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dapxsumkbn

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

Installation

npm install @stdlib/blas-ext-base-dapxsumkbn

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

dapxsumkbn( N, alpha, x, strideX )

Adds a scalar 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( x.length, 5.0, x, 1 );
// returns 16.0

The function has the following parameters:

• N: number of indexed elements.
• alpha: scalar constant.
• x: input Float64Array.
• strideX: stride length 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:

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, strideX, offsetX )

Adds a scalar 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( x.length, 5.0, x, 1, 0 );
// returns 16.0

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 access 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 = 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-array-discrete-uniform' );
var dapxsumkbn = require( '@stdlib/blas-ext-base-dapxsumkbn' );

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

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

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C APIs

Usage

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

stdlib_strided_dapxsumkbn( N, alpha, *X, strideX )

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

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

double v = stdlib_strided_dapxsumkbn( 4, 5.0, x, 1 );
// returns 30.0

The function accepts the following arguments:

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

double stdlib_strided_dapxsumkbn( const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX );

stdlib_strided_dapxsumkbn_ndarray( N, alpha, *X, strideX, offsetX )

Adds a scalar constant to each double-precision floating-point strided array element and computes the sum 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_dapxsumkbn_ndarray( 4, 5.0, x, 1, 0 );
// returns 30.0

The function accepts the following arguments:

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

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

Examples

#include "stdlib/blas/ext/base/dapxsumkbn.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 indexed elements:
    const int N = 8;

    // Specify a stride:
    const int strideX = 1;

    // Compute the sum:
    double v = stdlib_strided_dapxsumkbn( N, 5.0, x, strideX );

    // Print the result:
    printf( "Sum: %lf\n", sum );
}

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/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.

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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License

See LICENSE.

Copyright

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