gsort2hp

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

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.
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