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gsumkbn

Calculate the sum of strided array elements using an improved Kahan–Babuška algorithm.

Installation

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

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

gsumkbn( N, x, stride )

Computes the sum of strided array elements using an improved Kahan–Babuška algorithm.

var x = [ 1.0, -2.0, 2.0 ];
var N = x.length;

var v = gsumkbn( N, x, 1 );
// returns 1.0

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 compute the sum of 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 = gsumkbn( N, x, 2 );
// returns 5.0

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 = gsumkbn( N, x1, 2 );
// returns 5.0

gsumkbn.ndarray( N, x, stride, offset )

Computes the sum of strided array elements using an improved Kahan–Babuška algorithm and alternative indexing semantics.

var x = [ 1.0, -2.0, 2.0 ];
var N = x.length;

var v = gsumkbn.ndarray( N, x, 1, 0 );
// returns 1.0

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 calculate the sum of 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 = gsumkbn.ndarray( N, x, 2, 1 );
// returns 5.0

Notes

• If N <= 0, both functions return 0.0.
• Depending on the environment, the typed versions (dsum, ssum, 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 gsumkbn = require( '@stdlib/blas-ext-base-gsumkbn' );

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 = gsumkbn( x.length, x, 1 );
console.log( v );

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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.

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See Also

• @stdlib/blas-ext/base/dsumkbn: calculate the sum of double-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.
• @stdlib/blas-ext/base/gnansumkbn: calculate the sum of strided array elements, ignoring NaN values and using an improved Kahan–Babuška algorithm.
• @stdlib/blas-ext/base/gsum: calculate the sum of strided array elements.
• @stdlib/blas-ext/base/gsumkbn2: calculate the sum of strided array elements using a second-order iterative Kahan–Babuška algorithm.
• @stdlib/blas-ext/base/gsumors: calculate the sum of strided array elements using ordinary recursive summation.
• @stdlib/blas-ext/base/gsumpw: calculate the sum of strided array elements using pairwise summation.
• @stdlib/blas-ext/base/ssumkbn: calculate the sum of single-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.

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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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.