gnannsumkbn

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

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.