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# dsort2sh

> Simultaneously sort two double-precision floating-point strided arrays based on the sort order of the first array using Shellsort.

<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 floor = require( '@stdlib/math/base/special/floor' );

var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0 ] );
var y = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] );
var N = floor( x.length / 2 );

dsort2sh( N, -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' );
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...
dsort2sh( 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 ]
```

#### 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 class="links">

[@stdlib/array/float64]: https://github.com/stdlib-js/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

</section>

<!-- /.links -->
