# smeanlipw
> Calculate the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation.
The [arithmetic mean][arithmetic-mean] is defined as
## Usage
```javascript
var smeanlipw = require( '@stdlib/stats/base/smeanlipw' );
```
#### smeanlipw( N, x, stride )
Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array `x` using a one-pass trial mean algorithm with pairwise summation.
```javascript
var Float32Array = require( '@stdlib/array/float32' );
var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;
var v = smeanlipw( N, x, 1 );
// returns ~0.3333
```
The function has the following parameters:
- **N**: number of indexed elements.
- **x**: input [`Float32Array`][@stdlib/array/float32].
- **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 Float32Array = require( '@stdlib/array/float32' );
var floor = require( '@stdlib/math/base/special/floor' );
var x = new Float32Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
var N = floor( x.length / 2 );
var v = smeanlipw( 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 Float32Array = require( '@stdlib/array/float32' );
var floor = require( '@stdlib/math/base/special/floor' );
var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var N = floor( x0.length / 2 );
var v = smeanlipw( N, x1, 2 );
// returns 1.25
```
#### smeanlipw.ndarray( N, x, stride, offset )
Computes the [arithmetic mean][arithmetic-mean] of a single-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation and alternative indexing semantics.
```javascript
var Float32Array = require( '@stdlib/array/float32' );
var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;
var v = smeanlipw.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 Float32Array = require( '@stdlib/array/float32' );
var floor = require( '@stdlib/math/base/special/floor' );
var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var N = floor( x.length / 2 );
var v = smeanlipw.ndarray( N, x, 2, 1 );
// returns 1.25
```
## Notes
- If `N <= 0`, both functions return `NaN`.
- The underlying algorithm is a specialized case of Welford's algorithm. Similar to the method of assumed mean, the first strided array element is used as a trial mean. The trial mean is subtracted from subsequent data values, and the average deviations used to adjust the initial guess. Accordingly, the algorithm's accuracy is best when data is **unordered** (i.e., the data is **not** sorted in either ascending or descending order such that the first value is an "extreme" value).
## Examples
```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float32Array = require( '@stdlib/array/float32' );
var smeanlipw = require( '@stdlib/stats/base/smeanlipw' );
var x;
var i;
x = new Float32Array( 10 );
for ( i = 0; i < x.length; i++ ) {
x[ i ] = round( (randu()*100.0) - 50.0 );
}
console.log( x );
var v = smeanlipw( x.length, x, 1 );
console.log( v );
```
* * *
## References
- Welford, B. P. 1962. "Note on a Method for Calculating Corrected Sums of Squares and Products." _Technometrics_ 4 (3). Taylor & Francis: 419–20. doi:[10.1080/00401706.1962.10490022][@welford:1962a].
- van Reeken, A. J. 1968. "Letters to the Editor: Dealing with Neely's Algorithms." _Communications of the ACM_ 11 (3): 149–50. doi:[10.1145/362929.362961][@vanreeken:1968a].
- Ling, Robert F. 1974. "Comparison of Several Algorithms for Computing Sample Means and Variances." _Journal of the American Statistical Association_ 69 (348). American Statistical Association, Taylor & Francis, Ltd.: 859–66. doi:[10.2307/2286154][@ling:1974a].
- 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
[@stdlib/array/float32]: https://www.npmjs.com/package/@stdlib/array-float32
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
[@welford:1962a]: https://doi.org/10.1080/00401706.1962.10490022
[@vanreeken:1968a]: https://doi.org/10.1145/362929.362961
[@ling:1974a]: https://doi.org/10.2307/2286154
[@higham:1993a]: https://doi.org/10.1137/0914050
