gcusumkbn

Calculate the cumulative sum of strided array elements using an improved Kahan–Babuška algorithm.

Usage

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

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

Computes the cumulative sum of strided array elements using an improved Kahan–Babuška algorithm.

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

gcusumkbn( 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 ];

gcusumkbn( 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 = gcusumkbn( 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

gcusumkbn( 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 ]

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

Computes the cumulative sum of strided array elements using an improved Kahan–Babuška algorithm and alternative indexing semantics.

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

gcusumkbn.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 ];

gcusumkbn.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.
Depending on the environment, the typed versions (dcusum, scusum, etc.) are likely to be significantly more performant.

Examples

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

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

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

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

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.