@stdlib/blas-ext-base-gsort2hp
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Simultaneously sort two strided arrays based on the sort order of the first array using heapsort.
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# gsort2hp
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->
> Simultaneously sort two strided arrays based on the sort order of the first array using heapsort.
<section class="installation">
## Installation
```bash
npm install @stdlib/blas-ext-base-gsort2hp
```
</section>
<section class="usage">
## Usage
```javascript
var gsort2hp = require( '@stdlib/blas-ext-base-gsort2hp' );
```
#### gsort2hp( N, order, x, strideX, y, strideY )
Simultaneously sorts two strided arrays based on the sort order of the first array `x` using heapsort.
```javascript
var x = [ 1.0, -2.0, 3.0, -4.0 ];
var y = [ 0.0, 1.0, 2.0, 3.0 ];
gsort2hp( x.length, 1.0, x, 1, y, 1 );
console.log( x );
// => [ -4.0, -2.0, 1.0, 3.0 ]
console.log( y );
// => [ 3.0, 1.0, 0.0, 2.0 ]
```
The function has the following parameters:
- **N**: number of indexed elements.
- **order**: sort order. If `order < 0.0`, the input strided array `x` is sorted in **decreasing** order. If `order > 0.0`, the input strided array `x` is sorted in **increasing** order. If `order == 0.0`, the input strided arrays are left unchanged.
- **x**: first input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
- **strideX**: `x` index increment.
- **y**: second input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
- **strideY**: `y` index increment.
The `N` and `stride` parameters determine which elements in `x` and `y` 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 y = [ 0.0, 1.0, 2.0, 3.0 ];
var N = floor( x.length / 2 );
gsort2hp( N, -1.0, x, 2, y, 2 );
console.log( x );
// => [ 3.0, -2.0, 1.0, -4.0 ]
console.log( y );
// => [ 2.0, 1.0, 0.0, 3.0 ]
```
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 arrays...
var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
var y0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] );
// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var N = floor( x0.length/2 );
// Sort every other element...
gsort2hp( N, -1.0, x1, 2, y1, 2 );
console.log( x0 );
// => <Float64Array>[ 1.0, 4.0, 3.0, 2.0 ]
console.log( y0 );
// => <Float64Array>[ 0.0, 3.0, 2.0, 1.0 ]
```
#### gsort2hp.ndarray( N, order, x, strideX, offsetX, y, strideY, offsetY )
Simultaneously sorts two strided arrays based on the sort order of the first array `x` using heapsort and alternative indexing semantics.
```javascript
var x = [ 1.0, -2.0, 3.0, -4.0 ];
var y = [ 0.0, 1.0, 2.0, 3.0 ];
gsort2hp.ndarray( x.length, 1.0, x, 1, 0, y, 1, 0 );
console.log( x );
// => [ -4.0, -2.0, 1.0, 3.0 ]
console.log( y );
// => [ 3.0, 1.0, 0.0, 2.0 ]
```
The function has the following additional parameters:
- **offsetX**: `x` starting index.
- **offsetY**: `y` 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 ];
var y = [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ];
gsort2hp.ndarray( 3, 1.0, x, 1, x.length-3, y, 1, y.length-3 );
console.log( x );
// => [ 1.0, -2.0, 3.0, -6.0, -4.0, 5.0 ]
console.log( y );
// => [ 0.0, 1.0, 2.0, 5.0, 3.0, 4.0 ]
```
</section>
<!-- /.usage -->
<section class="notes">
## Notes
- If `N <= 0` or `order == 0.0`, both functions leave `x` and `y` 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^2)`.
- The algorithm is efficient for **small** strided arrays (typically `N <= 20`) and is particularly efficient for sorting strided arrays which are already substantially sorted.
- The algorithm has space complexity `O(1)` and time complexity `O(N log2 N)`.
- 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).
- Depending on the environment, the typed versions ([`dsort2hp`][@stdlib/blas/ext/base/dsort2hp], [`ssort2hp`][@stdlib/blas/ext/base/ssort2hp], 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 gsort2hp = require( '@stdlib/blas-ext-base-gsort2hp' );
var rand;
var sign;
var x;
var y;
var i;
x = new Float64Array( 10 );
y = new Float64Array( 10 ); // index array
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;
y[ i ] = i;
}
console.log( x );
console.log( y );
gsort2hp( x.length, -1.0, x, -1, y, -1 );
console.log( x );
console.log( y );
```
</section>
<!-- /.examples -->
* * *
<section class="references">
## References
- Williams, John William Joseph. 1964. "Algorithm 232: Heapsort." _Communications of the ACM_ 7 (6). New York, NY, USA: Association for Computing Machinery: 347–49. doi:[10.1145/512274.512284][@williams:1964a].
- Floyd, Robert W. 1964. "Algorithm 245: Treesort." _Communications of the ACM_ 7 (12). New York, NY, USA: Association for Computing Machinery: 701. doi:[10.1145/355588.365103][@floyd:1964a].
</section>
<section class="main-repo" >
* * *
## 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].
</section>
<!-- /.stdlib -->
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[deno-url]: https://github.com/stdlib-js/blas-ext-base-gsort2hp/tree/deno
[deno-readme]: https://github.com/stdlib-js/blas-ext-base-gsort2hp/blob/deno/README.md
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[esm-url]: https://github.com/stdlib-js/blas-ext-base-gsort2hp/tree/esm
[esm-readme]: https://github.com/stdlib-js/blas-ext-base-gsort2hp/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/blas-ext-base-gsort2hp/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/blas-ext-base-gsort2hp/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
[@stdlib/blas/ext/base/dsort2hp]: https://www.npmjs.com/package/@stdlib/blas-ext-base-dsort2hp
[@stdlib/blas/ext/base/ssort2hp]: https://www.npmjs.com/package/@stdlib/blas-ext-base-ssort2hp
[@williams:1964a]: https://doi.org/10.1145/512274.512284
[@floyd:1964a]: https://doi.org/10.1145/355588.365103
</section>
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