feat: add stats/meanwd

lib/node_modules/@stdlib/stats/meanwd/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 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.
+
+-->
+
+# meanwd
+
+> Compute the [arithmetic mean][arithmetic-mean] along one or more [ndarray][@stdlib/ndarray/ctor] dimensions using Welford's algorithm.
+
+<section class="intro">
+
+The [arithmetic mean][arithmetic-mean] is defined as
+
+<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->
+
+```math
+\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@42d8f64d805113ab899c79c7c39d6c6bac7fe25c/lib/node_modules/@stdlib/stats/strided/meanwd/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var meanwd = require( '@stdlib/stats/meanwd' );
+```
+
+#### meanwd( x\[, options] )
+
+Computes the [arithmetic mean][arithmetic-mean] along one or more [ndarray][@stdlib/ndarray/ctor] dimensions using Welford's algorithm.
+
+```javascript
+var array = require( '@stdlib/ndarray/array' );
+
+var x = array( [ 1.0, 2.0, -2.0, 4.0 ] );
+
+var y = meanwd( x );
+// returns <ndarray>[ 1.25 ]
+```
+
+The function has the following parameters:
+
+-   **x**: input [ndarray][@stdlib/ndarray/ctor]. Must have a real-valued or "generic" [data type][@stdlib/ndarray/dtypes].
+-   **options**: function options (_optional_).
+
+The function accepts the following options:
+
+-   **dims**: list of dimensions over which to perform a reduction. If not provided, the function performs a reduction over all elements in a provided input [ndarray][@stdlib/ndarray/ctor].
+-   **dtype**: output ndarray [data type][@stdlib/ndarray/dtypes]. Must be a real-valued floating-point or "generic" [data type][@stdlib/ndarray/dtypes].
+-   **keepdims**: boolean indicating whether the reduced dimensions should be included in the returned [ndarray][@stdlib/ndarray/ctor] as singleton dimensions. Default: `false`.
+
+By default, the function performs a reduction over all elements in a provided input [ndarray][@stdlib/ndarray/ctor]. To perform a reduction over specific dimensions, provide a `dims` option.
+
+```javascript
+var array = require( '@stdlib/ndarray/array' );
+
+var x = array( [ 1.0, 2.0, -2.0, 4.0 ], {
+    'shape': [ 2, 2 ],
+    'order': 'row-major'
+});
+// returns <ndarray>[ [ 1.0, 2.0 ], [ -2.0, 4.0 ] ]
+
+var y = meanwd( x, {
+    'dims': [ 0 ]
+});
+// returns <ndarray>[ -0.5, 3.0 ]
+
+y = meanwd( x, {
+    'dims': [ 1 ]
+});
+// returns <ndarray>[ 1.5, 1.0 ]
+
+y = meanwd( x, {
+    'dims': [ 0, 1 ]
+});
+// returns <ndarray>[ 1.25 ]
+```
+
+By default, the function excludes reduced dimensions from the output [ndarray][@stdlib/ndarray/ctor]. To include the reduced dimensions as singleton dimensions, set the `keepdims` option to `true`.
+
+```javascript
+var array = require( '@stdlib/ndarray/array' );
+
+var x = array( [ 1.0, 2.0, -2.0, 4.0 ], {
+    'shape': [ 2, 2 ],
+    'order': 'row-major'
+});
+// returns <ndarray>[ [ 1.0, 2.0 ], [ -2.0, 4.0 ] ]
+
+var y = meanwd( x, {
+    'dims': [ 0 ],
+    'keepdims': true
+});
+// returns <ndarray>[ [ -0.5, 3.0 ] ]
+
+y = meanwd( x, {
+    'dims': [ 1 ],
+    'keepdims': true
+});
+// returns <ndarray>[ [ 1.5 ], [ 1.0 ] ]
+
+y = meanwd( x, {
+    'dims': [ 0, 1 ],
+    'keepdims': true
+});
+// returns <ndarray>[ [ 1.25 ] ]
+```
+
+By default, the function returns an [ndarray][@stdlib/ndarray/ctor] having a [data type][@stdlib/ndarray/dtypes] determined by the function's output data type [policy][@stdlib/ndarray/output-dtype-policies]. To override the default behavior, set the `dtype` option.
+
+```javascript
+var getDType = require( '@stdlib/ndarray/dtype' );
+var array = require( '@stdlib/ndarray/array' );
+
+var x = array( [ 1.0, 2.0, -2.0, 4.0 ], {
+    'dtype': 'generic'
+});
+
+var y = meanwd( x, {
+    'dtype': 'float64'
+});
+// returns <ndarray>[ 1.25 ]
+
+var dt = String( getDType( y ) );
+// returns 'float64'
+```
+
+#### meanwd.assign( x, out\[, options] )
+
+Computes the [arithmetic mean][arithmetic-mean] along one or more [ndarray][@stdlib/ndarray/ctor] dimensions using Welford's algorithm and assigns results to a provided output [ndarray][@stdlib/ndarray/ctor].
+
+```javascript
+var array = require( '@stdlib/ndarray/array' );
+var zeros = require( '@stdlib/ndarray/zeros' );
+
+var x = array( [ 1.0, 2.0, -2.0, 4.0 ] );
+var y = zeros( [] );
+
+var out = meanwd.assign( x, y );
+// returns <ndarray>[ 1.25 ]
+
+var bool = ( out === y );
+// returns true
+```
+
+The method has the following parameters:
+
+-   **x**: input [ndarray][@stdlib/ndarray/ctor]. Must have a real-valued or generic [data type][@stdlib/ndarray/dtypes].
+-   **out**: output [ndarray][@stdlib/ndarray/ctor].
+-   **options**: function options (_optional_).
+
+The method accepts the following options:
+
+-   **dims**: list of dimensions over which to perform a reduction. If not provided, the function performs a reduction over all elements in a provided input [ndarray][@stdlib/ndarray/ctor].
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Setting the `keepdims` option to `true` can be useful when wanting to ensure that the output [ndarray][@stdlib/ndarray/ctor] is [broadcast-compatible][@stdlib/ndarray/base/broadcast-shapes] with ndarrays having the same shape as the input [ndarray][@stdlib/ndarray/ctor].
+-   The output data type [policy][@stdlib/ndarray/output-dtype-policies] only applies to the main function and specifies that, by default, the function must return an [ndarray][@stdlib/ndarray/ctor] having a real-valued floating-point or "generic" [data type][@stdlib/ndarray/dtypes]. For the `assign` method, the output [ndarray][@stdlib/ndarray/ctor] is allowed to have any supported output [data type][@stdlib/ndarray/dtypes].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var uniform = require( '@stdlib/random/uniform' );
+var getDType = require( '@stdlib/ndarray/dtype' );
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var meanwd = require( '@stdlib/stats/meanwd' );
+
+// Generate an array of random numbers:
+var x = uniform( [ 5, 5 ], 0.0, 20.0 );
+console.log( ndarray2array( x ) );
+
+// Perform a reduction:
+var y = meanwd( x, {
+    'dims': [ 0 ]
+});
+
+// Resolve the output array data type:
+var dt = getDType( y );
+console.log( dt );
+
+// Print the results:
+console.log( ndarray2array( y ) );
+```
+
+</section>
+
+<!-- /.examples -->
+
+* * *
+
+<section class="references">
+
+## References
+
+-   Welford, B. P. 1962. "Note on a Method for Calculating Corrected Sums of Squares and Products." _Technometrics_ 4 (3): 419–20. doi:[10.1080/00401706.1962.10490022][@welford:1962a].
+
+</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">
+
+[@stdlib/ndarray/ctor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/ndarray/ctor
+
+[@stdlib/ndarray/dtypes]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/ndarray/dtypes
+
+[@stdlib/ndarray/output-dtype-policies]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/ndarray/output-dtype-policies
+
+[@stdlib/ndarray/base/broadcast-shapes]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/ndarray/base/broadcast-shapes
+
+[@welford:1962a]: https://doi.org/10.1080/00401706.1962.10490022
+
+[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/meanwd/benchmark/benchmark.assign.js

@@ -0,0 +1,111 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var zeros = require( '@stdlib/array/zeros' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+var pkg = require( './../package.json' ).name;
+var meanwd = require( './../lib' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var out;
+	var x;
+
+	x = uniform( len, -50.0, 50.0, options );
+	x = new ndarray( options.dtype, x, [ len ], [ 1 ], 0, 'row-major' );
+
+	out = new ndarray( options.dtype, zeros( 1, options.dtype ), [], [ 0 ], 0, 'row-major' );
+
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var o;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			o = meanwd.assign( x, out );
+			if ( typeof o !== 'object' ) {
+				b.fail( 'should return an ndarray' );
+			}
+		}
+		b.toc();
+		if ( isnan( o.get() ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var len;
+	var min;
+	var max;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = pow( 10, i );
+		f = createBenchmark( len );
+		bench( pkg+':assign:dtype='+options.dtype+',len='+len, f );
+	}
+}
+
+main();