/*
    * Licensed to the Apache Software Foundation (ASF) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * The ASF licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
    * the License.  You may obtain a copy of the License at
    *
    *      http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  package org.apache.commons.math4.legacy.stat.descriptive;
  
  import java.util.Arrays;
  
  import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
  import org.apache.commons.math4.legacy.exception.MathIllegalStateException;
  import org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException;
  import org.apache.commons.math4.legacy.exception.NullArgumentException;
  import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException;
  import org.apache.commons.math4.legacy.exception.util.LocalizedFormats;
  import org.apache.commons.math4.core.jdkmath.JdkMath;
  import org.apache.commons.math4.legacy.core.MathArrays;
  
  /**
   * A variable length {@link DoubleArray} implementation that automatically
   * handles expanding and contracting its internal storage array as elements
   * are added and removed.
   * <p>
   * The internal storage array starts with capacity determined by the
   * {@code initialCapacity} property, which can be set by the constructor.
   * The default initial capacity is 16.  Adding elements using
   * {@link #addElement(double)} appends elements to the end of the array.
   * When there are no open entries at the end of the internal storage array,
   * the array is expanded.  The size of the expanded array depends on the
   * {@code expansionMode} and {@code expansionFactor} properties.
   * The {@code expansionMode} determines whether the size of the array is
   * multiplied by the {@code expansionFactor}
   * ({@link ExpansionMode#MULTIPLICATIVE}) or if the expansion is additive
   * ({@link ExpansionMode#ADDITIVE} -- {@code expansionFactor} storage
   * locations added).
   * The default {@code expansionMode} is {@code MULTIPLICATIVE} and the default
   * {@code expansionFactor} is 2.
   * <p>
   * The {@link #addElementRolling(double)} method adds a new element to the end
   * of the internal storage array and adjusts the "usable window" of the
   * internal array forward by one position (effectively making what was the
   * second element the first, and so on).  Repeated activations of this method
   * (or activation of {@link #discardFrontElements(int)}) will effectively orphan
   * the storage locations at the beginning of the internal storage array.  To
   * reclaim this storage, each time one of these methods is activated, the size
   * of the internal storage array is compared to the number of addressable
   * elements (the {@code numElements} property) and if the difference
   * is too large, the internal array is contracted to size
   * {@code numElements + 1}.  The determination of when the internal
   * storage array is "too large" depends on the {@code expansionMode} and
   * {@code contractionFactor} properties.  If  the {@code expansionMode}
   * is {@code MULTIPLICATIVE}, contraction is triggered when the
   * ratio between storage array length and {@code numElements} exceeds
   * {@code contractionFactor.}  If the {@code expansionMode}
   * is {@code ADDITIVE}, the number of excess storage locations
   * is compared to {@code contractionFactor}.
   * <p>
   * To avoid cycles of expansions and contractions, the
   * {@code expansionFactor} must not exceed the {@code contractionFactor}.
   * Constructors and mutators for both of these properties enforce this
   * requirement, throwing a {@code MathIllegalArgumentException} if it is
   * violated.
   * <p>
   * <b>Note:</b> this class is <b>NOT</b> thread-safe.
   */
  class ResizableDoubleArray implements DoubleArray { // Not in public API.
      /** Default value for initial capacity. */
      private static final int DEFAULT_INITIAL_CAPACITY = 16;
      /** Default value for array size modifier. */
      private static final double DEFAULT_EXPANSION_FACTOR = 2.0;
      /** Default value for expansion mode. */
      private static final ExpansionMode DEFAULT_EXPANSION_MODE = ExpansionMode.MULTIPLICATIVE;
      /**
       * Default value for the difference between {@link #contractionCriterion}
       * and {@link #expansionFactor}.
       */
      private static final double DEFAULT_CONTRACTION_DELTA = 0.5;
  
      /**
       * The contraction criteria determines when the internal array will be
       * contracted to fit the number of elements contained in the element
       *  array + 1.
       */
      private final double contractionCriterion;
  
      /**
       * The expansion factor of the array.  When the array needs to be expanded,
       * the new array size will be {@code internalArray.length * expansionFactor}
      * if {@code expansionMode} is set to MULTIPLICATIVE, or
      * {@code internalArray.length + expansionFactor} if
      * {@code expansionMode} is set to ADDITIVE.
      */
     private final double expansionFactor;
 
     /**
      * Determines whether array expansion by {@code expansionFactor}
      * is additive or multiplicative.
      */
     private final ExpansionMode expansionMode;
 
     /**
      * The internal storage array.
      */
     private double[] internalArray;
 
     /**
      * The number of addressable elements in the array.  Note that this
      * has nothing to do with the length of the internal storage array.
      */
     private int numElements;
 
     /**
      * The position of the first addressable element in the internal storage
      * array.  The addressable elements in the array are
      * {@code internalArray[startIndex],...,internalArray[startIndex + numElements - 1]}.
      */
     private int startIndex;
 
     /**
      * Specification of expansion algorithm.
      * @since 3.1
      */
     public enum ExpansionMode {
         /** Multiplicative expansion mode. */
         MULTIPLICATIVE,
         /** Additive expansion mode. */
         ADDITIVE
     }
 
     /**
      * Creates an instance with default properties.
      * <ul>
      *  <li>{@code initialCapacity = 16}</li>
      *  <li>{@code expansionMode = MULTIPLICATIVE}</li>
      *  <li>{@code expansionFactor = 2.0}</li>
      *  <li>{@code contractionCriterion = 2.5}</li>
      * </ul>
      */
     ResizableDoubleArray() {
         this(DEFAULT_INITIAL_CAPACITY);
     }
 
     /**
      * Creates an instance with the specified initial capacity.
      * <p>
      * Other properties take default values:
      * <ul>
      *  <li>{@code expansionMode = MULTIPLICATIVE}</li>
      *  <li>{@code expansionFactor = 2.0}</li>
      *  <li>{@code contractionCriterion = 2.5}</li>
      * </ul>
      * @param initialCapacity Initial size of the internal storage array.
      * @throws MathIllegalArgumentException if {@code initialCapacity <= 0}.
      */
     ResizableDoubleArray(int initialCapacity) throws MathIllegalArgumentException {
         this(initialCapacity, DEFAULT_EXPANSION_FACTOR);
     }
 
     /**
      * Creates an instance from an existing {@code double[]} with the
      * initial capacity and numElements corresponding to the size of
      * the supplied {@code double[]} array.
      * <p>
      * If the supplied array is null, a new empty array with the default
      * initial capacity will be created.
      * The input array is copied, not referenced.
      * Other properties take default values:
      * <ul>
      *  <li>{@code expansionMode = MULTIPLICATIVE}</li>
      *  <li>{@code expansionFactor = 2.0}</li>
      *  <li>{@code contractionCriterion = 2.5}</li>
      * </ul>
      *
      * @param initialArray initial array
      * @since 2.2
      */
     ResizableDoubleArray(double[] initialArray) {
         this(initialArray == null || initialArray.length == 0 ?
               DEFAULT_INITIAL_CAPACITY :
               initialArray.length,
              DEFAULT_EXPANSION_FACTOR,
              DEFAULT_CONTRACTION_DELTA + DEFAULT_EXPANSION_FACTOR,
              DEFAULT_EXPANSION_MODE,
              initialArray);
     }
 
     /**
      * Creates an instance with the specified initial capacity
      * and expansion factor.
      * <p>
      * The remaining properties take default values:
      * <ul>
      *  <li>{@code expansionMode = MULTIPLICATIVE}</li>
      *  <li>{@code contractionCriterion = 0.5 + expansionFactor}</li>
      * </ul>
      * <p>
      * Throws MathIllegalArgumentException if the following conditions
      * are not met:
      * <ul>
      *  <li>{@code initialCapacity > 0}</li>
      *  <li>{@code expansionFactor > 1}</li>
      * </ul>
      *
      * @param initialCapacity Initial size of the internal storage array.
      * @param expansionFactor The array will be expanded based on this parameter.
      * @throws MathIllegalArgumentException if parameters are not valid.
      * @since 3.1
      */
     ResizableDoubleArray(int initialCapacity, double expansionFactor) throws MathIllegalArgumentException {
         this(initialCapacity, expansionFactor, DEFAULT_CONTRACTION_DELTA + expansionFactor);
     }
 
     /**
      * Creates an instance with the specified initial capacity,
      * expansion factor, and contraction criteria.
      * <p>
      * The expansion mode will default to {@code MULTIPLICATIVE}.
      * <p>
      * Throws MathIllegalArgumentException if the following conditions
      * are not met:
      * <ul>
      *  <li>{@code initialCapacity > 0}</li>
      *  <li>{@code expansionFactor > 1}</li>
      *  <li>{@code contractionCriterion >= expansionFactor}</li>
      * </ul>
      *
      * @param initialCapacity Initial size of the internal storage array.
      * @param expansionFactor The array will be expanded based on this parameter.
      * @param contractionCriterion Contraction criterion.
      * @throws MathIllegalArgumentException if the parameters are not valid.
      * @since 3.1
      */
     ResizableDoubleArray(int initialCapacity, double expansionFactor, double contractionCriterion)
         throws MathIllegalArgumentException {
         this(initialCapacity, expansionFactor, contractionCriterion, DEFAULT_EXPANSION_MODE);
     }
 
     /**
      * Creates an instance with the specified properties.
      * <br>
      * Throws MathIllegalArgumentException if the following conditions
      * are not met:
      * <ul>
      *  <li>{@code initialCapacity > 0}</li>
      *  <li>{@code expansionFactor > 1}</li>
      *  <li>{@code contractionCriterion >= expansionFactor}</li>
      * </ul>
      *
      * @param initialCapacity Initial size of the internal storage array.
      * @param expansionFactor The array will be expanded based on this parameter.
      * @param contractionCriterion Contraction criteria.
      * @param expansionMode Expansion mode.
      * @param data Initial contents of the array.
      * @throws MathIllegalArgumentException if the parameters are not valid.
      * @throws NullArgumentException if expansionMode is null
      */
     ResizableDoubleArray(int initialCapacity,
                          double expansionFactor,
                          double contractionCriterion,
                          ExpansionMode expansionMode,
                          double ... data)
         throws MathIllegalArgumentException {
         if (initialCapacity <= 0) {
             throw new NotStrictlyPositiveException(LocalizedFormats.INITIAL_CAPACITY_NOT_POSITIVE,
                                                    initialCapacity);
         }
         checkContractExpand(contractionCriterion, expansionFactor);
         NullArgumentException.check(expansionMode);
 
         this.expansionFactor = expansionFactor;
         this.contractionCriterion = contractionCriterion;
         this.expansionMode = expansionMode;
         internalArray = new double[initialCapacity];
         numElements = 0;
         startIndex = 0;
 
         if (data != null && data.length > 0) {
             addElements(data);
         }
     }
 
     /**
      * Copy constructor.
      * <p>
      * Creates a new ResizableDoubleArray that is a deep, fresh copy of the original.
      * Original may not be null; otherwise a {@link NullArgumentException} is thrown.
      *
      * @param original array to copy
      * @exception NullArgumentException if original is null
      * @since 2.0
      */
     ResizableDoubleArray(final ResizableDoubleArray original)
         throws NullArgumentException {
         NullArgumentException.check(original);
         this.contractionCriterion = original.contractionCriterion;
         this.expansionFactor = original.expansionFactor;
         this.expansionMode = original.expansionMode;
         this.internalArray = new double[original.internalArray.length];
         System.arraycopy(original.internalArray, 0, this.internalArray, 0, this.internalArray.length);
         this.numElements = original.numElements;
         this.startIndex = original.startIndex;
     }
 
     /**
      * Adds an element to the end of this expandable array.
      *
      * @param value Value to be added to end of array.
      */
     @Override
     public void addElement(final double value) {
         if (internalArray.length <= startIndex + numElements) {
             expand();
         }
         internalArray[startIndex + numElements++] = value;
     }
 
     /**
      * Adds several element to the end of this expandable array.
      *
      * @param values Values to be added to end of array.
      * @since 2.2
      */
     @Override
     public void addElements(final double[] values) {
         final double[] tempArray = new double[numElements + values.length + 1];
         System.arraycopy(internalArray, startIndex, tempArray, 0, numElements);
         System.arraycopy(values, 0, tempArray, numElements, values.length);
         internalArray = tempArray;
         startIndex = 0;
         numElements += values.length;
     }
 
     /**
      * Adds an element to the end of the array and removes the first
      * element in the array.  Returns the discarded first element.
      * <p>
      * The effect is similar to a push operation in a FIFO queue.
      * <p>
      * Example: If the array contains the elements 1, 2, 3, 4 (in that order)
      * and addElementRolling(5) is invoked, the result is an array containing
      * the entries 2, 3, 4, 5 and the value returned is 1.
      *
      * @param value Value to be added to the array.
      * @return the value which has been discarded or "pushed" out of the array
      * by this rolling insert.
      */
     @Override
     public double addElementRolling(double value) {
         double discarded = internalArray[startIndex];
 
         if ((startIndex + (numElements + 1)) > internalArray.length) {
             expand();
         }
         // Increment the start index
         startIndex += 1;
 
         // Add the new value
         internalArray[startIndex + (numElements - 1)] = value;
 
         // Check the contraction criterion.
         if (shouldContract()) {
             contract();
         }
         return discarded;
     }
 
     /**
      * Substitutes {@code value} for the most recently added value.
      * <p>
      * Returns the value that has been replaced. If the array is empty (i.e.
      * if {@link #numElements} is zero), an MathIllegalStateException is thrown.
      *
      * @param value New value to substitute for the most recently added value
      * @return the value that has been replaced in the array.
      * @throws MathIllegalStateException if the array is empty
      * @since 2.0
      */
     public double substituteMostRecentElement(double value) throws MathIllegalStateException {
         if (numElements < 1) {
             throw new MathIllegalStateException(LocalizedFormats.CANNOT_SUBSTITUTE_ELEMENT_FROM_EMPTY_ARRAY);
         }
 
         final int substIndex = startIndex + (numElements - 1);
         final double discarded = internalArray[substIndex];
 
         internalArray[substIndex] = value;
 
         return discarded;
     }
 
     /**
      * Checks the expansion factor and the contraction criterion and raises
      * an exception if the contraction criterion is smaller than the
      * expansion criterion.
      *
      * @param contraction Criterion to be checked.
      * @param expansion Factor to be checked.
      * @throws NumberIsTooSmallException if {@code contraction < expansion}.
      * @throws NumberIsTooSmallException if {@code contraction <= 1}.
      * @throws NumberIsTooSmallException if {@code expansion <= 1 }.
      * @since 3.1
      */
     protected void checkContractExpand(double contraction, double expansion) throws NumberIsTooSmallException {
         if (contraction < expansion) {
             final NumberIsTooSmallException e = new NumberIsTooSmallException(contraction, 1, true);
             e.getContext().addMessage(LocalizedFormats.CONTRACTION_CRITERIA_SMALLER_THAN_EXPANSION_FACTOR,
                                       contraction, expansion);
             throw e;
         }
 
         if (contraction <= 1) {
             final NumberIsTooSmallException e = new NumberIsTooSmallException(contraction, 1, false);
             e.getContext().addMessage(LocalizedFormats.CONTRACTION_CRITERIA_SMALLER_THAN_ONE,
                                       contraction);
             throw e;
         }
 
         if (expansion <= 1) {
             final NumberIsTooSmallException e = new NumberIsTooSmallException(contraction, 1, false);
             e.getContext().addMessage(LocalizedFormats.EXPANSION_FACTOR_SMALLER_THAN_ONE,
                                       expansion);
             throw e;
         }
     }
 
     /**
      * Clear the array contents, resetting the number of elements to zero.
      */
     @Override
     public void clear() {
         numElements = 0;
         startIndex = 0;
     }
 
     /**
      * Contracts the storage array to the (size of the element set) + 1 - to avoid
      * a zero length array. This function also resets the startIndex to zero.
      */
     public void contract() {
         final double[] tempArray = new double[numElements + 1];
 
         // Copy and swap - copy only the element array from the src array.
         System.arraycopy(internalArray, startIndex, tempArray, 0, numElements);
         internalArray = tempArray;
 
         // Reset the start index to zero
         startIndex = 0;
     }
 
     /**
      * Discards the {@code i} initial elements of the array.
      * <p>
      * For example, if the array contains the elements 1,2,3,4, invoking
      * {@code discardFrontElements(2)} will cause the first two elements
      * to be discarded, leaving 3,4 in the array.
      *
      * @param i  the number of elements to discard from the front of the array
      * @throws MathIllegalArgumentException if i is greater than numElements.
      * @since 2.0
      */
     public void discardFrontElements(int i) throws MathIllegalArgumentException {
         discardExtremeElements(i,true);
     }
 
     /**
      * Discards the {@code i} last elements of the array.
      * <p>
      * For example, if the array contains the elements 1,2,3,4, invoking
      * {@code discardMostRecentElements(2)} will cause the last two elements
      * to be discarded, leaving 1,2 in the array.
      *
      * @param i  the number of elements to discard from the end of the array
      * @throws MathIllegalArgumentException if i is greater than numElements.
      * @since 2.0
      */
     public void discardMostRecentElements(int i) throws MathIllegalArgumentException {
         discardExtremeElements(i,false);
     }
 
     /**
      * Discards the {@code i} first or last elements of the array,
      * depending on the value of {@code front}.
      * <p>
      * For example, if the array contains the elements 1,2,3,4, invoking
      * {@code discardExtremeElements(2,false)} will cause the last two elements
      * to be discarded, leaving 1,2 in the array.
      * For example, if the array contains the elements 1,2,3,4, invoking
      * {@code discardExtremeElements(2,true)} will cause the first two elements
      * to be discarded, leaving 3,4 in the array.
      *
      * @param i  the number of elements to discard from the front/end of the array
      * @param front true if elements are to be discarded from the front
      * of the array, false if elements are to be discarded from the end
      * of the array
      * @throws MathIllegalArgumentException if i is greater than numElements.
      * @since 2.0
      */
     private void discardExtremeElements(int i, boolean front) throws MathIllegalArgumentException {
         if (i > numElements) {
             throw new MathIllegalArgumentException(
                     LocalizedFormats.TOO_MANY_ELEMENTS_TO_DISCARD_FROM_ARRAY,
                     i, numElements);
        } else if (i < 0) {
            throw new MathIllegalArgumentException(
                    LocalizedFormats.CANNOT_DISCARD_NEGATIVE_NUMBER_OF_ELEMENTS,
                    i);
         } else {
             // "Subtract" this number of discarded from numElements
             numElements -= i;
             if (front) {
                 startIndex += i;
             }
         }
         if (shouldContract()) {
             contract();
         }
     }
 
     /**
      * Expands the internal storage array using the expansion factor.
      * <p>
      * If {@code expansionMode} is set to MULTIPLICATIVE,
      * the new array size will be {@code internalArray.length * expansionFactor}.
      * If {@code expansionMode} is set to ADDITIVE, the length
      * after expansion will be {@code internalArray.length + expansionFactor}.
      */
     protected void expand() {
         // notice the use of JdkMath.ceil(), this guarantees that we will always
         // have an array of at least currentSize + 1.   Assume that the
         // current initial capacity is 1 and the expansion factor
         // is 1.000000000000000001.  The newly calculated size will be
         // rounded up to 2 after the multiplication is performed.
         int newSize = 0;
         if (expansionMode == ExpansionMode.MULTIPLICATIVE) {
             newSize = (int) JdkMath.ceil(internalArray.length * expansionFactor);
         } else {
             newSize = (int) (internalArray.length + JdkMath.round(expansionFactor));
         }
         final double[] tempArray = new double[newSize];
 
         // Copy and swap
         System.arraycopy(internalArray, 0, tempArray, 0, internalArray.length);
         internalArray = tempArray;
     }
 
     /**
      * Expands the internal storage array to the specified size.
      *
      * @param size Size of the new internal storage array.
      */
     private void expandTo(int size) {
         final double[] tempArray = new double[size];
         // Copy and swap
         System.arraycopy(internalArray, 0, tempArray, 0, internalArray.length);
         internalArray = tempArray;
     }
 
     /**
      * The contraction criterion defines when the internal array will contract
      * to store only the number of elements in the element array.
      * <p>
      * If the {@code expansionMode} is {@code MULTIPLICATIVE},
      * contraction is triggered when the ratio between storage array length
      * and {@code numElements} exceeds {@code contractionFactor}.
      * If the {@code expansionMode} is {@code ADDITIVE}, the
      * number of excess storage locations is compared to {@code contractionFactor}.
      *
      * @return the contraction criterion used to reclaim memory.
      * @since 3.1
      */
     public double getContractionCriterion() {
         return contractionCriterion;
     }
 
     /**
      * Returns the element at the specified index.
      *
      * @param index index to fetch a value from
      * @return value stored at the specified index
      * @throws ArrayIndexOutOfBoundsException if {@code index} is less than
      * zero or is greater than {@code getNumElements() - 1}.
      */
     @Override
     public double getElement(int index) {
         if (index >= numElements) {
             throw new ArrayIndexOutOfBoundsException(index);
         } else if (index >= 0) {
             return internalArray[startIndex + index];
         } else {
             throw new ArrayIndexOutOfBoundsException(index);
         }
     }
 
      /**
      * Returns a double array containing the elements of this ResizableArray.
      * <p>
      * This method returns a copy, not a reference to the underlying array,
      * so that changes made to the returned array have no effect on this ResizableArray.
      *
      * @return the double array.
      */
     @Override
     public double[] getElements() {
         final double[] elementArray = new double[numElements];
         System.arraycopy(internalArray, startIndex, elementArray, 0, numElements);
         return elementArray;
     }
 
     /**
      * The expansion factor controls the size of a new array when an array
      * needs to be expanded.
      * <p>
      * The {@code expansionMode} determines whether the size of the array
      * is multiplied by the {@code expansionFactor} (MULTIPLICATIVE) or if
      * the expansion is additive (ADDITIVE -- {@code expansionFactor}
      * storage locations added).  The default {@code expansionMode} is
      * MULTIPLICATIVE and the default {@code expansionFactor} is 2.0.
      *
      * @return the expansion factor of this expandable double array
      */
     public double getExpansionFactor() {
         return expansionFactor;
     }
 
     /**
      * The expansion mode determines whether the internal storage
      * array grows additively or multiplicatively when it is expanded.
      *
      * @return the expansion mode.
      */
     public ExpansionMode getExpansionMode() {
         return expansionMode;
     }
 
     /**
      * Gets the currently allocated size of the internal data structure used
      * for storing elements.
      * This is not to be confused with {@link #getNumElements() the number of
      * elements actually stored}.
      *
      * @return the length of the internal array.
      * @since 3.1
      */
     public int getCapacity() {
         return internalArray.length;
     }
 
     /**
      * Returns the number of elements currently in the array.  Please note
      * that this is different from the length of the internal storage array.
      *
      * @return the number of elements.
      */
     @Override
     public int getNumElements() {
         return numElements;
     }
 
     /**
      * Provides <em>direct</em> access to the internal storage array.
      * Please note that this method returns a reference to this object's
      * storage array, not a copy.
      * <p>
      * To correctly address elements of the array, the "start index" is
      * required (available via the {@link #getStartIndex() getStartIndex}
      * method.
      * <p>
      * This method should only be used to avoid copying the internal array.
      * The returned value <em>must</em> be used for reading only; other
      * uses could lead to this object becoming inconsistent.
      * <p>
      * The {@link #getElements} method has no such limitation since it
      * returns a copy of this array's addressable elements.
      *
      * @return the internal storage array used by this object.
      * @since 3.1
      */
     protected double[] getArrayRef() {
         return internalArray;
     }
 
     /**
      * Returns the "start index" of the internal array.
      * This index is the position of the first addressable element in the
      * internal storage array.
      * <p>
      * The addressable elements in the array are at indices contained in
      * the interval [{@link #getStartIndex()},
      *               {@link #getStartIndex()} + {@link #getNumElements()} - 1].
      *
      * @return the start index.
      * @since 3.1
      */
     protected int getStartIndex() {
         return startIndex;
     }
 
     /**
      * Performs an operation on the addressable elements of the array.
      *
      * @param f Function to be applied on this array.
      * @return the result.
      * @since 3.1
      */
     public double compute(MathArrays.Function f) {
         return f.evaluate(internalArray, startIndex, numElements);
     }
 
     /**
      * Sets the element at the specified index.
      * <p>
      * If the specified index is greater than {@code getNumElements() - 1},
      * the {@code numElements} property is increased to {@code index +1}
      * and additional storage is allocated (if necessary) for the new element and
      * all (uninitialized) elements between the new element and the previous end
      * of the array).
      *
      * @param index index to store a value in
      * @param value value to store at the specified index
      * @throws ArrayIndexOutOfBoundsException if {@code index < 0}.
      */
     @Override
     public void setElement(int index, double value) {
         if (index < 0) {
             throw new ArrayIndexOutOfBoundsException(index);
         }
         if (index + 1 > numElements) {
             numElements = index + 1;
         }
         if ((startIndex + index) >= internalArray.length) {
             expandTo(startIndex + (index + 1));
         }
         internalArray[startIndex + index] = value;
     }
 
     /**
      * This function allows you to control the number of elements contained
      * in this array, and can be used to "throw out" the last n values in an
      * array. This function will also expand the internal array as needed.
      *
      * @param i a new number of elements
      * @throws MathIllegalArgumentException if {@code i} is negative.
      */
     public void setNumElements(int i) throws MathIllegalArgumentException {
         // If index is negative thrown an error.
         if (i < 0) {
             throw new MathIllegalArgumentException(LocalizedFormats.INDEX_NOT_POSITIVE, i);
         }
 
         // Test the new num elements, check to see if the array needs to be
         // expanded to accommodate this new number of elements.
         final int newSize = startIndex + i;
         if (newSize > internalArray.length) {
             expandTo(newSize);
         }
 
         // Set the new number of elements to new value.
         numElements = i;
     }
 
     /**
      * Returns true if the internal storage array has too many unused
      * storage positions.
      *
      * @return true if array satisfies the contraction criteria
      */
     private boolean shouldContract() {
         if (expansionMode == ExpansionMode.MULTIPLICATIVE) {
             return (internalArray.length / ((float) numElements)) > contractionCriterion;
         } else {
             return (internalArray.length - numElements) > contractionCriterion;
         }
     }
 
     /**
      * Returns a copy of the ResizableDoubleArray.  Does not contract before
      * the copy, so the returned object is an exact copy of this.
      *
      * @return a new ResizableDoubleArray with the same data and configuration
      * properties as this
      * @since 2.0
      */
     public ResizableDoubleArray copy() {
         return new ResizableDoubleArray(this);
     }
 
     /**
      * Returns true iff object is a ResizableDoubleArray with the same properties
      * as this and an identical internal storage array.
      *
      * @param object object to be compared for equality with this
      * @return true iff object is a ResizableDoubleArray with the same data and
      * properties as this
      * @since 2.0
      */
     @Override
     public boolean equals(Object object) {
         if (object == this ) {
             return true;
         }
         if (!(object instanceof ResizableDoubleArray)) {
             return false;
         }
         boolean result = true;
         final ResizableDoubleArray other = (ResizableDoubleArray) object;
         result = result && other.contractionCriterion == contractionCriterion;
         result = result && other.expansionFactor == expansionFactor;
         result = result && other.expansionMode == expansionMode;
         result = result && other.numElements == numElements;
         result = result && other.startIndex == startIndex;
         if (!result) {
             return false;
         } else {
             return Arrays.equals(internalArray, other.internalArray);
         }
     }
 
     /**
      * Returns a hash code consistent with equals.
      *
      * @return the hash code representing this {@code ResizableDoubleArray}.
      * @since 2.0
      */
     @Override
     public int hashCode() {
         final int[] hashData = new int[6];
         hashData[0] = Double.valueOf(expansionFactor).hashCode();
         hashData[1] = Double.valueOf(contractionCriterion).hashCode();
         hashData[2] = expansionMode.hashCode();
         hashData[3] = Arrays.hashCode(internalArray);
         hashData[4] = numElements;
         hashData[5] = startIndex;
         return Arrays.hashCode(hashData);
     }
 }