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feat: add stats/meanpw #8810

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301 changes: 301 additions & 0 deletions lib/node_modules/@stdlib/stats/meanpw/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.

-->

# meanpw

> Compute the [arithmetic mean][arithmetic-mean] along one or more [ndarray][@stdlib/ndarray/ctor] dimensions using pairwise summation.

<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/meanpw/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
<br>
</div> -->

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var meanpw = require( '@stdlib/stats/meanpw' );
```

#### meanpw( x\[, options] )

Computes the [arithmetic mean][arithmetic-mean] along one or more [ndarray][@stdlib/ndarray/ctor] dimensions using pairwise summation.

```javascript
var array = require( '@stdlib/ndarray/array' );

var x = array( [ 1.0, 2.0, -2.0, 4.0 ] );

var y = meanpw( x );
// returns <ndarray>

var v = y.get();
// returns 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 ndarray2array = require( '@stdlib/ndarray/to-array' );
var array = require( '@stdlib/ndarray/array' );

var x = array( [ 1.0, 2.0, -2.0, 4.0 ], {
'shape': [ 2, 2 ],
'order': 'row-major'
});
var v = ndarray2array( x );
// returns [ [ 1.0, 2.0 ], [ -2.0, 4.0 ] ]

var y = meanpw( x, {
'dims': [ 0 ]
});
// returns <ndarray>

v = ndarray2array( y );
// returns [ -0.5, 3.0 ]

y = meanpw( x, {
'dims': [ 1 ]
});
// returns <ndarray>

v = ndarray2array( y );
// returns [ 1.5, 1.0 ]

y = meanpw( x, {
'dims': [ 0, 1 ]
});
// returns <ndarray>

v = y.get();
// returns 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 ndarray2array = require( '@stdlib/ndarray/to-array' );
var array = require( '@stdlib/ndarray/array' );

var x = array( [ 1.0, 2.0, -2.0, 4.0 ], {
'shape': [ 2, 2 ],
'order': 'row-major'
});

var v = ndarray2array( x );
// returns [ [ 1.0, 2.0 ], [ -2.0, 4.0 ] ]

var y = meanpw( x, {
'dims': [ 0 ],
'keepdims': true
});
// returns <ndarray>

v = ndarray2array( y );
// returns [ [ -0.5, 3.0 ] ]

y = meanpw( x, {
'dims': [ 1 ],
'keepdims': true
});
// returns <ndarray>

v = ndarray2array( y );
// returns [ [ 1.5 ], [ 1.0 ] ]

y = meanpw( x, {
'dims': [ 0, 1 ],
'keepdims': true
});
// returns <ndarray>

v = ndarray2array( y );
// returns [ [ 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 = meanpw( x, {
'dtype': 'float64'
});
// returns <ndarray>

var dt = String( getDType( y ) );
// returns 'float64'
```

#### meanpw.assign( x, out\[, options] )

Computes the [arithmetic mean][arithmetic-mean] along one or more [ndarray][@stdlib/ndarray/ctor] dimensions using pairwise summation 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 = meanpw.assign( x, y );
// returns <ndarray>

var v = out.get();
// returns 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].
- In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., "simple" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var uniform = require( '@stdlib/random/array/uniform' );
var getDType = require( '@stdlib/ndarray/dtype' );
var ndarray2array = require( '@stdlib/ndarray/to-array' );
var array = require( '@stdlib/ndarray/array' );
var meanpw = require( '@stdlib/stats/meanpw' );

// Generate an array of random numbers:
var x = array( uniform( 25, 0.0, 20.0 ), {
'shape': [ 5, 5 ]
});
console.log( ndarray2array( x ) );

// Perform a reduction:
var y = meanpw( 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

- Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050][@higham:1993a].

</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

[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean

[@higham:1993a]: https://doi.org/10.1137/0914050

</section>

<!-- /.links -->
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