feat: implementation of stats/base/dists/halfnormal/mgf

lib/node_modules/@stdlib/stats/base/dists/halfnormal/mgf/README.md

@@ -0,0 +1,264 @@
+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 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.
+
+-->
+
+# Moment-Generating Function
+
+> [Half-Normal][half-normal-distribution] distribution moment-generating function (MGF).
+
+<!-- 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 [moment-generating function][mgf] for a [half-normal][half-normal-distribution] random variable is
+
+<!-- <equation class="equation" label="eq:halfnormal_mgf_function" align="center" raw="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \exp\{ \frac{1}{2}\sigma^2t^2 \} \left( 1 + \text{erf}\left( \frac{\sigma t}{\sqrt{2}} \right) \right)" alt="Moment-generating function (MGF) for a half-normal distribution."> -->
+
+```math
+M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \exp\{ \frac{1}{2}\sigma^2t^2 \} \left( 1 + \text{erf}\left( \frac{\sigma t}{\sqrt{2}} \right) \right)
+```
+
+<!-- </equation> -->
+
+where `sigma > 0` is the scale parameter.
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var mgf = require( '@stdlib/stats/base/dists/halfnormal/mgf' );
+```
+
+#### mgf( t, sigma )
+
+Evaluates the [moment-generating function][mgf] (MGF) for a [half-normal][half-normal-distribution] distribution with parameter `sigma` (scale).
+
+```javascript
+var y = mgf( 2.0, 1.0 );
+// returns ~14.442
+
+y = mgf( 0.0, 1.0 );
+// returns 1.0
+
+y = mgf( -1.0, 2.0 );
+// returns ~0.336
+```
+
+If provided `NaN` as any argument, the function returns `NaN`.
+
+```javascript
+var y = mgf( NaN, 1.0 );
+// returns NaN
+
+y = mgf( 0.0, NaN );
+// returns NaN
+```
+
+If provided `sigma <= 0`, the function returns `NaN`.
+
+```javascript
+var y = mgf( 2.0, 0.0 );
+// returns NaN
+
+y = mgf( 2.0, -1.0 );
+// returns NaN
+```
+
+#### mgf.factory( sigma )
+
+Returns a function for evaluating the [moment-generating function][mgf] (MGF) of a [half-normal][half-normal-distribution] distribution with scale parameter `sigma`.
+
+```javascript
+var mymgf = mgf.factory( 2.0 );
+
+var y = mymgf( 1.0 );
+// returns ~14.442
+
+y = mymgf( 0.5 );
+// returns ~2.774
+```
+
+</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 logEachMap = require( '@stdlib/console/log-each-map' );
+var mgf = require( '@stdlib/stats/base/dists/halfnormal/mgf' );
+
+var opts = {
+    'dtype': 'float64'
+};
+var sigma = uniform( 10, 0.1, 20.0, opts );
+var t = uniform( 10, 0.0, 10.0, opts );
+
+logEachMap( 't: %lf, σ: %lf, M_X(t;σ): %lf', t, sigma, mgf );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- 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">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/stats/base/dists/halfnormal/mgf.h"
+```
+
+#### stdlib_base_dists_halfnormal_mgf( t, sigma )
+
+Evaluates the [moment-generating function][mgf] (MGF) for a [half-normal][half-normal-distribution] distribution with parameter `sigma` (scale).
+
+```c
+double y = stdlib_base_dists_halfnormal_mgf( 2.0, 1.0 );
+// returns ~14.442
+```
+
+The function accepts the following arguments:
+
+-   **t**: `[in] double` input value.
+-   **sigma**: `[in] double` scale parameter.
+
+```c
+double stdlib_base_dists_halfnormal_mgf( const double t, const double sigma );
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+#include "stdlib/stats/base/dists/halfnormal/mgf.h"
+#include "stdlib/constants/float64/eps.h"
+#include <stdlib.h>
+#include <stdio.h>
+
+static double random_uniform( const double min, const double max ) {
+     double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
+     return min + ( v*(max-min) );
+}
+
+int main( void ) {
+     double sigma;
+     double t;
+     double y;
+     int i;
+
+     for ( i = 0; i < 10; i++ ) {
+          t = random_uniform( 0.0, 1.0 );
+          sigma = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
+          y = stdlib_base_dists_halfnormal_mgf( t, sigma );
+          printf( "t: %lf, σ: %lf, M_X(t;σ): %lf\n", t, sigma, y );
+     }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- 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">
+
+[half-normal-distribution]: https://en.wikipedia.org/wiki/Half-normal_distribution
+
+[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/base/dists/halfnormal/mgf/benchmark/benchmark.js

@@ -0,0 +1,84 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var mgf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var sigma;
+	var len;
+	var t;
+	var y;
+	var i;
+
+	len = 100;
+	t = uniform( len, 0.0, 1.0);
+	sigma = uniform( len, EPS, 20.0);
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = mgf( t[ i % len ], sigma[ i % len ] );
+		if ( isnan( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( format( '%s::factory', pkg ), function benchmark( b ) {
+	var mymgf;
+	var sigma;
+	var t;
+	var y;
+	var i;
+
+	sigma = 1.5;
+	mymgf = mgf.factory( sigma );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		t = uniform( 0.0, 1.0 );
+		y = mymgf( t );
+		if ( isnan( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});