not complex.is_complex(complex_number)
runtime.error('MathComplex -> root(): "complex_number" has the wrong size.')
array.new_float(na)
else if not complex.is_complex(complex_exponent)
runtime.error('MathComplex -> root(): "complex_exponent" has the wrong size.')
array.new_float(na)
else
power(complex_number, complex_op.divide(complex.one(), complex_exponent))
//{ usage:
// console.queue_one(__C, str.format('root of complex number ("2+0i" √ "-5+12i") = {0} ', to_string(root(new(-5.0, 12.0), new(2.0, 0.0)), '#.##'))) //
//{ remarks:
// https://www.intmath.com/complex-numbers/7-powers-roots-demoivre.php
//}}}
// @function Square of complex_number (power 2).
// @param complex_number float array, pseudo complex number in the form of a array [real, imaginary].
// @returns float array, pseudo complex number in the form of a array [real, imaginary]
export square (float[] complex_number) => //{
if not complex.is_complex(complex_number)
runtime.error('MathComplex -> square(): "complex_number" has the wrong size.')
array.new_float(na)
else
float _re = complex.get_real(complex_number)
if complex.is_real(complex_number)
complex.new(math.pow(_re, 2.0), 0.0)
else
float _im = complex.get_imaginary(complex_number)
complex.new(math.pow(_re, 2.0) - math.pow(_im, 2.0), 2.0 * _re * _im)
//{ usage:
// console.queue_one(__C, str.format('square of complex number "12-6i"^2 = {0} ', to_string(square(new(12.0, -6.0)), '#.##'))) //
//{ remarks:
// https://docs.microsoft.com/en-us/dotnet/api/system.numerics.complex.pow?view=net-5.0
//}}}
// @function Square root of complex_number (power 1/2).
// @param complex_number float array, pseudo complex number in the form of a array [real, imaginary].
// @returns float array, pseudo complex number in the form of a array [real, imaginary]
export square_root (float[] complex_number) => //{
if not complex.is_complex(complex_number)
runtime.error('MathComplex -> square_root(): "complex_number" has the wrong size.')
array.new_float(na)
else
float _re = complex.get_real(complex_number)
if complex.is_real_non_negative(complex_number)
complex.new(math.sqrt(_re), 0.0)
else
float _im = complex.get_imaginary(complex_number)
float _abs_re = math.abs(_re)
float _abs_im = math.abs(_im)
float _w = 0.0
if _abs_re >= _abs_im
float _ratio = _im / _re
_w := math.sqrt(_abs_re) * math.sqrt(0.5 * (1.0 + math.sqrt(1.0 + math.pow(_ratio, 2))))
else
float _ratio = _re / _im
_w := math.sqrt(_abs_im) * math.sqrt(0.5 * (math.abs(_ratio) + math.sqrt(1.0 + math.pow(_ratio, 2))))
if _re >= 0.0
complex.new(_w, _im / (2.0 * _w))
else if _im >= 0.0
complex.new(_abs_im / (2.0 * _w), _w)
else
complex.new(_abs_im / (2.0 * _w), -_w)
//{ usage:
// console.queue_one(__C, str.format('square root of complex number "6-8i" = {0} ', to_string(square_root(new(6.0, -8.0)), '#.##'))) //
//{ remarks:
// https://www.brainkart.com/article/Square-roots-of-a-complex-number_39098/
//}}}
// @function Square root of complex_number (power 1/2).
// @param complex_number float array, pseudo complex number in the form of a array [real, imaginary].
// @returns tuple with 2 complex numbers.
export square_roots (float[] complex_number) => //{
if not complex.is_complex(complex_number)
runtime.error('MathComplex -> square_roots(): "complex_number" has the wrong size.')
[array.new_float(na), array.new_float(na)]
else
_principal = square_root(complex_number)
[_principal, complex_op.negative(_principal)]
//{ usage:
// [sr_pos, sr_neg] = square_roots(new(6.0, -8.0))
// console.queue_one(__C, str.format('square roots of complex number "6-8i" = {0} ___ {1}', to_string(sr_pos, '#.##'), to_string(sr_neg, '#.##'))) //
//{ remarks:
// https://github.com/mathnet/mathnet-numerics/blob/a50d68d52def605a53d129cc60ea3371a2e97548/src/Numerics/Complex32.cs#L492
//}}}
// @function Square root of complex_number (power 1/2).
// @param complex_number float array, pseudo complex number in the form of a array [real, imaginary].
// @returns tuple with 2 complex numbers.
export cubic_roots (float[] complex_number) => //{
if not complex.is_complex(complex_number)
runtime.error('MathComplex -> square_roots(): "complex_number" has the wrong size.')
[array.new_float(na), array.new_float(na), array.new_float(na)]
else
float _r = math.pow(complex_op.magnitude(complex_number), 1.0 / 3.0)
float _theta = get_phase(complex_number, true)
float _shift = mc.Pi2() / 3.0
[complex.from_polar_coordinates(_r, _theta), complex.from_polar_coordinates(_r, _theta + _shift), complex.from_polar_coordinates(_r, _theta - _shift)]
//{ usage:
// [cr_neu, cr_pos, cr_neg] = cubic_roots(new(6.0, -8.0))
// console.queue_one(__C, str.format('cubic roots of complex number "6-8i" = {0} ___ {1} ___ {2}', to_string(cr_neu, '#.##'), to_string(cr_pos, '#.##'), to_string(cr_neg, '#.##'))) //
//{ remarks:
// https://github.com/mathnet/mathnet-numerics/blob/a50d68d52def605a53d129cc60ea3371a2e97548/src/Numerics/Complex32.cs#L501
//}}}
// @function The polar form value of complex_number.
// @param complex_number float array, pseudo complex number in the form of a array [real, imaginary].
// @param in_radians boolean, value for the type of angle value, default=true, options=(true: radians, false: degrees)
// @returns float array, pseudo complex number in the form of a array [real, imaginary]
// ** returns a array [radius, phase]
export to_polar_form (float[] complex_number, bool in_radians=true) => //{
complex.new(complex_op.radius(complex_number), get_phase(complex_number, in_radians))
//{ usage:
// console.queue_one(__C, str.format('polar form of complex number "5.2+3.0i" = in radeans: {0} , in degrees: {1}', to_string(to_polar_form(new(5.2, 3.0), true), '#.##'), to_string(to_polar_form(new(5.2, 3.0), false), '#.##'))) //
// cn = to_polar_form(new(5.2, 3.0), false)
// plot(get_real(cn)), plot(get_imaginary(cn))
// // reactangular form "5.2+3.0i" converts to: "6+0.5i" in radeans || "6+30i" in degrees
//{ remarks:
// https://www.electronics-tutorials.ws/accircuits/complex-numbers.html
//}}}
if barstate.islastconfirmedhistory
A = complex.new(7.0, -6.0)
B = complex.new(-3.0, 4.0)
console.queue_one(__C, str.format('input parameters: (A: {0}, B: {1})', complex.to_string(A, '#.##'), complex.to_string(B, '#.##')))
console.queue_one(__C, str.format('\n## Extended ##\n', ''))
console.queue_one(__C, str.format('phase of A = (radeans: {0}, in degrees: {1})', get_phase(A, true), get_phase(A, false)))
console.queue_one(__C, str.format('Natural Logarithm (E) of A = {0}', complex.to_string(natural_logarithm(A), '#.##')))
console.queue_one(__C, str.format('Common Logarithm (10) of A = {0}', complex.to_string(common_logarithm(A), '#.##')))
console.queue_one(__C, str.format('Logarithm (base=10) of A = {0}', complex.to_string(logarithm(A, 10.0), '#.##')))
console.queue_one(__C, str.format('Power of A^B = {0}', complex.to_string(power(A, B), '#.##')))
console.queue_one(__C, str.format('Root of B√A = {0}', complex.to_string(root(A, B), '#.##')))
console.queue_one(__C, str.format('Square of A = {0}', complex.to_string(square(A), '#.##')))
console.queue_one(__C, str.format('Square Root of A = {0}', complex.to_string(square_root(A), '#.##')))
[Spos, Sneg] = square_roots(A)
[Cneu, Cpos, Cneg] = cubic_roots(A)
console.queue_one(__C, str.format('Square Roots of A = ({0}, {1})', complex.to_string(Spos, '#.##'), complex.to_string(Sneg, '#.##')))
console.queue_one(__C, str.format('Cubic Roots of A = ({0}, {1}, {2})', complex.to_string(Cneu, '#.##'), complex.to_string(Cpos, '#.##'), complex.to_string(Cneg, '#.##')))
console.queue_one(__C, str.format('Polar form of A = {0}', complex.to_string(to_polar_form(A), '#.##')))
// update console
console.update(__T, __C)
Overview
MathComplexExtension treats a complex value as a two-element float array of real and imaginary parts. It exports get_phase, which returns the argument in radians or degrees with quadrant and axis special cases, and natural_logarithm, which returns a complex result using magnitude and phase. Invalid array size raises a runtime error. It draws nothing and has no inputs.
- Phase of a complex number in radians or degrees
- Natural logarithm of a complex number
- Complex values stored as real and imaginary arrays
- Runtime error when the array size is invalid
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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