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

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.