npm package: @stdlib/stats-meankbn
Description: Compute the arithmetic mean along one or more ndarray dimensions using an improved Kahan–Babuška algorithm.
Author: The Stdlib Authors
Latest version: 0.1.1

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# meankbn

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute the [arithmetic mean][arithmetic-mean] along one or more [ndarray][@stdlib/ndarray/ctor] dimensions using an improved Kahan–Babuška 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."> -->

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

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-meankbn
```

</section>

<section class="usage">

## Usage

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

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

Computes the [arithmetic mean][arithmetic-mean] along one or more [ndarray][@stdlib/ndarray/ctor] dimensions using an improved Kahan–Babuška algorithm.

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

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

var y = meankbn( 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 = meankbn( x, {
    'dims': [ 0 ]
});
// returns <ndarray>[ -0.5, 3.0 ]

y = meankbn( x, {
    'dims': [ 1 ]
});
// returns <ndarray>[ 1.5, 1.0 ]

y = meankbn( 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 = meankbn( x, {
    'dims': [ 0 ],
    'keepdims': true
});
// returns <ndarray>[ [ -0.5, 3.0 ] ]

y = meankbn( x, {
    'dims': [ 1 ],
    'keepdims': true
});
// returns <ndarray>[ [ 1.5 ], [ 1.0 ] ]

y = meankbn( 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 = meankbn( x, {
    'dtype': 'float64'
});
// returns <ndarray>

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

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

Computes the [arithmetic mean][arithmetic-mean] along one or more [ndarray][@stdlib/ndarray/ctor] dimensions using an improved Kahan–Babuška 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 = meankbn.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 meankbn = require( '@stdlib/stats-meankbn' );

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

// Perform a reduction:
var y = meankbn( 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

-   Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." _Zeitschrift Für Angewandte Mathematik Und Mechanik_ 54 (1): 39–51. doi:[10.1002/zamm.19740540106][@neumaier:1974a].

</section>

<!-- /.references -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[deno-readme]: https://github.com/stdlib-js/stats-meankbn/blob/deno/README.md
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-meankbn/main/LICENSE

[@stdlib/ndarray/ctor]: https://www.npmjs.com/package/@stdlib/ndarray-ctor

[@stdlib/ndarray/dtypes]: https://www.npmjs.com/package/@stdlib/ndarray-dtypes

[@stdlib/ndarray/output-dtype-policies]: https://www.npmjs.com/package/@stdlib/ndarray-output-dtype-policies

[@stdlib/ndarray/base/broadcast-shapes]: https://www.npmjs.com/package/@stdlib/ndarray-base-broadcast-shapes

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

[@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106

</section>

<!-- /.links -->