gsumkbn2

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

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.