# meanpw
> Calculate the [arithmetic mean][arithmetic-mean] of a strided array using pairwise summation.
The [arithmetic mean][arithmetic-mean] is defined as
## Usage
```javascript
var meanpw = require( '@stdlib/stats/base/meanpw' );
```
#### meanpw( N, x, stride )
Computes the [arithmetic mean][arithmetic-mean] of a strided array `x` using pairwise summation.
```javascript
var x = [ 1.0, -2.0, 2.0 ];
var N = x.length;
var v = meanpw( N, x, 1 );
// returns ~0.3333
```
The function has the following parameters:
- **N**: number of indexed elements.
- **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
- **stride**: index increment 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 floor = require( '@stdlib/math/base/special/floor' );
var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];
var N = floor( x.length / 2 );
var v = meanpw( N, 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.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var floor = require( '@stdlib/math/base/special/floor' );
var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var N = floor( x0.length / 2 );
var v = meanpw( N, x1, 2 );
// returns 1.25
```
#### meanpw.ndarray( N, x, stride, offset )
Computes the [arithmetic mean][arithmetic-mean] of a strided array using pairwise summation and alternative indexing semantics.
```javascript
var x = [ 1.0, -2.0, 2.0 ];
var N = x.length;
var v = meanpw.ndarray( N, x, 1, 0 );
// returns ~0.33333
```
The function has the following additional parameters:
- **offset**: 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 value in `x` starting from the second value
```javascript
var floor = require( '@stdlib/math/base/special/floor' );
var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
var N = floor( x.length / 2 );
var v = meanpw.ndarray( N, x, 2, 1 );
// returns 1.25
```
## Notes
- If `N <= 0`, both functions return `NaN`.
- 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.
- Depending on the environment, the typed versions ([`dmeanpw`][@stdlib/stats/base/dmeanpw], [`smeanpw`][@stdlib/stats/base/smeanpw], etc.) are likely to be significantly more performant.
## Examples
```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var meanpw = require( '@stdlib/stats/base/meanpw' );
var x;
var i;
x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
x[ i ] = round( (randu()*100.0) - 50.0 );
}
console.log( x );
var v = meanpw( x.length, x, 1 );
console.log( v );
```
* * *
## 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].
[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean
[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
[@stdlib/stats/base/dmeanpw]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/dmeanpw
[@stdlib/stats/base/smeanpw]: https://www.npmjs.com/package/@stdlib/stats/tree/main/base/smeanpw
[@higham:1993a]: https://doi.org/10.1137/0914050
