npm package: @stdlib/stats-incr-mrmse
Description: Compute a moving root mean squared error (RMSE) incrementally.
Author: The Stdlib Authors
Latest version: 0.2.3

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# incrmrmse

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

> Compute a moving [root mean squared error][root-mean-squared-error] (RMSE) incrementally.

<section class="intro">

For a window of size `W`, the [**root mean squared error**][root-mean-squared-error] (also known as the **root mean square error** (RMSE) and **root mean square deviation** (RMSD)) is defined as

<!-- <equation class="equation" label="eq:root_mean_squared_error" align="center" raw="\operatorname{RMSE} = \sqrt{ \frac{1}{W} \sum_{i=0}^{W-1} (y_i - x_i)^2 }" alt="Equation for the root mean squared error."> -->

<div class="equation" align="center" data-raw-text="\operatorname{RMSE} = \sqrt{ \frac{1}{W} \sum_{i=0}^{W-1} (y_i - x_i)^2 }" data-equation="eq:root_mean_squared_error">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@6c360ad04d4b48c623a626d13723b4dc33ff0e8e/lib/node_modules/@stdlib/stats/incr/mrmse/docs/img/equation_root_mean_squared_error.svg" alt="Equation for the root mean squared error.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-incr-mrmse
```

</section>

<section class="usage">

## Usage

```javascript
var incrmrmse = require( '@stdlib/stats-incr-mrmse' );
```

#### incrmrmse( window )

Returns an accumulator `function` which incrementally computes a moving [root mean squared error][root-mean-squared-error]. The `window` parameter defines the number of values over which to compute the moving [root mean squared error][root-mean-squared-error].

```javascript
var accumulator = incrmrmse( 3 );
```

#### accumulator( \[x, y] )

If provided input values `x` and `y`, the accumulator function returns an updated [root mean squared error][root-mean-squared-error]. If not provided input values `x` and `y`, the accumulator function returns the current [root mean squared error][root-mean-squared-error].

```javascript
var accumulator = incrmrmse( 3 );

var r = accumulator();
// returns null

// Fill the window...
r = accumulator( 2.0, 3.0 ); // [(2.0,3.0)]
// returns 1.0

r = accumulator( -1.0, 4.0 ); // [(2.0,3.0), (-1.0,4.0)]
// returns ~3.61

r = accumulator( 3.0, 9.0 ); // [(2.0,3.0), (-1.0,4.0), (3.0,9.0)]
// returns ~4.55

// Window begins sliding...
r = accumulator( -7.0, 3.0 ); // [(-1.0,4.0), (3.0,9.0), (-7.0,3.0)]
// returns ~7.33

r = accumulator( -5.0, -3.0 ); // [(3.0,9.0), (-7.0,3.0), (-5.0,-3.0)]
// returns ~6.83

r = accumulator();
// returns ~6.83
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is `NaN` for **at least** `W-1` future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
-   As `W` (x,y) pairs are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random-base-randu' );
var incrmrmse = require( '@stdlib/stats-incr-mrmse' );

var accumulator;
var v1;
var v2;
var i;

// Initialize an accumulator:
accumulator = incrmrmse( 5 );

// For each simulated datum, update the moving root mean squared error...
for ( i = 0; i < 100; i++ ) {
    v1 = ( randu()*100.0 ) - 50.0;
    v2 = ( randu()*100.0 ) - 50.0;
    accumulator( v1, v2 );
}
console.log( accumulator() );
```

</section>

<!-- /.examples -->

<!-- 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-incr/mmse`][@stdlib/stats/incr/mmse]</span><span class="delimiter">: </span><span class="description">compute a moving mean squared error (MSE) incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/mrss`][@stdlib/stats/incr/mrss]</span><span class="delimiter">: </span><span class="description">compute a moving residual sum of squares (RSS) incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/rmse`][@stdlib/stats/incr/rmse]</span><span class="delimiter">: </span><span class="description">compute the root mean squared error (RMSE) incrementally.</span>

</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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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-incr-mrmse/main/LICENSE

[root-mean-squared-error]: https://en.wikipedia.org/wiki/Root-mean-square_deviation

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

[@stdlib/stats/incr/mmse]: https://www.npmjs.com/package/@stdlib/stats-incr-mmse

[@stdlib/stats/incr/mrss]: https://www.npmjs.com/package/@stdlib/stats-incr-mrss

[@stdlib/stats/incr/rmse]: https://www.npmjs.com/package/@stdlib/stats-incr-rmse

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</section>

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