<!-- @license Apache-2.0 Copyright (c) 2020 The Stdlib Authors. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. --> # gcusumkbn2 > Calculate the cumulative sum of strided array elements using a second-order iterative Kahan–Babuška algorithm. <section class="intro"> </section> <!-- /.intro --> <section class="usage"> ## Usage ```javascript 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. ```javascript 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`][mdn-array] or [`typed array`][mdn-typed-array]. - **strideX**: index increment for `x`. - **y**: output [`Array`][mdn-array] or [`typed array`][mdn-typed-array]. - **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`, ```javascript var floor = require( '@stdlib/math/base/special/floor' ); 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 N = floor( x.length / 2 ); var v = gcusumkbn2( N, 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`][mdn-typed-array] views. <!-- eslint-disable stdlib/capitalized-comments --> ```javascript var Float64Array = require( '@stdlib/array/float64' ); var floor = require( '@stdlib/math/base/special/floor' ); // 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 = floor( x0.length / 2 ); gcusumkbn2( 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 ] ``` #### 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. ```javascript 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`][mdn-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 ```javascript var floor = require( '@stdlib/math/base/special/floor' ); 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 ]; var N = floor( x.length / 2 ); gcusumkbn2.ndarray( N, 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 ] ``` </section> <!-- /.usage --> <section class="notes"> ## Notes - If `N <= 0`, both functions return `y` unchanged. - Depending on the environment, the typed versions ([`dcusumkbn2`][@stdlib/blas/ext/base/dcusumkbn2], [`scusumkbn2`][@stdlib/blas/ext/base/scusumkbn2], etc.) are likely to be significantly more performant. </section> <!-- /.notes --> <section class="examples"> ## Examples <!-- eslint no-undef: "error" --> ```javascript var randu = require( '@stdlib/random/base/randu' ); var round = require( '@stdlib/math/base/special/round' ); var Float64Array = require( '@stdlib/array/float64' ); var gcusumkbn2 = require( '@stdlib/blas/ext/base/gcusumkbn2' ); var y; var x; var i; x = new Float64Array( 10 ); y = new Float64Array( x.length ); for ( i = 0; i < x.length; i++ ) { x[ i ] = round( randu()*100.0 ); } console.log( x ); console.log( y ); gcusumkbn2( x.length, 0.0, x, 1, y, -1 ); console.log( y ); ``` </section> <!-- /.examples --> * * * <section class="references"> ## References - Klein, Andreas. 2005. "A Generalized Kahan-Babuška-Summation-Algorithm." _Computing_ 76 (3): 279–93. doi:[10.1007/s00607-005-0139-x][@klein:2005a]. </section> <!-- /.references --> <section class="links"> [mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray [@stdlib/blas/ext/base/dcusumkbn2]: https://www.npmjs.com/package/@stdlib/blas/tree/main/ext/base/dcusumkbn2 [@stdlib/blas/ext/base/scusumkbn2]: https://www.npmjs.com/package/@stdlib/blas/tree/main/ext/base/scusumkbn2 [@klein:2005a]: https://doi.org/10.1007/s00607-005-0139-x </section> <!-- /.links -->