time-to-botec

README.md (5572B)

---

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 # gasum
 
 > Compute the sum of [absolute values][@stdlib/math/base/special/abs] ([_L1_ norm][l1norm]).
 
 <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@30de397fadee10fa175a8332ae1447737f201818/lib/node_modules/@stdlib/blas/base/gasum/docs/img/equation_l1norm.svg" alt="L1 norm definition.">
     <br>
 </div>
 
 <!-- </equation> -->
 
 </section>
 
 <!-- /.intro -->
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var gasum = require( '@stdlib/blas/base/gasum' );
 ```
 
 #### gasum( N, x, stride )
 
 Computes the sum of [absolute values][@stdlib/math/base/special/abs].
 
 ```javascript
 var x = [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ];
 
 var sum = gasum( x.length, x, 1 );
 // returns 19.0
 ```
 
 The function has the following parameters:
 
 -   **N**: number of elements to sum.
 -   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
 -   **stride**: index increment.
 
 The `N` and `stride` parameters determine which elements in `x` are used to compute the sum. For example, to sum every other value,
 
 ```javascript
 var floor = require( '@stdlib/math/base/special/floor' );
 
 var x = [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ];
 
 var N = floor( x.length / 2 );
 var stride = 2;
 
 var sum = gasum( N, x, stride );
 // returns 10.0
 ```
 
 Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
 
 var floor = require( '@stdlib/math/base/special/floor' );
 
 // Initial array...
 var x0 = new Float64Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );
 
 // Create an offset view...
 var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
 
 var N = floor( x0.length / 2 );
 
 // Sum every other value...
 var sum = gasum( N, x1, 2 );
 // returns 12.0
 ```
 
 If either `N` or `stride` is less than or equal to `0`, the function returns `0`.
 
 #### gasum.ndarray( N, x, stride, offset )
 
 Computes the sum of [absolute values][@stdlib/math/base/special/abs] using alternative indexing semantics.
 
 ```javascript
 var x = [ -2.0, 1.0, 3.0, -5.0, 4.0, 0.0, -1.0, -3.0 ];
 
 var sum = gasum.ndarray( x.length, x, 1, 0 );
 // returns 19.0
 ```
 
 The function has the following additional parameters:
 
 -   **offset**: starting index.
 
 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 sum the last three elements,
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
 
 var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );
 
 var sum = gasum.ndarray( 3, x, 1, x.length-3 );
 // returns 15.0
 
 // Using a negative stride to sum from the last element:
 sum = gasum.ndarray( 3, x, -1, x.length-1 );
 // returns 15.0
 ```
 
 </section>
 
 <!-- /.usage -->
 
 <section class="notes">
 
 ## Notes
 
 -   If `N <= 0`, both functions return `0`.
 -   `gasum()` corresponds to the [BLAS][blas] level 1 function [`dasum`][dasum] with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions ([`dasum`][@stdlib/blas/base/dasum], [`sasum`][@stdlib/blas/base/sasum], etc.) are likely to be significantly more performant.
 
 </section>
 
 <!-- /.notes -->
 
 <section class="examples">
 
 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 var round = require( '@stdlib/math/base/special/round' );
 var randu = require( '@stdlib/random/base/randu' );
 var gasum = require( '@stdlib/blas/base/gasum' );
 
 var rand;
 var sign;
 var x;
 var i;
 
 x = [];
 for ( i = 0; i < 100; i++ ) {
     rand = round( randu()*100.0 );
     sign = randu();
     if ( sign < 0.5 ) {
         sign = -1.0;
     } else {
         sign = 1.0;
     }
     x.push( sign*rand );
 }
 console.log( gasum( x.length, x, 1 ) );
 ```
 
 </section>
 
 <!-- /.examples -->
 
 <section class="links">
 
 [blas]: http://www.netlib.org/blas
 
 [dasum]: http://www.netlib.org/lapack/explore-html/de/da4/group__double__blas__level1.html
 
 [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
 
 [l1norm]: http://en.wikipedia.org/wiki/Norm_%28mathematics%29
 
 [@stdlib/math/base/special/abs]: https://www.npmjs.com/package/@stdlib/math-base-special-abs
 
 [@stdlib/blas/base/dasum]: https://www.npmjs.com/package/@stdlib/blas/tree/main/base/dasum
 
 [@stdlib/blas/base/sasum]: https://www.npmjs.com/package/@stdlib/blas/tree/main/base/sasum
 
 </section>
 
 <!-- /.links -->