# gsort2hp
> Simultaneously sort two strided arrays based on the sort order of the first array using heapsort.
## 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 );
// => [ 1.0, 4.0, 3.0, 2.0 ]
console.log( y0 );
// => [ 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 ]
```
## 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.
## Examples
```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 );
```
* * *
## 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].
[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://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