README.md

gsumpw

Compute the sum of all elements in a one-dimensional ndarray using pairwise summation.

Usage

var gsumpw= require( '@stdlib/blas/ext/base/ndarray/gsumpw' );

gsumpw( arrays )

Computes the sum of all elements in a one-dimensional ndarray using pairwise summation.

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

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

var v = gsumpw( [ x ] );
// returns 10.0

The function has the following parameters:

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

Notes

• If provided an empty real-valued one-dimensional ndarray, the function returns 0.0.
• 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.

Examples

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

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

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

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