stdlib-js / blas-ext-base-dcusumkbn2

Calculate the cumulative sum of double-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.

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dcusumkbn2

Calculate the cumulative sum of double-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.

Installation

npm install @stdlib/blas-ext-base-dcusumkbn2

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 dcusumkbn2 = require( '@stdlib/blas-ext-base-dcusumkbn2' );

dcusumkbn2( N, sum, x, strideX, y, strideY )

Computes the cumulative sum of double-precision floating-point strided array elements using a second-order iterative 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 );

dcusumkbn2( 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 );

dcusumkbn2( 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: index increment for x.
• y: output Float64Array.
• strideY: index increment for y.

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

var N = 4;

var v = dcusumkbn2( N, 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

var N = 4;

dcusumkbn2( N, 0.0, x1, -2, y1, 1 );
// y0 => <Float64Array>[ 0.0, 0.0, 0.0, 4.0, 6.0, 4.0, 5.0, 0.0 ]

dcusumkbn2.ndarray( N, sum, x, strideX, offsetX, y, strideY, offsetY )

Computes the cumulative sum of double-precision floating-point strided array elements using a second-order iterative 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 );

dcusumkbn2.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, offsetX and offsetY parameters support indexing semantics based on a starting indices. For example, to calculate the cumulative sum of every other value in x starting from the second value and to store in the last N elements of y 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 );

var N = 4;

dcusumkbn2.ndarray( N, 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 dcusumkbn2 = require( '@stdlib/blas-ext-base-dcusumkbn2' );

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

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

dcusumkbn2( x.length, 0.0, x, 1, y, -1 );
console.log( y );

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C APIs

Usage

#include "stdlib/blas/ext/base/dcusumkbn2.h"

stdlib_strided_dcusumkbn2( N, sum, *X, strideX, *Y, strideY )

Computes the cumulative sum of double-precision floating-point strided array elements using a second-order iterative 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_dcusumkbn2( 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 index increment for X.
• Y: [out] double* output array.
• strideY: [in] CBLAS_INT index increment for Y.

void stdlib_strided_dcusumkbn2( const CBLAS_INT N, const double sum, const double *X, const CBLAS_INT strideX, double *Y, const CBLAS_INT strideY );

stdlib_strided_dcusumkbn2_ndarray( N, sum, *X, strideX, offsetX, *Y, strideY, offsetY )

Computes the cumulative sum of double-precision floating-point strided array elements using a second-order iterative 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_dcusumkbn2_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 index increment for X.
• offsetX: [in] CBLAS_INT starting index for X.
• Y: [out] double* output array.
• strideY: [in] CBLAS_INT index increment for Y.
• offsetY: [in] CBLAS_INT starting index for Y.

void stdlib_strided_dcusumkbn2_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/dcusumkbn2.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_dcusumkbn2( 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

• Klein, Andreas. 2005. "A Generalized Kahan-Babuška-Summation-Algorithm." Computing 76 (3): 279–93. doi:10.1007/s00607-005-0139-x.

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See Also

• @stdlib/blas-ext/base/dcusum: calculate the cumulative sum of double-precision floating-point strided array elements.
• @stdlib/blas-ext/base/gcusumkbn2: calculate the cumulative sum of strided array elements using a second-order iterative Kahan–Babuška algorithm.
• @stdlib/blas-ext/base/scusumkbn2: calculate the cumulative sum of single-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.

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Notice

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

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License

See LICENSE.

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