@stdlib/blas-ext-base-dsort2sh
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Simultaneously sort two double-precision floating-point strided arrays based on the sort order of the first array using Shellsort.
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# dsort2sh
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> Simultaneously sort two double-precision floating-point strided arrays based on the sort order of the first array using Shellsort.
<section class="installation">
## Installation
```bash
npm install @stdlib/blas-ext-base-dsort2sh
```
</section>
<section class="usage">
## Usage
```javascript
var dsort2sh = require( '@stdlib/blas-ext-base-dsort2sh' );
```
#### dsort2sh( N, order, x, strideX, y, strideY )
Simultaneously sorts two double-precision floating-point strided arrays based on the sort order of the first array `x` using Shellsort.
```javascript
var Float64Array = require( '@stdlib/array-float64' );
var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0 ] );
var y = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] );
dsort2sh( x.length, 1.0, x, 1, y, 1 );
console.log( x );
// => <Float64Array>[ -4.0, -2.0, 1.0, 3.0 ]
console.log( y );
// => <Float64Array>[ 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 [`Float64Array`][@stdlib/array/float64].
- **strideX**: `x` index increment.
- **y**: second input [`Float64Array`][@stdlib/array/float64].
- **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 Float64Array = require( '@stdlib/array-float64' );
var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0 ] );
var y = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] );
dsort2sh( 2, -1.0, x, 2, y, 2 );
console.log( x );
// => <Float64Array>[ 3.0, -2.0, 1.0, -4.0 ]
console.log( y );
// => <Float64Array>[ 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' );
// 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
// Sort every other element...
dsort2sh( 2, -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 ]
```
#### dsort2sh.ndarray( N, order, x, strideX, offsetX, y, strideY, offsetY )
Simultaneously sorts two double-precision floating-point strided arrays based on the sort order of the first array `x` using Shellsort and alternative indexing semantics.
```javascript
var Float64Array = require( '@stdlib/array-float64' );
var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0 ] );
var y = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] );
dsort2sh.ndarray( x.length, 1.0, x, 1, 0, y, 1, 0 );
console.log( x );
// => <Float64Array>[ -4.0, -2.0, 1.0, 3.0 ]
console.log( y );
// => <Float64Array>[ 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 Float64Array = require( '@stdlib/array-float64' );
var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );
var y = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );
dsort2sh.ndarray( 3, 1.0, x, 1, x.length-3, y, 1, y.length-3 );
console.log( x );
// => <Float64Array>[ 1.0, -2.0, 3.0, -6.0, -4.0, 5.0 ]
console.log( y );
// => <Float64Array>[ 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^(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 arrays are sorted **in-place** (i.e., the input strided arrays are **mutated**).
</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 dsort2sh = require( '@stdlib/blas-ext-base-dsort2sh' );
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 );
dsort2sh( x.length, -1.0, x, -1, y, -1 );
console.log( x );
console.log( y );
```
</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 for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
<section class="related">
* * *
## See Also
- <span class="package-name">[`@stdlib/blas-ext/base/dsortsh`][@stdlib/blas/ext/base/dsortsh]</span><span class="delimiter">: </span><span class="description">sort a double-precision floating-point strided array using Shellsort.</span>
- <span class="package-name">[`@stdlib/blas-ext/base/gsort2sh`][@stdlib/blas/ext/base/gsort2sh]</span><span class="delimiter">: </span><span class="description">simultaneously sort two strided arrays based on the sort order of the first array using Shellsort.</span>
- <span class="package-name">[`@stdlib/blas-ext/base/ssort2sh`][@stdlib/blas/ext/base/ssort2sh]</span><span class="delimiter">: </span><span class="description">simultaneously sort two single-precision floating-point strided arrays based on the sort order of the first array using Shellsort.</span>
</section>
<!-- /.related -->
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<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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[esm-url]: https://github.com/stdlib-js/blas-ext-base-dsort2sh/tree/esm
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[@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
[@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
<!-- <related-links> -->
[@stdlib/blas/ext/base/dsortsh]: https://www.npmjs.com/package/@stdlib/blas-ext-base-dsortsh
[@stdlib/blas/ext/base/gsort2sh]: https://www.npmjs.com/package/@stdlib/blas-ext-base-gsort2sh
[@stdlib/blas/ext/base/ssort2sh]: https://www.npmjs.com/package/@stdlib/blas-ext-base-ssort2sh
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