About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Normalized Hermite Polynomial

Evaluate a normalized Hermite polynomial using double-precision floating-point arithmetic.

The normalized (aka "probabilist") Hermite polynomials are given by

$$He_{n}(x)=(-1)^{n} e^{\frac{x^2}{2}} \frac{\mathrm d^{n}}{\mathrm d x^{n}} e^{-\frac{x^2}{2}}$$

Installation

npm install @stdlib/math-base-tools-normhermitepoly

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var normhermitepoly = require( '@stdlib/math-base-tools-normhermitepoly' );

normhermitepoly( n, x )

Evaluates a normalized Hermite polynomial of degree n using double-precision floating-point arithmetic.

var v = normhermitepoly( 1, 1.0 );
// returns 1.0

v = normhermitepoly( 1, 0.5 );
// returns 0.5

v = normhermitepoly( 0, 0.5 );
// returns 1.0

v = normhermitepoly( 2, 0.5 );
// returns -0.75

v = normhermitepoly( -1, 0.5 );
// returns NaN

normhermitepoly.factory( n )

Returns a function for evaluating a normalized Hermite polynomial of degree n using double-precision floating-point arithmetic.

var polyval = normhermitepoly.factory( 2 );

var v = polyval( 0.5 );
// returns -0.75

Examples

var uniform = require( '@stdlib/random-array-uniform' );
var zeros = require( '@stdlib/array-zeros' );
var dmap = require( '@stdlib/strided-base-dmap' );
var logEach = require( '@stdlib/console-log-each' );
var normhermitepoly = require( '@stdlib/math-base-tools-normhermitepoly' );

// Generate random values at which to evaluate a polynomial:
var x = uniform( 10, -50.0, 50.0, {
    'dtype': 'float64'
});

// Create a polynomial function of degree 1:
var f = normhermitepoly.factory( 1 );

// Allocate an output array:
var y = zeros( x.length, 'float64' );

// Evaluate the polynomial:
dmap( x.length, x, 1, y, 1, f );
logEach( 'He_%d(%.3f) = %.3f', 1, x, y );

// Create a polynomial function of degree 2:
f = normhermitepoly.factory( 2 );

// Allocate an output array:
y = zeros( x.length, 'float64' );

// Evaluate the polynomial:
dmap( x.length, x, 1, y, 1, f );
logEach( 'He_%d(%.3f) = %.3f', 2, x, y );

// Create a polynomial function of degree 3:
f = normhermitepoly.factory( 3 );

// Allocate an output array:
y = zeros( x.length, 'float64' );

// Evaluate the polynomial:
dmap( x.length, x, 1, y, 1, f );
logEach( 'He_%d(%.3f) = %.3f', 3, x, y );

---

See Also

• @stdlib/math-base/tools/evalpoly: evaluate a polynomial.
• @stdlib/math-base/tools/hermitepoly: evaluate a physicist's Hermite polynomial.

---

Notice

This package is part of 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, see the main project repository.

Community

---

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.