time-to-botec

README.md (6179B)

---

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 # gsortsh
 
 > Sort a strided array using Shellsort.
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var gsortsh = require( '@stdlib/blas/ext/base/gsortsh' );
 ```
 
 #### gsortsh( N, order, x, stride )
 
 Sorts a strided array `x` using Shellsort.
 
 ```javascript
 var x = [ 1.0, -2.0, 3.0, -4.0 ];
 
 gsortsh( x.length, 1.0, x, 1 );
 // x => [ -4.0, -2.0, 1.0, 3.0 ]
 ```
 
 The function has the following parameters:
 
 -   **N**: number of indexed elements.
 -   **order**: sort order. If `order < 0.0`, the input strided array is sorted in **decreasing** order. If `order > 0.0`, the input strided array is sorted in **increasing** order. If `order == 0.0`, the input strided array is left unchanged.
 -   **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 accessed at runtime. For example, to sort every other element
 
 ```javascript
 var floor = require( '@stdlib/math/base/special/floor' );
 
 var x = [ 1.0, -2.0, 3.0, -4.0 ];
 var N = floor( x.length / 2 );
 
 gsortsh( N, -1.0, x, 2 );
 // x => [ 3.0, -2.0, 1.0, -4.0 ]
 ```
 
 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 ] );
 
 // 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 );
 
 // Sort every other element...
 gsortsh( N, -1.0, x1, 2 );
 // x0 => <Float64Array>[ 1.0, 4.0, 3.0, 2.0 ]
 ```
 
 #### gsortsh.ndarray( N, order, x, stride, offset )
 
 Sorts a strided array `x` using Shellsort and alternative indexing semantics.
 
 ```javascript
 var x = [ 1.0, -2.0, 3.0, -4.0 ];
 
 gsortsh.ndarray( x.length, 1.0, x, 1, 0 );
 // x => [ -4.0, -2.0, 1.0, 3.0 ]
 ```
 
 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 access only the last three elements of `x`
 
 ```javascript
 var x = [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ];
 
 gsortsh.ndarray( 3, 1.0, x, 1, x.length-3 );
 // x => [ 1.0, -2.0, 3.0, -6.0, -4.0, 5.0 ]
 ```
 
 </section>
 
 <!-- /.usage -->
 
 <section class="notes">
 
 ## Notes
 
 -   If `N <= 0` or `order == 0.0`, both functions return `x` unchanged.
 -   The algorithm distinguishes between `-0` and `+0`. When sorted in increasing order, `-0` is sorted before `+0`. When sorted in decreasing order, `-0` is sorted after `+0`.
 -   The algorithm sorts `NaN` values to the end. When sorted in increasing order, `NaN` values are sorted last. When sorted in decreasing order, `NaN` values are sorted first.
 -   The algorithm has space complexity `O(1)` and worst case time complexity `O(N^(4/3))`.
 -   The algorithm is efficient for **shorter** strided arrays (typically `N <= 50`).
 -   The algorithm is **unstable**, meaning that the algorithm may change the order of strided array elements which are equal or equivalent (e.g., `NaN` values).
 -   The input strided array is sorted **in-place** (i.e., the input strided array is **mutated**).
 -   Depending on the environment, the typed versions ([`dsortsh`][@stdlib/blas/ext/base/dsortsh], [`ssortsh`][@stdlib/blas/ext/base/ssortsh], 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 Float64Array = require( '@stdlib/array/float64' );
 var gsortsh = require( '@stdlib/blas/ext/base/gsortsh' );
 
 var rand;
 var sign;
 var x;
 var i;
 
 x = new Float64Array( 10 );
 for ( i = 0; i < x.length; i++ ) {
     rand = round( randu()*100.0 );
     sign = randu();
     if ( sign < 0.5 ) {
         sign = -1.0;
     } else {
         sign = 1.0;
     }
     x[ i ] = sign * rand;
 }
 console.log( x );
 
 gsortsh( x.length, -1.0, x, -1 );
 console.log( x );
 ```
 
 </section>
 
 <!-- /.examples -->
 
 * * *
 
 <section class="references">
 
 ## References
 
 -   Shell, Donald L. 1959. "A High-Speed Sorting Procedure." _Communications of the ACM_ 2 (7). Association for Computing Machinery: 30–32. doi:[10.1145/368370.368387][@shell:1959a].
 -   Sedgewick, Robert. 1986. "A new upper bound for Shellsort." _Journal of Algorithms_ 7 (2): 159–73. doi:[10.1016/0196-6774(86)90001-5][@sedgewick:1986a].
 -   Ciura, Marcin. 2001. "Best Increments for the Average Case of Shellsort." In _Fundamentals of Computation Theory_, 106–17. Springer Berlin Heidelberg. doi:[10.1007/3-540-44669-9_12][@ciura:2001a].
 
 </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/dsortsh]: https://www.npmjs.com/package/@stdlib/blas/tree/main/ext/base/dsortsh
 
 [@stdlib/blas/ext/base/ssortsh]: https://www.npmjs.com/package/@stdlib/blas/tree/main/ext/base/ssortsh
 
 [@shell:1959a]: https://doi.org/10.1145/368370.368387
 
 [@sedgewick:1986a]: https://doi.org/10.1016/0196-6774(86)90001-5
 
 [@ciura:2001a]: https://doi.org/10.1007/3-540-44669-9_12
 
 </section>
 
 <!-- /.links -->