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About stdlib...

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dmeanpw

NPM version Build Status Coverage Status

Calculate the arithmetic mean of a double-precision floating-point strided array using pairwise summation.

The arithmetic mean is defined as

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

Usage

import dmeanpw from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dmeanpw@esm/index.mjs';

dmeanpw( N, x, stride )

Computes the arithmetic mean of a double-precision floating-point strided array x using pairwise summation.

import Float64Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float64@esm/index.mjs';

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

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

The function has the following parameters:

  • N: number of indexed elements.
  • x: input Float64Array.
  • 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,

import Float64Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float64@esm/index.mjs';
import floor from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-floor@esm/index.mjs';

var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
var N = floor( x.length / 2 );

var v = dmeanpw( N, x, 2 );
// returns 1.25

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

import Float64Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float64@esm/index.mjs';
import floor from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-floor@esm/index.mjs';

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

dmeanpw.ndarray( N, x, stride, offset )

Computes the arithmetic mean of a double-precision floating-point strided array using pairwise summation and alternative indexing semantics.

import Float64Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float64@esm/index.mjs';

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

var v = dmeanpw.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

import Float64Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float64@esm/index.mjs';
import floor from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-floor@esm/index.mjs';

var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var N = floor( x.length / 2 );

var v = dmeanpw.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.

Examples

<!DOCTYPE html>
<html lang="en">
<body>
<script type="module">

import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@esm/index.mjs';
import round from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-round@esm/index.mjs';
import Float64Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float64@esm/index.mjs';
import dmeanpw from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dmeanpw@esm/index.mjs';

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 = dmeanpw( x.length, x, 1 );
console.log( v );

</script>
</body>
</html>

References

  • Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." SIAM Journal on Scientific Computing 14 (4): 783–99. doi:10.1137/0914050.

See Also

Notice

This package is part of stdlib, a standard library 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.

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.