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# gsort2hp

> Simultaneously sort two strided arrays based on the sort order of the first array using heapsort.

<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 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**: stride length for `x`.
-   **y**: second input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
-   **strideY**: stride length for `y`.

The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to sort every other element:

```javascript
var x = [ 1.0, -2.0, 3.0, -4.0 ];
var y = [ 0.0, 1.0, 2.0, 3.0 ];

gsort2hp( 2, -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' );

// 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...
gsort2hp( 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 ]
```

#### gsort2hp.ndarray( N, order, x, strideX, offsetX, y, strideY, offsetY )

Simultaneously sorts two strided arrays based on the sort order of the first array 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**: starting index for `x`.
-   **offsetY**: starting index for `y`.

While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, to access only the last three elements:

```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.
-   Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor]).
-   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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var gsort2hp = require( '@stdlib/blas/ext/base/gsort2hp' );

var x = discreteUniform( 10, -100, 100, {
    'dtype': 'float64'
});
var y = discreteUniform( 10, -100, 100, {
    'dtype': 'float64'
});
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>

<!-- /.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/array/base/accessor]: https://www.npmjs.com/package/@stdlib/array-base-accessor

[@stdlib/blas/ext/base/dsort2hp]: https://github.com/stdlib-js/blas/tree/main/ext/base/dsort2hp

[@stdlib/blas/ext/base/ssort2hp]: https://github.com/stdlib-js/blas/tree/main/ext/base/ssort2hp

[@williams:1964a]: https://doi.org/10.1145/512274.512284

[@floyd:1964a]: https://doi.org/10.1145/355588.365103

</section>

<!-- /.links -->
