Skip to content

Latest commit

 

History

History
357 lines (230 loc) · 13.1 KB

README.md

File metadata and controls

357 lines (230 loc) · 13.1 KB
Raw
About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

ssort2sh

NPM version Build Status Coverage Status

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

Usage

import ssort2sh from 'https://cdn.jsdelivr.net/gh/stdlib-js/blas-ext-base-ssort2sh@esm/index.mjs';

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.

import Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';

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

import Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';
import floor from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-floor@esm/index.mjs';

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.

import Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';
import floor from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-floor@esm/index.mjs';

// 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.

import Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';

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

import Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';

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

<!DOCTYPE html>
<html lang="en">
<body>
<script type="module">

import round from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-round@esm/index.mjs';
import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@esm/index.mjs';
import Float32Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float32@esm/index.mjs';
import ssort2sh from 'https://cdn.jsdelivr.net/gh/stdlib-js/blas-ext-base-ssort2sh@esm/index.mjs';

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 );

</script>
</body>
</html>

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.

See Also

Notice

This package is part of stdlib, a standard library 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.

Community

Chat

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.