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About stdlib...

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smeanlipw

NPM version Build Status Coverage Status

Calculate the arithmetic mean of a single-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation.

The arithmetic mean is defined as

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

Usage

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

smeanlipw( N, x, stride )

Computes the arithmetic mean of a single-precision floating-point strided array x using a one-pass trial mean algorithm with pairwise summation.

import Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';

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.
  • 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 Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';
import floor from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-floor@esm/index.mjs';

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 views.

import Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';
import floor from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-floor@esm/index.mjs';

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 of a single-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation and alternative indexing semantics.

import Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';

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 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 Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';
import floor from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-floor@esm/index.mjs';

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

<!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 Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';
import smeanlipw from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-smeanlipw@esm/index.mjs';

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 );

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

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.
  • 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.
  • 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.
  • 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

  • @stdlib/stats-base/dmeanlipw: calculate the arithmetic mean of a double-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation.
  • @stdlib/stats-base/smean: calculate the arithmetic mean of a single-precision floating-point strided array.
  • @stdlib/stats-base/smeanli: calculate the arithmetic mean of a single-precision floating-point strided array using a one-pass trial mean algorithm.

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.