@stdlib/blas-ext-base-gnannsumkbn

Calculate the sum of strided array elements, ignoring NaN values and using an improved Kahan–Babuška algorithm.

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README

gnannsumkbn

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Calculate the sum of strided array elements, ignoring NaN values and using an improved Kahan–Babuška algorithm.

Installation

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

Usage

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

gnannsumkbn( N, x, strideX, out, strideOut )

Computes the sum of strided array elements, ignoring NaN values and using an improved Kahan–Babuška algorithm.

var x = [ 1.0, -2.0, NaN, 2.0 ];
var out = [ 0.0, 0 ];

var v = gnannsumkbn( x.length, x, 1, out, 1 );
// returns [ 1.0, 3 ]

The function has the following parameters:

  • N: number of indexed elements.
  • x: input Array or typed array.
  • strideX: index increment for x.
  • out: output Array or typed array whose first element is the sum and whose second element is the number of non-NaN elements.
  • strideOut: index increment for out.

The N and stride parameters determine which elements 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, NaN, -7.0, NaN, 3.0, 4.0, 2.0 ];
var out = [ 0.0, 0 ];
var N = floor( x.length / 2 );

var v = gnannsumkbn( N, x, 2, out, 1 );
// returns [ 5.0, 2 ]

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, NaN, -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 out0 = new Float64Array( 4 );
var out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

var N = floor( x0.length / 2 );

var v = gnannsumkbn( N, x1, 2, out1, 1 );
// returns <Float64Array>[ 5.0, 4 ]

gnannsumkbn.ndarray( N, x, strideX, offsetX, out, strideOut, offsetOut )

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

var x = [ 1.0, -2.0, NaN, 2.0 ];
var out = [ 0.0, 0 ];

var v = gnannsumkbn.ndarray( x.length, x, 1, 0, out, 1, 0 );
// returns [ 1.0, 3 ]

The function has the following additional parameters:

  • offsetX: starting index for x.
  • offsetOut: starting index for out.

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, NaN, -2.0, -2.0, 2.0, 3.0, 4.0 ];
var out = [ 0.0, 0.0, 0.0, 0 ];
var N = floor( x.length / 2 );

var v = gnannsumkbn.ndarray( N, x, 2, 1, out, 2, 1 );
// returns <Float64Array>[ 0.0, 5.0, 0.0, 4 ]

Notes

  • If N <= 0, both functions return a sum equal to 0.0.

Examples

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

var x;
var i;

x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    if ( randu() < 0.2 ) {
        x[ i ] = NaN;
    } else {
        x[ i ] = round( randu()*100.0 );
    }
}
console.log( x );

var out = new Float64Array( 2 );
gnannsumkbn( x.length, x, 1, out, 1 );
console.log( out );

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.

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License

See LICENSE.

Copyright

Copyright © 2016-2022. The Stdlib Authors.