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https://github.com/stdlib-js/blas-ext-base-gsortsh

Sort a strided array using Shellsort.
https://github.com/stdlib-js/blas-ext-base-gsortsh

arrange array blas extended insertion javascript math mathematics ndarray node node-js nodejs order permute shell shellsort sort stdlib strided

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Sort a strided array using Shellsort.

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README 

        



  

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# gsortsh



[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] 



> Sort a strided array using Shellsort.



## Installation



```bash

npm install @stdlib/blas-ext-base-gsortsh

```



Alternatively,



-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).

-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).

-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).



The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.



To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.



## 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 => [ 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 ]

```



## 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.



## Examples



```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 );

```



* * *



## 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].



* * *



## See Also



-   [`@stdlib/blas-ext/base/dsortsh`][@stdlib/blas/ext/base/dsortsh]: sort a double-precision floating-point strided array using Shellsort.

-   [`@stdlib/blas-ext/base/gsort2sh`][@stdlib/blas/ext/base/gsort2sh]: simultaneously sort two strided arrays based on the sort order of the first array using Shellsort.

-   [`@stdlib/blas-ext/base/ssortsh`][@stdlib/blas/ext/base/ssortsh]: sort a single-precision floating-point strided array using Shellsort.



* * *



## Notice



This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.



For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].



#### Community



[![Chat][chat-image]][chat-url]



---



## License



See [LICENSE][stdlib-license].



## Copyright



Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/blas-ext-base-gsortsh.svg

[npm-url]: https://npmjs.org/package/@stdlib/blas-ext-base-gsortsh



[test-image]: https://github.com/stdlib-js/blas-ext-base-gsortsh/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/blas-ext-base-gsortsh/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/blas-ext-base-gsortsh/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/blas-ext-base-gsortsh?branch=main



[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im



[stdlib]: https://github.com/stdlib-js/stdlib



[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors



[umd]: https://github.com/umdjs/umd

[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules



[deno-url]: https://github.com/stdlib-js/blas-ext-base-gsortsh/tree/deno

[deno-readme]: https://github.com/stdlib-js/blas-ext-base-gsortsh/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/blas-ext-base-gsortsh/tree/umd

[umd-readme]: https://github.com/stdlib-js/blas-ext-base-gsortsh/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/blas-ext-base-gsortsh/tree/esm

[esm-readme]: https://github.com/stdlib-js/blas-ext-base-gsortsh/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/blas-ext-base-gsortsh/blob/main/branches.md



[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/blas-ext-base-gsortsh/main/LICENSE



[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



[@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



[@stdlib/blas/ext/base/dsortsh]: https://github.com/stdlib-js/blas-ext-base-dsortsh



[@stdlib/blas/ext/base/gsort2sh]: https://github.com/stdlib-js/blas-ext-base-gsort2sh



[@stdlib/blas/ext/base/ssortsh]: https://github.com/stdlib-js/blas-ext-base-ssortsh