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base/tools/normhermitepolyf/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2024 The Stdlib Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# Normalized Hermite Polynomial
+
+> Evaluate a normalized [Hermite polynomial][hermite-polynomial] using single-precision floating-point arithmetic.
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+The normalized (aka "probabilist") [Hermite polynomials][hermite-polynomial] are given by
+
+<!-- <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."> -->
+
+```math
+He_{n}(x)=(-1)^{n} e^{\frac{x^2}{2}} \frac{\mathrm d^{n}}{\mathrm d x^{n}} e^{-\frac{x^2}{2}}
+```
+
+<!-- <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">
+    <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.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## 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
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- Package usage examples. -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```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 );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- 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. -->
+
+<section class="references">
+
+</section>
+
+<!-- /.references -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[hermite-polynomial]: https://en.wikipedia.org/wiki/Hermite_polynomials
+
+</section>
+
+<!-- /.links -->

base/tools/normhermitepolyf/benchmark/benchmark.factory.js

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

base/tools/normhermitepolyf/benchmark/benchmark.js

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