# incrmrmse
> Compute a moving [root mean squared error][root-mean-squared-error] (RMSE) incrementally.
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
## 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
```
## 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.
## Examples
```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() );
```
[root-mean-squared-error]: https://en.wikipedia.org/wiki/Root-mean-square_deviation
