gcusumkbn2

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

Installation

npm install @stdlib/blas-ext-base-gcusumkbn2

Usage

var gcusumkbn2 = require( '@stdlib/blas-ext-base-gcusumkbn2' );

gcusumkbn2( N, sum, x, strideX, y, strideY )

Computes the cumulative sum of strided array elements using a second-order iterative Kahan–Babuška algorithm.

var x = [ 1.0, -2.0, 2.0 ];
var y = [ 0.0, 0.0, 0.0 ];

gcusumkbn2( x.length, 0.0, x, 1, y, 1 );
// y => [ 1.0, -1.0, 1.0 ]

x = [ 1.0, -2.0, 2.0 ];
y = [ 0.0, 0.0, 0.0 ];

gcusumkbn2( x.length, 10.0, x, 1, y, 1 );
// y => [ 11.0, 9.0, 11.0 ]

The function has the following parameters:

• N: number of indexed elements.
• sum: initial sum.
• x: input Array or typed array.
• strideX: stride length for x.
• y: output Array or typed array.
• 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 x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ];
var y = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];

var v = gcusumkbn2( 4, 0.0, x, 2, y, 1 );
// y => [ 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

gcusumkbn2( 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 ]

gcusumkbn2.ndarray( N, sum, x, strideX, offsetX, y, strideY, offsetY )

Computes the cumulative sum of strided array elements using a second-order iterative Kahan–Babuška algorithm and alternative indexing semantics.

var x = [ 1.0, -2.0, 2.0 ];
var y = [ 0.0, 0.0, 0.0 ];

gcusumkbn2.ndarray( x.length, 0.0, x, 1, 0, y, 1, 0 );
// y => [ 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, offset parameters support indexing semantics based on starting indices. For example, to calculate the cumulative sum of every other element in the strided input array starting from the second element and to store in the last N elements of the strided output array starting from the last element:

var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ];
var y = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];

gcusumkbn2.ndarray( 4, 0.0, x, 2, 1, y, -1, y.length-1 );
// y => [ 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.
• Both functions support array-like objects having getter and setter accessors for array element access (e.g., @stdlib/array-base/accessor).
• Depending on the environment, the typed versions (dcusumkbn2, scusumkbn2, etc.) are likely to be significantly more performant.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var Float64Array = require( '@stdlib/array-float64' );
var gcusumkbn2 = require( '@stdlib/blas-ext-base-gcusumkbn2' );

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

gcusumkbn2( x.length, 0.0, x, 1, y, -1 );
console.log( y );

References

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

See Also

• @stdlib/blas-ext/base/dcusumkbn2: calculate the cumulative sum of double-precision floating-point strided array elements using a second-order iterative Kahan–Babuška algorithm.
• @stdlib/blas-ext/base/gcusum: calculate the cumulative sum of 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/scusumkbn2: calculate the cumulative sum of single-precision floating-point strided array elements using a second-order iterative 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.

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License

See LICENSE.

Copyright

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