https://github.com/stdlib-js/stats-strided-dsmeanpw

Calculate the arithmetic mean of a single-precision floating-point strided array using pairwise summation with extended accumulation and returning an extended precision result.
https://github.com/stdlib-js/stats-strided-dsmeanpw

arithmetic-mean array average avg central-tendency javascript math mathematics mean node node-js nodejs pairwise pw statistics stats stdlib strided strided-array typed

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Calculate the arithmetic mean of a single-precision floating-point strided array using pairwise summation with extended accumulation and returning an extended precision result.

Host: GitHub
URL: https://github.com/stdlib-js/stats-strided-dsmeanpw
Owner: stdlib-js
License: apache-2.0
Created: 2025-03-29T20:26:10.000Z (about 1 month ago)
Default Branch: main
Last Pushed: 2025-03-29T23:18:14.000Z (about 1 month ago)
Last Synced: 2025-03-29T23:25:28.592Z (about 1 month ago)
Topics: arithmetic-mean, array, average, avg, central-tendency, javascript, math, mathematics, mean, node, node-js, nodejs, pairwise, pw, statistics, stats, stdlib, strided, strided-array, typed
Language: JavaScript
Homepage: https://github.com/stdlib-js/stdlib
Size: 207 KB
Stars: 0
Watchers: 2
Forks: 0
Open Issues: 0
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md

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# dsmeanpw

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

> Calculate the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using pairwise summation with extended accumulation and returning an extended precision result.

The [arithmetic mean][arithmetic-mean] is defined as

```math

\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i

```

## Installation

```bash

npm install @stdlib/stats-strided-dsmeanpw

```

Alternatively,

-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).

-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).

-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).

The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

## Usage

```javascript

var dsmeanpw = require( '@stdlib/stats-strided-dsmeanpw' );

```

#### dsmeanpw( N, x, strideX )

Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array `x` using pairwise summation with extended accumulation and returning an extended precision result.

```javascript

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var v = dsmeanpw( x.length, x, 1 );

// returns ~0.3333

```

The function has the following parameters:

-   **N**: number of indexed elements.

-   **x**: input [`Float32Array`][@stdlib/array/float32].

-   **strideX**: stride length 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 Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var v = dsmeanpw( 4, 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.

```javascript

var Float32Array = require( '@stdlib/array-float32' );

var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var v = dsmeanpw( 4, x1, 2 );

// returns 1.25

```

#### dsmeanpw.ndarray( N, x, strideX, offsetX )

Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using pairwise summation with extended accumulation and alternative indexing semantics and returning an extended precision result.

```javascript

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );

var v = dsmeanpw.ndarray( x.length, x, 1, 0 );

// returns ~0.33333

```

The function has the following additional parameters:

-   **offsetX**: 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 element in `x` starting from the second element

```javascript

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var v = dsmeanpw.ndarray( 4, x, 2, 1 );

// returns 1.25

```

## Notes

-   If `N <= 0`, both functions return `NaN`.

-   Accumulated intermediate values are stored as double-precision floating-point numbers.

-   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.

## Examples

```javascript

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );

var dsmeanpw = require( '@stdlib/stats-strided-dsmeanpw' );

var x = discreteUniform( 10, -50, 50, {

    'dtype': 'float32'

});

console.log( x );

var v = dsmeanpw( x.length, x, 1 );

console.log( v );

```

* * *

## C APIs

### Usage

```c

#include "stdlib/stats/strided/dsmeanpw.h"

```

#### stdlib_strided_dsmeanpw( N, \*X, strideX )

Computes the arithmetic mean of a single-precision floating-point strided array using pairwise summation with extended accumulation and returning an extended precision result.

```c

const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };

double v = stdlib_strided_dsmeanpw( 4, x, 2 );

// returns 4.0

```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.

-   **X**: `[in] float*` input array.

-   **strideX**: `[in] CBLAS_INT` stride length for `X`.

```c

double stdlib_strided_dsmeanpw( const CBLAS_INT N, const float *X, const CBLAS_INT strideX );

```

#### stdlib_strided_dsmeanpw_ndarray( N, \*X, strideX, offsetX )

Computes the arithmetic mean of a single-precision floating-point strided array using pairwise summation with extended accumulation and alternative indexing semantics and returning an extended precision result.

```c

const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };

double v = stdlib_strided_dsmeanpw_ndarray( 4, x, 2, 0 );

// returns 4.0

```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.

-   **X**: `[in] float*` input array.

-   **strideX**: `[in] CBLAS_INT` stride length for `X`.

-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.

```c

double stdlib_strided_dsmeanpw_ndarray( const CBLAS_INT N, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );

```

### Examples

```c

#include "stdlib/stats/strided/dsmeanpw.h"

#include 

int main( void ) {

    // Create a strided array:

    const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };

    // Specify the number of elements:

    const int  N = 4;

    // Specify the stride length:

    const int  strideX = 2;

    // Compute the arithmetic mean:

    double v = stdlib_strided_dsmeanpw( N, x, strideX );

    // Print the result:

    printf( "mean: %lf\n", v );

}

```

* * *

## 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].

* * *

## See Also

-   [`@stdlib/stats-strided/dmeanpw`][@stdlib/stats/strided/dmeanpw]: calculate the arithmetic mean of a double-precision floating-point strided array using pairwise summation.

-   [`@stdlib/stats-strided/dsmean`][@stdlib/stats/strided/dsmean]: calculate the arithmetic mean of a single-precision floating-point strided array using extended accumulation and returning an extended precision result.

-   [`@stdlib/stats-base/meanpw`][@stdlib/stats/base/meanpw]: calculate the arithmetic mean of a strided array using pairwise summation.

-   [`@stdlib/stats-strided/smeanpw`][@stdlib/stats/strided/smeanpw]: calculate the arithmetic mean of a single-precision floating-point strided array using pairwise summation.

* * *

## 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].

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[npm-url]: https://npmjs.org/package/@stdlib/stats-strided-dsmeanpw

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[coverage-url]: https://codecov.io/github/stdlib-js/stats-strided-dsmeanpw?branch=main

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[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd

[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/stats-strided-dsmeanpw/tree/deno

[deno-readme]: https://github.com/stdlib-js/stats-strided-dsmeanpw/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/stats-strided-dsmeanpw/tree/umd

[umd-readme]: https://github.com/stdlib-js/stats-strided-dsmeanpw/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/stats-strided-dsmeanpw/tree/esm

[esm-readme]: https://github.com/stdlib-js/stats-strided-dsmeanpw/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/stats-strided-dsmeanpw/blob/main/branches.md

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

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

[@stdlib/array/float32]: https://github.com/stdlib-js/array-float32

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

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

[@stdlib/stats/strided/dmeanpw]: https://github.com/stdlib-js/stats-strided-dmeanpw

[@stdlib/stats/strided/dsmean]: https://github.com/stdlib-js/stats-strided-dsmean

[@stdlib/stats/base/meanpw]: https://github.com/stdlib-js/stats-base-meanpw

[@stdlib/stats/strided/smeanpw]: https://github.com/stdlib-js/stats-strided-smeanpw

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