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README.md

meankbn

Compute the arithmetic mean along one or more ndarray dimensions using an improved Kahan–Babuška algorithm.

The arithmetic mean is defined as

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

Usage

var meankbn = require( '@stdlib/stats/meankbn' );

meankbn( x[, options] )

Computes the arithmetic mean along one or more ndarray dimensions using an improved Kahan–Babuška algorithm.

var array = require( '@stdlib/ndarray/array' );

var x = array( [ 1.0, 2.0, -2.0, 4.0 ] );

var y = meankbn( x );
// returns <ndarray>[ 1.25 ]

The function has the following parameters:

  • x: input ndarray. Must have a real-valued or "generic" data type.
  • options: function options (optional).

The function accepts the following options:

  • dims: list of dimensions over which to perform a reduction. If not provided, the function performs a reduction over all elements in a provided input ndarray.
  • dtype: output ndarray data type. Must be a real-valued floating-point or "generic" data type.
  • keepdims: boolean indicating whether the reduced dimensions should be included in the returned ndarray as singleton dimensions. Default: false.

By default, the function performs a reduction over all elements in a provided input ndarray. To perform a reduction over specific dimensions, provide a dims option.

var array = require( '@stdlib/ndarray/array' );

var x = array( [ 1.0, 2.0, -2.0, 4.0 ], {
    'shape': [ 2, 2 ],
    'order': 'row-major'
});
// returns <ndarray>[ [ 1.0, 2.0 ], [ -2.0, 4.0 ] ]

var y = meankbn( x, {
    'dims': [ 0 ]
});
// returns <ndarray>[ -0.5, 3.0 ]

y = meankbn( x, {
    'dims': [ 1 ]
});
// returns <ndarray>[ 1.5, 1.0 ]

y = meankbn( x, {
    'dims': [ 0, 1 ]
});
// returns <ndarray>[ 1.25 ]

By default, the function excludes reduced dimensions from the output ndarray. To include the reduced dimensions as singleton dimensions, set the keepdims option to true.

var array = require( '@stdlib/ndarray/array' );

var x = array( [ 1.0, 2.0, -2.0, 4.0 ], {
    'shape': [ 2, 2 ],
    'order': 'row-major'
});
// returns <ndarray>[ [ 1.0, 2.0 ], [ -2.0, 4.0 ] ]

var y = meankbn( x, {
    'dims': [ 0 ],
    'keepdims': true
});
// returns <ndarray>[ [ -0.5, 3.0 ] ]

y = meankbn( x, {
    'dims': [ 1 ],
    'keepdims': true
});
// returns <ndarray>[ [ 1.5 ], [ 1.0 ] ]

y = meankbn( x, {
    'dims': [ 0, 1 ],
    'keepdims': true
});
// returns <ndarray>[ [ 1.25 ] ]

By default, the function returns an ndarray having a data type determined by the function's output data type policy. To override the default behavior, set the dtype option.

var getDType = require( '@stdlib/ndarray/dtype' );
var array = require( '@stdlib/ndarray/array' );

var x = array( [ 1.0, 2.0, -2.0, 4.0 ], {
    'dtype': 'generic'
});

var y = meankbn( x, {
    'dtype': 'float64'
});
// returns <ndarray>

var dt = String( getDType( y ) );
// returns 'float64'

meankbn.assign( x, out[, options] )

Computes the arithmetic mean along one or more ndarray dimensions using an improved Kahan–Babuška algorithm and assigns results to a provided output ndarray.

var array = require( '@stdlib/ndarray/array' );
var zeros = require( '@stdlib/ndarray/zeros' );

var x = array( [ 1.0, 2.0, -2.0, 4.0 ] );
var y = zeros( [] );

var out = meankbn.assign( x, y );
// returns <ndarray>[ 1.25 ]

var bool = ( out === y );
// returns true

The method has the following parameters:

  • x: input ndarray. Must have a real-valued or "generic" data type.
  • out: output ndarray.
  • options: function options (optional).

The method accepts the following options:

  • dims: list of dimensions over which to perform a reduction. If not provided, the function performs a reduction over all elements in a provided input ndarray.

Notes

  • Setting the keepdims option to true can be useful when wanting to ensure that the output ndarray is broadcast-compatible with ndarrays having the same shape as the input ndarray.
  • The output data type policy only applies to the main function and specifies that, by default, the function must return an ndarray having a real-valued floating-point or "generic" data type. For the assign method, the output ndarray is allowed to have any supported output data type.

Examples

var uniform = require( '@stdlib/random/uniform' );
var getDType = require( '@stdlib/ndarray/dtype' );
var ndarray2array = require( '@stdlib/ndarray/to-array' );
var meankbn = require( '@stdlib/stats/meankbn' );

// Generate an array of random numbers:
var x = uniform( [ 5, 5 ], 0.0, 20.0 );
console.log( ndarray2array( x ) );

// Perform a reduction:
var y = meankbn( x, {
    'dims': [ 0 ]
});

// Resolve the output array data type:
var dt = getDType( y );
console.log( dt );

// Print the results:
console.log( ndarray2array( y ) );

References

  • Neumaier, Arnold. 1974. "Rounding Error Analysis of Some Methods for Summing Finite Sums." Zeitschrift Für Angewandte Mathematik Und Mechanik 54 (1): 39–51. doi:10.1002/zamm.19740540106.