@stdlib/math-base-tools-normhermitepolyf
v0.0.3TypeScript
Evaluate a normalized Hermite polynomial using single-precision floating-point arithmetic.
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Published by The Stdlib Authors
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About stdlib...
Normalized Hermite Polynomial
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> Evaluate a normalized [Hermite polynomial][hermite-polynomial] using single-precision floating-point arithmetic.
The normalized (aka "probabilist") [Hermite polynomials][hermite-polynomial] are given by
Installation
``bash`
npm install @stdlib/math-base-tools-normhermitepolyf
Usage
`javascript`
var normhermitepolyf = require( '@stdlib/math-base-tools-normhermitepolyf' );
#### normhermitepolyf( n, x )
Evaluates a normalized [Hermite polynomial][hermite-polynomial] of degree n using single-precision floating-point arithmetic.
`javascript
var v = normhermitepolyf( 1, 1.0 );
// returns 1.0
v = normhermitepolyf( 1, 0.5 );
// returns 0.5
v = normhermitepolyf( 0, 0.5 );
// returns 1.0
v = normhermitepolyf( 2, 0.5 );
// returns -0.75
v = normhermitepolyf( -1, 0.5 );
// returns NaN
`
#### normhermitepolyf.factory( n )
Returns a function for evaluating a normalized [Hermite polynomial][hermite-polynomial] of degree n using single-precision floating-point arithmetic.
`javascript
var polyval = normhermitepolyf.factory( 2 );
var v = polyval( 0.5 );
// returns -0.75
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var zeros = require( '@stdlib/array-zeros' );
var smap = require( '@stdlib/strided-base-smap' );
var logEach = require( '@stdlib/console-log-each' );
var normhermitepolyf = require( '@stdlib/math-base-tools-normhermitepolyf' );
// Generate random values at which to evaluate a polynomial:
var x = uniform( 10, -50.0, 50.0, {
'dtype': 'float32'
});
// Create a polynomial function of degree 1:
var f = normhermitepolyf.factory( 1 );
// Allocate an output array:
var y = zeros( x.length, 'float32' );
// Evaluate the polynomial:
smap( x.length, x, 1, y, 1, f );
logEach( 'He_%d(%.3f) = %.3f', 1, x, y );
// Create a polynomial function of degree 2:
f = normhermitepolyf.factory( 2 );
// Allocate an output array:
y = zeros( x.length, 'float32' );
// Evaluate the polynomial:
smap( x.length, x, 1, y, 1, f );
logEach( 'He_%d(%.3f) = %.3f', 2, x, y );
// Create a polynomial function of degree 3:
f = normhermitepolyf.factory( 3 );
// Allocate an output array:
y = zeros( x.length, 'float32' );
// Evaluate the polynomial:
smap( x.length, x, 1, y, 1, f );
logEach( 'He_%d(%.3f) = %.3f', 3, x, y );
`
*
Notice
This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[test-url]: https://github.com/stdlib-js/math-base-tools-normhermitepolyf/actions/workflows/test.yml?query=branch:v0.0.3
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-tools-normhermitepolyf/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/math-base-tools-normhermitepolyf?branch=main
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[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/math-base-tools-normhermitepolyf/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-tools-normhermitepolyf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-tools-normhermitepolyf/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-tools-normhermitepolyf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-tools-normhermitepolyf/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-tools-normhermitepolyf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-tools-normhermitepolyf/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-tools-normhermitepolyf/main/LICENSE
[hermite-polynomial]: https://en.wikipedia.org/wiki/Hermite_polynomials