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Calculate the cumulative sum of double-precision floating-point strided array elements using pairwise summation.
npm install @stdlib/blas-ext-base-dcusumpwvar dcusumpw = require( '@stdlib/blas-ext-base-dcusumpw' );Computes the cumulative sum of double-precision floating-point strided array elements using pairwise summation.
var Float64Array = require( '@stdlib/array-float64' );
var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var y = new Float64Array( x.length );
dcusumpw( 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 );
dcusumpw( 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 the strided arrays are accessed at runtime. For example, to compute the cumulative sum of every other element in the strided input array,
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 = dcusumpw( 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
dcusumpw( 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 ]Computes the cumulative sum of double-precision floating-point strided array elements using pairwise summation 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 );
dcusumpw.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 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 );
dcusumpw.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 ]- If
N <= 0, both functions returnyunchanged. - In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., "simple" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques.
var discreteUniform = require( '@stdlib/random-base-discrete-uniform' ).factory;
var filledarrayBy = require( '@stdlib/array-filled-by' );
var Float64Array = require( '@stdlib/array-float64' );
var dcusumpw = require( '@stdlib/blas-ext-base-dcusumpw' );
var x = filledarrayBy( 10, 'float64', discreteUniform( 0, 100 ) );
var y = new Float64Array( x.length );
console.log( x );
console.log( y );
dcusumpw( x.length, 0.0, x, 1, y, -1 );
console.log( y );- Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." SIAM Journal on Scientific Computing 14 (4): 783–99. doi:10.1137/0914050.
-
@stdlib/blas-ext/base/dcusum: calculate the cumulative sum of double-precision floating-point strided array elements. -
@stdlib/blas-ext/base/gcusumpw: calculate the cumulative sum of strided array elements using pairwise summation. -
@stdlib/blas-ext/base/scusumpw: calculate the cumulative sum of single-precision floating-point strided array elements using pairwise summation.
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.
See LICENSE.
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