time-to-botec

README.md (5917B)

---

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 # 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 -->