npm package: @stdlib/stats-base-meanpw
Description: Calculate the arithmetic mean of a strided array using pairwise summation.
Author: The Stdlib Authors
Latest version: 0.2.2

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</details>

# meanpw

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

> Calculate the [arithmetic mean][arithmetic-mean] of a strided array 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."> -->

<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@e4a1cd44f903f1758776279afedd500ce2dc6ddd/lib/node_modules/@stdlib/stats/base/meanpw/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-base-meanpw
```

</section>

<section class="usage">

## Usage

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

#### meanpw( N, x, stride )

Computes the [arithmetic mean][arithmetic-mean] of a strided array `x` using pairwise summation.

```javascript
var x = [ 1.0, -2.0, 2.0 ];
var N = x.length;

var v = meanpw( N, x, 1 );
// returns ~0.3333
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
-   **stride**: index increment for `x`.

The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to compute the [arithmetic mean][arithmetic-mean] of every other element in `x`,

```javascript
var floor = require( '@stdlib/math-base-special-floor' );

var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];
var N = floor( x.length / 2 );

var v = meanpw( N, x, 2 );
// returns 1.25
```

Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.

<!-- eslint-disable stdlib/capitalized-comments -->

```javascript
var Float64Array = require( '@stdlib/array-float64' );
var floor = require( '@stdlib/math-base-special-floor' );

var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var N = floor( x0.length / 2 );

var v = meanpw( N, x1, 2 );
// returns 1.25
```

#### meanpw.ndarray( N, x, stride, offset )

Computes the [arithmetic mean][arithmetic-mean] of a strided array using pairwise summation and alternative indexing semantics.

```javascript
var x = [ 1.0, -2.0, 2.0 ];
var N = x.length;

var v = meanpw.ndarray( N, x, 1, 0 );
// returns ~0.33333
```

The function has the following additional parameters:

-   **offset**: starting index for `x`.

While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying `buffer`, the `offset` parameter supports indexing semantics based on a starting index. For example, to calculate the [arithmetic mean][arithmetic-mean] for every other value in `x` starting from the second value

```javascript
var floor = require( '@stdlib/math-base-special-floor' );

var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
var N = floor( x.length / 2 );

var v = meanpw.ndarray( N, x, 2, 1 );
// returns 1.25
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `NaN`.
-   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.
-   Depending on the environment, the typed versions ([`dmeanpw`][@stdlib/stats/base/dmeanpw], [`smeanpw`][@stdlib/stats/base/smeanpw], etc.) are likely to be significantly more performant.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var Float64Array = require( '@stdlib/array-float64' );
var meanpw = require( '@stdlib/stats-base-meanpw' );

var x;
var i;

x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    x[ i ] = round( (randu()*100.0) - 50.0 );
}
console.log( x );

var v = meanpw( x.length, x, 1 );
console.log( v );
```

</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">

* * *

## See Also

-   <span class="package-name">[`@stdlib/stats-base/dmeanpw`][@stdlib/stats/base/dmeanpw]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a double-precision floating-point strided array using pairwise summation.</span>
-   <span class="package-name">[`@stdlib/stats-base/mean`][@stdlib/stats/base/mean]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a strided array.</span>
-   <span class="package-name">[`@stdlib/stats-base/smeanpw`][@stdlib/stats/base/smeanpw]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a single-precision floating-point strided array using pairwise summation.</span>

</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="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; 2016-2024. The Stdlib [Authors][stdlib-authors].

</section>

<!-- /.stdlib -->

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[umd]: https://github.com/umdjs/umd
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[deno-url]: https://github.com/stdlib-js/stats-base-meanpw/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-meanpw/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-meanpw/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-meanpw/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-meanpw/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-meanpw/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-meanpw/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-meanpw/main/LICENSE

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

[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array

[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray

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

<!-- <related-links> -->

[@stdlib/stats/base/dmeanpw]: https://www.npmjs.com/package/@stdlib/stats-base-dmeanpw

[@stdlib/stats/base/mean]: https://www.npmjs.com/package/@stdlib/stats-base-mean

[@stdlib/stats/base/smeanpw]: https://www.npmjs.com/package/@stdlib/stats-base-smeanpw

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</section>

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