# gsortins
> Sort a strided array using insertion sort.
## Usage
```javascript
var gsortins = require( '@stdlib/blas/ext/base/gsortins' );
```
#### gsortins( N, order, x, stride )
Sorts a strided array `x` using insertion sort.
```javascript
var x = [ 1.0, -2.0, 3.0, -4.0 ];
gsortins( x.length, 1.0, x, 1 );
// x => [ -4.0, -2.0, 1.0, 3.0 ]
```
The function has the following parameters:
- **N**: number of indexed elements.
- **order**: sort order. If `order < 0.0`, the input strided array is sorted in **decreasing** order. If `order > 0.0`, the input strided array is sorted in **increasing** order. If `order == 0.0`, the input strided array is left unchanged.
- **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
- **stride**: index increment.
The `N` and `stride` parameters determine which elements in `x` 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 N = floor( x.length / 2 );
gsortins( N, -1.0, x, 2 );
// x => [ 3.0, -2.0, 1.0, -4.0 ]
```
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 array...
var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
// Create an offset view...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var N = floor( x0.length/2 );
// Sort every other element...
gsortins( N, -1.0, x1, 2 );
// x0 => [ 1.0, 4.0, 3.0, 2.0 ]
```
#### gsortins.ndarray( N, order, x, stride, offset )
Sorts a strided array `x` using insertion sort and alternative indexing semantics.
```javascript
var x = [ 1.0, -2.0, 3.0, -4.0 ];
gsortins.ndarray( x.length, 1.0, x, 1, 0 );
// x => [ -4.0, -2.0, 1.0, 3.0 ]
```
The function has the following additional parameters:
- **offset**: 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 ];
gsortins.ndarray( 3, 1.0, x, 1, x.length-3 );
// x => [ 1.0, -2.0, 3.0, -6.0, -4.0, 5.0 ]
```
## Notes
- If `N <= 0` or `order == 0.0`, both functions return `x` 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 is **stable**, meaning that the algorithm does **not** change the order of strided array elements which are equal or equivalent (e.g., `NaN` values).
- The input strided array is sorted **in-place** (i.e., the input strided array is **mutated**).
- Depending on the environment, the typed versions ([`dsortins`][@stdlib/blas/ext/base/dsortins], [`ssortins`][@stdlib/blas/ext/base/ssortins], 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 gsortins = require( '@stdlib/blas/ext/base/gsortins' );
var rand;
var sign;
var x;
var i;
x = new Float64Array( 10 );
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;
}
console.log( x );
gsortins( x.length, -1.0, x, -1 );
console.log( x );
```
[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/dsortins]: https://github.com/stdlib-js/blas/tree/main/ext/base/dsortins
[@stdlib/blas/ext/base/gsort2ins]: https://github.com/stdlib-js/blas/tree/main/ext/base/gsort2ins
[@stdlib/blas/ext/base/ssortins]: https://github.com/stdlib-js/blas/tree/main/ext/base/ssortins