Skip to content

Latest commit

 

History

History
200 lines (118 loc) · 6.49 KB

README.md

File metadata and controls

200 lines (118 loc) · 6.49 KB

dapxsumkbn

Add a constant to each double-precision floating-point strided array element and compute the sum using an improved Kahan–Babuška algorithm.

Usage

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

dapxsumkbn( N, alpha, x, stride )

Adds a constant to each double-precision floating-point strided array element and computes the sum using an improved Kahan–Babuška algorithm.

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

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

var v = dapxsumkbn( 3, 5.0, x, 1 );
// returns 16.0

The function has the following parameters:

  • N: number of indexed elements.
  • x: input Float64Array.
  • stride: index increment for x.

The N and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to access every other element in x,

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

var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );

var v = dapxsumkbn( 4, 5.0, x, 2 );
// returns 25.0

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

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

var 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 v = dapxsumkbn( 4, 5.0, x1, 2 );
// returns 25.0

dapxsumkbn.ndarray( N, alpha, x, stride, offset )

Adds a constant to each double-precision floating-point strided array element and computes the sum using an improved Kahan–Babuška algorithm and alternative indexing semantics.

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

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

var v = dapxsumkbn.ndarray( 3, 5.0, x, 1, 0 );
// returns 16.0

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 access every other value in x starting from the second value

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

var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );

var v = dapxsumkbn.ndarray( 4, 5.0, x, 2, 1 );
// returns 25.0

Notes

  • If N <= 0, both functions return 0.0.

Examples

var discreteUniform = require( '@stdlib/random/base/discrete-uniform' ).factory;
var filledarrayBy = require( '@stdlib/array/filled-by' );
var dapxsumkbn = require( '@stdlib/blas/ext/base/dapxsumkbn' );

var x = filledarrayBy( 10, 'float64', discreteUniform( 0, 100 ) );
console.log( x );

var v = dapxsumkbn( x.length, 5.0, x, 1 );
console.log( v );

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.

See Also

  • @stdlib/blas/ext/base/dapxsum: adds a constant to each double-precision floating-point strided array element and computes the sum.
  • @stdlib/blas/ext/base/dsumkbn: calculate the sum of double-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.
  • @stdlib/blas/ext/base/gapxsumkbn: adds a constant to each strided array element and computes the sum using an improved Kahan–Babuška algorithm.
  • @stdlib/blas/ext/base/sapxsumkbn: adds a constant to each single-precision floating-point strided array element and computes the sum using an improved Kahan–Babuška algorithm.