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README.md

meanwd

Calculate the arithmetic mean of a strided array using Welford's algorithm.

The arithmetic mean is defined as

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

Usage

var meanwd = require( '@stdlib/stats/strided/meanwd' );

meanwd( N, x, strideX )

Computes the arithmetic mean of a strided array x using Welford's algorithm.

var x = [ 1.0, -2.0, 2.0 ];
var N = x.length;

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

The function has the following parameters:

  • N: number of indexed elements.
  • x: input Array or typed array.
  • strideX: stride length for x.

The N and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the arithmetic mean of every other element in x,

var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];

var v = meanwd( 4, 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 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 v = meanwd( 4, x1, 2 );
// returns 1.25

meanwd.ndarray( N, x, strideX, offsetX )

Computes the arithmetic mean of a strided array using Welford's algorithm and alternative indexing semantics.

var x = [ 1.0, -2.0, 2.0 ];

var v = meanwd.ndarray( 3, x, 1, 0 );
// returns ~0.33333

The function has the following additional parameters:

  • offsetX: 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 element in the strided array starting from the second element

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 v = meanwd.ndarray( 4, x, 2, 1 );
// returns 1.25

Notes

  • If N <= 0, both functions return NaN.
  • Both functions support array-like objects having getter and setter accessors for array element access (e.g., @stdlib/array/base/accessor).
  • Depending on the environment, the typed versions (dmeanwd, smeanwd, etc.) are likely to be significantly more performant.

Examples

var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var meanwd = require( '@stdlib/stats/strided/meanwd' );

var x = discreteUniform( 10, -50, 50, {
    'dtype': 'float64'
});
console.log( x );

var v = meanwd( x.length, x, 1 );
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.

See Also