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: stride length 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: stride length for out.

The N and stride parameters determine which elements are accessed at runtime. For example, to compute the sum of every other element:

var x = [ 1.0, 2.0, NaN, -7.0, NaN, 3.0, 4.0, 2.0 ];
var out = [ 0.0, 0 ];

var v = gnannsumkbn( 4, 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 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 v = gnannsumkbn( 4, 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 parameters support indexing semantics based on starting indices. For example, to calculate the sum of every other element starting from the second element:

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 v = gnannsumkbn.ndarray( 4, 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 bernoulli = require( '@stdlib/random/base/bernoulli' );
var discreteUniform = require( '@stdlib/random/base/discrete-uniform' );
var filledarrayBy = require( '@stdlib/array/filled-by' );
var Float64Array = require( '@stdlib/array/float64' );
var gnannsumkbn = require( '@stdlib/blas/ext/base/gnannsumkbn' );

function rand() {
    if ( bernoulli( 0.8 ) > 0 ) {
        return discreteUniform( 0, 100 );
    }
    return NaN;
}

var x = filledarrayBy( 10, 'float64', rand );
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.