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feat: add math/base/special/chebyshev-t-polynomial #5774

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@anandkaranubc anandkaranubc commented Mar 4, 2025 •
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Progresses #123

Description

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This pull request:

  • Adds the JS implementation of the function to evaluate a Chebyshev polynomial of the first kind at a value x.

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@stdlib-bot stdlib-bot added Math Issue or pull request specific to math functionality. Needs Review A pull request which needs code review. labels Mar 4, 2025
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@stdlib-bot stdlib-bot added the bot: In Progress Pull request is currently awaiting automation. label Mar 4, 2025
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stdlib-bot commented Mar 4, 2025 •
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Coverage Report

Package Statements Branches Functions Lines
math/base/special/chebyshev-t-polynomial $\color{green}137/137$
$\color{green}+100.00\%$ 		$\color{green}7/7$
$\color{green}+100.00\%$ 		$\color{green}1/1$
$\color{green}+100.00\%$ 		$\color{green}137/137$
$\color{green}+100.00\%$

The above coverage report was generated for the changes in this PR.

@stdlib-bot stdlib-bot removed the bot: In Progress Pull request is currently awaiting automation. label Mar 4, 2025
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anandkaranubc commented Mar 4, 2025 •
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Time to bring hyp2f1 to life! 🚀

Once this is approved, I will also add its respective C implementation. 😄

delta = abs( y - expected[ i ] );

// NOTE: The tolerance is higher due to the numerical differences between the `hyp2f1` implementation in JavaScript and its reference implementation in SciPy.
tol = 755.0 * EPS * abs( expected[ i ] );
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I expected this from the start. Fortunately, they are not as crazy as hyp2f1. The test coverage report also confirms that this function only uses parts of the helper functions hyp2f1ra and hys2f1 that rely on evaluating the hypergeometric function through power series expansion. Thus, numerical differences...

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def main():
"""Generate fixture data."""
x = np.linspace(-1, 1, 1000)
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In the text fixture generation, I have kept x in the [-1,1] range, where these polynomials are typically considered. Is it also necessary to test outside of this interval?

For |x| > 1, the polynomials grow exponentially rather than oscillating. Our implementation can handle that since there is no restriction on x.

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I'm fine leaving it in [-1,1] is that is the typical range.

) {
return NaN;
}
return hyp2f1( -n, n, 0.5, 0.5*(1-x) );
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No restrictions on x over here :)

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anandkaranubc and others added 3 commits March 3, 2025 21:38 
Signed-off-by: Karan Anand <119553199+anandkaranubc@users.noreply.github.com>
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@anandkaranubc anandkaranubc added the JavaScript Issue involves or relates to JavaScript. label Mar 4, 2025
anandkaranubc and others added 2 commits April 1, 2025 22:58 
Co-authored-by: Karan Anand <119553199+anandkaranubc@users.noreply.github.com>
Signed-off-by: Athan <kgryte@gmail.com>
# chebyshevtpoly

> [Chebyshev Polynomial][chebyshev-polynomial] of the first kind.
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Suggested change
> [Chebyshev Polynomial][chebyshev-polynomial] of the first kind.
> [Chebyshev polynomial][chebyshev-polynomial] of the first kind.

"polynomial" does not need to be capitalized. Applies here and elsewhere throughout this package.


where `n` is the polynomial degree.

The [Chebyshev Polynomial][chebyshev-polynomial] of the first kind is related to the Gaussian hypergeometric function via the following equation
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The [Chebyshev Polynomial][chebyshev-polynomial] of the first kind is related to the Gaussian hypergeometric function via the following equation
The [Chebyshev Polynomial][chebyshev-polynomial] of the first kind is related to the [Gaussian hypergeometric function][@stdlib/math/base/special/hyp2f1] via the following equation

You'll need to add the link defn below in the links section. Also double-check that I used the correct package name.

// returns NaN
```

If provided a polynomial degree `n` which is not a nonnegative integer, the function returns `NaN`.
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Why do we restrict to only integer degrees? Why not follow SciPy and state that non-integer values are resolved relative to the hypergeometric function?

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random/base/randu' );
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We can update this example to use console/log-each-map.


<section class="links">

[chebyshev-polynomial]: https://en.wikipedia.org/wiki/Chebyshev_polynomials#Definitions
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You can drop #Definitions here.

@@ -0,0 +1,38 @@

{{alias}}( n, x )
Evaluates the Chebyshev polynomial of the first kind
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Your line wrapping is off here.

'use strict';

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
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Same comment as README.

function chebyshevtpoly( n, x ) {
if (
isnan( x ) ||
!isInteger( n ) ||
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Not clear to me that we need to apply this restriction.

) {
return NaN;
}
return hyp2f1( -n, n, 0.5, 0.5*(1.0-x) );
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For integer x, why not use the recurrence relation directly, as in SciPy?

{
"name": "@stdlib/math/base/special/chebyshev-t-polynomial",
"version": "0.0.0",
"description": "Evaluates the Chebyshev polynomial of the first kind.",
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Suggested change
"description": "Evaluates the Chebyshev polynomial of the first kind.",
"description": "Evaluate the Chebyshev polynomial of the first kind.",

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Left an initial round of comments.

@kgryte kgryte added Needs Changes Pull request which needs changes before being merged. and removed Needs Review A pull request which needs code review. labels Apr 2, 2025
@anandkaranubc anandkaranubc marked this pull request as draft April 11, 2025 07:31
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