The arithmetic mean is defined as

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

Computes the arithmetic mean along one or more ndarray dimensions using pairwise summation.

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

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

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

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

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

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

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

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

Computes the arithmetic mean along one or more ndarray dimensions using pairwise summation 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 = meanpw.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.

• 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.
• In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., "simple" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques.

• Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." SIAM Journal on Scientific Computing 14 (4): 783–99. doi:10.1137/0914050.