About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

gapxsumkbn

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

Installation

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

gapxsumkbn( N, alpha, x, stride )

Adds a 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 N = x.length;

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

The function has the following parameters:

• N: number of indexed elements.
• x: input Array or typed array.
• stride: index increment for x.

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

var floor = require( '@stdlib/math-base-special-floor' );

var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];
var N = floor( x.length / 2 );

var v = gapxsumkbn( N, 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 floor = require( '@stdlib/math-base-special-floor' );

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 N = floor( x0.length / 2 );

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

gapxsumkbn.ndarray( N, alpha, x, stride, offset )

Adds a 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 N = x.length;

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

The function has the following additional parameters:

• offset: starting index for x.

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 value in x starting from the second value

var floor = require( '@stdlib/math-base-special-floor' );

var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
var N = floor( x.length / 2 );

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

Notes

• If N <= 0, both functions return 0.0.
• Depending on the environment, the typed versions (dapxsumkbn, sapxsumkbn, etc.) are likely to be significantly more performant.

Examples

var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var Float64Array = require( '@stdlib/array-float64' );
var gapxsumkbn = require( '@stdlib/blas-ext-base-gapxsumkbn' );

var x;
var i;

x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    x[ i ] = round( randu()*100.0 );
}
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: adds a constant to each double-precision floating-point strided array element and computes the sum using an improved Kahan–Babuška algorithm.
• @stdlib/blas-ext/base/gapxsum: adds a constant to each strided array element and computes 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: adds a constant to each single-precision floating-point strided array element and computes 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 © 2016-2024. The Stdlib Authors.