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README.md |
gnansumpw
Calculate the sum of strided array elements, ignoring
NaN
values and using pairwise summation.
Usage
var gnansumpw = require( '@stdlib/blas/ext/base/gnansumpw' );
gnansumpw( N, x, stride )
Computes the sum of strided array elements, ignoring NaN
values and using pairwise summation.
var x = [ 1.0, -2.0, NaN, 2.0 ];
var N = x.length;
var v = gnansumpw( N, x, 1 );
// returns 1.0
The function has the following parameters:
- N: number of indexed elements.
- x: input
Array
ortyped 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, NaN, NaN ];
var N = floor( x.length / 2 );
var v = gnansumpw( 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 = gnansumpw( N, x1, 2 );
// returns 5.0
gnansumpw.ndarray( N, x, stride, offset )
Computes the sum of strided array elements, ignoring NaN
values and using pairwise summation and alternative indexing semantics.
var x = [ 1.0, -2.0, NaN, 2.0 ];
var N = x.length;
var v = gnansumpw.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, NaN, NaN ];
var N = floor( x.length / 2 );
var v = gnansumpw.ndarray( N, x, 2, 1 );
// returns 5.0
Notes
- If
N <= 0
, both functions return0.0
. - 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.
- Depending on the environment, the typed versions (
dnansumpw
,snansumpw
, 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 gnansumpw = require( '@stdlib/blas/ext/base/gnansumpw' );
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 v = gnansumpw( x.length, x, 1 );
console.log( v );
References
- Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." SIAM Journal on Scientific Computing 14 (4): 783–99. doi:10.1137/0914050.