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https://github.com/antononcube/raku-math-polynomial-chebyshev
Raku package for functionalities based on Chebyshev polynomials.
https://github.com/antononcube/raku-math-polynomial-chebyshev
chebyshev-polynomials orthogonal-polynomials polynomials raku rakulang
Last synced: 15 days ago
JSON representation
Raku package for functionalities based on Chebyshev polynomials.
- Host: GitHub
- URL: https://github.com/antononcube/raku-math-polynomial-chebyshev
- Owner: antononcube
- License: artistic-2.0
- Created: 2024-06-19T21:56:50.000Z (5 months ago)
- Default Branch: main
- Last Pushed: 2024-06-20T21:39:34.000Z (5 months ago)
- Last Synced: 2024-10-11T20:41:41.311Z (about 1 month ago)
- Topics: chebyshev-polynomials, orthogonal-polynomials, polynomials, raku, rakulang
- Language: Raku
- Homepage: https://raku.land/zef:antononcube/Math::Polynomial::Chebyshev
- Size: 34.2 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README-work.md
- License: LICENSE
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README
# Math::Polynomial::Chebyshev
Raku package for functionalities based on Chebyshev polynomials.
------
## Installation
From Zef ecosystem:
```
zef install Math::Polynomial::Chebyshev
```
From GitHub:
```
zef install https://github.com/antononcube/Raku-Math-Polynomial-Chebyshev.git
```
-------
## Usage examples
Evaluate the numerical value of the Chebyshev polynomial of first kind $T_2(3)$:
```perl6
use Math::Polynomial::Chebyshev;
chebyshev-t(2, 0.3)
```
The default method is "recursive":
```perl6
chebyshev-t(2, 6, method => 'recursive')
```
Here is an invocation of the "trigonometric" method:
```perl6
chebyshev-t(2, 3, method => 'trigonometric')
```
**Remark:** Currently, the trigonometric method is implemented only for the Chebyshev polynomials of first kind
(Chebyshev-T.)
Plot the 7th Chebyshev-T polynomial:
```perl6
use Text::Plot;
my @x = (-1, -0.99 ... 1);
text-list-plot(@x, chebyshev-t(6, @x), width => 60)
```
Here we make a Chebyshev-T function:
```perl6
chebyshev-u(4)
```
A list of Chebyshev polynomials can be used as a basis for the models in
["Math::Fitting"](), [AAp2].
Here is an example:
```perl6
use Math::Fitting;
my @basis = (^4).map({ chebyshev-t($_) });
my @data = [2.rand - 1, 10.rand] xx 20;
my &lm = linear-model-fit(@data, :@basis);
```
Here is a plot of the data and the fit:
```perl6
my @fit = (-1, -0.98 ... 1).map({ [$_, &lm($_)] });
say Z=> <* □>;
say text-list-plot([@fit, @data])
```
--------
## References
### Articles
[WK1] Wolfram Koepf,
["Efficient Computation of Chebyshev Polynomials in Computer Algebra"](https://www.researchgate.net/publication/2321141_Efficient_Computation_of_Chebyshev_Polynomials_in_Computer_Algebra).
(1999),
Computer Algebra Systems: A Practical Guide. 79-99.
[Wk1] Wikipedia entry, [Chebyshev polynomials](https://en.wikipedia.org/wiki/Chebyshev_polynomials).
### Packages
[AAp1] Anton Antonov,
[Text::Plot Raku package](https://github.com/antononcube/Raku-Text-Plot),
(2022-2023),
[GitHub/antononcube](https://github.com/antononcube).
[AAp2] Anton Antonov,
[Math::Fitting Raku package](https://github.com/antononcube/Raku-Math-Fitting),
(2024),
[GitHub/antononcube](https://github.com/antononcube).
[SFp1] Solomon Foster,
[Math::ChebyshevPolynomial Raku package](https://github.com/colomon/Math-ChebyshevPolynomial),
(2013-2015),
[GitHub/colomon](https://github.com/colomon).