time-to-botec

README.md (5990B)

---

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 # dasumpw
 
 > Calculate the sum of absolute values ([_L1_ norm][l1norm]) of double-precision floating-point strided array elements using pairwise summation.
 
 <section class="intro">
 
 The [_L1_ norm][l1norm] is defined as
 
 <!-- <equation class="equation" label="eq:l1norm" align="center" raw="\|\mathbf{x}\|_1 = \sum_{i=0}^{n-1} \vert x_i \vert" alt="L1 norm definition."> -->
 
 <div class="equation" align="center" data-raw-text="\|\mathbf{x}\|_1 = \sum_{i=0}^{n-1} \vert x_i \vert" data-equation="eq:l1norm">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@4fc193be4e7ddee6645fe1071f68a85d9a4c54f0/lib/node_modules/@stdlib/blas/ext/base/dasumpw/docs/img/equation_l1norm.svg" alt="L1 norm definition.">
     <br>
 </div>
 
 <!-- </equation> -->
 
 </section>
 
 <!-- /.intro -->
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var dasumpw = require( '@stdlib/blas/ext/base/dasumpw' );
 ```
 
 #### dasumpw( N, x, stride )
 
 Computes the sum of absolute values ([_L1_ norm][l1norm]) of double-precision floating-point strided array elements using pairwise summation.
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
 
 var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
 var N = x.length;
 
 var v = dasumpw( N, x, 1 );
 // returns 5.0
 ```
 
 The function has the following parameters:
 
 -   **N**: number of indexed elements.
 -   **x**: input [`Float64Array`][@stdlib/array/float64].
 -   **stride**: index increment for `x`.
 
 The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to compute the sum of absolute values of every other element in `x`,
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
 var floor = require( '@stdlib/math/base/special/floor' );
 
 var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
 var N = floor( x.length / 2 );
 
 var v = dasumpw( N, x, 2 );
 // returns 9.0
 ```
 
 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' );
 
 var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
 var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
 
 var N = floor( x0.length / 2 );
 
 var v = dasumpw( N, x1, 2 );
 // returns 9.0
 ```
 
 #### dasumpw.ndarray( N, x, stride, offset )
 
 Computes the sum of absolute values ([_L1_ norm][l1norm]) of double-precision floating-point strided array elements using pairwise summation and alternative indexing semantics.
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
 
 var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
 var N = x.length;
 
 var v = dasumpw.ndarray( N, x, 1, 0 );
 // returns 5.0
 ```
 
 The function has the following additional parameters:
 
 -   **offset**: starting index for `x`.
 
 While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying `buffer`, the `offset` parameter supports indexing semantics based on a starting index. For example, to calculate the sum of absolute values of every other value in `x` starting from the second value
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
 var floor = require( '@stdlib/math/base/special/floor' );
 
 var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
 var N = floor( x.length / 2 );
 
 var v = dasumpw.ndarray( N, x, 2, 1 );
 // returns 9.0
 ```
 
 </section>
 
 <!-- /.usage -->
 
 <section class="notes">
 
 ## Notes
 
 -   If `N <= 0`, both functions return `0.0`.
 -   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.
 
 </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 dasumpw = require( '@stdlib/blas/ext/base/dasumpw' );
 
 var x;
 var i;
 
 x = new Float64Array( 10 );
 for ( i = 0; i < x.length; i++ ) {
     x[ i ] = round( randu()*100.0 );
 }
 console.log( x );
 
 var v = dasumpw( x.length, x, 1 );
 console.log( v );
 ```
 
 </section>
 
 <!-- /.examples -->
 
 * * *
 
 <section class="references">
 
 ## References
 
 -   Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050][@higham:1993a].
 
 </section>
 
 <!-- /.references -->
 
 <section class="links">
 
 [@stdlib/array/float64]: https://www.npmjs.com/package/@stdlib/array-float64
 
 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
 
 [l1norm]: http://en.wikipedia.org/wiki/Norm_%28mathematics%29
 
 [@higham:1993a]: https://doi.org/10.1137/0914050
 
 </section>
 
 <!-- /.links -->