# @stdlib/stats-base-dsmeanpw

Calculate the arithmetic mean of a single-precision floating-point strided array using pairwise summation with extended accumulation and returning an extended precision result.

## Usage no npm install needed!

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import stdlibStatsBaseDsmeanpw from 'https://cdn.skypack.dev/@stdlib/stats-base-dsmeanpw';
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# dsmeanpw

Calculate the arithmetic mean of a single-precision floating-point strided array using pairwise summation with extended accumulation and returning an extended precision result.

The arithmetic mean is defined as

## Installation

npm install @stdlib/stats-base-dsmeanpw


## Usage

var dsmeanpw = require( '@stdlib/stats-base-dsmeanpw' );


#### dsmeanpw( N, x, stride )

Computes the arithmetic mean of a single-precision floating-point strided array x using pairwise summation with extended accumulation and returning an extended precision result.

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

var v = dsmeanpw( N, x, 1 );
// returns ~0.3333


The function has the following parameters:

The N and stride parameters determine which elements in x are accessed at runtime. For example, to compute the arithmetic mean of every other element in x,

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 = dsmeanpw( N, x, 2 );
// returns 1.25


Note that indexing is relative to the first index. To introduce an offset, use typed array views.

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 = dsmeanpw( N, x1, 2 );
// returns 1.25


#### dsmeanpw.ndarray( N, x, stride, offset )

Computes the arithmetic mean of a single-precision floating-point strided array using pairwise summation with extended accumulation and alternative indexing semantics and returning an extended precision result.

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

var v = dsmeanpw.ndarray( N, x, 1, 0 );
// returns ~0.33333


The function has the following additional parameters:

• offset: starting index for x.

While 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 for every other value in x starting from the second value

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 = dsmeanpw.ndarray( N, x, 2, 1 );
// returns 1.25


## Notes

• If N <= 0, both functions return NaN.
• Accumulated intermediate values are stored as double-precision floating-point numbers.
• 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.

## Examples

var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var Float32Array = require( '@stdlib/array-float32' );
var dsmeanpw = require( '@stdlib/stats-base-dsmeanpw' );

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 = dsmeanpw( 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.

## Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.