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Add strided interface to compute a cumulative using an improved Kahan-Babuska algorithm
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‎lib/node_modules/@stdlib/blas/ext/base/dcusumkbn/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2020 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# dcusumkbn
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> Calculate the cumulative sum of double-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.
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<section class="intro">
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var dcusumkbn = require( '@stdlib/blas/ext/base/dcusumkbn' );
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```
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#### dcusumkbn( N, sum, x, strideX, y, strideY )
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Computes the cumulative sum of double-precision floating-point strided array elements using an improved Kahan–Babuška algorithm.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
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var y = new Float64Array( x.length );
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dcusumkbn( x.length, 0.0, x, 1, y, 1 );
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// y => <Float64Array>[ 1.0, -1.0, 1.0 ]
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x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
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y = new Float64Array( x.length );
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dcusumkbn( x.length, 10.0, x, 1, y, 1 );
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// y => <Float64Array>[ 11.0, 9.0, 11.0 ]
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```
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The function has the following parameters:
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- **N**: number of indexed elements.
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- **sum**: initial sum.
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- **x**: input [`Float64Array`][@stdlib/array/float64].
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- **strideX**: index increment for `x`.
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- **y**: output [`Float64Array`][@stdlib/array/float64].
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- **strideY**: index increment for `y`.
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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`,
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var floor = require( '@stdlib/math/base/special/floor' );
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var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
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var y = new Float64Array( x.length );
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var N = floor( x.length / 2 );
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var v = dcusumkbn( N, 0.0, x, 2, y, 1 );
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// y => <Float64Array>[ 1.0, 3.0, 1.0, 5.0, 0.0, 0.0, 0.0, 0.0 ]
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```
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var floor = require( '@stdlib/math/base/special/floor' );
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// Initial arrays...
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var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
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var y0 = new Float64Array( x0.length );
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// Create offset views...
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var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element
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var N = floor( x0.length / 2 );
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dcusumkbn( N, 0.0, x1, -2, y1, 1 );
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// y0 => <Float64Array>[ 0.0, 0.0, 0.0, 0.0, 4.0, 6.0, 4.0, 5.0 ]
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```
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#### dcusumkbn.ndarray( N, sum, x, strideX, offsetX, y, strideY, offsetY )
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Computes the cumulative sum of double-precision floating-point strided array elements using an improved Kahan–Babuška algorithm and alternative indexing semantics.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
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var y = new Float64Array( x.length );
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dcusumkbn.ndarray( x.length, 0.0, x, 1, 0, y, 1, 0 );
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// y => <Float64Array>[ 1.0, -1.0, 1.0 ]
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```
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The function has the following additional parameters:
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- **offsetX**: starting index for `x`.
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- **offsetY**: starting index for `y`.
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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
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var floor = require( '@stdlib/math/base/special/floor' );
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var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
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var y = new Float64Array( x.length );
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var N = floor( x.length / 2 );
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dcusumkbn.ndarray( N, 0.0, x, 2, 1, y, -1, y.length-1 );
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// y => <Float64Array>[ 0.0, 0.0, 0.0, 0.0, 5.0, 1.0, -1.0, 1.0 ]
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- If `N <= 0`, both functions return `y` unchanged.
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var randu = require( '@stdlib/random/base/randu' );
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var round = require( '@stdlib/math/base/special/round' );
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var Float64Array = require( '@stdlib/array/float64' );
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var dcusumkbn = require( '@stdlib/blas/ext/base/dcusumkbn' );
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var y;
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var x;
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var i;
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x = new Float64Array( 10 );
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y = new Float64Array( x.length );
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for ( i = 0; i < x.length; i++ ) {
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x[ i ] = round( randu()*100.0 );
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}
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console.log( x );
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console.log( y );
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dcusumkbn( x.length, 0.0, x, 1, y, -1 );
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console.log( y );
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```
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</section>
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<!-- /.examples -->
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* * *
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<section class="references">
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## References
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- 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][@neumaier:1974a].
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</section>
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<!-- /.references -->
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<section class="links">
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[@stdlib/array/float64]: https://github.com/stdlib-js/stdlib
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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[@neumaier:1974a]: https://doi.org/10.1002/zamm.19740540106
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/blas/ext/base/dcusumkbn/benchmark/benchmark.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2020 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var randu = require( '@stdlib/random/base/randu' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var Float64Array = require( '@stdlib/array/float64' );
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var pkg = require( './../package.json' ).name;
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var dcusumkbn = require( './../lib/dcusumkbn.js' );
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var y;
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var x;
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var i;
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x = new Float64Array( len );
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y = new Float64Array( len );
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for ( i = 0; i < x.length; i++ ) {
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x[ i ] = ( randu()*20.0 ) - 10.0;
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}
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return benchmark;
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function benchmark( b ) {
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var v;
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var i;
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for ( i = 0; i < len; i++ ) {
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y[ i ] = 0.0;
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}
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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x[ 0 ] += 1.0;
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v = dcusumkbn( x.length, 0.0, x, 1, y, 1 );
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if ( isnan( v[ i%len ] ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( v[ i%len ] ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( pkg+':len='+len, f );
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}
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}
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main();

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