gsortsh

Sort a strided array using Shellsort.

Usage

var gsortsh = require( '@stdlib/blas/ext/base/gsortsh' );

gsortsh( N, order, x, stride )

Sorts a strided array x using Shellsort.

var x = [ 1.0, -2.0, 3.0, -4.0 ];

gsortsh( 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 or 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

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

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

gsortsh( 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 views.

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...
gsortsh( N, -1.0, x1, 2 );
// x0 => <Float64Array>[ 1.0, 4.0, 3.0, 2.0 ]

gsortsh.ndarray( N, order, x, stride, offset )

Sorts a strided array x using Shellsort and alternative indexing semantics.

var x = [ 1.0, -2.0, 3.0, -4.0 ];

gsortsh.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 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

var x = [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ];

gsortsh.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^(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 array is sorted in-place (i.e., the input strided array is mutated).
Depending on the environment, the typed versions (dsortsh, ssortsh, etc.) are likely to be significantly more performant.

Examples

var round = require( '@stdlib/math/base/special/round' );
var randu = require( '@stdlib/random/base/randu' );
var Float64Array = require( '@stdlib/array/float64' );
var gsortsh = require( '@stdlib/blas/ext/base/gsortsh' );

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 );

gsortsh( x.length, -1.0, x, -1 );
console.log( x );

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.
Sedgewick, Robert. 1986. "A new upper bound for Shellsort." Journal of Algorithms 7 (2): 159–73. doi:10.1016/0196-6774(86)90001-5.
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.