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feat: add math/base/tools/normhermitepolyf
PR-URL: #2151 Closes: #2029 Co-authored-by: Athan Reines <kgryte@gmail.com> Reviewed-by: Athan Reines <kgryte@gmail.com>
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‎lib/node_modules/@stdlib/math/base/tools/normhermitepolyf/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2024 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# Normalized Hermite Polynomial
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> Evaluate a normalized [Hermite polynomial][hermite-polynomial] using single-precision floating-point arithmetic.
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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The normalized (aka "probabilist") [Hermite polynomials][hermite-polynomial] are given by
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<!-- <equation class="equation" label="eq:normalized_hermite_polynomials" align="center" raw="He_{n}(x)=(-1)^{n} e^{\frac{x^2}{2}} \frac{\mathrm d^{n}}{\mathrm d x^{n}} e^{-\frac{x^2}{2}}" alt="Equation for normalized Hermite polynomials."> -->
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```math
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He_{n}(x)=(-1)^{n} e^{\frac{x^2}{2}} \frac{\mathrm d^{n}}{\mathrm d x^{n}} e^{-\frac{x^2}{2}}
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```
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<!-- <div class="equation" align="center" data-raw-text="He_{n}(x)=(-1)^{n} e^{\frac{x^2}{2}} \frac{\mathrm{d}^{n}}{\mathrm{d}x^n} e^{-\frac{x^2}{2}}" data-equation="eq:normalized_hermite_polynomials">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bea0101eb61892f160eec8d97dc79188fd937523/lib/node_modules/@stdlib/math/base/tools/normhermitepoly/docs/img/equation_normalized_hermite_polynomials.svg" alt="Equation for normalized Hermite polynomials.">
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<br>
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</div> -->
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<!-- Package usage documentation. -->
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<section class="usage">
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## Usage
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```javascript
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var normhermitepolyf = require( '@stdlib/math/base/tools/normhermitepolyf' );
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```
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#### normhermitepolyf( n, x )
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Evaluates a normalized [Hermite polynomial][hermite-polynomial] of degree `n` using single-precision floating-point arithmetic.
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```javascript
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var v = normhermitepolyf( 1, 1.0 );
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// returns 1.0
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v = normhermitepolyf( 1, 0.5 );
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// returns 0.5
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v = normhermitepolyf( 0, 0.5 );
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// returns 1.0
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v = normhermitepolyf( 2, 0.5 );
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// returns -0.75
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v = normhermitepolyf( -1, 0.5 );
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// returns NaN
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```
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#### normhermitepolyf.factory( n )
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Returns a function for evaluating a normalized [Hermite polynomial][hermite-polynomial] of degree `n` using single-precision floating-point arithmetic.
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```javascript
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var polyval = normhermitepolyf.factory( 2 );
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var v = polyval( 0.5 );
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// returns -0.75
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```
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</section>
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<!-- /.usage -->
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<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- Package usage examples. -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var uniform = require( '@stdlib/random/array/uniform' );
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var zeros = require( '@stdlib/array/zeros' );
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var smap = require( '@stdlib/strided/base/smap' );
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var logEach = require( '@stdlib/console/log-each' );
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var normhermitepolyf = require( '@stdlib/math/base/tools/normhermitepolyf' );
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// Generate random values at which to evaluate a polynomial:
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var x = uniform( 10, -50.0, 50.0, {
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'dtype': 'float32'
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});
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// Create a polynomial function of degree 1:
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var f = normhermitepolyf.factory( 1 );
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// Allocate an output array:
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var y = zeros( x.length, 'float32' );
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// Evaluate the polynomial:
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smap( x.length, x, 1, y, 1, f );
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logEach( 'He_%d(%.3f) = %.3f', 1, x, y );
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// Create a polynomial function of degree 2:
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f = normhermitepolyf.factory( 2 );
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// Allocate an output array:
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y = zeros( x.length, 'float32' );
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// Evaluate the polynomial:
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smap( x.length, x, 1, y, 1, f );
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logEach( 'He_%d(%.3f) = %.3f', 2, x, y );
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// Create a polynomial function of degree 3:
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f = normhermitepolyf.factory( 3 );
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// Allocate an output array:
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y = zeros( x.length, 'float32' );
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// Evaluate the polynomial:
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smap( x.length, x, 1, y, 1, f );
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logEach( 'He_%d(%.3f) = %.3f', 3, x, y );
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```
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</section>
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<!-- /.examples -->
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<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="references">
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</section>
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<!-- /.references -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[hermite-polynomial]: https://en.wikipedia.org/wiki/Hermite_polynomials
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/math/base/tools/normhermitepolyf/benchmark/benchmark.factory.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
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var pkg = require( './../package.json' ).name;
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var factory = require( './../lib/factory.js' );
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// MAIN //
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bench( pkg+'::create:factory', function benchmark( b ) {
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var n;
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var f;
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var i;
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n = discreteUniform( 10, 1, 10, {
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'dtype': 'float32'
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});
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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f = factory( n[ i%n.length ] );
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if ( typeof f !== 'function' ) {
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b.fail( 'should return a function' );
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}
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}
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b.toc();
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if ( typeof f !== 'function' ) {
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b.fail( 'should return a function' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+'::evaluate:factory', function benchmark( b ) {
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var x;
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var v;
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var f;
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var i;
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f = factory( 2 );
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x = uniform( 10, -5.0, 5.0, {
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'dtype': 'float32'
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});
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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v = f( x[ i%x.length ] );
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if ( isnanf( v ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnanf( v ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

‎lib/node_modules/@stdlib/math/base/tools/normhermitepolyf/benchmark/benchmark.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
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var pkg = require( './../package.json' ).name;
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var normhermitepolyf = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var opts;
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var x;
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var y;
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var i;
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opts = {
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'dtype': 'float32'
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};
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x = uniform( 10, -5.0, 5.0, opts );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = normhermitepolyf( 2, x[ i%x.length ] );
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if ( isnanf( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnanf( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

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