Normalized Hermite Polynomial

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

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

Installation

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

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.