## Usage ```javascript var gsort2ins = require( '@stdlib/blas/ext/base/gsort2ins' ); ``` #### gsort2ins( N, order, x, strideX, y, strideY ) Simultaneously sorts two strided arrays based on the sort order of the first array `x` using insertion sort. ```javascript var x = [ 1.0, -2.0, 3.0, -4.0 ]; var y = [ 0.0, 1.0, 2.0, 3.0 ]; gsort2ins( 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 ); gsort2ins( 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... gsort2ins( 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 ] ``` #### gsort2ins.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 insertion sort 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 ]; gsort2ins.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 ]; gsort2ins.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 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 arrays are sorted **in-place** (i.e., the input strided arrays are **mutated**). - Depending on the environment, the typed versions ([`dsort2ins`][@stdlib/blas/ext/base/dsort2ins], [`ssort2ins`][@stdlib/blas/ext/base/ssort2ins], etc.) are likely to be significantly more performant.