Skip to content

README.md

Latest commit

 

History

History
153 lines (93 loc) · 4.97 KB

README.md

File metadata and controls

153 lines (93 loc) · 4.97 KB

smeanlipw

Compute the arithmetic mean of a one-dimensional double-precision floating-point ndarray 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

var smeanlipw = require( '@stdlib/stats/base/ndarray/smeanlipw' );

smeanlipw( arrays )

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

var Float32Array = require( '@stdlib/array/float32' );
var ndarray = require( '@stdlib/ndarray/base/ctor' );

var xbuf = new Float32Array( [ 1.0, 3.0, 4.0, 2.0 ] );
var x = new ndarray( 'float32', xbuf, [ 4 ], [ 1 ], 0, 'row-major' );

var v = smeanlipw( [ x ] );
// returns 2.5

The function has the following parameters:

  • arrays: array-like object containing a one-dimensional input ndarray.

Notes

  • If provided an empty one-dimensional ndarray, the function returns NaN.
  • The underlying algorithm is a specialized case of Welford's algorithm. Similar to the method of assumed mean, the first ndarray 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

var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var ndarray = require( '@stdlib/ndarray/base/ctor' );
var ndarray2array = require( '@stdlib/ndarray/to-array' );
var smeanlipw = require( '@stdlib/stats/base/ndarray/smeanlipw' );

var xbuf = discreteUniform( 10, -50, 50, {
    'dtype': 'float32'
});
var x = new ndarray( 'float32', xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
console.log( ndarray2array( x ) );

var v = smeanlipw( [ x ] );
console.log( v );

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.