dcusumkbn

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

Installation

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

Usage

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

dcusumkbn( N, sum, x, strideX, y, strideY )

Computes the cumulative 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 y = new Float64Array( x.length );

dcusumkbn( x.length, 0.0, x, 1, y, 1 );
// y => <Float64Array>[ 1.0, -1.0, 1.0 ]

x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
y = new Float64Array( x.length );

dcusumkbn( x.length, 10.0, x, 1, y, 1 );
// y => <Float64Array>[ 11.0, 9.0, 11.0 ]

The function has the following parameters:

• N: number of indexed elements.
• sum: initial sum.
• x: input Float64Array.
• strideX: stride length for x.
• y: output Float64Array.
• strideY: stride length for y.

The N and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to compute the cumulative 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 y = new Float64Array( x.length );

var v = dcusumkbn( 4, 0.0, x, 2, y, 1 );
// y => <Float64Array>[ 1.0, 3.0, 1.0, 5.0, 0.0, 0.0, 0.0, 0.0 ]

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

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

// Initial arrays...
var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var y0 = new Float64Array( x0.length );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element

dcusumkbn( 4, 0.0, x1, -2, y1, 1 );
// y0 => <Float64Array>[ 0.0, 0.0, 0.0, 4.0, 6.0, 4.0, 5.0, 0.0 ]

dcusumkbn.ndarray( N, sum, x, strideX, offsetX, y, strideY, offsetY )

Computes the cumulative 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 y = new Float64Array( x.length );

dcusumkbn.ndarray( x.length, 0.0, x, 1, 0, y, 1, 0 );
// y => <Float64Array>[ 1.0, -1.0, 1.0 ]

The function has the following additional parameters:

• offsetX: starting index for x.
• offsetY: starting index for y.

While typed array views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, to calculate the cumulative sum of every other value in the strided input array starting from the second value and to store in the last N elements of the strided output array starting from the last 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 y = new Float64Array( x.length );

dcusumkbn.ndarray( 4, 0.0, x, 2, 1, y, -1, y.length-1 );
// y => <Float64Array>[ 0.0, 0.0, 0.0, 0.0, 5.0, 1.0, -1.0, 1.0 ]

Notes

• If N <= 0, both functions return y unchanged.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var Float64Array = require( '@stdlib/array-float64' );
var dcusumkbn = require( '@stdlib/blas-ext-base-dcusumkbn' );

var x = discreteUniform( 10, -100, 100, {
    'dtype': 'float64'
});
var y = new Float64Array( x.length );

console.log( x );
console.log( y );

dcusumkbn( x.length, 0.0, x, 1, y, -1 );
console.log( y );

C APIs

Usage

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

stdlib_strided_dcusumkbn( N, sum, *X, strideX, *Y, strideY )

Computes the cumulative 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 y[] = { 0.0, 0.0, 0.0, 0.0 };

stdlib_strided_dcusumkbn( 4, 0.0, x, 1, y, 1 );

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• sum: [in] double initial sum.
• X: [in] double* input array.
• strideX: [in] CBLAS_INT stride length for X.
• Y: [out] double* output array.
• strideY: [in] CBLAS_INT stride length for Y.

void stdlib_strided_dcusumkbn( const CBLAS_INT N, const double sum, const double *X, const CBLAS_INT strideX, double *Y, const CBLAS_INT strideY );

stdlib_strided_dcusumkbn_ndarray( N, sum, *X, strideX, offsetX, *Y, strideY, offsetY )

Computes the cumulative 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 y[] = { 0.0, 0.0, 0.0, 0.0 };

stdlib_strided_dcusumkbn_ndarray( 4, 0.0, x, 1, 0, y, 1, 0 );

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• sum: [in] double initial sum.
• X: [in] double* input array.
• strideX: [in] CBLAS_INT stride length for X.
• offsetX: [in] CBLAS_INT starting index for X.
• Y: [out] double* output array.
• strideY: [in] CBLAS_INT stride length for Y.
• offsetY: [in] CBLAS_INT starting index for Y.

void stdlib_strided_dcusumkbn_ndarray( const CBLAS_INT N, const double sum, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );

Examples

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

int main( void ) {
    // Create strided arrays:
    const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
    double y[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };

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

    // Specify stride lengths:
    const int strideX = 2;
    const int strideY = -2;

    // Compute the cumulative sum:
    stdlib_strided_dcusumkbn( N, 0.0, x, strideX, y, strideY );

    // Print the result:
    for ( int i = 0; i < 8; i++ ) {
        printf( "y[ %d ] = %lf\n", i, y[ i ] );
    }
}

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/dcusum: calculate the cumulative sum of double-precision floating-point strided array elements.
• @stdlib/blas-ext/base/gcusumkbn: calculate the cumulative sum of strided array elements using an improved Kahan–Babuška algorithm.
• @stdlib/blas-ext/base/scusumkbn: calculate the cumulative sum of single-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.

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

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.