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Calculate the arithmetic mean of a single-precision floating-point strided array using a one-pass trial mean algorithm.
The arithmetic mean is defined as
To use in Observable,
smeanli = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-smeanli@umd/browser.js' )
To vendor stdlib functionality and avoid installing dependency trees for Node.js, you can use the UMD server build:
var smeanli = require( 'path/to/vendor/umd/stats-base-smeanli/index.js' )
To include the bundle in a webpage,
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-smeanli@umd/browser.js"></script>
If no recognized module system is present, access bundle contents via the global scope:
<script type="text/javascript">
(function () {
window.smeanli;
})();
</script>
Computes the arithmetic mean of a single-precision floating-point strided array x
using a one-pass trial mean algorithm.
var Float32Array = require( '@stdlib/array-float32' );
var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;
var v = smeanli( 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
,
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 = smeanli( 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 = smeanli( N, x1, 2 );
// returns 1.25
Computes the arithmetic mean of a single-precision floating-point strided array using a one-pass trial mean algorithm and alternative indexing semantics.
var Float32Array = require( '@stdlib/array-float32' );
var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;
var v = smeanli.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 = smeanli.ndarray( N, x, 2, 1 );
// returns 1.25
- If
N <= 0
, both functions returnNaN
. - 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).
<!DOCTYPE html>
<html lang="en">
<body>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-round@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-smeanli@umd/browser.js"></script>
<script type="text/javascript">
(function () {
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 = smeanli( x.length, x, 1 );
console.log( v );
})();
</script>
</body>
</html>
- 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.
@stdlib/stats-base/dmeanli
: calculate the arithmetic mean of a double-precision floating-point strided array using a one-pass trial mean algorithm.@stdlib/stats-base/smean
: calculate the arithmetic mean of a single-precision floating-point strided array.@stdlib/stats-base/smeanlipw
: calculate the arithmetic mean of a single-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation.
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.
See LICENSE.
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