/*
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*/
/**
 * Copyright (c) 2011, The University of Southampton and the individual contributors.
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without modification,
 * are permitted provided that the following conditions are met:
 *
 *   *  Redistributions of source code must retain the above copyright notice,
 *      this list of conditions and the following disclaimer.
 *
 *   *  Redistributions in binary form must reproduce the above copyright notice,
 *      this list of conditions and the following disclaimer in the documentation
 *      and/or other materials provided with the distribution.
 *
 *   *  Neither the name of the University of Southampton nor the names of its
 *      contributors may be used to endorse or promote products derived from this
 *      software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
 * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
 * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
package org.openimaj.util.array;

import java.lang.reflect.Array;

/**
 * Collection of utilities for primitive arrays.
 * 
 * @author Jonathan Hare
 * @author Sina Samangooei
 * 
 */
public class ArrayUtils {
    private ArrayUtils () {
        
    }

    
        /**
         * Format the array as a string, using the provided format 
         * string to control how each value is printed.
         * 
         * @param arr
         *            array of double
         * @param fmt
         *            format string for each element
         * @return the value
         */
    public static String toString(double[] arr, String fmt) {
                StringBuffer localStringBuffer = new StringBuffer();
                localStringBuffer.append("[");
                int i = arr.length - 1;
                for (int j = 0; j <= i; ++j)
                {
                        localStringBuffer.append(String.format(fmt, arr[j]));
                        if (j >= i)
                                continue;
                        localStringBuffer.append(", ");
                }
                localStringBuffer.append("]");
                return localStringBuffer.toString();
        }
    
    
        /**
         * Format the array as a string, using the provided format 
         * string to control how each value is printed.
         * 
         * @param arr
         *            array of float
         * @param fmt
         *            format string for each element
         * @return the value
         */
    public static String toString(float[] arr, String fmt) {
                StringBuffer localStringBuffer = new StringBuffer();
                localStringBuffer.append("[");
                int i = arr.length - 1;
                for (int j = 0; j <= i; ++j)
                {
                        localStringBuffer.append(String.format(fmt, arr[j]));
                        if (j >= i)
                                continue;
                        localStringBuffer.append(", ");
                }
                localStringBuffer.append("]");
                return localStringBuffer.toString();
        }
    
    
        /**
         * Format the array as a string, using the provided format 
         * string to control how each value is printed.
         * 
         * @param arr
         *            array of int
         * @param fmt
         *            format string for each element
         * @return the value
         */
    public static String toString(int[] arr, String fmt) {
                StringBuffer localStringBuffer = new StringBuffer();
                localStringBuffer.append("[");
                int i = arr.length - 1;
                for (int j = 0; j <= i; ++j)
                {
                        localStringBuffer.append(String.format(fmt, arr[j]));
                        if (j >= i)
                                continue;
                        localStringBuffer.append(", ");
                }
                localStringBuffer.append("]");
                return localStringBuffer.toString();
        }
    
    
        /**
         * Format the array as a string, using the provided format 
         * string to control how each value is printed.
         * 
         * @param arr
         *            array of long
         * @param fmt
         *            format string for each element
         * @return the value
         */
    public static String toString(long[] arr, String fmt) {
                StringBuffer localStringBuffer = new StringBuffer();
                localStringBuffer.append("[");
                int i = arr.length - 1;
                for (int j = 0; j <= i; ++j)
                {
                        localStringBuffer.append(String.format(fmt, arr[j]));
                        if (j >= i)
                                continue;
                        localStringBuffer.append(", ");
                }
                localStringBuffer.append("]");
                return localStringBuffer.toString();
        }
    
    
        /**
         * Format the array as a string, using the provided format 
         * string to control how each value is printed.
         * 
         * @param arr
         *            array of byte
         * @param fmt
         *            format string for each element
         * @return the value
         */
    public static String toString(byte[] arr, String fmt) {
                StringBuffer localStringBuffer = new StringBuffer();
                localStringBuffer.append("[");
                int i = arr.length - 1;
                for (int j = 0; j <= i; ++j)
                {
                        localStringBuffer.append(String.format(fmt, arr[j]));
                        if (j >= i)
                                continue;
                        localStringBuffer.append(", ");
                }
                localStringBuffer.append("]");
                return localStringBuffer.toString();
        }
    
    
        /**
         * Format the array as a string, using the provided format 
         * string to control how each value is printed.
         * 
         * @param arr
         *            array of short
         * @param fmt
         *            format string for each element
         * @return the value
         */
    public static String toString(short[] arr, String fmt) {
                StringBuffer localStringBuffer = new StringBuffer();
                localStringBuffer.append("[");
                int i = arr.length - 1;
                for (int j = 0; j <= i; ++j)
                {
                        localStringBuffer.append(String.format(fmt, arr[j]));
                        if (j >= i)
                                continue;
                        localStringBuffer.append(", ");
                }
                localStringBuffer.append("]");
                return localStringBuffer.toString();
        }
    
    
        /**
         * Returns the largest value in the array.
         * 
         * @param arr
         *            array of double
         * @return the value
         */
        public static double maxValue(final double[] arr) {
                if (arr.length < 0)
                        return 0;

                double max = arr[0];
                for (int i = 1; i < arr.length; i++) {
                        if (arr[i] > max) {
                                max = arr[i];
                        }
                }

                return max;
        }

    
        /**
         * Returns the largest value in the array.
         * 
         * @param arr
         *            array of float
         * @return the value
         */
        public static float maxValue(final float[] arr) {
                if (arr.length < 0)
                        return 0;

                float max = arr[0];
                for (int i = 1; i < arr.length; i++) {
                        if (arr[i] > max) {
                                max = arr[i];
                        }
                }

                return max;
        }

    
        /**
         * Returns the largest value in the array.
         * 
         * @param arr
         *            array of int
         * @return the value
         */
        public static int maxValue(final int[] arr) {
                if (arr.length < 0)
                        return 0;

                int max = arr[0];
                for (int i = 1; i < arr.length; i++) {
                        if (arr[i] > max) {
                                max = arr[i];
                        }
                }

                return max;
        }

    
        /**
         * Returns the largest value in the array.
         * 
         * @param arr
         *            array of long
         * @return the value
         */
        public static long maxValue(final long[] arr) {
                if (arr.length < 0)
                        return 0;

                long max = arr[0];
                for (int i = 1; i < arr.length; i++) {
                        if (arr[i] > max) {
                                max = arr[i];
                        }
                }

                return max;
        }

    
        /**
         * Returns the largest value in the array.
         * 
         * @param arr
         *            array of byte
         * @return the value
         */
        public static byte maxValue(final byte[] arr) {
                if (arr.length < 0)
                        return 0;

                byte max = arr[0];
                for (int i = 1; i < arr.length; i++) {
                        if (arr[i] > max) {
                                max = arr[i];
                        }
                }

                return max;
        }

    
        /**
         * Returns the largest value in the array.
         * 
         * @param arr
         *            array of short
         * @return the value
         */
        public static short maxValue(final short[] arr) {
                if (arr.length < 0)
                        return 0;

                short max = arr[0];
                for (int i = 1; i < arr.length; i++) {
                        if (arr[i] > max) {
                                max = arr[i];
                        }
                }

                return max;
        }

    
        /**
         * Returns the smallest value in the array.
         * 
         * @param arr
         *            array of double
         * @return the value
         */
        public static double minValue(final double[] arr) {
                if (arr.length < 0)
                        return 0;

                double min = arr[0];
                for (int i = 1; i < arr.length; i++) {
                        if (arr[i] < min) {
                                min = arr[i];
                        }
                }

                return min;
        }

    
        /**
         * Returns the smallest value in the array.
         * 
         * @param arr
         *            array of float
         * @return the value
         */
        public static float minValue(final float[] arr) {
                if (arr.length < 0)
                        return 0;

                float min = arr[0];
                for (int i = 1; i < arr.length; i++) {
                        if (arr[i] < min) {
                                min = arr[i];
                        }
                }

                return min;
        }

    
        /**
         * Returns the smallest value in the array.
         * 
         * @param arr
         *            array of int
         * @return the value
         */
        public static int minValue(final int[] arr) {
                if (arr.length < 0)
                        return 0;

                int min = arr[0];
                for (int i = 1; i < arr.length; i++) {
                        if (arr[i] < min) {
                                min = arr[i];
                        }
                }

                return min;
        }

    
        /**
         * Returns the smallest value in the array.
         * 
         * @param arr
         *            array of long
         * @return the value
         */
        public static long minValue(final long[] arr) {
                if (arr.length < 0)
                        return 0;

                long min = arr[0];
                for (int i = 1; i < arr.length; i++) {
                        if (arr[i] < min) {
                                min = arr[i];
                        }
                }

                return min;
        }

    
        /**
         * Returns the smallest value in the array.
         * 
         * @param arr
         *            array of byte
         * @return the value
         */
        public static byte minValue(final byte[] arr) {
                if (arr.length < 0)
                        return 0;

                byte min = arr[0];
                for (int i = 1; i < arr.length; i++) {
                        if (arr[i] < min) {
                                min = arr[i];
                        }
                }

                return min;
        }

    
        /**
         * Returns the smallest value in the array.
         * 
         * @param arr
         *            array of short
         * @return the value
         */
        public static short minValue(final short[] arr) {
                if (arr.length < 0)
                        return 0;

                short min = arr[0];
                for (int i = 1; i < arr.length; i++) {
                        if (arr[i] < min) {
                                min = arr[i];
                        }
                }

                return min;
        }

    
        /**
         * Returns the index to the biggest value in the array.
         * 
         * @param arr
         *            array of double
         * @return the index
         */
        public static int maxIndex(final double[] arr) {
                double max = Double.MIN_VALUE;
                int index = 0;
                for (int i = 0; i < arr.length; i++) {
                        if (arr[i] > max) {
                                max = arr[i];
                                index = i;
                        }
                }

                return index;
        }

    
        /**
         * Returns the index to the biggest value in the array.
         * 
         * @param arr
         *            array of float
         * @return the index
         */
        public static int maxIndex(final float[] arr) {
                float max = Float.MIN_VALUE;
                int index = 0;
                for (int i = 0; i < arr.length; i++) {
                        if (arr[i] > max) {
                                max = arr[i];
                                index = i;
                        }
                }

                return index;
        }

    
        /**
         * Returns the index to the biggest value in the array.
         * 
         * @param arr
         *            array of int
         * @return the index
         */
        public static int maxIndex(final int[] arr) {
                int max = Integer.MIN_VALUE;
                int index = 0;
                for (int i = 0; i < arr.length; i++) {
                        if (arr[i] > max) {
                                max = arr[i];
                                index = i;
                        }
                }

                return index;
        }

    
        /**
         * Returns the index to the biggest value in the array.
         * 
         * @param arr
         *            array of long
         * @return the index
         */
        public static int maxIndex(final long[] arr) {
                long max = Long.MIN_VALUE;
                int index = 0;
                for (int i = 0; i < arr.length; i++) {
                        if (arr[i] > max) {
                                max = arr[i];
                                index = i;
                        }
                }

                return index;
        }

    
        /**
         * Returns the index to the biggest value in the array.
         * 
         * @param arr
         *            array of byte
         * @return the index
         */
        public static int maxIndex(final byte[] arr) {
                byte max = Byte.MIN_VALUE;
                int index = 0;
                for (int i = 0; i < arr.length; i++) {
                        if (arr[i] > max) {
                                max = arr[i];
                                index = i;
                        }
                }

                return index;
        }

    
        /**
         * Returns the index to the biggest value in the array.
         * 
         * @param arr
         *            array of short
         * @return the index
         */
        public static int maxIndex(final short[] arr) {
                short max = Short.MIN_VALUE;
                int index = 0;
                for (int i = 0; i < arr.length; i++) {
                        if (arr[i] > max) {
                                max = arr[i];
                                index = i;
                        }
                }

                return index;
        }

    
        /**
         * Returns the index to the smallest value in the array.
         * 
         * @param arr
         *            array of double
         * @return the index
         */
        public static int minIndex(final double[] arr) {
                double min = Double.MAX_VALUE;
                int index = 0;
                for (int i = 0; i < arr.length; i++) {
                        if (arr[i] < min) {
                                min = arr[i];
                                index = i;
                        }
                }

                return index;
        }

    
        /**
         * Returns the index to the smallest value in the array.
         * 
         * @param arr
         *            array of float
         * @return the index
         */
        public static int minIndex(final float[] arr) {
                float min = Float.MAX_VALUE;
                int index = 0;
                for (int i = 0; i < arr.length; i++) {
                        if (arr[i] < min) {
                                min = arr[i];
                                index = i;
                        }
                }

                return index;
        }

    
        /**
         * Returns the index to the smallest value in the array.
         * 
         * @param arr
         *            array of int
         * @return the index
         */
        public static int minIndex(final int[] arr) {
                int min = Integer.MAX_VALUE;
                int index = 0;
                for (int i = 0; i < arr.length; i++) {
                        if (arr[i] < min) {
                                min = arr[i];
                                index = i;
                        }
                }

                return index;
        }

    
        /**
         * Returns the index to the smallest value in the array.
         * 
         * @param arr
         *            array of long
         * @return the index
         */
        public static int minIndex(final long[] arr) {
                long min = Long.MAX_VALUE;
                int index = 0;
                for (int i = 0; i < arr.length; i++) {
                        if (arr[i] < min) {
                                min = arr[i];
                                index = i;
                        }
                }

                return index;
        }

    
        /**
         * Returns the index to the smallest value in the array.
         * 
         * @param arr
         *            array of byte
         * @return the index
         */
        public static int minIndex(final byte[] arr) {
                byte min = Byte.MAX_VALUE;
                int index = 0;
                for (int i = 0; i < arr.length; i++) {
                        if (arr[i] < min) {
                                min = arr[i];
                                index = i;
                        }
                }

                return index;
        }

    
        /**
         * Returns the index to the smallest value in the array.
         * 
         * @param arr
         *            array of short
         * @return the index
         */
        public static int minIndex(final short[] arr) {
                short min = Short.MAX_VALUE;
                int index = 0;
                for (int i = 0; i < arr.length; i++) {
                        if (arr[i] < min) {
                                min = arr[i];
                                index = i;
                        }
                }

                return index;
        }

    
        /**
         * Element-wise summation of two arrays, output writes over first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static double[][] sum(final double[][] a1, final double[][] a2) {
                for (int j = 0; j < a1.length; j++) {
                        sum(a1[j], a2[j]);
                }
                return a1;
        }

        /**
         * Element-wise summation of two arrays, output writes over first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static double[] sum(final double[] a1, final double[] a2) {
                for (int j = 0; j < a1.length; j++) {
                        a1[j] += a2[j];
                }
                return a1;
        }

    
        /**
         * Element-wise summation of two arrays, output writes over first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static float[][] sum(final float[][] a1, final float[][] a2) {
                for (int j = 0; j < a1.length; j++) {
                        sum(a1[j], a2[j]);
                }
                return a1;
        }

        /**
         * Element-wise summation of two arrays, output writes over first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static float[] sum(final float[] a1, final float[] a2) {
                for (int j = 0; j < a1.length; j++) {
                        a1[j] += a2[j];
                }
                return a1;
        }

    
        /**
         * Element-wise summation of two arrays, output writes over first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static int[][] sum(final int[][] a1, final int[][] a2) {
                for (int j = 0; j < a1.length; j++) {
                        sum(a1[j], a2[j]);
                }
                return a1;
        }

        /**
         * Element-wise summation of two arrays, output writes over first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static int[] sum(final int[] a1, final int[] a2) {
                for (int j = 0; j < a1.length; j++) {
                        a1[j] += a2[j];
                }
                return a1;
        }

    
        /**
         * Element-wise summation of two arrays, output writes over first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static long[][] sum(final long[][] a1, final long[][] a2) {
                for (int j = 0; j < a1.length; j++) {
                        sum(a1[j], a2[j]);
                }
                return a1;
        }

        /**
         * Element-wise summation of two arrays, output writes over first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static long[] sum(final long[] a1, final long[] a2) {
                for (int j = 0; j < a1.length; j++) {
                        a1[j] += a2[j];
                }
                return a1;
        }

    
        /**
         * Element-wise summation of two arrays, output writes over first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static byte[][] sum(final byte[][] a1, final byte[][] a2) {
                for (int j = 0; j < a1.length; j++) {
                        sum(a1[j], a2[j]);
                }
                return a1;
        }

        /**
         * Element-wise summation of two arrays, output writes over first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static byte[] sum(final byte[] a1, final byte[] a2) {
                for (int j = 0; j < a1.length; j++) {
                        a1[j] += a2[j];
                }
                return a1;
        }

    
        /**
         * Element-wise summation of two arrays, output writes over first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static short[][] sum(final short[][] a1, final short[][] a2) {
                for (int j = 0; j < a1.length; j++) {
                        sum(a1[j], a2[j]);
                }
                return a1;
        }

        /**
         * Element-wise summation of two arrays, output writes over first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static short[] sum(final short[] a1, final short[] a2) {
                for (int j = 0; j < a1.length; j++) {
                        a1[j] += a2[j];
                }
                return a1;
        }

    
        /**
         * Element-wise subtraction of two arrays. Second array is subtracted from
         * first, overwriting the first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static double[][] subtract(final double[][] a1, final double[][] a2) {
                for (int j = 0; j < a1.length; j++) {
                        subtract(a1[j], a2[j]);
                }
                return a1;
        }

        /**
         * Element-wise subtraction of two arrays. Second array is subtracted from
         * first, overwriting the first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static double[] subtract(final double[] a1, final double[] a2) {
                for (int j = 0; j < a1.length; j++) {
                        a1[j] -= a2[j];
                }
                return a1;
        }

        
        /**
         * Element-wise subtraction of two arrays. Second array is subtracted from
         * first, overwriting the first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static float[][] subtract(final float[][] a1, final float[][] a2) {
                for (int j = 0; j < a1.length; j++) {
                        subtract(a1[j], a2[j]);
                }
                return a1;
        }

        /**
         * Element-wise subtraction of two arrays. Second array is subtracted from
         * first, overwriting the first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static float[] subtract(final float[] a1, final float[] a2) {
                for (int j = 0; j < a1.length; j++) {
                        a1[j] -= a2[j];
                }
                return a1;
        }

        
        /**
         * Element-wise subtraction of two arrays. Second array is subtracted from
         * first, overwriting the first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static int[][] subtract(final int[][] a1, final int[][] a2) {
                for (int j = 0; j < a1.length; j++) {
                        subtract(a1[j], a2[j]);
                }
                return a1;
        }

        /**
         * Element-wise subtraction of two arrays. Second array is subtracted from
         * first, overwriting the first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static int[] subtract(final int[] a1, final int[] a2) {
                for (int j = 0; j < a1.length; j++) {
                        a1[j] -= a2[j];
                }
                return a1;
        }

        
        /**
         * Element-wise subtraction of two arrays. Second array is subtracted from
         * first, overwriting the first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static long[][] subtract(final long[][] a1, final long[][] a2) {
                for (int j = 0; j < a1.length; j++) {
                        subtract(a1[j], a2[j]);
                }
                return a1;
        }

        /**
         * Element-wise subtraction of two arrays. Second array is subtracted from
         * first, overwriting the first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static long[] subtract(final long[] a1, final long[] a2) {
                for (int j = 0; j < a1.length; j++) {
                        a1[j] -= a2[j];
                }
                return a1;
        }

        
        /**
         * Element-wise subtraction of two arrays. Second array is subtracted from
         * first, overwriting the first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static byte[][] subtract(final byte[][] a1, final byte[][] a2) {
                for (int j = 0; j < a1.length; j++) {
                        subtract(a1[j], a2[j]);
                }
                return a1;
        }

        /**
         * Element-wise subtraction of two arrays. Second array is subtracted from
         * first, overwriting the first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static byte[] subtract(final byte[] a1, final byte[] a2) {
                for (int j = 0; j < a1.length; j++) {
                        a1[j] -= a2[j];
                }
                return a1;
        }

        
        /**
         * Element-wise subtraction of two arrays. Second array is subtracted from
         * first, overwriting the first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static short[][] subtract(final short[][] a1, final short[][] a2) {
                for (int j = 0; j < a1.length; j++) {
                        subtract(a1[j], a2[j]);
                }
                return a1;
        }

        /**
         * Element-wise subtraction of two arrays. Second array is subtracted from
         * first, overwriting the first array
         * 
         * @param a1
         *            first array
         * @param a2
         *            second array
         * @return the first array
         */
        public static short[] subtract(final short[] a1, final short[] a2) {
                for (int j = 0; j < a1.length; j++) {
                        a1[j] -= a2[j];
                }
                return a1;
        }

        
        /**
         * Subtracts <code>s</code> from all elements in <code>a1</code> overwriting
         * the array. This is syntactic sugar for <code>add( a1, -s )</code>.
         * 
         * @param a1
         *            The array
         * @param s
         *            The scalar
         * @return the array
         */
        public static double[] subtract(final double[] a1, final double s)
        {
                return add(a1, (double)(-s));
        }

    
        /**
         * Subtracts <code>s</code> from all elements in <code>a1</code> overwriting
         * the array. This is syntactic sugar for <code>add( a1, -s )</code>.
         * 
         * @param a1
         *            The array
         * @param s
         *            The scalar
         * @return the array
         */
        public static float[] subtract(final float[] a1, final float s)
        {
                return add(a1, (float)(-s));
        }

    
        /**
         * Subtracts <code>s</code> from all elements in <code>a1</code> overwriting
         * the array. This is syntactic sugar for <code>add( a1, -s )</code>.
         * 
         * @param a1
         *            The array
         * @param s
         *            The scalar
         * @return the array
         */
        public static int[] subtract(final int[] a1, final int s)
        {
                return add(a1, (int)(-s));
        }

    
        /**
         * Subtracts <code>s</code> from all elements in <code>a1</code> overwriting
         * the array. This is syntactic sugar for <code>add( a1, -s )</code>.
         * 
         * @param a1
         *            The array
         * @param s
         *            The scalar
         * @return the array
         */
        public static long[] subtract(final long[] a1, final long s)
        {
                return add(a1, (long)(-s));
        }

    
        /**
         * Subtracts <code>s</code> from all elements in <code>a1</code> overwriting
         * the array. This is syntactic sugar for <code>add( a1, -s )</code>.
         * 
         * @param a1
         *            The array
         * @param s
         *            The scalar
         * @return the array
         */
        public static byte[] subtract(final byte[] a1, final byte s)
        {
                return add(a1, (byte)(-s));
        }

    
        /**
         * Subtracts <code>s</code> from all elements in <code>a1</code> overwriting
         * the array. This is syntactic sugar for <code>add( a1, -s )</code>.
         * 
         * @param a1
         *            The array
         * @param s
         *            The scalar
         * @return the array
         */
        public static short[] subtract(final short[] a1, final short s)
        {
                return add(a1, (short)(-s));
        }

    
        /**
         * Add a constant to all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to add
         * @return the input array
         */
        public static double[] add(final double[] ds, final double x) {
                for (int i = 0; i < ds.length; i++) {
                        ds[i] += x;
                }
                return ds;
        }

    
        /**
         * Add a constant to all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to add
         * @return the input array
         */
        public static float[] add(final float[] ds, final float x) {
                for (int i = 0; i < ds.length; i++) {
                        ds[i] += x;
                }
                return ds;
        }

    
        /**
         * Add a constant to all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to add
         * @return the input array
         */
        public static int[] add(final int[] ds, final int x) {
                for (int i = 0; i < ds.length; i++) {
                        ds[i] += x;
                }
                return ds;
        }

    
        /**
         * Add a constant to all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to add
         * @return the input array
         */
        public static long[] add(final long[] ds, final long x) {
                for (int i = 0; i < ds.length; i++) {
                        ds[i] += x;
                }
                return ds;
        }

    
        /**
         * Add a constant to all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to add
         * @return the input array
         */
        public static byte[] add(final byte[] ds, final byte x) {
                for (int i = 0; i < ds.length; i++) {
                        ds[i] += x;
                }
                return ds;
        }

    
        /**
         * Add a constant to all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to add
         * @return the input array
         */
        public static short[] add(final short[] ds, final short x) {
                for (int i = 0; i < ds.length; i++) {
                        ds[i] += x;
                }
                return ds;
        }

    
    /**
         * Multiply by a constant all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to multiply by
         * @return input
         */
        public static double[] multiply(final double[] ds, final double x) {
                for (int i = 0; i < ds.length; i++) {
                        ds[i] *= x;
                }
                return ds;
        }
        
        /**
         * Multiply by a constant all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to multiply by
         * @return input
         */
        public static double[][] multiply(final double[][] ds, final double x) {
                for (int i = 0; i < ds.length; i++) {
                        multiply(ds[i], x);
                }
                return ds;
        }

    
    /**
         * Multiply by a constant all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to multiply by
         * @return input
         */
        public static float[] multiply(final float[] ds, final float x) {
                for (int i = 0; i < ds.length; i++) {
                        ds[i] *= x;
                }
                return ds;
        }
        
        /**
         * Multiply by a constant all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to multiply by
         * @return input
         */
        public static float[][] multiply(final float[][] ds, final float x) {
                for (int i = 0; i < ds.length; i++) {
                        multiply(ds[i], x);
                }
                return ds;
        }

    
    /**
         * Multiply by a constant all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to multiply by
         * @return input
         */
        public static int[] multiply(final int[] ds, final int x) {
                for (int i = 0; i < ds.length; i++) {
                        ds[i] *= x;
                }
                return ds;
        }
        
        /**
         * Multiply by a constant all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to multiply by
         * @return input
         */
        public static int[][] multiply(final int[][] ds, final int x) {
                for (int i = 0; i < ds.length; i++) {
                        multiply(ds[i], x);
                }
                return ds;
        }

    
    /**
         * Multiply by a constant all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to multiply by
         * @return input
         */
        public static long[] multiply(final long[] ds, final long x) {
                for (int i = 0; i < ds.length; i++) {
                        ds[i] *= x;
                }
                return ds;
        }
        
        /**
         * Multiply by a constant all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to multiply by
         * @return input
         */
        public static long[][] multiply(final long[][] ds, final long x) {
                for (int i = 0; i < ds.length; i++) {
                        multiply(ds[i], x);
                }
                return ds;
        }

    
    /**
         * Multiply by a constant all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to multiply by
         * @return input
         */
        public static byte[] multiply(final byte[] ds, final byte x) {
                for (int i = 0; i < ds.length; i++) {
                        ds[i] *= x;
                }
                return ds;
        }
        
        /**
         * Multiply by a constant all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to multiply by
         * @return input
         */
        public static byte[][] multiply(final byte[][] ds, final byte x) {
                for (int i = 0; i < ds.length; i++) {
                        multiply(ds[i], x);
                }
                return ds;
        }

    
    /**
         * Multiply by a constant all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to multiply by
         * @return input
         */
        public static short[] multiply(final short[] ds, final short x) {
                for (int i = 0; i < ds.length; i++) {
                        ds[i] *= x;
                }
                return ds;
        }
        
        /**
         * Multiply by a constant all elements and return the input
         * 
         * @param ds
         *            input array
         * @param x
         *            constant to multiply by
         * @return input
         */
        public static short[][] multiply(final short[][] ds, final short x) {
                for (int i = 0; i < ds.length; i++) {
                        multiply(ds[i], x);
                }
                return ds;
        }

    
        /**
         * Element-wise multiplication, overwriting a1
         * 
         * @param a1
         *            The first array
         * @param a2
         *            the second array
         * @return The first array
         */
        public static double[] multiply(final double[] a1, final double[] a2)
        {
                for (int j = 0; j < a1.length; j++)
                        a1[j] *= a2[j];
                return a1;
        }

        /**
         * Element-wise multiplication, overwriting a1.
         * 
         * @param a1
         *            First array
         * @param a2
         *            second array
         * @return Updated first array
         */
        public static double[][] multiply(final double[][] a1, final double[][] a2)
        {
                for (int j = 0; j < a1.length; j++)
                        multiply(a1[j], a2[j]);
                return a1;
        }

    
        /**
         * Element-wise multiplication, overwriting a1
         * 
         * @param a1
         *            The first array
         * @param a2
         *            the second array
         * @return The first array
         */
        public static float[] multiply(final float[] a1, final float[] a2)
        {
                for (int j = 0; j < a1.length; j++)
                        a1[j] *= a2[j];
                return a1;
        }

        /**
         * Element-wise multiplication, overwriting a1.
         * 
         * @param a1
         *            First array
         * @param a2
         *            second array
         * @return Updated first array
         */
        public static float[][] multiply(final float[][] a1, final float[][] a2)
        {
                for (int j = 0; j < a1.length; j++)
                        multiply(a1[j], a2[j]);
                return a1;
        }

    
        /**
         * Element-wise multiplication, overwriting a1
         * 
         * @param a1
         *            The first array
         * @param a2
         *            the second array
         * @return The first array
         */
        public static int[] multiply(final int[] a1, final int[] a2)
        {
                for (int j = 0; j < a1.length; j++)
                        a1[j] *= a2[j];
                return a1;
        }

        /**
         * Element-wise multiplication, overwriting a1.
         * 
         * @param a1
         *            First array
         * @param a2
         *            second array
         * @return Updated first array
         */
        public static int[][] multiply(final int[][] a1, final int[][] a2)
        {
                for (int j = 0; j < a1.length; j++)
                        multiply(a1[j], a2[j]);
                return a1;
        }

    
        /**
         * Element-wise multiplication, overwriting a1
         * 
         * @param a1
         *            The first array
         * @param a2
         *            the second array
         * @return The first array
         */
        public static long[] multiply(final long[] a1, final long[] a2)
        {
                for (int j = 0; j < a1.length; j++)
                        a1[j] *= a2[j];
                return a1;
        }

        /**
         * Element-wise multiplication, overwriting a1.
         * 
         * @param a1
         *            First array
         * @param a2
         *            second array
         * @return Updated first array
         */
        public static long[][] multiply(final long[][] a1, final long[][] a2)
        {
                for (int j = 0; j < a1.length; j++)
                        multiply(a1[j], a2[j]);
                return a1;
        }

    
        /**
         * Element-wise multiplication, overwriting a1
         * 
         * @param a1
         *            The first array
         * @param a2
         *            the second array
         * @return The first array
         */
        public static byte[] multiply(final byte[] a1, final byte[] a2)
        {
                for (int j = 0; j < a1.length; j++)
                        a1[j] *= a2[j];
                return a1;
        }

        /**
         * Element-wise multiplication, overwriting a1.
         * 
         * @param a1
         *            First array
         * @param a2
         *            second array
         * @return Updated first array
         */
        public static byte[][] multiply(final byte[][] a1, final byte[][] a2)
        {
                for (int j = 0; j < a1.length; j++)
                        multiply(a1[j], a2[j]);
                return a1;
        }

    
        /**
         * Element-wise multiplication, overwriting a1
         * 
         * @param a1
         *            The first array
         * @param a2
         *            the second array
         * @return The first array
         */
        public static short[] multiply(final short[] a1, final short[] a2)
        {
                for (int j = 0; j < a1.length; j++)
                        a1[j] *= a2[j];
                return a1;
        }

        /**
         * Element-wise multiplication, overwriting a1.
         * 
         * @param a1
         *            First array
         * @param a2
         *            second array
         * @return Updated first array
         */
        public static short[][] multiply(final short[][] a1, final short[][] a2)
        {
                for (int j = 0; j < a1.length; j++)
                        multiply(a1[j], a2[j]);
                return a1;
        }

    
        /**
         * Divide by a constant, all elements and return the input
         * 
         * @param fs
         *            The input array
         * @param x
         *            the constant to divide by
         * @return THe input
         */
        public static double[] divide(final double[] fs, final double x)
        {
                for (int i = 0; i < fs.length; i++)
                        fs[i] /= x;
                return fs;
        }

    
        /**
         * Divide by a constant, all elements and return the input
         * 
         * @param fs
         *            The input array
         * @param x
         *            the constant to divide by
         * @return THe input
         */
        public static float[] divide(final float[] fs, final float x)
        {
                for (int i = 0; i < fs.length; i++)
                        fs[i] /= x;
                return fs;
        }

    
        /**
         * Divide by a constant, all elements and return the input
         * 
         * @param fs
         *            The input array
         * @param x
         *            the constant to divide by
         * @return THe input
         */
        public static int[] divide(final int[] fs, final int x)
        {
                for (int i = 0; i < fs.length; i++)
                        fs[i] /= x;
                return fs;
        }

    
        /**
         * Divide by a constant, all elements and return the input
         * 
         * @param fs
         *            The input array
         * @param x
         *            the constant to divide by
         * @return THe input
         */
        public static long[] divide(final long[] fs, final long x)
        {
                for (int i = 0; i < fs.length; i++)
                        fs[i] /= x;
                return fs;
        }

    
        /**
         * Divide by a constant, all elements and return the input
         * 
         * @param fs
         *            The input array
         * @param x
         *            the constant to divide by
         * @return THe input
         */
        public static byte[] divide(final byte[] fs, final byte x)
        {
                for (int i = 0; i < fs.length; i++)
                        fs[i] /= x;
                return fs;
        }

    
        /**
         * Divide by a constant, all elements and return the input
         * 
         * @param fs
         *            The input array
         * @param x
         *            the constant to divide by
         * @return THe input
         */
        public static short[] divide(final short[] fs, final short x)
        {
                for (int i = 0; i < fs.length; i++)
                        fs[i] /= x;
                return fs;
        }

    
        /**
         * Normalise length of array to 1.0. Writes over array. If the array is all
         * zeros, it will be unchanged.
         * 
         * @param array
         *            the array
         * @return the array
         */
        public static float[] normalise(final float[] array) {
                float sumsq = 0.0f;
                for (int i = 0; i < array.length; i++)
                        sumsq += array[i] * array[i];

                if (sumsq == 0)
                        return array;

                final float weight = 1.0f / (float) Math.sqrt(sumsq);
                for (int i = 0; i < array.length; i++)
                        array[i] *= weight;
                return array;
        }

        /**
         * Normalise length of array to 1.0. Writes over array. If the array is all
         * zeros, it will be unchanged.
         * 
         * @param array
         *            the array
         * @return the array
         */
        public static double[] normalise(final double[] array) {
                double sumsq = 0.0f;
                for (int i = 0; i < array.length; i++)
                        sumsq += array[i] * array[i];

                if (sumsq == 0)
                        return array;

                final double weight = 1.0f / Math.sqrt(sumsq);
                for (int i = 0; i < array.length; i++)
                        array[i] *= weight;
                return array;
        }

    
        /**
         * Reverse the elements in the input and return the input.
         * 
         * @param ds
         *            input array
         * @return input
         */
        public static double[] reverse(final double[] ds) {
                final int len = ds.length;
                final int hlen = len / 2;

                for (int i = 0; i < hlen; i++) {
                        final double tmp = ds[i];
                        ds[i] = ds[len - i - 1];
                        ds[len - i - 1] = tmp;
                }
                return ds;
        }

    
        /**
         * Reverse the elements in the input and return the input.
         * 
         * @param ds
         *            input array
         * @return input
         */
        public static float[] reverse(final float[] ds) {
                final int len = ds.length;
                final int hlen = len / 2;

                for (int i = 0; i < hlen; i++) {
                        final float tmp = ds[i];
                        ds[i] = ds[len - i - 1];
                        ds[len - i - 1] = tmp;
                }
                return ds;
        }

    
        /**
         * Reverse the elements in the input and return the input.
         * 
         * @param ds
         *            input array
         * @return input
         */
        public static int[] reverse(final int[] ds) {
                final int len = ds.length;
                final int hlen = len / 2;

                for (int i = 0; i < hlen; i++) {
                        final int tmp = ds[i];
                        ds[i] = ds[len - i - 1];
                        ds[len - i - 1] = tmp;
                }
                return ds;
        }

    
        /**
         * Reverse the elements in the input and return the input.
         * 
         * @param ds
         *            input array
         * @return input
         */
        public static long[] reverse(final long[] ds) {
                final int len = ds.length;
                final int hlen = len / 2;

                for (int i = 0; i < hlen; i++) {
                        final long tmp = ds[i];
                        ds[i] = ds[len - i - 1];
                        ds[len - i - 1] = tmp;
                }
                return ds;
        }

    
        /**
         * Reverse the elements in the input and return the input.
         * 
         * @param ds
         *            input array
         * @return input
         */
        public static byte[] reverse(final byte[] ds) {
                final int len = ds.length;
                final int hlen = len / 2;

                for (int i = 0; i < hlen; i++) {
                        final byte tmp = ds[i];
                        ds[i] = ds[len - i - 1];
                        ds[len - i - 1] = tmp;
                }
                return ds;
        }

    
        /**
         * Reverse the elements in the input and return the input.
         * 
         * @param ds
         *            input array
         * @return input
         */
        public static short[] reverse(final short[] ds) {
                final int len = ds.length;
                final int hlen = len / 2;

                for (int i = 0; i < hlen; i++) {
                        final short tmp = ds[i];
                        ds[i] = ds[len - i - 1];
                        ds[len - i - 1] = tmp;
                }
                return ds;
        }

    
        /**
         * Convert a double array to a double array.
         * 
         * @param array
         *            array of doubles to convert
         * @return array of doubles
         */
        public static double[] convertToDouble(final double[] array) {
                final double[] darr = new double[array.length];

                for (int i = 0; i < array.length; i++) {
                        darr[i] = array[i];
                }
                return darr;
        }

        /**
         * Convert a double array to a double array.
         * 
         * @param array
         *            array of doubles to convert
         * @return array of doubles
         */
        public static double[][] convertToDouble(final double[][] array)
        {
                final double[][] darr = new double[array.length][];
                for (int i = 0; i < array.length; i++)
                        darr[i] = convertToDouble(array[i]);
                return darr;
        }

    
        /**
         * Convert a float array to a double array.
         * 
         * @param array
         *            array of floats to convert
         * @return array of doubles
         */
        public static double[] convertToDouble(final float[] array) {
                final double[] darr = new double[array.length];

                for (int i = 0; i < array.length; i++) {
                        darr[i] = array[i];
                }
                return darr;
        }

        /**
         * Convert a float array to a double array.
         * 
         * @param array
         *            array of floats to convert
         * @return array of doubles
         */
        public static double[][] convertToDouble(final float[][] array)
        {
                final double[][] darr = new double[array.length][];
                for (int i = 0; i < array.length; i++)
                        darr[i] = convertToDouble(array[i]);
                return darr;
        }

    
        /**
         * Convert a int array to a double array.
         * 
         * @param array
         *            array of ints to convert
         * @return array of doubles
         */
        public static double[] convertToDouble(final int[] array) {
                final double[] darr = new double[array.length];

                for (int i = 0; i < array.length; i++) {
                        darr[i] = array[i];
                }
                return darr;
        }

        /**
         * Convert a int array to a double array.
         * 
         * @param array
         *            array of ints to convert
         * @return array of doubles
         */
        public static double[][] convertToDouble(final int[][] array)
        {
                final double[][] darr = new double[array.length][];
                for (int i = 0; i < array.length; i++)
                        darr[i] = convertToDouble(array[i]);
                return darr;
        }

    
        /**
         * Convert a long array to a double array.
         * 
         * @param array
         *            array of longs to convert
         * @return array of doubles
         */
        public static double[] convertToDouble(final long[] array) {
                final double[] darr = new double[array.length];

                for (int i = 0; i < array.length; i++) {
                        darr[i] = array[i];
                }
                return darr;
        }

        /**
         * Convert a long array to a double array.
         * 
         * @param array
         *            array of longs to convert
         * @return array of doubles
         */
        public static double[][] convertToDouble(final long[][] array)
        {
                final double[][] darr = new double[array.length][];
                for (int i = 0; i < array.length; i++)
                        darr[i] = convertToDouble(array[i]);
                return darr;
        }

    
        /**
         * Convert a byte array to a double array.
         * 
         * @param array
         *            array of bytes to convert
         * @return array of doubles
         */
        public static double[] convertToDouble(final byte[] array) {
                final double[] darr = new double[array.length];

                for (int i = 0; i < array.length; i++) {
                        darr[i] = array[i];
                }
                return darr;
        }

        /**
         * Convert a byte array to a double array.
         * 
         * @param array
         *            array of bytes to convert
         * @return array of doubles
         */
        public static double[][] convertToDouble(final byte[][] array)
        {
                final double[][] darr = new double[array.length][];
                for (int i = 0; i < array.length; i++)
                        darr[i] = convertToDouble(array[i]);
                return darr;
        }

    
        /**
         * Convert a short array to a double array.
         * 
         * @param array
         *            array of shorts to convert
         * @return array of doubles
         */
        public static double[] convertToDouble(final short[] array) {
                final double[] darr = new double[array.length];

                for (int i = 0; i < array.length; i++) {
                        darr[i] = array[i];
                }
                return darr;
        }

        /**
         * Convert a short array to a double array.
         * 
         * @param array
         *            array of shorts to convert
         * @return array of doubles
         */
        public static double[][] convertToDouble(final short[][] array)
        {
                final double[][] darr = new double[array.length][];
                for (int i = 0; i < array.length; i++)
                        darr[i] = convertToDouble(array[i]);
                return darr;
        }

    
        /**
         * Convert a double array to a float array.
         * 
         * @param array
         *            array of doubles to convert
         * @return array of floats
         */
        public static float[] convertToFloat(final double[] array) {
                final float[] farr = new float[array.length];

                for (int i = 0; i < array.length; i++) {
                        farr[i] = (float) array[i];
                }
                return farr;
        }

    /**
         * Convert a double array to a float array.
         * 
         * @param array
         *            array of doubles to convert
         * @return array of doubles
         */
        public static float[][] convertToFloat(final double[][] array)
        {
                final float[][] darr = new float[array.length][];
                for (int i = 0; i < array.length; i++)
                        darr[i] = convertToFloat(array[i]);
                return darr;
        }

    
        /**
         * Convert a float array to a float array.
         * 
         * @param array
         *            array of floats to convert
         * @return array of floats
         */
        public static float[] convertToFloat(final float[] array) {
                final float[] farr = new float[array.length];

                for (int i = 0; i < array.length; i++) {
                        farr[i] = (float) array[i];
                }
                return farr;
        }

    /**
         * Convert a float array to a float array.
         * 
         * @param array
         *            array of floats to convert
         * @return array of doubles
         */
        public static float[][] convertToFloat(final float[][] array)
        {
                final float[][] darr = new float[array.length][];
                for (int i = 0; i < array.length; i++)
                        darr[i] = convertToFloat(array[i]);
                return darr;
        }

    
        /**
         * Convert a int array to a float array.
         * 
         * @param array
         *            array of ints to convert
         * @return array of floats
         */
        public static float[] convertToFloat(final int[] array) {
                final float[] farr = new float[array.length];

                for (int i = 0; i < array.length; i++) {
                        farr[i] = (float) array[i];
                }
                return farr;
        }

    /**
         * Convert a int array to a float array.
         * 
         * @param array
         *            array of ints to convert
         * @return array of doubles
         */
        public static float[][] convertToFloat(final int[][] array)
        {
                final float[][] darr = new float[array.length][];
                for (int i = 0; i < array.length; i++)
                        darr[i] = convertToFloat(array[i]);
                return darr;
        }

    
        /**
         * Convert a long array to a float array.
         * 
         * @param array
         *            array of longs to convert
         * @return array of floats
         */
        public static float[] convertToFloat(final long[] array) {
                final float[] farr = new float[array.length];

                for (int i = 0; i < array.length; i++) {
                        farr[i] = (float) array[i];
                }
                return farr;
        }

    /**
         * Convert a long array to a float array.
         * 
         * @param array
         *            array of longs to convert
         * @return array of doubles
         */
        public static float[][] convertToFloat(final long[][] array)
        {
                final float[][] darr = new float[array.length][];
                for (int i = 0; i < array.length; i++)
                        darr[i] = convertToFloat(array[i]);
                return darr;
        }

    
        /**
         * Convert a byte array to a float array.
         * 
         * @param array
         *            array of bytes to convert
         * @return array of floats
         */
        public static float[] convertToFloat(final byte[] array) {
                final float[] farr = new float[array.length];

                for (int i = 0; i < array.length; i++) {
                        farr[i] = (float) array[i];
                }
                return farr;
        }

    /**
         * Convert a byte array to a float array.
         * 
         * @param array
         *            array of bytes to convert
         * @return array of doubles
         */
        public static float[][] convertToFloat(final byte[][] array)
        {
                final float[][] darr = new float[array.length][];
                for (int i = 0; i < array.length; i++)
                        darr[i] = convertToFloat(array[i]);
                return darr;
        }

    
        /**
         * Convert a short array to a float array.
         * 
         * @param array
         *            array of shorts to convert
         * @return array of floats
         */
        public static float[] convertToFloat(final short[] array) {
                final float[] farr = new float[array.length];

                for (int i = 0; i < array.length; i++) {
                        farr[i] = (float) array[i];
                }
                return farr;
        }

    /**
         * Convert a short array to a float array.
         * 
         * @param array
         *            array of shorts to convert
         * @return array of doubles
         */
        public static float[][] convertToFloat(final short[][] array)
        {
                final float[][] darr = new float[array.length][];
                for (int i = 0; i < array.length; i++)
                        darr[i] = convertToFloat(array[i]);
                return darr;
        }

    
        /**
         * Return the first non-null item from an array.
         * 
         * @param <T>
         *            the type of the elements in the array
         * @param array
         *            the array
         * @return the first non-null object, or null if not found.
         */
        public static <T> T firstNonNull(final T[] array) {
                if (array == null)
                        return null;

                for (final T obj : array) {
                        if (obj != null) {
                                return obj;
                        }
                }

                return null;
        }

    
        /**
         * Concatenate multiple arrays into a single new array.
         * 
         * @param <T>
         *            Type of elements in the array.
         * @param arrays
         *            the arrays to concatenate.
         * @return the new concatenated array
         */
        @SafeVarargs
        public static <T> T[] concatenate(final T[]... arrays) {
                int length = 0;
                Class<?> type = null;

                for (final T[] arr : arrays) {
                        if (arr != null) {
                                length += arr.length;

                                if (type == null) {
                                        type = arr.getClass().getComponentType();
                                }
                        }
                }

                @SuppressWarnings("unchecked")
                final T[] concat = (T[]) Array.newInstance(type, length);

                int current = 0;
                for (final T[] arr : arrays) {
                        System.arraycopy(arr, 0, concat, current, arr.length);
                        current += arr.length;
                }

                return concat;
        }

    
        /**
         * Concatenate multiple arrays into a single new array.
         * 
         * @param arrays
         *            the arrays to concatenate.
         * @return the new concatenated array
         */
        public static double[] concatenate(final double[]... arrays) {
                int length = 0;
                for (final double[] arr : arrays) {
                        length += (arr == null ? 0 : arr.length);
                }

                final double[] concat = new double[length];

                int current = 0;
                for (final double[] arr : arrays) {
                        System.arraycopy(arr, 0, concat, current, arr.length);
                        current += arr.length;
                }

                return concat;
        }
        
         
        /**
         * Concatenate multiple arrays into a single new array.
         * 
         * @param arrays
         *            the arrays to concatenate.
         * @return the new concatenated array
         */
        public static float[] concatenate(final float[]... arrays) {
                int length = 0;
                for (final float[] arr : arrays) {
                        length += (arr == null ? 0 : arr.length);
                }

                final float[] concat = new float[length];

                int current = 0;
                for (final float[] arr : arrays) {
                        System.arraycopy(arr, 0, concat, current, arr.length);
                        current += arr.length;
                }

                return concat;
        }
        
         
        /**
         * Concatenate multiple arrays into a single new array.
         * 
         * @param arrays
         *            the arrays to concatenate.
         * @return the new concatenated array
         */
        public static int[] concatenate(final int[]... arrays) {
                int length = 0;
                for (final int[] arr : arrays) {
                        length += (arr == null ? 0 : arr.length);
                }

                final int[] concat = new int[length];

                int current = 0;
                for (final int[] arr : arrays) {
                        System.arraycopy(arr, 0, concat, current, arr.length);
                        current += arr.length;
                }

                return concat;
        }
        
         
        /**
         * Concatenate multiple arrays into a single new array.
         * 
         * @param arrays
         *            the arrays to concatenate.
         * @return the new concatenated array
         */
        public static long[] concatenate(final long[]... arrays) {
                int length = 0;
                for (final long[] arr : arrays) {
                        length += (arr == null ? 0 : arr.length);
                }

                final long[] concat = new long[length];

                int current = 0;
                for (final long[] arr : arrays) {
                        System.arraycopy(arr, 0, concat, current, arr.length);
                        current += arr.length;
                }

                return concat;
        }
        
         
        /**
         * Concatenate multiple arrays into a single new array.
         * 
         * @param arrays
         *            the arrays to concatenate.
         * @return the new concatenated array
         */
        public static byte[] concatenate(final byte[]... arrays) {
                int length = 0;
                for (final byte[] arr : arrays) {
                        length += (arr == null ? 0 : arr.length);
                }

                final byte[] concat = new byte[length];

                int current = 0;
                for (final byte[] arr : arrays) {
                        System.arraycopy(arr, 0, concat, current, arr.length);
                        current += arr.length;
                }

                return concat;
        }
        
         
        /**
         * Concatenate multiple arrays into a single new array.
         * 
         * @param arrays
         *            the arrays to concatenate.
         * @return the new concatenated array
         */
        public static short[] concatenate(final short[]... arrays) {
                int length = 0;
                for (final short[] arr : arrays) {
                        length += (arr == null ? 0 : arr.length);
                }

                final short[] concat = new short[length];

                int current = 0;
                for (final short[] arr : arrays) {
                        System.arraycopy(arr, 0, concat, current, arr.length);
                        current += arr.length;
                }

                return concat;
        }
        
         
        /**
         * Concatenate multiple arrays into a single new array.
         * 
         * @param arrays
         *            the arrays to concatenate.
         * @return the new concatenated array
         */
        public static double[][] concatenate(final double[][]... arrays) {
                final double[][] concat = new double[arrays[0].length][];
                for(int i = 0; i < concat.length; i++){
                        final double[][] row = new double[arrays.length][];
                        for(int j = 0; j < row.length; j++){
                                row[j] = arrays[j][i];
                        } 
                        concat[i] = concatenate(row);
                }
                
                return concat;
        }

        
        /**
         * Concatenate multiple arrays into a single new array.
         * 
         * @param arrays
         *            the arrays to concatenate.
         * @return the new concatenated array
         */
        public static float[][] concatenate(final float[][]... arrays) {
                final float[][] concat = new float[arrays[0].length][];
                for(int i = 0; i < concat.length; i++){
                        final float[][] row = new float[arrays.length][];
                        for(int j = 0; j < row.length; j++){
                                row[j] = arrays[j][i];
                        } 
                        concat[i] = concatenate(row);
                }
                
                return concat;
        }

        
        /**
         * Concatenate multiple arrays into a single new array.
         * 
         * @param arrays
         *            the arrays to concatenate.
         * @return the new concatenated array
         */
        public static int[][] concatenate(final int[][]... arrays) {
                final int[][] concat = new int[arrays[0].length][];
                for(int i = 0; i < concat.length; i++){
                        final int[][] row = new int[arrays.length][];
                        for(int j = 0; j < row.length; j++){
                                row[j] = arrays[j][i];
                        } 
                        concat[i] = concatenate(row);
                }
                
                return concat;
        }

        
        /**
         * Concatenate multiple arrays into a single new array.
         * 
         * @param arrays
         *            the arrays to concatenate.
         * @return the new concatenated array
         */
        public static long[][] concatenate(final long[][]... arrays) {
                final long[][] concat = new long[arrays[0].length][];
                for(int i = 0; i < concat.length; i++){
                        final long[][] row = new long[arrays.length][];
                        for(int j = 0; j < row.length; j++){
                                row[j] = arrays[j][i];
                        } 
                        concat[i] = concatenate(row);
                }
                
                return concat;
        }

        
        /**
         * Concatenate multiple arrays into a single new array.
         * 
         * @param arrays
         *            the arrays to concatenate.
         * @return the new concatenated array
         */
        public static byte[][] concatenate(final byte[][]... arrays) {
                final byte[][] concat = new byte[arrays[0].length][];
                for(int i = 0; i < concat.length; i++){
                        final byte[][] row = new byte[arrays.length][];
                        for(int j = 0; j < row.length; j++){
                                row[j] = arrays[j][i];
                        } 
                        concat[i] = concatenate(row);
                }
                
                return concat;
        }

        
        /**
         * Concatenate multiple arrays into a single new array.
         * 
         * @param arrays
         *            the arrays to concatenate.
         * @return the new concatenated array
         */
        public static short[][] concatenate(final short[][]... arrays) {
                final short[][] concat = new short[arrays[0].length][];
                for(int i = 0; i < concat.length; i++){
                        final short[][] row = new short[arrays.length][];
                        for(int j = 0; j < row.length; j++){
                                row[j] = arrays[j][i];
                        } 
                        concat[i] = concatenate(row);
                }
                
                return concat;
        }

        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static double sumValues(final double[] vector) {
                double sum = 0;

                for (final double v : vector)
                        sum += v;

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static float sumValues(final float[] vector) {
                float sum = 0;

                for (final float v : vector)
                        sum += v;

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static long sumValues(final int[] vector) {
                long sum = 0;

                for (final int v : vector)
                        sum += v;

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static long sumValues(final long[] vector) {
                long sum = 0;

                for (final long v : vector)
                        sum += v;

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static int sumValues(final byte[] vector) {
                int sum = 0;

                for (final byte v : vector)
                        sum += v;

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static int sumValues(final short[] vector) {
                int sum = 0;

                for (final short v : vector)
                        sum += v;

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in a 2d array
         * 
         * @param array
         * @return the sum of all values
         */
        public static double sumValues(final double[][] array) {
                double sum = 0;

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[i].length; j++)
                                sum += array[i][j];

                return sum;
        }

    
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in a 2d array
         * 
         * @param array
         * @return the sum of all values
         */
        public static float sumValues(final float[][] array) {
                float sum = 0;

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[i].length; j++)
                                sum += array[i][j];

                return sum;
        }

    
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in a 2d array
         * 
         * @param array
         * @return the sum of all values
         */
        public static long sumValues(final int[][] array) {
                long sum = 0;

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[i].length; j++)
                                sum += array[i][j];

                return sum;
        }

    
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in a 2d array
         * 
         * @param array
         * @return the sum of all values
         */
        public static long sumValues(final long[][] array) {
                long sum = 0;

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[i].length; j++)
                                sum += array[i][j];

                return sum;
        }

    
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in a 2d array
         * 
         * @param array
         * @return the sum of all values
         */
        public static int sumValues(final byte[][] array) {
                int sum = 0;

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[i].length; j++)
                                sum += array[i][j];

                return sum;
        }

    
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in a 2d array
         * 
         * @param array
         * @return the sum of all values
         */
        public static int sumValues(final short[][] array) {
                int sum = 0;

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[i].length; j++)
                                sum += array[i][j];

                return sum;
        }

    
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values squared in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static double sumValuesSquared(final double[] vector) {
                double sum = 0;

                for (final double v : vector)
                        sum += v * v;

                return sum;
        }

        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values squared in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static float sumValuesSquared(final float[] vector) {
                float sum = 0;

                for (final float v : vector)
                        sum += v * v;

                return sum;
        }

        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values squared in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static long sumValuesSquared(final int[] vector) {
                long sum = 0;

                for (final int v : vector)
                        sum += v * v;

                return sum;
        }

        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values squared in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static long sumValuesSquared(final long[] vector) {
                long sum = 0;

                for (final long v : vector)
                        sum += v * v;

                return sum;
        }

        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values squared in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static int sumValuesSquared(final byte[] vector) {
                int sum = 0;

                for (final byte v : vector)
                        sum += v * v;

                return sum;
        }

        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values squared in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static int sumValuesSquared(final short[] vector) {
                int sum = 0;

                for (final short v : vector)
                        sum += v * v;

                return sum;
        }

        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the cumulative sum of values in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static double[] cumulativeSum(final double[] vector) {
                double[] sum = new double[vector.length];

                if (vector.length == 0) return sum;

                sum[0] = vector[0];
                for (int i=1; i<vector.length; i++)
                        sum[i] = vector[i] + sum[i-1];

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the cumulative sum of values in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static float[] cumulativeSum(final float[] vector) {
                float[] sum = new float[vector.length];

                if (vector.length == 0) return sum;

                sum[0] = vector[0];
                for (int i=1; i<vector.length; i++)
                        sum[i] = vector[i] + sum[i-1];

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the cumulative sum of values in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static long[] cumulativeSum(final int[] vector) {
                long[] sum = new long[vector.length];

                if (vector.length == 0) return sum;

                sum[0] = vector[0];
                for (int i=1; i<vector.length; i++)
                        sum[i] = vector[i] + sum[i-1];

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the cumulative sum of values in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static long[] cumulativeSum(final long[] vector) {
                long[] sum = new long[vector.length];

                if (vector.length == 0) return sum;

                sum[0] = vector[0];
                for (int i=1; i<vector.length; i++)
                        sum[i] = vector[i] + sum[i-1];

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the cumulative sum of values in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static int[] cumulativeSum(final byte[] vector) {
                int[] sum = new int[vector.length];

                if (vector.length == 0) return sum;

                sum[0] = vector[0];
                for (int i=1; i<vector.length; i++)
                        sum[i] = vector[i] + sum[i-1];

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the cumulative sum of values in an array
         * 
         * @param vector
         * @return the sum of all values
         */
        public static int[] cumulativeSum(final short[] vector) {
                int[] sum = new int[vector.length];

                if (vector.length == 0) return sum;

                sum[0] = vector[0];
                for (int i=1; i<vector.length; i++)
                        sum[i] = vector[i] + sum[i-1];

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in each row of a 2d array
         * 
         * @param array the array 
         * @return the sum of each row
         */
        public static double[] rowSum(final double[][] array) {
                double[] sum = new double[array.length];

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[i].length; j++)
                                sum[i] += array[i][j];

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in each row of a 2d array
         * 
         * @param array the array 
         * @return the sum of each row
         */
        public static float[] rowSum(final float[][] array) {
                float[] sum = new float[array.length];

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[i].length; j++)
                                sum[i] += array[i][j];

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in each row of a 2d array
         * 
         * @param array the array 
         * @return the sum of each row
         */
        public static long[] rowSum(final int[][] array) {
                long[] sum = new long[array.length];

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[i].length; j++)
                                sum[i] += array[i][j];

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in each row of a 2d array
         * 
         * @param array the array 
         * @return the sum of each row
         */
        public static long[] rowSum(final long[][] array) {
                long[] sum = new long[array.length];

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[i].length; j++)
                                sum[i] += array[i][j];

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in each row of a 2d array
         * 
         * @param array the array 
         * @return the sum of each row
         */
        public static int[] rowSum(final byte[][] array) {
                int[] sum = new int[array.length];

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[i].length; j++)
                                sum[i] += array[i][j];

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in each row of a 2d array
         * 
         * @param array the array 
         * @return the sum of each row
         */
        public static int[] rowSum(final short[][] array) {
                int[] sum = new int[array.length];

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[i].length; j++)
                                sum[i] += array[i][j];

                return sum;
        }
        
        
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in each column of a 2d array
         * 
         * @param array the array 
         * @return the sum of each column
         */
        public static double[] colSum(final double[][] array) {
                double[] sum = new double[array[0].length];

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[0].length; j++)
                                sum[j] += array[i][j];

                return sum;
        }

    
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in each column of a 2d array
         * 
         * @param array the array 
         * @return the sum of each column
         */
        public static float[] colSum(final float[][] array) {
                float[] sum = new float[array[0].length];

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[0].length; j++)
                                sum[j] += array[i][j];

                return sum;
        }

    
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in each column of a 2d array
         * 
         * @param array the array 
         * @return the sum of each column
         */
        public static long[] colSum(final int[][] array) {
                long[] sum = new long[array[0].length];

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[0].length; j++)
                                sum[j] += array[i][j];

                return sum;
        }

    
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in each column of a 2d array
         * 
         * @param array the array 
         * @return the sum of each column
         */
        public static long[] colSum(final long[][] array) {
                long[] sum = new long[array[0].length];

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[0].length; j++)
                                sum[j] += array[i][j];

                return sum;
        }

    
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in each column of a 2d array
         * 
         * @param array the array 
         * @return the sum of each column
         */
        public static int[] colSum(final byte[][] array) {
                int[] sum = new int[array[0].length];

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[0].length; j++)
                                sum[j] += array[i][j];

                return sum;
        }

    
        /*** 
        { m -> 
                if (m['T'] == DOUBLE) {
                        return (m['R'] == DOUBLE);              
                }
                if (m['T'] == LONG) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == INT) {
                        return (m['R'] == LONG);
                }
                if (m['T'] == SHORT) {
                        return (m['R'] == INT);
                }
                if (m['T'] == BYTE) {
                        return (m['R'] == INT);
                }
                return (m['R'] == FLOAT);
        }
    ***/
        /**
         * Compute the sum of values in each column of a 2d array
         * 
         * @param array the array 
         * @return the sum of each column
         */
        public static int[] colSum(final short[][] array) {
                int[] sum = new int[array[0].length];

                for (int i=0; i<array.length; i++)
                        for (int j=0; j<array[0].length; j++)
                                sum[j] += array[i][j];

                return sum;
        }

    
        /**
         * Extract a range
         * 
         * @param start
         * @param length
         * @return [start...length] (inclusive)
         */
        public static int[] range(final int start, final int length) {
                final int[] range = new int[length - start + 1];
                for (int i = start; i <= length; i++) {
                        range[i - start] = i;
                }
                return range;
        }

    
        /**
         * Find the given value in the array, and return all indices at which it occurs.
         * 
         * @param a
         *            array to search
         * @param value
         *                        value to search for
         * @return the found values
         */
        public static int[] search(final double[] a, double value) {
                int count = 0;

                for (int i = 0; i < a.length; i++)
                        if (a[i] == value) 
                                count++;
                
                int [] ret = new int[count];
                for (int i = 0, j=0; i < a.length; i++)
                        if (a[i] == value) ret[j++] = i;
                
                return ret;
        }

    
        /**
         * Find the given value in the array, and return all indices at which it occurs.
         * 
         * @param a
         *            array to search
         * @param value
         *                        value to search for
         * @return the found values
         */
        public static int[] search(final float[] a, float value) {
                int count = 0;

                for (int i = 0; i < a.length; i++)
                        if (a[i] == value) 
                                count++;
                
                int [] ret = new int[count];
                for (int i = 0, j=0; i < a.length; i++)
                        if (a[i] == value) ret[j++] = i;
                
                return ret;
        }

    
        /**
         * Find the given value in the array, and return all indices at which it occurs.
         * 
         * @param a
         *            array to search
         * @param value
         *                        value to search for
         * @return the found values
         */
        public static int[] search(final int[] a, int value) {
                int count = 0;

                for (int i = 0; i < a.length; i++)
                        if (a[i] == value) 
                                count++;
                
                int [] ret = new int[count];
                for (int i = 0, j=0; i < a.length; i++)
                        if (a[i] == value) ret[j++] = i;
                
                return ret;
        }

    
        /**
         * Find the given value in the array, and return all indices at which it occurs.
         * 
         * @param a
         *            array to search
         * @param value
         *                        value to search for
         * @return the found values
         */
        public static int[] search(final long[] a, long value) {
                int count = 0;

                for (int i = 0; i < a.length; i++)
                        if (a[i] == value) 
                                count++;
                
                int [] ret = new int[count];
                for (int i = 0, j=0; i < a.length; i++)
                        if (a[i] == value) ret[j++] = i;
                
                return ret;
        }

    
        /**
         * Find the given value in the array, and return all indices at which it occurs.
         * 
         * @param a
         *            array to search
         * @param value
         *                        value to search for
         * @return the found values
         */
        public static int[] search(final byte[] a, byte value) {
                int count = 0;

                for (int i = 0; i < a.length; i++)
                        if (a[i] == value) 
                                count++;
                
                int [] ret = new int[count];
                for (int i = 0, j=0; i < a.length; i++)
                        if (a[i] == value) ret[j++] = i;
                
                return ret;
        }

    
        /**
         * Find the given value in the array, and return all indices at which it occurs.
         * 
         * @param a
         *            array to search
         * @param value
         *                        value to search for
         * @return the found values
         */
        public static int[] search(final short[] a, short value) {
                int count = 0;

                for (int i = 0; i < a.length; i++)
                        if (a[i] == value) 
                                count++;
                
                int [] ret = new int[count];
                for (int i = 0, j=0; i < a.length; i++)
                        if (a[i] == value) ret[j++] = i;
                
                return ret;
        }

    
        /**
         * Reshape a 2D array into a 1D array
         * 
         * @param a
         *            array to reshape
         * @return the reshaped array
         */
        public static double[] reshape(final double[][] a) {
                final double[] ret = new double[a.length * a[0].length];

                for (int r = 0, i = 0; r < a.length; r++)
                        for (int c = 0; c < a[0].length; c++, i++)
                                ret[i] = a[r][c];

                return ret;
        }

    
        /**
         * Reshape a 2D array into a 1D array
         * 
         * @param a
         *            array to reshape
         * @return the reshaped array
         */
        public static float[] reshape(final float[][] a) {
                final float[] ret = new float[a.length * a[0].length];

                for (int r = 0, i = 0; r < a.length; r++)
                        for (int c = 0; c < a[0].length; c++, i++)
                                ret[i] = a[r][c];

                return ret;
        }

    
        /**
         * Reshape a 2D array into a 1D array
         * 
         * @param a
         *            array to reshape
         * @return the reshaped array
         */
        public static int[] reshape(final int[][] a) {
                final int[] ret = new int[a.length * a[0].length];

                for (int r = 0, i = 0; r < a.length; r++)
                        for (int c = 0; c < a[0].length; c++, i++)
                                ret[i] = a[r][c];

                return ret;
        }

    
        /**
         * Reshape a 2D array into a 1D array
         * 
         * @param a
         *            array to reshape
         * @return the reshaped array
         */
        public static long[] reshape(final long[][] a) {
                final long[] ret = new long[a.length * a[0].length];

                for (int r = 0, i = 0; r < a.length; r++)
                        for (int c = 0; c < a[0].length; c++, i++)
                                ret[i] = a[r][c];

                return ret;
        }

    
        /**
         * Reshape a 2D array into a 1D array
         * 
         * @param a
         *            array to reshape
         * @return the reshaped array
         */
        public static byte[] reshape(final byte[][] a) {
                final byte[] ret = new byte[a.length * a[0].length];

                for (int r = 0, i = 0; r < a.length; r++)
                        for (int c = 0; c < a[0].length; c++, i++)
                                ret[i] = a[r][c];

                return ret;
        }

    
        /**
         * Reshape a 2D array into a 1D array
         * 
         * @param a
         *            array to reshape
         * @return the reshaped array
         */
        public static short[] reshape(final short[][] a) {
                final short[] ret = new short[a.length * a[0].length];

                for (int r = 0, i = 0; r < a.length; r++)
                        for (int c = 0; c < a[0].length; c++, i++)
                                ret[i] = a[r][c];

                return ret;
        }

    
        /**
         * Reshape a 2D array into a 1D array of doubles
         * 
         * @param a
         *            array to reshape
         * @return the reshaped array
         */
        public static double[] reshapeDouble(final double[][] a) {
                final double[] ret = new double[a.length * a[0].length];

                for (int r = 0, i = 0; r < a.length; r++)
                        for (int c = 0; c < a[0].length; c++, i++)
                                ret[i] = a[r][c];

                return ret;
        }

    
        /**
         * Reshape a 2D array into a 1D array of doubles
         * 
         * @param a
         *            array to reshape
         * @return the reshaped array
         */
        public static double[] reshapeDouble(final float[][] a) {
                final double[] ret = new double[a.length * a[0].length];

                for (int r = 0, i = 0; r < a.length; r++)
                        for (int c = 0; c < a[0].length; c++, i++)
                                ret[i] = a[r][c];

                return ret;
        }

    
        /**
         * Reshape a 2D array into a 1D array of doubles
         * 
         * @param a
         *            array to reshape
         * @return the reshaped array
         */
        public static double[] reshapeDouble(final int[][] a) {
                final double[] ret = new double[a.length * a[0].length];

                for (int r = 0, i = 0; r < a.length; r++)
                        for (int c = 0; c < a[0].length; c++, i++)
                                ret[i] = a[r][c];

                return ret;
        }

    
        /**
         * Reshape a 2D array into a 1D array of doubles
         * 
         * @param a
         *            array to reshape
         * @return the reshaped array
         */
        public static double[] reshapeDouble(final long[][] a) {
                final double[] ret = new double[a.length * a[0].length];

                for (int r = 0, i = 0; r < a.length; r++)
                        for (int c = 0; c < a[0].length; c++, i++)
                                ret[i] = a[r][c];

                return ret;
        }

    
        /**
         * Reshape a 2D array into a 1D array of doubles
         * 
         * @param a
         *            array to reshape
         * @return the reshaped array
         */
        public static double[] reshapeDouble(final byte[][] a) {
                final double[] ret = new double[a.length * a[0].length];

                for (int r = 0, i = 0; r < a.length; r++)
                        for (int c = 0; c < a[0].length; c++, i++)
                                ret[i] = a[r][c];

                return ret;
        }

    
        /**
         * Reshape a 2D array into a 1D array of doubles
         * 
         * @param a
         *            array to reshape
         * @return the reshaped array
         */
        public static double[] reshapeDouble(final short[][] a) {
                final double[] ret = new double[a.length * a[0].length];

                for (int r = 0, i = 0; r < a.length; r++)
                        for (int c = 0; c < a[0].length; c++, i++)
                                ret[i] = a[r][c];

                return ret;
        }

    
        /**
         * Reshape a 1D array into a 2D array
         * 
         * @param a
         *            array to reshape
         * @param out
         *            the return array, correctly sized
         * @return the reshaped array
         */
        public static double[][] reshape(final double[] a, final double[][] out) {
                for (int r = 0, i = 0; r < out.length; r++)
                        for (int c = 0; c < out[0].length; c++, i++)
                                out[r][c] = a[i];

                return out;
        }

        /**
         * Reshape a 1D array into a 2D array
         * 
         * @param a
         *            array to reshape
         * @param width
         *            the width of the return array
         * @param height
         *            the height of the return array
         * @return the reshaped array
         */
        public static double[][] reshape(final double[] a, final int width, final int height) {
                final double[][] ret = new double[height][width];
                return reshape(a, ret);
        }

    
        /**
         * Reshape a 1D array into a 2D array
         * 
         * @param a
         *            array to reshape
         * @param out
         *            the return array, correctly sized
         * @return the reshaped array
         */
        public static float[][] reshape(final float[] a, final float[][] out) {
                for (int r = 0, i = 0; r < out.length; r++)
                        for (int c = 0; c < out[0].length; c++, i++)
                                out[r][c] = a[i];

                return out;
        }

        /**
         * Reshape a 1D array into a 2D array
         * 
         * @param a
         *            array to reshape
         * @param width
         *            the width of the return array
         * @param height
         *            the height of the return array
         * @return the reshaped array
         */
        public static float[][] reshape(final float[] a, final int width, final int height) {
                final float[][] ret = new float[height][width];
                return reshape(a, ret);
        }

    
        /**
         * Reshape a 1D array into a 2D array
         * 
         * @param a
         *            array to reshape
         * @param out
         *            the return array, correctly sized
         * @return the reshaped array
         */
        public static int[][] reshape(final int[] a, final int[][] out) {
                for (int r = 0, i = 0; r < out.length; r++)
                        for (int c = 0; c < out[0].length; c++, i++)
                                out[r][c] = a[i];

                return out;
        }

        /**
         * Reshape a 1D array into a 2D array
         * 
         * @param a
         *            array to reshape
         * @param width
         *            the width of the return array
         * @param height
         *            the height of the return array
         * @return the reshaped array
         */
        public static int[][] reshape(final int[] a, final int width, final int height) {
                final int[][] ret = new int[height][width];
                return reshape(a, ret);
        }

    
        /**
         * Reshape a 1D array into a 2D array
         * 
         * @param a
         *            array to reshape
         * @param out
         *            the return array, correctly sized
         * @return the reshaped array
         */
        public static long[][] reshape(final long[] a, final long[][] out) {
                for (int r = 0, i = 0; r < out.length; r++)
                        for (int c = 0; c < out[0].length; c++, i++)
                                out[r][c] = a[i];

                return out;
        }

        /**
         * Reshape a 1D array into a 2D array
         * 
         * @param a
         *            array to reshape
         * @param width
         *            the width of the return array
         * @param height
         *            the height of the return array
         * @return the reshaped array
         */
        public static long[][] reshape(final long[] a, final int width, final int height) {
                final long[][] ret = new long[height][width];
                return reshape(a, ret);
        }

    
        /**
         * Reshape a 1D array into a 2D array
         * 
         * @param a
         *            array to reshape
         * @param out
         *            the return array, correctly sized
         * @return the reshaped array
         */
        public static byte[][] reshape(final byte[] a, final byte[][] out) {
                for (int r = 0, i = 0; r < out.length; r++)
                        for (int c = 0; c < out[0].length; c++, i++)
                                out[r][c] = a[i];

                return out;
        }

        /**
         * Reshape a 1D array into a 2D array
         * 
         * @param a
         *            array to reshape
         * @param width
         *            the width of the return array
         * @param height
         *            the height of the return array
         * @return the reshaped array
         */
        public static byte[][] reshape(final byte[] a, final int width, final int height) {
                final byte[][] ret = new byte[height][width];
                return reshape(a, ret);
        }

    
        /**
         * Reshape a 1D array into a 2D array
         * 
         * @param a
         *            array to reshape
         * @param out
         *            the return array, correctly sized
         * @return the reshaped array
         */
        public static short[][] reshape(final short[] a, final short[][] out) {
                for (int r = 0, i = 0; r < out.length; r++)
                        for (int c = 0; c < out[0].length; c++, i++)
                                out[r][c] = a[i];

                return out;
        }

        /**
         * Reshape a 1D array into a 2D array
         * 
         * @param a
         *            array to reshape
         * @param width
         *            the width of the return array
         * @param height
         *            the height of the return array
         * @return the reshaped array
         */
        public static short[][] reshape(final short[] a, final int width, final int height) {
                final short[][] ret = new short[height][width];
                return reshape(a, ret);
        }

    
        /**
         * Reshape a 1D array into a 2D array
         * 
         * @param a
         *            array to reshape
         * @param out
         *            the return array, correctly sized
         * @return the reshaped array
         */
        public static float[][] reshapeFloat(final double[] a, final float[][] out) {
                for (int r = 0, i = 0; r < out.length; r++)
                        for (int c = 0; c < out[0].length; c++, i++)
                                out[r][c] = (float) a[i];

                return out;
        }

        /**
         * Reshape a 1D array into a 2D array
         * 
         * @param a
         *            array to reshape
         * @param width
         *            the width of the return array
         * @param height
         *            the height of the return array
         * @return the reshaped array
         */
        public static float[][] reshapeFloat(final double[] a, final int width, final int height) {
                final float[][] ret = new float[height][width];
                return reshapeFloat(a, ret);
        }

    
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final double[] main, final double[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final double[] main, final double[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final double[] a, final double[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final double[] main, final float[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final double[] main, final float[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final double[] a, final float[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final double[] main, final int[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final double[] main, final int[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final double[] a, final int[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final double[] main, final long[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final double[] main, final long[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final double[] a, final long[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final double[] main, final byte[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final double[] main, final byte[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final double[] a, final byte[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final double[] main, final short[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final double[] main, final short[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final double[] a, final short[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final float[] main, final double[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final float[] main, final double[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final float[] a, final double[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final float[] main, final float[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final float[] main, final float[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final float[] a, final float[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final float[] main, final int[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final float[] main, final int[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final float[] a, final int[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final float[] main, final long[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final float[] main, final long[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final float[] a, final long[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final float[] main, final byte[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final float[] main, final byte[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final float[] a, final byte[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final float[] main, final short[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final float[] main, final short[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final float[] a, final short[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final int[] main, final double[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final int[] main, final double[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final int[] a, final double[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final int[] main, final float[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final int[] main, final float[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final int[] a, final float[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final int[] main, final int[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final int[] main, final int[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final int[] a, final int[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final int[] main, final long[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final int[] main, final long[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final int[] a, final long[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final int[] main, final byte[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final int[] main, final byte[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final int[] a, final byte[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final int[] main, final short[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final int[] main, final short[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final int[] a, final short[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final long[] main, final double[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final long[] main, final double[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final long[] a, final double[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final long[] main, final float[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final long[] main, final float[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final long[] a, final float[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final long[] main, final int[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final long[] main, final int[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final long[] a, final int[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final long[] main, final long[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final long[] main, final long[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final long[] a, final long[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final long[] main, final byte[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final long[] main, final byte[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final long[] a, final byte[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final long[] main, final short[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final long[] main, final short[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final long[] a, final short[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final byte[] main, final double[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final byte[] main, final double[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final byte[] a, final double[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final byte[] main, final float[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final byte[] main, final float[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final byte[] a, final float[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final byte[] main, final int[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final byte[] main, final int[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final byte[] a, final int[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final byte[] main, final long[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final byte[] main, final long[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final byte[] a, final long[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final byte[] main, final byte[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final byte[] main, final byte[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final byte[] a, final byte[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final byte[] main, final short[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final byte[] main, final short[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final byte[] a, final short[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final short[] main, final double[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final short[] main, final double[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final short[] a, final double[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final short[] main, final float[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final short[] main, final float[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final short[] a, final float[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final short[] main, final int[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final short[] main, final int[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final short[] a, final int[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final short[] main, final long[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final short[] main, final long[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final short[] a, final long[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final short[] main, final byte[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final short[] main, final byte[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final short[] a, final byte[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortDescending(final short[] main, final short[] indices) {
                parallelQuicksortDescending(main, indices, 0, indices.length - 1);
        }

        /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into descending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void parallelQuicksortDescending(final short[] main, final short[] indices, final int left,
                        final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionDesc(main, indices, left, right);

                parallelQuicksortDescending(main, indices, left, i - 1);
                parallelQuicksortDescending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionDesc(final short[] a, final short[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] > a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] > a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }
        
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final double[] main, final double[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final double[] main, final double[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final double[] a, final double[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final double[] main, final float[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final double[] main, final float[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final double[] a, final float[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final double[] main, final int[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final double[] main, final int[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final double[] a, final int[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final double[] main, final long[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final double[] main, final long[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final double[] a, final long[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final double[] main, final byte[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final double[] main, final byte[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final double[] a, final byte[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final double[] main, final short[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final double[] main, final short[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final double[] a, final short[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final float[] main, final double[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final float[] main, final double[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final float[] a, final double[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final float[] main, final float[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final float[] main, final float[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final float[] a, final float[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final float[] main, final int[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final float[] main, final int[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final float[] a, final int[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final float[] main, final long[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final float[] main, final long[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final float[] a, final long[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final float[] main, final byte[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final float[] main, final byte[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final float[] a, final byte[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final float[] main, final short[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final float[] main, final short[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final float[] a, final short[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final int[] main, final double[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final int[] main, final double[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final int[] a, final double[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final int[] main, final float[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final int[] main, final float[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final int[] a, final float[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final int[] main, final int[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final int[] main, final int[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final int[] a, final int[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final int[] main, final long[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final int[] main, final long[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final int[] a, final long[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final int[] main, final byte[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final int[] main, final byte[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final int[] a, final byte[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final int[] main, final short[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final int[] main, final short[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final int[] a, final short[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final long[] main, final double[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final long[] main, final double[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final long[] a, final double[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final long[] main, final float[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final long[] main, final float[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final long[] a, final float[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final long[] main, final int[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final long[] main, final int[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final long[] a, final int[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final long[] main, final long[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final long[] main, final long[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final long[] a, final long[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final long[] main, final byte[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final long[] main, final byte[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final long[] a, final byte[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final long[] main, final short[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final long[] main, final short[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final long[] a, final short[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final byte[] main, final double[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final byte[] main, final double[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final byte[] a, final double[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final byte[] main, final float[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final byte[] main, final float[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final byte[] a, final float[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final byte[] main, final int[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final byte[] main, final int[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final byte[] a, final int[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final byte[] main, final long[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final byte[] main, final long[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final byte[] a, final long[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final byte[] main, final byte[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final byte[] main, final byte[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final byte[] a, final byte[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final byte[] main, final short[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final byte[] main, final short[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final byte[] a, final short[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final short[] main, final double[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final short[] main, final double[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final short[] a, final double[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final short[] main, final float[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final short[] main, final float[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final short[] a, final float[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final short[] main, final int[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final short[] main, final int[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final short[] a, final int[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final short[] main, final long[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final short[] main, final long[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final short[] a, final long[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final short[] main, final byte[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final short[] main, final byte[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final short[] a, final byte[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         */
        public static void parallelQuicksortAscending(final short[] main, final short[] indices) {
                ArrayUtils.parallelQuicksortAscending(main, indices, 0, indices.length - 1);
        }
        
    /**
         * Sort parallel arrays. Arrays are sorted in-place. The first array
         * determines the order, and is sorted into ascending order.
         * <p>
         * Implementation inspired by this stackoverflow page: <a href=
         * "http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-get-a-sorted-list-of-indices-of-an-array"
         * > http://stackoverflow.com/questions/951848/java-array-sort-quick-way-to-
         * get-a-sorted-list-of-indices-of-an-array </a>
         * 
         * @param main
         *            the values to use for determining the order
         * @param indices
         *            the second array
         * @param left
         *            the starting index
         * @param right
         *            the ending index
         */
        public static void
                        parallelQuicksortAscending(final short[] main, final short[] indices, final int left, final int right)
        {
                if (right <= left)
                        return;

                final int i = partitionAsc(main, indices, left, right);

                parallelQuicksortAscending(main, indices, left, i - 1);
                parallelQuicksortAscending(main, indices, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partitionAsc(final short[] a, final short[] index, final int left, final int right) {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[++i] < a[right])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[right] < a[--j])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(a, index, i, j); // swap two elements into place
                }
                exch(a, index, i, right); // swap with partition element
                return i;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final double[] a, final double[] index, final int i, final int j) {
                final double swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final double b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final double[] a, final float[] index, final int i, final int j) {
                final double swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final float b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final double[] a, final int[] index, final int i, final int j) {
                final double swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final int b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final double[] a, final long[] index, final int i, final int j) {
                final double swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final long b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final double[] a, final byte[] index, final int i, final int j) {
                final double swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final byte b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final double[] a, final short[] index, final int i, final int j) {
                final double swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final short b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final float[] a, final double[] index, final int i, final int j) {
                final float swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final double b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final float[] a, final float[] index, final int i, final int j) {
                final float swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final float b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final float[] a, final int[] index, final int i, final int j) {
                final float swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final int b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final float[] a, final long[] index, final int i, final int j) {
                final float swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final long b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final float[] a, final byte[] index, final int i, final int j) {
                final float swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final byte b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final float[] a, final short[] index, final int i, final int j) {
                final float swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final short b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final int[] a, final double[] index, final int i, final int j) {
                final int swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final double b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final int[] a, final float[] index, final int i, final int j) {
                final int swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final float b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final int[] a, final int[] index, final int i, final int j) {
                final int swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final int b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final int[] a, final long[] index, final int i, final int j) {
                final int swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final long b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final int[] a, final byte[] index, final int i, final int j) {
                final int swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final byte b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final int[] a, final short[] index, final int i, final int j) {
                final int swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final short b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final long[] a, final double[] index, final int i, final int j) {
                final long swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final double b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final long[] a, final float[] index, final int i, final int j) {
                final long swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final float b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final long[] a, final int[] index, final int i, final int j) {
                final long swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final int b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final long[] a, final long[] index, final int i, final int j) {
                final long swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final long b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final long[] a, final byte[] index, final int i, final int j) {
                final long swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final byte b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final long[] a, final short[] index, final int i, final int j) {
                final long swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final short b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final byte[] a, final double[] index, final int i, final int j) {
                final byte swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final double b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final byte[] a, final float[] index, final int i, final int j) {
                final byte swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final float b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final byte[] a, final int[] index, final int i, final int j) {
                final byte swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final int b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final byte[] a, final long[] index, final int i, final int j) {
                final byte swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final long b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final byte[] a, final byte[] index, final int i, final int j) {
                final byte swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final byte b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final byte[] a, final short[] index, final int i, final int j) {
                final byte swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final short b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final short[] a, final double[] index, final int i, final int j) {
                final short swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final double b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final short[] a, final float[] index, final int i, final int j) {
                final short swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final float b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final short[] a, final int[] index, final int i, final int j) {
                final short swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final int b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final short[] a, final long[] index, final int i, final int j) {
                final short swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final long b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final short[] a, final byte[] index, final int i, final int j) {
                final short swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final byte b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
    // exchange a[i] and a[j]
        private static void exch(final short[] a, final short[] index, final int i, final int j) {
                final short swap = a[i];
                a[i] = a[j];
                a[j] = swap;

                final short b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
        /**
         * Determine the indices of the given array if it were to be sorted into
         * ascending order.
         * 
         * @param arr
         *            the array
         * @return the sorted indices
         */
        public static int[] indexSort(final double[] arr) {
                final int[] index = new int[arr.length];

                for (int i = 0; i < index.length; i++)
                        index[i] = i;

                quicksort(arr, index, 0, index.length - 1);

                return index;
        }

        // quicksort a[left] to a[right]
        private static void quicksort(final double[] a, final int[] index, final int left, final int right) {
                if (right <= left)
                        return;
                final int i = partition(a, index, left, right);
                quicksort(a, index, left, i - 1);
                quicksort(a, index, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partition(final double[] a, final int[] index,
                        final int left, final int right)
        {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[index[++i]] < a[index[right]])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[index[right]] < a[index[--j]])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(index, i, j); // swap two elements into place
                }
                exch(index, i, right); // swap with partition element
                return i;
        }

    
        /**
         * Determine the indices of the given array if it were to be sorted into
         * ascending order.
         * 
         * @param arr
         *            the array
         * @return the sorted indices
         */
        public static int[] indexSort(final float[] arr) {
                final int[] index = new int[arr.length];

                for (int i = 0; i < index.length; i++)
                        index[i] = i;

                quicksort(arr, index, 0, index.length - 1);

                return index;
        }

        // quicksort a[left] to a[right]
        private static void quicksort(final float[] a, final int[] index, final int left, final int right) {
                if (right <= left)
                        return;
                final int i = partition(a, index, left, right);
                quicksort(a, index, left, i - 1);
                quicksort(a, index, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partition(final float[] a, final int[] index,
                        final int left, final int right)
        {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[index[++i]] < a[index[right]])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[index[right]] < a[index[--j]])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(index, i, j); // swap two elements into place
                }
                exch(index, i, right); // swap with partition element
                return i;
        }

    
        /**
         * Determine the indices of the given array if it were to be sorted into
         * ascending order.
         * 
         * @param arr
         *            the array
         * @return the sorted indices
         */
        public static int[] indexSort(final int[] arr) {
                final int[] index = new int[arr.length];

                for (int i = 0; i < index.length; i++)
                        index[i] = i;

                quicksort(arr, index, 0, index.length - 1);

                return index;
        }

        // quicksort a[left] to a[right]
        private static void quicksort(final int[] a, final int[] index, final int left, final int right) {
                if (right <= left)
                        return;
                final int i = partition(a, index, left, right);
                quicksort(a, index, left, i - 1);
                quicksort(a, index, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partition(final int[] a, final int[] index,
                        final int left, final int right)
        {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[index[++i]] < a[index[right]])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[index[right]] < a[index[--j]])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(index, i, j); // swap two elements into place
                }
                exch(index, i, right); // swap with partition element
                return i;
        }

    
        /**
         * Determine the indices of the given array if it were to be sorted into
         * ascending order.
         * 
         * @param arr
         *            the array
         * @return the sorted indices
         */
        public static int[] indexSort(final long[] arr) {
                final int[] index = new int[arr.length];

                for (int i = 0; i < index.length; i++)
                        index[i] = i;

                quicksort(arr, index, 0, index.length - 1);

                return index;
        }

        // quicksort a[left] to a[right]
        private static void quicksort(final long[] a, final int[] index, final int left, final int right) {
                if (right <= left)
                        return;
                final int i = partition(a, index, left, right);
                quicksort(a, index, left, i - 1);
                quicksort(a, index, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partition(final long[] a, final int[] index,
                        final int left, final int right)
        {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[index[++i]] < a[index[right]])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[index[right]] < a[index[--j]])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(index, i, j); // swap two elements into place
                }
                exch(index, i, right); // swap with partition element
                return i;
        }

    
        /**
         * Determine the indices of the given array if it were to be sorted into
         * ascending order.
         * 
         * @param arr
         *            the array
         * @return the sorted indices
         */
        public static int[] indexSort(final byte[] arr) {
                final int[] index = new int[arr.length];

                for (int i = 0; i < index.length; i++)
                        index[i] = i;

                quicksort(arr, index, 0, index.length - 1);

                return index;
        }

        // quicksort a[left] to a[right]
        private static void quicksort(final byte[] a, final int[] index, final int left, final int right) {
                if (right <= left)
                        return;
                final int i = partition(a, index, left, right);
                quicksort(a, index, left, i - 1);
                quicksort(a, index, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partition(final byte[] a, final int[] index,
                        final int left, final int right)
        {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[index[++i]] < a[index[right]])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[index[right]] < a[index[--j]])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(index, i, j); // swap two elements into place
                }
                exch(index, i, right); // swap with partition element
                return i;
        }

    
        /**
         * Determine the indices of the given array if it were to be sorted into
         * ascending order.
         * 
         * @param arr
         *            the array
         * @return the sorted indices
         */
        public static int[] indexSort(final short[] arr) {
                final int[] index = new int[arr.length];

                for (int i = 0; i < index.length; i++)
                        index[i] = i;

                quicksort(arr, index, 0, index.length - 1);

                return index;
        }

        // quicksort a[left] to a[right]
        private static void quicksort(final short[] a, final int[] index, final int left, final int right) {
                if (right <= left)
                        return;
                final int i = partition(a, index, left, right);
                quicksort(a, index, left, i - 1);
                quicksort(a, index, i + 1, right);
        }

        // partition a[left] to a[right], assumes left < right
        private static int partition(final short[] a, final int[] index,
                        final int left, final int right)
        {
                int i = left - 1;
                int j = right;
                while (true) {
                        while (a[index[++i]] < a[index[right]])
                                // find item on left to swap
                                ; // a[right] acts as sentinel
                        while (a[index[right]] < a[index[--j]])
                                // find item on right to swap
                                if (j == left)
                                        break; // don't go out-of-bounds
                        if (i >= j)
                                break; // check if pointers cross
                        exch(index, i, j); // swap two elements into place
                }
                exch(index, i, right); // swap with partition element
                return i;
        }

    
        // exchange a[i] and a[j]
        static void exch(final int[] index, final int i, final int j) {
                final int b = index[i];
                index[i] = index[j];
                index[j] = b;
        }

    
        /**
         * Normalise and scale the values so that the maximum value in the array is
         * 1.
         * 
         * @param array
         *            The array to normalise
         * @return The array
         */
        public static double[] normaliseMax(final double[] array) {
                return normaliseMax(array, 1d);
        }

        /**
         * Normalise and scale the values so that the maximum value in the array is
         * max
         * 
         * @param array
         *            The array to normalise
         * @param max
         *            The maximum value
         * @return The array
         */
        public static double[] normaliseMax(final double[] array, final double max) {
                final double m = maxValue(array);
                for (int i = 0; i < array.length; i++)
                        array[i] = (array[i] / m) * max;
                return array;
        }

    
        /**
         * Convert the array to a {@link String} by joining the elements with the
         * given glue.
         * 
         * @param s
         *            the array
         * @param glue
         *            the glue
         * @return the string
         */
        public static String toString(final String[] s, final String glue) {
                final int k = s.length;

                if (k == 0)
                        return null;

                final StringBuilder out = new StringBuilder();
                out.append(s[0]);

                for (int x = 1; x < k; ++x)
                        out.append(glue).append(s[x]);

                return out.toString();
        }

    
        /**
         * Fill the array with the value
         * 
         * @param a1
         *            The array
         * @param i
         *            The value
         * @return The array
         */
        public static double[][] fill(final double[][] a1, final double i)
        {
                for (int j = 0; j < a1.length; j++)
                        fill(a1[j], i);
                return a1;
        }

        /**
         * Fill the array with the value from the start index for the length given
         * 
         * @param a1
         *            The array to fill
         * @param i
         *            The value to fill with
         * @param s
         *            The start index
         * @param l
         *            The length of the fill
         * @return The array
         */
        public static double[] fill(final double[] a1, final double i, final int s, final int l)
        {
                for (int j = s; j < s + l; j++)
                        a1[j] = i;
                return a1;
        }

        /**
         * Fill the array with the value
         * 
         * @param a1
         *            The array
         * @param i
         *            The value
         * @return The array
         */
        public static double[] fill(final double[] a1, final double i)
        {
                for (int j = 0; j < a1.length; j++)
                        a1[j] = i;
                return a1;
        }

    
        /**
         * Fill the array with the value
         * 
         * @param a1
         *            The array
         * @param i
         *            The value
         * @return The array
         */
        public static float[][] fill(final float[][] a1, final float i)
        {
                for (int j = 0; j < a1.length; j++)
                        fill(a1[j], i);
                return a1;
        }

        /**
         * Fill the array with the value from the start index for the length given
         * 
         * @param a1
         *            The array to fill
         * @param i
         *            The value to fill with
         * @param s
         *            The start index
         * @param l
         *            The length of the fill
         * @return The array
         */
        public static float[] fill(final float[] a1, final float i, final int s, final int l)
        {
                for (int j = s; j < s + l; j++)
                        a1[j] = i;
                return a1;
        }

        /**
         * Fill the array with the value
         * 
         * @param a1
         *            The array
         * @param i
         *            The value
         * @return The array
         */
        public static float[] fill(final float[] a1, final float i)
        {
                for (int j = 0; j < a1.length; j++)
                        a1[j] = i;
                return a1;
        }

    
        /**
         * Fill the array with the value
         * 
         * @param a1
         *            The array
         * @param i
         *            The value
         * @return The array
         */
        public static int[][] fill(final int[][] a1, final int i)
        {
                for (int j = 0; j < a1.length; j++)
                        fill(a1[j], i);
                return a1;
        }

        /**
         * Fill the array with the value from the start index for the length given
         * 
         * @param a1
         *            The array to fill
         * @param i
         *            The value to fill with
         * @param s
         *            The start index
         * @param l
         *            The length of the fill
         * @return The array
         */
        public static int[] fill(final int[] a1, final int i, final int s, final int l)
        {
                for (int j = s; j < s + l; j++)
                        a1[j] = i;
                return a1;
        }

        /**
         * Fill the array with the value
         * 
         * @param a1
         *            The array
         * @param i
         *            The value
         * @return The array
         */
        public static int[] fill(final int[] a1, final int i)
        {
                for (int j = 0; j < a1.length; j++)
                        a1[j] = i;
                return a1;
        }

    
        /**
         * Fill the array with the value
         * 
         * @param a1
         *            The array
         * @param i
         *            The value
         * @return The array
         */
        public static long[][] fill(final long[][] a1, final long i)
        {
                for (int j = 0; j < a1.length; j++)
                        fill(a1[j], i);
                return a1;
        }

        /**
         * Fill the array with the value from the start index for the length given
         * 
         * @param a1
         *            The array to fill
         * @param i
         *            The value to fill with
         * @param s
         *            The start index
         * @param l
         *            The length of the fill
         * @return The array
         */
        public static long[] fill(final long[] a1, final long i, final int s, final int l)
        {
                for (int j = s; j < s + l; j++)
                        a1[j] = i;
                return a1;
        }

        /**
         * Fill the array with the value
         * 
         * @param a1
         *            The array
         * @param i
         *            The value
         * @return The array
         */
        public static long[] fill(final long[] a1, final long i)
        {
                for (int j = 0; j < a1.length; j++)
                        a1[j] = i;
                return a1;
        }

    
        /**
         * Fill the array with the value
         * 
         * @param a1
         *            The array
         * @param i
         *            The value
         * @return The array
         */
        public static byte[][] fill(final byte[][] a1, final byte i)
        {
                for (int j = 0; j < a1.length; j++)
                        fill(a1[j], i);
                return a1;
        }

        /**
         * Fill the array with the value from the start index for the length given
         * 
         * @param a1
         *            The array to fill
         * @param i
         *            The value to fill with
         * @param s
         *            The start index
         * @param l
         *            The length of the fill
         * @return The array
         */
        public static byte[] fill(final byte[] a1, final byte i, final int s, final int l)
        {
                for (int j = s; j < s + l; j++)
                        a1[j] = i;
                return a1;
        }

        /**
         * Fill the array with the value
         * 
         * @param a1
         *            The array
         * @param i
         *            The value
         * @return The array
         */
        public static byte[] fill(final byte[] a1, final byte i)
        {
                for (int j = 0; j < a1.length; j++)
                        a1[j] = i;
                return a1;
        }

    
        /**
         * Fill the array with the value
         * 
         * @param a1
         *            The array
         * @param i
         *            The value
         * @return The array
         */
        public static short[][] fill(final short[][] a1, final short i)
        {
                for (int j = 0; j < a1.length; j++)
                        fill(a1[j], i);
                return a1;
        }

        /**
         * Fill the array with the value from the start index for the length given
         * 
         * @param a1
         *            The array to fill
         * @param i
         *            The value to fill with
         * @param s
         *            The start index
         * @param l
         *            The length of the fill
         * @return The array
         */
        public static short[] fill(final short[] a1, final short i, final int s, final int l)
        {
                for (int j = s; j < s + l; j++)
                        a1[j] = i;
                return a1;
        }

        /**
         * Fill the array with the value
         * 
         * @param a1
         *            The array
         * @param i
         *            The value
         * @return The array
         */
        public static short[] fill(final short[] a1, final short i)
        {
                for (int j = 0; j < a1.length; j++)
                        a1[j] = i;
                return a1;
        }

    
        /**
         * Fills the array with ordinal values
         * 
         * @param array
         *            The array to fill
         * @return the array
         */
        public static int[] fill(final int[] array)
        {
                for (int i = 0; i < array.length; i++)
                        array[i] = i;
                return array;
        }

    
        /**
         * Truncates the given array to the given size.
         * 
         * @param array
         *            The array to truncate
         * @param index
         *            The size to truncate it to
         * @return The truncated array
         */
        public static double[] truncate(final double[] array, final int index)
        {
                final double[] d = new double[index];
                System.arraycopy(array, 0, d, 0, index);
                return d;
        }

        /**
         * Truncates every element in the given array to the given size.
         * 
         * @param array
         *            The array to truncate
         * @param index
         *            The size to truncate it to
         * @return The truncated array
         */
        public static double[][] truncate(final double[][] array, final int index)
        {
                final double[][] d = new double[Math.min(array.length, index)][index];
                for (int i = 0; i < d.length; i++)
                        d[i] = truncate(array[i], index);
                return d;
        }

    
        /**
         * Truncates the given array to the given size.
         * 
         * @param array
         *            The array to truncate
         * @param index
         *            The size to truncate it to
         * @return The truncated array
         */
        public static float[] truncate(final float[] array, final int index)
        {
                final float[] d = new float[index];
                System.arraycopy(array, 0, d, 0, index);
                return d;
        }

        /**
         * Truncates every element in the given array to the given size.
         * 
         * @param array
         *            The array to truncate
         * @param index
         *            The size to truncate it to
         * @return The truncated array
         */
        public static float[][] truncate(final float[][] array, final int index)
        {
                final float[][] d = new float[Math.min(array.length, index)][index];
                for (int i = 0; i < d.length; i++)
                        d[i] = truncate(array[i], index);
                return d;
        }

    
        /**
         * Truncates the given array to the given size.
         * 
         * @param array
         *            The array to truncate
         * @param index
         *            The size to truncate it to
         * @return The truncated array
         */
        public static int[] truncate(final int[] array, final int index)
        {
                final int[] d = new int[index];
                System.arraycopy(array, 0, d, 0, index);
                return d;
        }

        /**
         * Truncates every element in the given array to the given size.
         * 
         * @param array
         *            The array to truncate
         * @param index
         *            The size to truncate it to
         * @return The truncated array
         */
        public static int[][] truncate(final int[][] array, final int index)
        {
                final int[][] d = new int[Math.min(array.length, index)][index];
                for (int i = 0; i < d.length; i++)
                        d[i] = truncate(array[i], index);
                return d;
        }

    
        /**
         * Truncates the given array to the given size.
         * 
         * @param array
         *            The array to truncate
         * @param index
         *            The size to truncate it to
         * @return The truncated array
         */
        public static long[] truncate(final long[] array, final int index)
        {
                final long[] d = new long[index];
                System.arraycopy(array, 0, d, 0, index);
                return d;
        }

        /**
         * Truncates every element in the given array to the given size.
         * 
         * @param array
         *            The array to truncate
         * @param index
         *            The size to truncate it to
         * @return The truncated array
         */
        public static long[][] truncate(final long[][] array, final int index)
        {
                final long[][] d = new long[Math.min(array.length, index)][index];
                for (int i = 0; i < d.length; i++)
                        d[i] = truncate(array[i], index);
                return d;
        }

    
        /**
         * Truncates the given array to the given size.
         * 
         * @param array
         *            The array to truncate
         * @param index
         *            The size to truncate it to
         * @return The truncated array
         */
        public static byte[] truncate(final byte[] array, final int index)
        {
                final byte[] d = new byte[index];
                System.arraycopy(array, 0, d, 0, index);
                return d;
        }

        /**
         * Truncates every element in the given array to the given size.
         * 
         * @param array
         *            The array to truncate
         * @param index
         *            The size to truncate it to
         * @return The truncated array
         */
        public static byte[][] truncate(final byte[][] array, final int index)
        {
                final byte[][] d = new byte[Math.min(array.length, index)][index];
                for (int i = 0; i < d.length; i++)
                        d[i] = truncate(array[i], index);
                return d;
        }

    
        /**
         * Truncates the given array to the given size.
         * 
         * @param array
         *            The array to truncate
         * @param index
         *            The size to truncate it to
         * @return The truncated array
         */
        public static short[] truncate(final short[] array, final int index)
        {
                final short[] d = new short[index];
                System.arraycopy(array, 0, d, 0, index);
                return d;
        }

        /**
         * Truncates every element in the given array to the given size.
         * 
         * @param array
         *            The array to truncate
         * @param index
         *            The size to truncate it to
         * @return The truncated array
         */
        public static short[][] truncate(final short[][] array, final int index)
        {
                final short[][] d = new short[Math.min(array.length, index)][index];
                for (int i = 0; i < d.length; i++)
                        d[i] = truncate(array[i], index);
                return d;
        }

    
        /**
         * Quick Select algorithm for getting the nth item from the array as if it
         * were sorted. Expected complexity is O(N); worst case is O(N^2). The input
         * array will be reordered; clone it first if this is a problem.
         * Implementation based on public domain code from Nicolas Devillard.
         * 
         * @see "http://ndevilla.free.fr/median/median/src/quickselect.c"
         * 
         * @param arr
         *            the array to select from
         * @param n
         *            the item to select
         * @return the selected item
         */
        public static double quickSelect(double arr[], int n) {
                return quickSelect(arr, n, 0, arr.length - 1);
        }

        /**
         * Quick Select algorithm for getting the nth item from a sub-array as if it
         * were sorted. Expected complexity is O(N); worst case is O(N^2). The input
         * array will be reordered; clone it first if this is a problem.
         * Implementation based on public domain code from Nicolas Devillard.
         * 
         * @see "http://ndevilla.free.fr/median/median/src/quickselect.c"
         * 
         * @param arr
         *            the array to select from
         * @param n
         *            the item to select
         * @param low
         *            the starting position in the array (inclusive)
         * @param high
         *            the ending position in the array (exclusive)
         * @return the selected item
         */
        public static double quickSelect(double arr[], int n, int low, int high) {
                high--; // make high inclusive

                int middle, ll, hh;
                double tmp = 0;
                final int median = (low + high) / 2;

                while (true) {
                        if (high <= low) /* One element only */
                                return arr[median];

                        if (high == low + 1) { /* Two elements only */
                                if (arr[low] > arr[high]) {
                                        tmp = arr[low];
                                        arr[low] = arr[high];
                                        arr[high] = tmp;
                                }
                                return arr[median];
                        }

                        /* Find median of low, middle and high items; swap into position low */
                        middle = (low + high) / 2;
                        if (arr[middle] > arr[high]) {
                                tmp = arr[middle];
                                arr[middle] = arr[high];
                                arr[high] = tmp;
                                ;
                        }
                        if (arr[low] > arr[high]) {
                                tmp = arr[low];
                                arr[low] = arr[high];
                                arr[high] = tmp;
                        }
                        if (arr[middle] > arr[low]) {
                                tmp = arr[low];
                                arr[low] = arr[middle];
                                arr[middle] = tmp;
                        }

                        /* Swap low item (now in position middle) into position (low+1) */
                        tmp = arr[middle];
                        arr[middle] = arr[low + 1];
                        arr[low + 1] = tmp;

                        /* Nibble from each end towards middle, swapping items when stuck */
                        ll = low + 1;
                        hh = high;
                        for (;;) {
                                do
                                        ll++;
                                while (arr[low] > arr[ll]);
                                do
                                        hh--;
                                while (arr[hh] > arr[low]);

                                if (hh < ll)
                                        break;

                                tmp = arr[ll];
                                arr[ll] = arr[hh];
                                arr[hh] = tmp;
                        }

                        /* Swap middle item (in position low) back into correct position */
                        tmp = arr[low];
                        arr[low] = arr[hh];
                        arr[hh] = tmp;

                        /* Re-set active partition */
                        if (hh <= median)
                                low = ll;
                        if (hh >= median)
                                high = hh - 1;
                }
        }       

        
        /**
         * Quick Select algorithm for getting the nth item from the array as if it
         * were sorted. Expected complexity is O(N); worst case is O(N^2). The input
         * array will be reordered; clone it first if this is a problem.
         * Implementation based on public domain code from Nicolas Devillard.
         * 
         * @see "http://ndevilla.free.fr/median/median/src/quickselect.c"
         * 
         * @param arr
         *            the array to select from
         * @param n
         *            the item to select
         * @return the selected item
         */
        public static float quickSelect(float arr[], int n) {
                return quickSelect(arr, n, 0, arr.length - 1);
        }

        /**
         * Quick Select algorithm for getting the nth item from a sub-array as if it
         * were sorted. Expected complexity is O(N); worst case is O(N^2). The input
         * array will be reordered; clone it first if this is a problem.
         * Implementation based on public domain code from Nicolas Devillard.
         * 
         * @see "http://ndevilla.free.fr/median/median/src/quickselect.c"
         * 
         * @param arr
         *            the array to select from
         * @param n
         *            the item to select
         * @param low
         *            the starting position in the array (inclusive)
         * @param high
         *            the ending position in the array (exclusive)
         * @return the selected item
         */
        public static float quickSelect(float arr[], int n, int low, int high) {
                high--; // make high inclusive

                int middle, ll, hh;
                float tmp = 0;
                final int median = (low + high) / 2;

                while (true) {
                        if (high <= low) /* One element only */
                                return arr[median];

                        if (high == low + 1) { /* Two elements only */
                                if (arr[low] > arr[high]) {
                                        tmp = arr[low];
                                        arr[low] = arr[high];
                                        arr[high] = tmp;
                                }
                                return arr[median];
                        }

                        /* Find median of low, middle and high items; swap into position low */
                        middle = (low + high) / 2;
                        if (arr[middle] > arr[high]) {
                                tmp = arr[middle];
                                arr[middle] = arr[high];
                                arr[high] = tmp;
                                ;
                        }
                        if (arr[low] > arr[high]) {
                                tmp = arr[low];
                                arr[low] = arr[high];
                                arr[high] = tmp;
                        }
                        if (arr[middle] > arr[low]) {
                                tmp = arr[low];
                                arr[low] = arr[middle];
                                arr[middle] = tmp;
                        }

                        /* Swap low item (now in position middle) into position (low+1) */
                        tmp = arr[middle];
                        arr[middle] = arr[low + 1];
                        arr[low + 1] = tmp;

                        /* Nibble from each end towards middle, swapping items when stuck */
                        ll = low + 1;
                        hh = high;
                        for (;;) {
                                do
                                        ll++;
                                while (arr[low] > arr[ll]);
                                do
                                        hh--;
                                while (arr[hh] > arr[low]);

                                if (hh < ll)
                                        break;

                                tmp = arr[ll];
                                arr[ll] = arr[hh];
                                arr[hh] = tmp;
                        }

                        /* Swap middle item (in position low) back into correct position */
                        tmp = arr[low];
                        arr[low] = arr[hh];
                        arr[hh] = tmp;

                        /* Re-set active partition */
                        if (hh <= median)
                                low = ll;
                        if (hh >= median)
                                high = hh - 1;
                }
        }       

        
        /**
         * Quick Select algorithm for getting the nth item from the array as if it
         * were sorted. Expected complexity is O(N); worst case is O(N^2). The input
         * array will be reordered; clone it first if this is a problem.
         * Implementation based on public domain code from Nicolas Devillard.
         * 
         * @see "http://ndevilla.free.fr/median/median/src/quickselect.c"
         * 
         * @param arr
         *            the array to select from
         * @param n
         *            the item to select
         * @return the selected item
         */
        public static int quickSelect(int arr[], int n) {
                return quickSelect(arr, n, 0, arr.length - 1);
        }

        /**
         * Quick Select algorithm for getting the nth item from a sub-array as if it
         * were sorted. Expected complexity is O(N); worst case is O(N^2). The input
         * array will be reordered; clone it first if this is a problem.
         * Implementation based on public domain code from Nicolas Devillard.
         * 
         * @see "http://ndevilla.free.fr/median/median/src/quickselect.c"
         * 
         * @param arr
         *            the array to select from
         * @param n
         *            the item to select
         * @param low
         *            the starting position in the array (inclusive)
         * @param high
         *            the ending position in the array (exclusive)
         * @return the selected item
         */
        public static int quickSelect(int arr[], int n, int low, int high) {
                high--; // make high inclusive

                int middle, ll, hh;
                int tmp = 0;
                final int median = (low + high) / 2;

                while (true) {
                        if (high <= low) /* One element only */
                                return arr[median];

                        if (high == low + 1) { /* Two elements only */
                                if (arr[low] > arr[high]) {
                                        tmp = arr[low];
                                        arr[low] = arr[high];
                                        arr[high] = tmp;
                                }
                                return arr[median];
                        }

                        /* Find median of low, middle and high items; swap into position low */
                        middle = (low + high) / 2;
                        if (arr[middle] > arr[high]) {
                                tmp = arr[middle];
                                arr[middle] = arr[high];
                                arr[high] = tmp;
                                ;
                        }
                        if (arr[low] > arr[high]) {
                                tmp = arr[low];
                                arr[low] = arr[high];
                                arr[high] = tmp;
                        }
                        if (arr[middle] > arr[low]) {
                                tmp = arr[low];
                                arr[low] = arr[middle];
                                arr[middle] = tmp;
                        }

                        /* Swap low item (now in position middle) into position (low+1) */
                        tmp = arr[middle];
                        arr[middle] = arr[low + 1];
                        arr[low + 1] = tmp;

                        /* Nibble from each end towards middle, swapping items when stuck */
                        ll = low + 1;
                        hh = high;
                        for (;;) {
                                do
                                        ll++;
                                while (arr[low] > arr[ll]);
                                do
                                        hh--;
                                while (arr[hh] > arr[low]);

                                if (hh < ll)
                                        break;

                                tmp = arr[ll];
                                arr[ll] = arr[hh];
                                arr[hh] = tmp;
                        }

                        /* Swap middle item (in position low) back into correct position */
                        tmp = arr[low];
                        arr[low] = arr[hh];
                        arr[hh] = tmp;

                        /* Re-set active partition */
                        if (hh <= median)
                                low = ll;
                        if (hh >= median)
                                high = hh - 1;
                }
        }       

        
        /**
         * Quick Select algorithm for getting the nth item from the array as if it
         * were sorted. Expected complexity is O(N); worst case is O(N^2). The input
         * array will be reordered; clone it first if this is a problem.
         * Implementation based on public domain code from Nicolas Devillard.
         * 
         * @see "http://ndevilla.free.fr/median/median/src/quickselect.c"
         * 
         * @param arr
         *            the array to select from
         * @param n
         *            the item to select
         * @return the selected item
         */
        public static long quickSelect(long arr[], int n) {
                return quickSelect(arr, n, 0, arr.length - 1);
        }

        /**
         * Quick Select algorithm for getting the nth item from a sub-array as if it
         * were sorted. Expected complexity is O(N); worst case is O(N^2). The input
         * array will be reordered; clone it first if this is a problem.
         * Implementation based on public domain code from Nicolas Devillard.
         * 
         * @see "http://ndevilla.free.fr/median/median/src/quickselect.c"
         * 
         * @param arr
         *            the array to select from
         * @param n
         *            the item to select
         * @param low
         *            the starting position in the array (inclusive)
         * @param high
         *            the ending position in the array (exclusive)
         * @return the selected item
         */
        public static long quickSelect(long arr[], int n, int low, int high) {
                high--; // make high inclusive

                int middle, ll, hh;
                long tmp = 0;
                final int median = (low + high) / 2;

                while (true) {
                        if (high <= low) /* One element only */
                                return arr[median];

                        if (high == low + 1) { /* Two elements only */
                                if (arr[low] > arr[high]) {
                                        tmp = arr[low];
                                        arr[low] = arr[high];
                                        arr[high] = tmp;
                                }
                                return arr[median];
                        }

                        /* Find median of low, middle and high items; swap into position low */
                        middle = (low + high) / 2;
                        if (arr[middle] > arr[high]) {
                                tmp = arr[middle];
                                arr[middle] = arr[high];
                                arr[high] = tmp;
                                ;
                        }
                        if (arr[low] > arr[high]) {
                                tmp = arr[low];
                                arr[low] = arr[high];
                                arr[high] = tmp;
                        }
                        if (arr[middle] > arr[low]) {
                                tmp = arr[low];
                                arr[low] = arr[middle];
                                arr[middle] = tmp;
                        }

                        /* Swap low item (now in position middle) into position (low+1) */
                        tmp = arr[middle];
                        arr[middle] = arr[low + 1];
                        arr[low + 1] = tmp;

                        /* Nibble from each end towards middle, swapping items when stuck */
                        ll = low + 1;
                        hh = high;
                        for (;;) {
                                do
                                        ll++;
                                while (arr[low] > arr[ll]);
                                do
                                        hh--;
                                while (arr[hh] > arr[low]);

                                if (hh < ll)
                                        break;

                                tmp = arr[ll];
                                arr[ll] = arr[hh];
                                arr[hh] = tmp;
                        }

                        /* Swap middle item (in position low) back into correct position */
                        tmp = arr[low];
                        arr[low] = arr[hh];
                        arr[hh] = tmp;

                        /* Re-set active partition */
                        if (hh <= median)
                                low = ll;
                        if (hh >= median)
                                high = hh - 1;
                }
        }       

        
        /**
         * Quick Select algorithm for getting the nth item from the array as if it
         * were sorted. Expected complexity is O(N); worst case is O(N^2). The input
         * array will be reordered; clone it first if this is a problem.
         * Implementation based on public domain code from Nicolas Devillard.
         * 
         * @see "http://ndevilla.free.fr/median/median/src/quickselect.c"
         * 
         * @param arr
         *            the array to select from
         * @param n
         *            the item to select
         * @return the selected item
         */
        public static byte quickSelect(byte arr[], int n) {
                return quickSelect(arr, n, 0, arr.length - 1);
        }

        /**
         * Quick Select algorithm for getting the nth item from a sub-array as if it
         * were sorted. Expected complexity is O(N); worst case is O(N^2). The input
         * array will be reordered; clone it first if this is a problem.
         * Implementation based on public domain code from Nicolas Devillard.
         * 
         * @see "http://ndevilla.free.fr/median/median/src/quickselect.c"
         * 
         * @param arr
         *            the array to select from
         * @param n
         *            the item to select
         * @param low
         *            the starting position in the array (inclusive)
         * @param high
         *            the ending position in the array (exclusive)
         * @return the selected item
         */
        public static byte quickSelect(byte arr[], int n, int low, int high) {
                high--; // make high inclusive

                int middle, ll, hh;
                byte tmp = 0;
                final int median = (low + high) / 2;

                while (true) {
                        if (high <= low) /* One element only */
                                return arr[median];

                        if (high == low + 1) { /* Two elements only */
                                if (arr[low] > arr[high]) {
                                        tmp = arr[low];
                                        arr[low] = arr[high];
                                        arr[high] = tmp;
                                }
                                return arr[median];
                        }

                        /* Find median of low, middle and high items; swap into position low */
                        middle = (low + high) / 2;
                        if (arr[middle] > arr[high]) {
                                tmp = arr[middle];
                                arr[middle] = arr[high];
                                arr[high] = tmp;
                                ;
                        }
                        if (arr[low] > arr[high]) {
                                tmp = arr[low];
                                arr[low] = arr[high];
                                arr[high] = tmp;
                        }
                        if (arr[middle] > arr[low]) {
                                tmp = arr[low];
                                arr[low] = arr[middle];
                                arr[middle] = tmp;
                        }

                        /* Swap low item (now in position middle) into position (low+1) */
                        tmp = arr[middle];
                        arr[middle] = arr[low + 1];
                        arr[low + 1] = tmp;

                        /* Nibble from each end towards middle, swapping items when stuck */
                        ll = low + 1;
                        hh = high;
                        for (;;) {
                                do
                                        ll++;
                                while (arr[low] > arr[ll]);
                                do
                                        hh--;
                                while (arr[hh] > arr[low]);

                                if (hh < ll)
                                        break;

                                tmp = arr[ll];
                                arr[ll] = arr[hh];
                                arr[hh] = tmp;
                        }

                        /* Swap middle item (in position low) back into correct position */
                        tmp = arr[low];
                        arr[low] = arr[hh];
                        arr[hh] = tmp;

                        /* Re-set active partition */
                        if (hh <= median)
                                low = ll;
                        if (hh >= median)
                                high = hh - 1;
                }
        }       

        
        /**
         * Quick Select algorithm for getting the nth item from the array as if it
         * were sorted. Expected complexity is O(N); worst case is O(N^2). The input
         * array will be reordered; clone it first if this is a problem.
         * Implementation based on public domain code from Nicolas Devillard.
         * 
         * @see "http://ndevilla.free.fr/median/median/src/quickselect.c"
         * 
         * @param arr
         *            the array to select from
         * @param n
         *            the item to select
         * @return the selected item
         */
        public static short quickSelect(short arr[], int n) {
                return quickSelect(arr, n, 0, arr.length - 1);
        }

        /**
         * Quick Select algorithm for getting the nth item from a sub-array as if it
         * were sorted. Expected complexity is O(N); worst case is O(N^2). The input
         * array will be reordered; clone it first if this is a problem.
         * Implementation based on public domain code from Nicolas Devillard.
         * 
         * @see "http://ndevilla.free.fr/median/median/src/quickselect.c"
         * 
         * @param arr
         *            the array to select from
         * @param n
         *            the item to select
         * @param low
         *            the starting position in the array (inclusive)
         * @param high
         *            the ending position in the array (exclusive)
         * @return the selected item
         */
        public static short quickSelect(short arr[], int n, int low, int high) {
                high--; // make high inclusive

                int middle, ll, hh;
                short tmp = 0;
                final int median = (low + high) / 2;

                while (true) {
                        if (high <= low) /* One element only */
                                return arr[median];

                        if (high == low + 1) { /* Two elements only */
                                if (arr[low] > arr[high]) {
                                        tmp = arr[low];
                                        arr[low] = arr[high];
                                        arr[high] = tmp;
                                }
                                return arr[median];
                        }

                        /* Find median of low, middle and high items; swap into position low */
                        middle = (low + high) / 2;
                        if (arr[middle] > arr[high]) {
                                tmp = arr[middle];
                                arr[middle] = arr[high];
                                arr[high] = tmp;
                                ;
                        }
                        if (arr[low] > arr[high]) {
                                tmp = arr[low];
                                arr[low] = arr[high];
                                arr[high] = tmp;
                        }
                        if (arr[middle] > arr[low]) {
                                tmp = arr[low];
                                arr[low] = arr[middle];
                                arr[middle] = tmp;
                        }

                        /* Swap low item (now in position middle) into position (low+1) */
                        tmp = arr[middle];
                        arr[middle] = arr[low + 1];
                        arr[low + 1] = tmp;

                        /* Nibble from each end towards middle, swapping items when stuck */
                        ll = low + 1;
                        hh = high;
                        for (;;) {
                                do
                                        ll++;
                                while (arr[low] > arr[ll]);
                                do
                                        hh--;
                                while (arr[hh] > arr[low]);

                                if (hh < ll)
                                        break;

                                tmp = arr[ll];
                                arr[ll] = arr[hh];
                                arr[hh] = tmp;
                        }

                        /* Swap middle item (in position low) back into correct position */
                        tmp = arr[low];
                        arr[low] = arr[hh];
                        arr[hh] = tmp;

                        /* Re-set active partition */
                        if (hh <= median)
                                low = ll;
                        if (hh >= median)
                                high = hh - 1;
                }
        }       

        
        /**
         * Convert from Double[] to double[]. This will create a new array and copy the contents.
         *
         * @param array input array
         * @return the converted array
         */
        public double[] convert(Double[] array) {
                double[] out = new double[array.length];
                
                for (int i=0; i<array.length; i++) {
                        out[i] = array[i];
                }
                
                return out;
        }
        
        /**
         * Convert from Double[] to Double[]. This will create a new array and copy the contents.
         *
         * @param array input array
         * @return the converted array
         */
        public Double[] convert(double[] array) {
                Double[] out = new Double[array.length];
                
                for (int i=0; i<array.length; i++) {
                        out[i] = array[i];
                }
                
                return out;
        }

        
        /**
         * Convert from Float[] to float[]. This will create a new array and copy the contents.
         *
         * @param array input array
         * @return the converted array
         */
        public float[] convert(Float[] array) {
                float[] out = new float[array.length];
                
                for (int i=0; i<array.length; i++) {
                        out[i] = array[i];
                }
                
                return out;
        }
        
        /**
         * Convert from Float[] to Float[]. This will create a new array and copy the contents.
         *
         * @param array input array
         * @return the converted array
         */
        public Float[] convert(float[] array) {
                Float[] out = new Float[array.length];
                
                for (int i=0; i<array.length; i++) {
                        out[i] = array[i];
                }
                
                return out;
        }

        
        /**
         * Convert from Integer[] to int[]. This will create a new array and copy the contents.
         *
         * @param array input array
         * @return the converted array
         */
        public int[] convert(Integer[] array) {
                int[] out = new int[array.length];
                
                for (int i=0; i<array.length; i++) {
                        out[i] = array[i];
                }
                
                return out;
        }
        
        /**
         * Convert from Int[] to Integer[]. This will create a new array and copy the contents.
         *
         * @param array input array
         * @return the converted array
         */
        public Integer[] convert(int[] array) {
                Integer[] out = new Integer[array.length];
                
                for (int i=0; i<array.length; i++) {
                        out[i] = array[i];
                }
                
                return out;
        }

        
        /**
         * Convert from Long[] to long[]. This will create a new array and copy the contents.
         *
         * @param array input array
         * @return the converted array
         */
        public long[] convert(Long[] array) {
                long[] out = new long[array.length];
                
                for (int i=0; i<array.length; i++) {
                        out[i] = array[i];
                }
                
                return out;
        }
        
        /**
         * Convert from Long[] to Long[]. This will create a new array and copy the contents.
         *
         * @param array input array
         * @return the converted array
         */
        public Long[] convert(long[] array) {
                Long[] out = new Long[array.length];
                
                for (int i=0; i<array.length; i++) {
                        out[i] = array[i];
                }
                
                return out;
        }

        
        /**
         * Convert from Byte[] to byte[]. This will create a new array and copy the contents.
         *
         * @param array input array
         * @return the converted array
         */
        public byte[] convert(Byte[] array) {
                byte[] out = new byte[array.length];
                
                for (int i=0; i<array.length; i++) {
                        out[i] = array[i];
                }
                
                return out;
        }
        
        /**
         * Convert from Byte[] to Byte[]. This will create a new array and copy the contents.
         *
         * @param array input array
         * @return the converted array
         */
        public Byte[] convert(byte[] array) {
                Byte[] out = new Byte[array.length];
                
                for (int i=0; i<array.length; i++) {
                        out[i] = array[i];
                }
                
                return out;
        }

        
        /**
         * Convert from Short[] to short[]. This will create a new array and copy the contents.
         *
         * @param array input array
         * @return the converted array
         */
        public short[] convert(Short[] array) {
                short[] out = new short[array.length];
                
                for (int i=0; i<array.length; i++) {
                        out[i] = array[i];
                }
                
                return out;
        }
        
        /**
         * Convert from Short[] to Short[]. This will create a new array and copy the contents.
         *
         * @param array input array
         * @return the converted array
         */
        public Short[] convert(short[] array) {
                Short[] out = new Short[array.length];
                
                for (int i=0; i<array.length; i++) {
                        out[i] = array[i];
                }
                
                return out;
        }

        
        /**
         * Compute the p-norm of the array
         * 
         * @param array the array 
         * @param p the p value
         * @return the p-norm
         */
        public static double pnorm(final double[] array, final int p) {
                double sum = 0;

                for (int i=0; i<array.length; i++)
                        sum += Math.pow(Math.abs(array[i]), p);

                return Math.pow(sum, 1.0/p);
        }

        
        /**
         * Compute the p-norm of the array
         * 
         * @param array the array 
         * @param p the p value
         * @return the p-norm
         */
        public static double pnorm(final float[] array, final int p) {
                double sum = 0;

                for (int i=0; i<array.length; i++)
                        sum += Math.pow(Math.abs(array[i]), p);

                return Math.pow(sum, 1.0/p);
        }

        
        /**
         * Compute the p-norm of the array
         * 
         * @param array the array 
         * @param p the p value
         * @return the p-norm
         */
        public static double pnorm(final int[] array, final int p) {
                double sum = 0;

                for (int i=0; i<array.length; i++)
                        sum += Math.pow(Math.abs(array[i]), p);

                return Math.pow(sum, 1.0/p);
        }

        
        /**
         * Compute the p-norm of the array
         * 
         * @param array the array 
         * @param p the p value
         * @return the p-norm
         */
        public static double pnorm(final long[] array, final int p) {
                double sum = 0;

                for (int i=0; i<array.length; i++)
                        sum += Math.pow(Math.abs(array[i]), p);

                return Math.pow(sum, 1.0/p);
        }

        
        /**
         * Compute the p-norm of the array
         * 
         * @param array the array 
         * @param p the p value
         * @return the p-norm
         */
        public static double pnorm(final byte[] array, final int p) {
                double sum = 0;

                for (int i=0; i<array.length; i++)
                        sum += Math.pow(Math.abs(array[i]), p);

                return Math.pow(sum, 1.0/p);
        }

        
        /**
         * Compute the p-norm of the array
         * 
         * @param array the array 
         * @param p the p value
         * @return the p-norm
         */
        public static double pnorm(final short[] array, final int p) {
                double sum = 0;

                for (int i=0; i<array.length; i++)
                        sum += Math.pow(Math.abs(array[i]), p);

                return Math.pow(sum, 1.0/p);
        }

        
}