gsort2ins

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

Usage

var gsort2ins = require( '@stdlib/blas/ext/base/gsort2ins' );

gsort2ins( N, order, x, strideX, y, strideY )

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

var x = [ 1.0, -2.0, 3.0, -4.0 ];
var y = [ 0.0, 1.0, 2.0, 3.0 ];

gsort2ins( 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 );

gsort2ins( 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...
gsort2ins( 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 ]

gsort2ins.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 insertion sort and alternative indexing semantics.

var x = [ 1.0, -2.0, 3.0, -4.0 ];
var y = [ 0.0, 1.0, 2.0, 3.0 ];

gsort2ins.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 ];

gsort2ins.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 is stable, meaning that the algorithm does not 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 (dsort2ins, ssort2ins, 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 gsort2ins = require( '@stdlib/blas/ext/base/gsort2ins' );

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 );

gsort2ins( x.length, -1.0, x, -1, y, -1 );
console.log( x );
console.log( y );