Skip to content

README.md

Latest commit

 

History

History
146 lines (90 loc) · 4.06 KB

README.md

File metadata and controls

146 lines (90 loc) · 4.06 KB

gcusumpw

Compute the cumulative sum of a one-dimensional ndarray using pairwise summation.

Usage

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

gcusumpw( arrays )

Computes the cumulative sum of a one-dimensional ndarray using pairwise summation.

var ndarray2array = require( '@stdlib/ndarray/to-array' );
var scalar2ndarray = require( '@stdlib/ndarray/base/from-scalar' );
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 ybuf = [ 0.0, 0.0, 0.0, 0.0 ];
var y = new ndarray( 'generic', ybuf, [ 4 ], [ 1 ], 0, 'row-major' );

var initial = scalar2ndarray( 0.0, 'generic', 'row-major' );

var v = gcusumpw( [ x, y, initial ] );
// returns <ndarray>

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

var arr = ndarray2array( v );
// returns [ 1.0, 4.0, 8.0, 10.0 ]

The function has the following parameters:

  • arrays: array-like object containing a one-dimensional input ndarray, a one-dimensional output ndarray, and a zero-dimensional ndarray containing the initial sum.

Notes

  • If provided an empty one-dimensional input ndarray, the function returns the output ndarray unchanged.
  • 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 zerosLike = require( '@stdlib/ndarray/zeros-like' );
var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
var ndarray2array = require( '@stdlib/ndarray/to-array' );
var gcusumpw = require( '@stdlib/blas/ext/base/ndarray/gcusumpw' );

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 y = zerosLike( x );
console.log( ndarray2array( y ) );

var initial = scalar2ndarray( 100.0, {
    'dtype': 'generic'
});

var v = gcusumpw( [ x, y, initial ] );
console.log( ndarray2array( v ) );

References

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