dnannsumpw

Calculate the sum of double-precision floating-point strided array elements, ignoring NaN values and using pairwise summation.

Usage

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

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

Computes the sum of double-precision floating-point strided array elements, ignoring NaN values and using pairwise summation.

var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] );
var out = new Float64Array( 2 );

var v = dnannsumpw( x.length, x, 1, out, 1 );
// returns <Float64Array>[ 1.0, 3 ]

The function has the following parameters:

N: number of indexed elements.
x: input Float64Array.
strideX: index increment for x.
out: output Float64Array 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 Float64Array = require( '@stdlib/array/float64' );
var floor = require( '@stdlib/math/base/special/floor' );

var x = new Float64Array( [ 1.0, 2.0, NaN, -7.0, NaN, 3.0, 4.0, 2.0 ] );
var out = new Float64Array( 2 );
var N = floor( x.length / 2 );

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

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

Computes the sum of double-precision floating-point strided array elements, ignoring NaN values and using pairwise summation and alternative indexing semantics.

var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] );
var out = new Float64Array( 2 );

var v = dnannsumpw.ndarray( x.length, x, 1, 0, out, 1, 0 );
// returns <Float64Array>[ 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 Float64Array = require( '@stdlib/array/float64' );
var floor = require( '@stdlib/math/base/special/floor' );

var x = new Float64Array( [ 2.0, 1.0, NaN, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var out = new Float64Array( 4 );
var N = floor( x.length / 2 );

var v = dnannsumpw.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.
In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., "simple" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques.

Examples

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

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 );
dnannsumpw( x.length, x, 1, out, 1 );
console.log( out );

References

Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." SIAM Journal on Scientific Computing 14 (4): 783–99. doi:10.1137/0914050.