@stdlib/stats/incr/sum/README.md

Standard library statistical functions.

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# incrsum

> Compute a sum incrementally.

<section class="intro">

The sum is defined as

<!-- <equation class="equation" label="eq:sum" align="center" raw="s = \sum_{i=0}^{n-1} x_i" alt="Equation for the sum."> -->

<div class="equation" align="center" data-raw-text="s = \sum_{i=0}^{n-1} x_i" data-equation="eq:sum">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/sum/docs/img/equation_sum.svg" alt="Equation for the sum.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var incrsum = require( '@stdlib/stats/incr/sum' );
```

#### incrsum()

Returns an accumulator `function` which incrementally computes a sum.

```javascript
var accumulator = incrsum();
```

#### accumulator( \[x] )

If provided an input value `x`, the accumulator function returns an updated sum. If not provided an input value `x`, the accumulator function returns the current sum.

```javascript
var accumulator = incrsum();

var sum = accumulator( 2.0 );
// returns 2.0

sum = accumulator( 1.0 );
// returns 3.0

sum = accumulator( 3.0 );
// returns 6.0

sum = accumulator();
// returns 6.0
```

</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 **all** 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.
-   For long running accumulations or accumulations of large numbers, care should be taken to prevent overflow.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var incrsum = require( '@stdlib/stats/incr/sum' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = incrsum();

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

</section>

<!-- /.examples -->

* * *

<section class="references">

## References

-   Klein, Andreas. 2005. "A Generalized Kahan-Babuška-Summation-Algorithm." _Computing_ 76 (3): 279–93. doi:[10.1007/s00607-005-0139-x][@klein:2005a].

</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/incr/count`][@stdlib/stats/incr/count]</span><span class="delimiter">: </span><span class="description">compute a count incrementally.</span>
-   <span class="package-name">[`@stdlib/stats/incr/mean`][@stdlib/stats/incr/mean]</span><span class="delimiter">: </span><span class="description">compute an arithmetic mean incrementally.</span>
-   <span class="package-name">[`@stdlib/stats/incr/msum`][@stdlib/stats/incr/msum]</span><span class="delimiter">: </span><span class="description">compute a moving sum incrementally.</span>
-   <span class="package-name">[`@stdlib/stats/incr/prod`][@stdlib/stats/incr/prod]</span><span class="delimiter">: </span><span class="description">compute a product incrementally.</span>
-   <span class="package-name">[`@stdlib/stats/incr/summary`][@stdlib/stats/incr/summary]</span><span class="delimiter">: </span><span class="description">compute a statistical summary incrementally.</span>

</section>

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<section class="links">

[@klein:2005a]: https://doi.org/10.1007/s00607-005-0139-x

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[@stdlib/stats/incr/count]: https://github.com/stdlib-js/stats/tree/main/incr/count

[@stdlib/stats/incr/mean]: https://github.com/stdlib-js/stats/tree/main/incr/mean

[@stdlib/stats/incr/msum]: https://github.com/stdlib-js/stats/tree/main/incr/msum

[@stdlib/stats/incr/prod]: https://github.com/stdlib-js/stats/tree/main/incr/prod

[@stdlib/stats/incr/summary]: https://github.com/stdlib-js/stats/tree/main/incr/summary

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

</section>

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