@stdlib/blas-ext-base-gsort2hp/lib/ndarray.js

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

/**
* @license Apache-2.0
*
* Copyright (c) 2020 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
*    http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/

'use strict';

// MODULES //

var isPositiveZero = require( '@stdlib/math-base-assert-is-positive-zero' );
var isnan = require( '@stdlib/math-base-assert-is-nan' );
var floor = require( '@stdlib/math-base-special-floor' );


// MAIN //

/**
* Simultaneously sorts two double-precision floating-point strided arrays based on the sort order of the first array using heapsort.
*
* ## Notes
*
* -   This implementation uses an in-place algorithm derived from the work of Floyd (1964).
*
* ## 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](https://doi.org/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](https://doi.org/10.1145/355588.365103).
*
* @param {PositiveInteger} N - number of indexed elements
* @param {number} order - sort order
* @param {NumericArray} x - first input array
* @param {integer} strideX - `x` index increment
* @param {NonNegativeInteger} offsetX - `x` starting index
* @param {NumericArray} y - second input array
* @param {integer} strideY - `y` index increment
* @param {NonNegativeInteger} offsetY - `y` starting index
* @returns {NumericArray} `x`
*
* @example
* 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, 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 ]
*/
function gsort2hp( N, order, x, strideX, offsetX, y, strideY, offsetY ) {
	var parent;
	var child;
	var v1;
	var v2;
	var tx;
	var ty;
	var ix;
	var iy;
	var n;
	var j;
	var k;

	if ( N <= 0 || order === 0.0 ) {
		return x;
	}
	// For a positive stride, sorting in decreasing order is equivalent to providing a negative stride and sorting in increasing order, and, for a negative stride, sorting in decreasing order is equivalent to providing a positive stride and sorting in increasing order...
	if ( order < 0.0 ) {
		strideX *= -1;
		strideY *= -1;
		offsetX -= (N-1) * strideX;
		offsetY -= (N-1) * strideY;
	}
	// Set the initial heap size:
	n = N;

	// Specify an initial "parent" index for building the heap:
	parent = floor( N / 2 );

	// Continue looping until the array is sorted...
	while ( true ) {
		if ( parent > 0 ) {
			// We need to build the heap...
			parent -= 1;
			tx = x[ offsetX+(parent*strideX) ];
			ty = y[ offsetY+(parent*strideY) ];
		} else {
			// Reduce the heap size:
			n -= 1;

			// Check if the heap is empty, and, if so, we are finished sorting...
			if ( n === 0 ) {
				return x;
			}
			// Store the last heap value in a temporary variable in order to make room for the heap root being placed into its sorted position:
			ix = offsetX + (n*strideX);
			tx = x[ ix ];
			iy = offsetY + (n*strideY);
			ty = y[ iy ];

			// Move the heap root to its sorted position:
			x[ ix ] = x[ offsetX ];
			y[ iy ] = y[ offsetY ];
		}
		// We need to "sift down", pushing `t` down the heap to in order to replace the parent and satisfy the heap property...

		// Start at the parent index:
		j = parent;

		// Get the "left" child index:
		child = (j*2) + 1;

		while ( child < n ) {
			// Find the largest child...
			k = child + 1;
			if ( k < n ) {
				v1 = x[ offsetX+(k*strideX) ];
				v2 = x[ offsetX+(child*strideX) ];

				// Check if a "right" child exists and is "bigger"...
				if ( v1 > v2 || isnan( v1 ) || (v1 === v2 && isPositiveZero( v1 ) ) ) { // eslint-disable-line max-len
					child += 1;
				}
			}
			// Check if the largest child is bigger than `t`...
			v1 = x[ offsetX+(child*strideX) ];
			if ( v1 > tx || isnan( v1 ) || ( v1 === tx && isPositiveZero( v1 ) ) ) { // eslint-disable-line max-len
				// Insert the larger child value:
				x[ offsetX+(j*strideX) ] = v1;
				y[ offsetY+(j*strideY) ] = y[ offsetY+(child*strideY) ];

				// Update `j` to point to the child index:
				j = child;

				// Get the "left" child index and repeat...
				child = (j*2) + 1;
			} else {
				// We've found `t`'s place in the heap...
				break;
			}
		}
		// Insert `t` into the heap:
		x[ offsetX+(j*strideX) ] = tx;
		y[ offsetY+(j*strideY) ] = ty;
	}
}


// EXPORTS //

module.exports = gsort2hp;