gapxsumkbn

Add a scalar constant to each strided array element and compute the sum using an improved Kahan–Babuška algorithm.

Installation

npm install @stdlib/blas-ext-base-gapxsumkbn

Usage

var gapxsumkbn = require( '@stdlib/blas-ext-base-gapxsumkbn' );

gapxsumkbn( N, alpha, x, strideX )

Adds a scalar constant to each strided array element and computes the sum using an improved Kahan–Babuška algorithm.

var x = [ 1.0, -2.0, 2.0 ];

var v = gapxsumkbn( x.length, 5.0, x, 1 );
// returns 16.0

The function has the following parameters:

• N: number of indexed elements.
• alpha: scalar constant.
• x: input Array or typed array.
• strideX: stride length.

The N and stride parameters determine which elements in the strided array are accessed at runtime. For example, to access every other element:

var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];

var v = gapxsumkbn( 4, 5.0, x, 2 );
// returns 25.0

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

var Float64Array = require( '@stdlib/array-float64' );

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 v = gapxsumkbn( 4, 5.0, x1, 2 );
// returns 25.0

gapxsumkbn.ndarray( N, alpha, x, strideX, offsetX )

Adds a scalar constant to each strided array element and computes the sum using an improved Kahan–Babuška algorithm and alternative indexing semantics.

var x = [ 1.0, -2.0, 2.0 ];

var v = gapxsumkbn.ndarray( x.length, 5.0, x, 1, 0 );
// returns 16.0

The function has the following additional parameters:

• offsetX: starting index.

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 access every other element starting from the second element:

var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];

var v = gapxsumkbn.ndarray( 4, 5.0, x, 2, 1 );
// returns 25.0

Notes

• If N <= 0, both functions return 0.0.
• Both functions support array-like objects having getter and setter accessors for array element access (e.g., @stdlib/array-base/accessor).
• Depending on the environment, the typed versions (dapxsumkbn, sapxsumkbn, etc.) are likely to be significantly more performant.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var gapxsumkbn = require( '@stdlib/blas-ext-base-gapxsumkbn' );

var x = discreteUniform( 10, -100, 100, {
    'dtype': 'float64'
});
console.log( x );

var v = gapxsumkbn( x.length, 5.0, x, 1 );
console.log( v );

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.

See Also

• @stdlib/blas-ext/base/dapxsumkbn: add a constant to each double-precision floating-point strided array element and compute the sum using an improved Kahan–Babuška algorithm.
• @stdlib/blas-ext/base/gapxsum: add a scalar constant to each strided array element and compute the sum.
• @stdlib/blas-ext/base/gsumkbn: calculate the sum of strided array elements using an improved Kahan–Babuška algorithm.
• @stdlib/blas-ext/base/sapxsumkbn: add a scalar constant to each single-precision floating-point strided array element and compute the sum using an improved Kahan–Babuška 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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.