@stdlib/blas-ext-base-gsort2hp
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    gsort2hp

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    Simultaneously sort two strided arrays based on the sort order of the first array using heapsort.

    Installation

    npm install @stdlib/blas-ext-base-gsort2hp

    Usage

    var gsort2hp = require( '@stdlib/blas-ext-base-gsort2hp' );

    gsort2hp( N, order, x, strideX, y, strideY )

    Simultaneously sorts two strided arrays based on the sort order of the first array x using heapsort.

    var x = [ 1.0, -2.0, 3.0, -4.0 ];
    var y = [ 0.0, 1.0, 2.0, 3.0 ];
    
    gsort2hp( 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 or typed array.
    • strideX: x index increment.
    • y: second input Array or 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

    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 );
    
    gsort2hp( 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...
    gsort2hp( 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 ]

    gsort2hp.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 heapsort and alternative indexing semantics.

    var x = [ 1.0, -2.0, 3.0, -4.0 ];
    var y = [ 0.0, 1.0, 2.0, 3.0 ];
    
    gsort2hp.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 ];
    
    gsort2hp.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 has space complexity O(1) and time complexity O(N log2 N).
    • 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).
    • Depending on the environment, the typed versions (dsort2hp, ssort2hp, 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 gsort2hp = require( '@stdlib/blas-ext-base-gsort2hp' );
    
    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 );
    
    gsort2hp( x.length, -1.0, x, -1, y, -1 );
    console.log( x );
    console.log( y );

    References

    • Williams, John William Joseph. 1964. "Algorithm 232: Heapsort." Communications of the ACM 7 (6). New York, NY, USA: Association for Computing Machinery: 347–49. doi:10.1145/512274.512284.
    • Floyd, Robert W. 1964. "Algorithm 245: Treesort." Communications of the ACM 7 (12). New York, NY, USA: Association for Computing Machinery: 701. doi:10.1145/355588.365103.

    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.

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    License

    See LICENSE.

    Copyright

    Copyright © 2016-2021. The Stdlib Authors.

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    npm i @stdlib/blas-ext-base-gsort2hp

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