@stdlib/blas-ext-base-ssort2sh NPM

ssort2sh

Simultaneously sort two single-precision floating-point strided arrays based on the sort order of the first array using Shellsort.

Installation

npm install @stdlib/blas-ext-base-ssort2sh

Usage

var ssort2sh = require( '@stdlib/blas-ext-base-ssort2sh' );

ssort2sh( N, order, x, strideX, y, strideY )

Simultaneously sorts two single-precision floating-point strided arrays based on the sort order of the first array x using Shellsort.

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 3.0, -4.0 ] );
var y = new Float32Array( [ 0.0, 1.0, 2.0, 3.0 ] );

ssort2sh( x.length, 1.0, x, 1, y, 1 );

console.log( x );
// => <Float32Array>[ -4.0, -2.0, 1.0, 3.0 ]

console.log( y );
// => <Float32Array>[ 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 Float32Array.
strideX: x index increment.
y: second input Float32Array.
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 Float32Array = require( '@stdlib/array-float32' );
var floor = require( '@stdlib/math-base-special-floor' );

var x = new Float32Array( [ 1.0, -2.0, 3.0, -4.0 ] );
var y = new Float32Array( [ 0.0, 1.0, 2.0, 3.0 ] );
var N = floor( x.length / 2 );

ssort2sh( N, -1.0, x, 2, y, 2 );

console.log( x );
// => <Float32Array>[ 3.0, -2.0, 1.0, -4.0 ]

console.log( y );
// => <Float32Array>[ 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 Float32Array = require( '@stdlib/array-float32' );
var floor = require( '@stdlib/math-base-special-floor' );

// Initial arrays...
var x0 = new Float32Array( [ 1.0, 2.0, 3.0, 4.0 ] );
var y0 = new Float32Array( [ 0.0, 1.0, 2.0, 3.0 ] );

// Create offset views...
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float32Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var N = floor( x0.length/2 );

// Sort every other element...
ssort2sh( N, -1.0, x1, 2, y1, 2 );

console.log( x0 );
// => <Float32Array>[ 1.0, 4.0, 3.0, 2.0 ]

console.log( y0 );
// => <Float32Array>[ 0.0, 3.0, 2.0, 1.0 ]

ssort2sh.ndarray( N, order, x, strideX, offsetX, y, strideY, offsetY )

Simultaneously sorts two single-precision floating-point strided arrays based on the sort order of the first array x using Shellsort and alternative indexing semantics.

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 3.0, -4.0 ] );
var y = new Float32Array( [ 0.0, 1.0, 2.0, 3.0 ] );

ssort2sh.ndarray( x.length, 1.0, x, 1, 0, y, 1, 0 );

console.log( x );
// => <Float32Array>[ -4.0, -2.0, 1.0, 3.0 ]

console.log( y );
// => <Float32Array>[ 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 Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );
var y = new Float32Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );

ssort2sh.ndarray( 3, 1.0, x, 1, x.length-3, y, 1, y.length-3 );

console.log( x );
// => <Float32Array>[ 1.0, -2.0, 3.0, -6.0, -4.0, 5.0 ]

console.log( y );
// => <Float32Array>[ 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^(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).

Examples

var round = require( '@stdlib/math-base-special-round' );
var randu = require( '@stdlib/random-base-randu' );
var Float32Array = require( '@stdlib/array-float32' );
var ssort2sh = require( '@stdlib/blas-ext-base-ssort2sh' );

var rand;
var sign;
var x;
var y;
var i;

x = new Float32Array( 10 );
y = new Float32Array( 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 );

ssort2sh( 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.

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.