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

anandkaranubc · 2025-03-04T05:14:40Z

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.

Related Issues

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This pull request:

progresses [RFC]: evaluate a Chebyshev polynomial of the first kind at a value x #123

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anandkaranubc · 2025-03-04T05:15:33Z

/stdlib update-copyright-years

stdlib-bot · 2025-03-04T05:16:13Z

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.

anandkaranubc · 2025-03-04T05:16:32Z

Time to bring hyp2f1 to life! 🚀

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

anandkaranubc · 2025-03-04T05:23:32Z

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/test/test.js

+			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 ] );


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…

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/README.md

anandkaranubc · 2025-03-04T05:33:47Z

...node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/test/fixtures/python/runner.py

+
+def main():
+    """Generate fixture data."""
+    x = np.linspace(-1, 1, 1000)


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.

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

anandkaranubc · 2025-03-04T05:34:31Z

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/lib/main.js

+	) {
+		return NaN;
+	}
+	return hyp2f1( -n, n, 0.5, 0.5*(1-x) );


No restrictions on x over here :)

Signed-off-by: Karan Anand <119553199+anandkaranubc@users.noreply.github.com>

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Co-authored-by: Karan Anand <119553199+anandkaranubc@users.noreply.github.com> Signed-off-by: Athan <kgryte@gmail.com>

kgryte · 2025-04-02T23:22:49Z

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/README.md

+
+# chebyshevtpoly
+
+> [Chebyshev Polynomial][chebyshev-polynomial] of the first kind.


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.

kgryte · 2025-04-02T23:24:18Z

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/README.md

+
+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


Suggested change

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.

kgryte · 2025-04-02T23:25:52Z

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/README.md

+// returns NaN
+```
+
+If provided a polynomial degree `n` which is not a nonnegative integer, the function returns `NaN`.


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?

kgryte · 2025-04-02T23:26:21Z

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/README.md

+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );


We can update this example to use console/log-each-map.

kgryte · 2025-04-02T23:26:38Z

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/README.md

+
+<section class="links">
+
+[chebyshev-polynomial]: https://en.wikipedia.org/wiki/Chebyshev_polynomials#Definitions


You can drop #Definitions here.

kgryte · 2025-04-02T23:27:14Z

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/docs/repl.txt

@@ -0,0 +1,38 @@
+
+{{alias}}( n, x )
+    Evaluates the Chebyshev polynomial of the first kind


Your line wrapping is off here.

kgryte · 2025-04-02T23:27:45Z

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/examples/index.js

+'use strict';
+
+var randu = require( '@stdlib/random/base/randu' );
+var round = require( '@stdlib/math/base/special/round' );


Same comment as README.

kgryte · 2025-04-02T23:28:17Z

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/lib/main.js

+function chebyshevtpoly( n, x ) {
+	if (
+		isnan( x ) ||
+		!isInteger( n ) ||


Not clear to me that we need to apply this restriction.

kgryte · 2025-04-02T23:30:06Z

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/lib/main.js

+	) {
+		return NaN;
+	}
+	return hyp2f1( -n, n, 0.5, 0.5*(1.0-x) );


For integer x, why not use the recurrence relation directly, as in SciPy?

kgryte · 2025-04-02T23:30:39Z

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/package.json

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


Suggested change

"description": "Evaluates the Chebyshev polynomial of the first kind.",

"description": "Evaluate the Chebyshev polynomial of the first kind.",

kgryte

Left an initial round of comments.

anandkaranubc added 5 commits February 19, 2025 01:35

feat: temp commit

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chore: update copyright years

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Merge branch 'stdlib-js:develop' into feat/chebyshevtpoly

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Signed-off-by: Karan Anand <119553199+anandkaranubc@users.noreply.github.com>

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Merge branch 'stdlib-js:develop' into feat/chebyshevtpoly

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Co-authored-by: Karan Anand <119553199+anandkaranubc@users.noreply.github.com> Signed-off-by: Athan <kgryte@gmail.com>

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

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		# chebyshevtpoly

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


		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


		<section class="links">

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

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

		{{alias}}( n, x )
		Evaluates the Chebyshev polynomial of the first kind

	"description": "Evaluates the Chebyshev polynomial of the first kind.",
	"description": "Evaluate the Chebyshev polynomial of the first kind.",

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

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

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

anandkaranubc commented Mar 4, 2025 •

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