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meanpw

Calculate the arithmetic mean of a strided array using pairwise summation.

The arithmetic mean is defined as

$$\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i$$

Installation

npm install @stdlib/stats-base-meanpw

Alternatively,

To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
If you are using Deno, visit the deno branch (see README for usage intructions).
For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

meanpw( N, x, stride )

Computes the arithmetic mean of a strided array x using pairwise summation.

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 or 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 of every other element in x,

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 views.

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 of a strided array using pairwise summation and alternative indexing semantics.

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 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 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, smeanpw, etc.) are likely to be significantly more performant.

Examples

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.

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.

Community

License

See LICENSE.

stdlib-js/stats-base-meanpw