gsumkbn2

Calculate the sum of strided array elements using a second-order iterative Kahan–Babuška algorithm.

Installation

npm install @stdlib/blas-ext-base-gsumkbn2

Usage

var gsumkbn2 = require( '@stdlib/blas-ext-base-gsumkbn2' );

gsumkbn2( N, x, stride )

Computes the sum of strided array elements using a second-order iterative Kahan–Babuška algorithm.

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

var v = gsumkbn2( 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 = gsumkbn2( 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 = gsumkbn2( N, x1, 2 );
// returns 5.0

gsumkbn2.ndarray( N, x, stride, offset )

Computes the sum of strided array elements using a second-order iterative Kahan–Babuška algorithm and alternative indexing semantics.

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

var v = gsumkbn2.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 = gsumkbn2.ndarray( N, x, 2, 1 );
// returns 5.0

Notes

• If N <= 0, both functions return 0.0.
• Depending on the environment, the typed versions (dsumkbn2, ssumkbn2, 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 gsumkbn2 = require( '@stdlib/blas-ext-base-gsumkbn2' );

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 = gsumkbn2( x.length, x, 1 );
console.log( v );

References

• Klein, Andreas. 2005. "A Generalized Kahan-Babuška-Summation-Algorithm." Computing 76 (3): 279–93. doi:10.1007/s00607-005-0139-x.

See Also

• @stdlib/blas-ext/base/dsumkbn2: calculate the sum of double-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.
• @stdlib/blas-ext/base/gnansumkbn2: calculate the sum of strided array elements, ignoring NaN values and using a second-order iterative Kahan–Babuška algorithm.
• @stdlib/blas-ext/base/gsum: calculate the sum of strided array elements.
• @stdlib/blas-ext/base/gsumkbn: calculate the sum of strided array elements using an improved 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/ssumkbn2: calculate the sum of single-precision floating-point strided array elements using a second-order iterative 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.

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.