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    @stdlib/stats-base-meanpn
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    0.0.7 • Public • Published

    meanpn

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    Calculate the arithmetic mean of a strided array using a two-pass error correction algorithm.

    The arithmetic mean is defined as

    Equation for the arithmetic mean.

    Installation

    npm install @stdlib/stats-base-meanpn

    Usage

    var meanpn = require( '@stdlib/stats-base-meanpn' );

    meanpn( N, x, stride )

    Computes the arithmetic mean of a strided array x using a two-pass error correction algorithm.

    var x = [ 1.0, -2.0, 2.0 ];
    var N = x.length;
    
    var v = meanpn( N, x, 1 );
    // returns ~0.3333

    The function has the following parameters:

    • N: number of indexed elements.
    • x: input Array or typed array.
    • 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 floor = require( '@stdlib/math-base-special-floor' );
    
    var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];
    var N = floor( x.length / 2 );
    
    var v = meanpn( N, 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 floor = require( '@stdlib/math-base-special-floor' );
    
    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 = meanpn( N, x1, 2 );
    // returns 1.25

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

    Computes the arithmetic mean of a strided array using a two-pass error correction algorithm and alternative indexing semantics.

    var x = [ 1.0, -2.0, 2.0 ];
    var N = x.length;
    
    var v = meanpn.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 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 N = floor( x.length / 2 );
    
    var v = meanpn.ndarray( N, x, 2, 1 );
    // returns 1.25

    Notes

    • If N <= 0, both functions return NaN.
    • Depending on the environment, the typed versions (dmeanpn, smeanpn, etc.) are likely to be significantly more performant.

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var round = require( '@stdlib/math-base-special-round' );
    var Float64Array = require( '@stdlib/array-float64' );
    var meanpn = require( '@stdlib/stats-base-meanpn' );
    
    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 = meanpn( x.length, x, 1 );
    console.log( v );

    References

    • Neely, Peter M. 1966. "Comparison of Several Algorithms for Computation of Means, Standard Deviations and Correlation Coefficients." Communications of the ACM 9 (7). Association for Computing Machinery: 496–99. doi:10.1145/365719.365958.
    • Schubert, Erich, and Michael Gertz. 2018. "Numerically Stable Parallel Computation of (Co-)Variance." In Proceedings of the 30th International Conference on Scientific and Statistical Database Management. New York, NY, USA: Association for Computing Machinery. doi:10.1145/3221269.3223036.

    See Also

    • @stdlib/stats/base/dmeanpn: calculate the arithmetic mean of a double-precision floating-point strided array using a two-pass error correction algorithm.
    • @stdlib/stats/base/mean: calculate the arithmetic mean of a strided array.
    • @stdlib/stats/base/nanmeanpn: calculate the arithmetic mean of a strided array, ignoring NaN values and using a two-pass error correction algorithm.
    • @stdlib/stats/base/smeanpn: calculate the arithmetic mean of a single-precision floating-point strided array using a two-pass error correction algorithm.

    Notice

    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.

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    License

    See LICENSE.

    Copyright

    Copyright © 2016-2022. The Stdlib Authors.

    Install

    npm i @stdlib/stats-base-meanpn

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