npm

@stdlib/blas-ext-base-gsumkbn

0.0.9 • Public • Published

gsumkbn

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

Installation

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

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:

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 );```

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.

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.

Install

`npm i @stdlib/blas-ext-base-gsumkbn`

stdlib.io

1,543

0.0.9

Apache-2.0

38.5 kB

10