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# incrmgmean

> Compute a moving [geometric mean][geometric-mean] incrementally.

<section class="intro">

The [geometric mean][geometric-mean] is defined as the nth root of a product of _n_ numbers.

<!-- <equation class="equation" label="eq:geometric_mean" align="center" raw="\biggl( \prod_{i=0}^{n-1} \biggr)^{\frac{1}{n}} = \sqrt[n]{x_0 x_1 \cdots x_{n-1}}" alt="Equation for the geometric mean."> -->

<div class="equation" align="center" data-raw-text="\biggl( \prod_{i=0}^{n-1} \biggr)^{\frac{1}{n}} = \sqrt[n]{x_0 x_1 \cdots x_{n-1}}" data-equation="eq:geometric_mean">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/27e2a43c70db648bb5bbc3fd0cdee050c25adc0b/lib/node_modules/@stdlib/stats/incr/mgmean/docs/img/equation_geometric_mean.svg" alt="Equation for the geometric mean.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var incrmgmean = require( '@stdlib/stats/incr/mgmean' );
```

#### incrmgmean( window )

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

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

#### accumulator( \[x] )

If provided an input value `x`, the accumulator function returns an updated [geometric mean][geometric-mean]. If not provided an input value `x`, the accumulator function returns the current [geometric-mean][geometric-mean].

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

var v = accumulator();
// returns null

// Fill the window...
v = accumulator( 2.0 ); // [2.0]
// returns 2.0

v = accumulator( 1.0 ); // [2.0, 1.0]
// returns ~1.41

v = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
// returns ~1.82

// Window begins sliding...
v = accumulator( 7.0 ); // [1.0, 3.0, 7.0]
// returns ~2.76

v = accumulator( 5.0 ); // [3.0, 7.0, 5.0]
// returns ~4.72

v = accumulator();
// returns ~4.72
```

</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` values 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 incrmgmean = require( '@stdlib/stats/incr/mgmean' );

var accumulator;
var v;
var i;

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

// For each simulated datum, update the moving geometric mean...
for ( i = 0; i < 100; i++ ) {
    v = randu() * 100.0;
    accumulator( v );
}
console.log( accumulator() );
```

</section>

<!-- /.examples -->

<section class="links">

[geometric-mean]: https://en.wikipedia.org/wiki/Geometric_mean

</section>

<!-- /.links -->
