npm package: @stdlib/stats-strided-dsmeanpw
Description: Calculate the arithmetic mean of a single-precision floating-point strided array using pairwise summation with extended accumulation and returning an extended precision result.
Author: The Stdlib Authors
Latest version: 0.1.1

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# dsmeanpw

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> 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.

<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@bef48a7ab1318364d0bf178f0e69d081a61688c3/lib/node_modules/@stdlib/stats/strided/dsmeanpw/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-strided-dsmeanpw
```

</section>

<section class="usage">

## 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.

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

```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
```

</section>

<!-- /.usage -->

<section class="notes">

## 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.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```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 );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### 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 );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/stats/strided/dsmeanpw.h"
#include <stdio.h>

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 );
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

* * *

<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-strided/dmeanpw`][@stdlib/stats/strided/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-strided/dsmean`][@stdlib/stats/strided/dsmean]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a single-precision floating-point strided array using extended accumulation and returning an extended precision result.</span>
-   <span class="package-name">[`@stdlib/stats-strided/meanpw`][@stdlib/stats/strided/meanpw]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a strided array using pairwise summation.</span>
-   <span class="package-name">[`@stdlib/stats-strided/smeanpw`][@stdlib/stats/strided/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; 2016-2026. The Stdlib [Authors][stdlib-authors].

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

[@stdlib/array/float32]: https://www.npmjs.com/package/@stdlib/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

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

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

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

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