gsort2sh
Simultaneously sort two strided arrays based on the sort order of the first array using Shellsort.
Usage
var gsort2sh = require( '@stdlib/blas/ext/base/gsort2sh' );
gsort2sh( N, order, x, strideX, y, strideY )
Simultaneously sorts two strided arrays based on the sort order of the first array x
using Shellsort.
var x = [ 1.0, -2.0, 3.0, -4.0 ];
var y = [ 0.0, 1.0, 2.0, 3.0 ];
gsort2sh( 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 arrayx
is sorted in decreasing order. Iforder > 0.0
, the input strided arrayx
is sorted in increasing order. Iforder == 0.0
, the input strided arrays are left unchanged. - x: first input
Array
ortyped array
. - strideX:
x
index increment. - y: second input
Array
ortyped 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
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 );
gsort2sh( 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
views.
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...
gsort2sh( N, -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 ]
gsort2sh.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 Shellsort and alternative indexing semantics.
var x = [ 1.0, -2.0, 3.0, -4.0 ];
var y = [ 0.0, 1.0, 2.0, 3.0 ];
gsort2sh.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
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 ];
var y = [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ];
gsort2sh.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
ororder == 0.0
, both functions leavex
andy
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 complexityO(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 arrays are sorted in-place (i.e., the input strided arrays are mutated).
- Depending on the environment, the typed versions (
dsort2sh
,ssort2sh
, 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 gsort2sh = require( '@stdlib/blas/ext/base/gsort2sh' );
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 );
gsort2sh( x.length, -1.0, x, -1, y, -1 );
console.log( x );
console.log( y );
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.