dsumkbn

Calculate the sum of double-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.

Usage

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

dsumkbn( N, x, strideX )

Computes the sum of double-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.

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

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

var v = dsumkbn( x.length, x, 1 );
// returns 1.0

The function has the following parameters:

• N: number of indexed elements.
• x: input Float64Array.
• strideX: stride length for x.

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

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 = dsumkbn( 4, 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 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 = dsumkbn( 4, x1, 2 );
// returns 5.0

dsumkbn.ndarray( N, x, strideX, offsetX )

Computes the sum of double-precision floating-point strided array elements 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 = dsumkbn.ndarray( 3, x, 1, 0 );
// returns 1.0

The function has the following additional parameters:

• offsetX: 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 element starting from the second element:

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 = dsumkbn.ndarray( 4, x, 2, 1 );
// returns 5.0

Notes

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

Examples

var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var dsumkbn = require( '@stdlib/blas/ext/base/dsumkbn' );

var x = discreteUniform( 10, -100, 100, {
    'dtype': 'float64'
});
console.log( x );

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

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C APIs

Usage

#include "stdlib/blas/ext/base/dsumkbn.h"

stdlib_strided_dsumkbn( N, *X, strideX )

Computes the sum of double-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.

const double x[] = { 1.0, 2.0, 3.0, 4.0 };

double v = stdlib_strided_dsumkbn( 4, x, 1 );
// returns 10.0

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] double* input array.
• strideX: [in] CBLAS_INT stride length for X.

double stdlib_strided_dsumkbn( const CBLAS_INT N, const double *X, const CBLAS_INT strideX );

stdlib_strided_dsumkbn_ndarray( N, *X, strideX, offsetX )

Computes the sum of double-precision floating-point strided array elements using an improved Kahan–Babuška algorithm and alternative indexing semantics.

const double x[] = { 1.0, 2.0, 3.0, 4.0 };

double v = stdlib_strided_dsumkbn_ndarray( 4, x, 1, 0 );
// returns 10.0

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• X: [in] double* input array.
• strideX: [in] CBLAS_INT stride length for X.
• offsetX: [in] CBLAS_INT starting index for X.

double stdlib_strided_dsumkbn_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX );

Examples

#include "stdlib/blas/ext/base/dsumkbn.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array:
    const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };

    // Specify the number of elements:
    const int N = 4;

    // Specify the stride length:
    const int strideX = 2;

    // Compute the sum:
    double v = stdlib_strided_dsumkbn( N, x, strideX );

    // Print the result:
    printf( "sum: %lf\n", 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.

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See Also

• @stdlib/blas/ext/base/dnansumkbn: calculate the sum of double-precision floating-point strided array elements, ignoring NaN values and using an improved Kahan–Babuška algorithm.
• @stdlib/blas/ext/base/dsum: calculate the sum of double-precision floating-point strided array elements.
• @stdlib/blas/ext/base/dsumkbn2: calculate the sum of double-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.
• @stdlib/blas/ext/base/dsumors: calculate the sum of double-precision floating-point strided array elements using ordinary recursive summation.
• @stdlib/blas/ext/base/dsumpw: calculate the sum of double-precision floating-point strided array elements using pairwise summation.
• @stdlib/blas/ext/base/gsumkbn: calculate the sum of strided array elements using an improved Kahan–Babuška algorithm.
• @stdlib/blas/ext/base/ssumkbn: calculate the sum of single-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.