/*
    * 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.linear;
  
  import java.io.Serializable;
  import java.util.Arrays;
  
  import org.apache.commons.math4.legacy.core.Field;
  import org.apache.commons.math4.legacy.core.FieldElement;
  import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
  import org.apache.commons.math4.legacy.exception.MathArithmeticException;
  import org.apache.commons.math4.legacy.exception.NotPositiveException;
  import org.apache.commons.math4.legacy.exception.NullArgumentException;
  import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException;
  import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException;
  import org.apache.commons.math4.legacy.exception.OutOfRangeException;
  import org.apache.commons.math4.legacy.exception.ZeroException;
  import org.apache.commons.math4.legacy.exception.util.LocalizedFormats;
  import org.apache.commons.math4.legacy.core.MathArrays;
  
  /**
   * This class implements the {@link FieldVector} interface with a {@link FieldElement} array.
   * @param <T> the type of the field elements
   * @since 2.0
   */
  public class ArrayFieldVector<T extends FieldElement<T>> implements FieldVector<T>, Serializable {
      /** Serializable version identifier. */
      private static final long serialVersionUID = 7648186910365927050L;
  
      /** Entries of the vector. */
      private T[] data;
  
      /** Field to which the elements belong. */
      private final Field<T> field;
  
      /**
       * Build a 0-length vector.
       * Zero-length vectors may be used to initialize construction of vectors
       * by data gathering. We start with zero-length and use either the {@link
       * #ArrayFieldVector(FieldVector, FieldVector)} constructor
       * or one of the {@code append} methods ({@link #add(FieldVector)} or
       * {@link #append(ArrayFieldVector)}) to gather data into this vector.
       *
       * @param field field to which the elements belong
       */
      public ArrayFieldVector(final Field<T> field) {
          this(field, 0);
      }
  
      /**
       * Construct a vector of zeroes.
       *
       * @param field Field to which the elements belong.
       * @param size Size of the vector.
       */
      public ArrayFieldVector(Field<T> field, int size) {
          this.field = field;
          this.data  = MathArrays.buildArray(field, size);
      }
  
      /**
       * Construct a vector with preset values.
       *
       * @param size Size of the vector.
       * @param preset All entries will be set with this value.
       */
      public ArrayFieldVector(int size, T preset) {
          this(preset.getField(), size);
          Arrays.fill(data, preset);
      }
  
      /**
       * Construct a vector from an array, copying the input array.
       * This constructor needs a non-empty {@code d} array to retrieve
       * the field from its first element. This implies it cannot build
       * 0 length vectors. To build vectors from any size, one should
       * use the {@link #ArrayFieldVector(Field, FieldElement[])} constructor.
       *
       * @param d Array.
       * @throws NullArgumentException if {@code d} is {@code null}.
       * @throws ZeroException if {@code d} is empty.
       * @see #ArrayFieldVector(Field, FieldElement[])
       */
      public ArrayFieldVector(T[] d)
              throws NullArgumentException, ZeroException {
         NullArgumentException.check(d);
         try {
             field = d[0].getField();
             data = d.clone();
         } catch (ArrayIndexOutOfBoundsException e) {
             throw new ZeroException(LocalizedFormats.VECTOR_MUST_HAVE_AT_LEAST_ONE_ELEMENT);
         }
     }
 
     /**
      * Construct a vector from an array, copying the input array.
      *
      * @param field Field to which the elements belong.
      * @param d Array.
      * @throws NullArgumentException if {@code d} is {@code null}.
      * @see #ArrayFieldVector(FieldElement[])
      */
     public ArrayFieldVector(Field<T> field, T[] d)
             throws NullArgumentException {
         NullArgumentException.check(d);
         this.field = field;
         data = d.clone();
     }
 
     /**
      * Create a new ArrayFieldVector using the input array as the underlying
      * data array.
      * If an array is built specially in order to be embedded in a
      * ArrayFieldVector and not used directly, the {@code copyArray} may be
      * set to {@code false}. This will prevent the copying and improve
      * performance as no new array will be built and no data will be copied.
      * This constructor needs a non-empty {@code d} array to retrieve
      * the field from its first element. This implies it cannot build
      * 0 length vectors. To build vectors from any size, one should
      * use the {@link #ArrayFieldVector(Field, FieldElement[], boolean)}
      * constructor.
      *
      * @param d Data for the new vector.
      * @param copyArray If {@code true}, the input array will be copied,
      * otherwise it will be referenced.
      * @throws NullArgumentException if {@code d} is {@code null}.
      * @throws ZeroException if {@code d} is empty.
      * @see #ArrayFieldVector(FieldElement[])
      * @see #ArrayFieldVector(Field, FieldElement[], boolean)
      */
     public ArrayFieldVector(T[] d, boolean copyArray)
             throws NullArgumentException, ZeroException {
         NullArgumentException.check(d);
         if (d.length == 0) {
             throw new ZeroException(LocalizedFormats.VECTOR_MUST_HAVE_AT_LEAST_ONE_ELEMENT);
         }
         field = d[0].getField();
         data = copyArray ? d.clone() : d;
     }
 
     /**
      * Create a new ArrayFieldVector using the input array as the underlying
      * data array.
      * If an array is built specially in order to be embedded in a
      * ArrayFieldVector and not used directly, the {@code copyArray} may be
      * set to {@code false}. This will prevent the copying and improve
      * performance as no new array will be built and no data will be copied.
      *
      * @param field Field to which the elements belong.
      * @param d Data for the new vector.
      * @param copyArray If {@code true}, the input array will be copied,
      * otherwise it will be referenced.
      * @throws NullArgumentException if {@code d} is {@code null}.
      * @see #ArrayFieldVector(FieldElement[], boolean)
      */
     public ArrayFieldVector(Field<T> field, T[] d, boolean copyArray)
             throws NullArgumentException {
         NullArgumentException.check(d);
         this.field = field;
         data = copyArray ? d.clone() :  d;
     }
 
     /**
      * Construct a vector from part of a array.
      *
      * @param d Array.
      * @param pos Position of the first entry.
      * @param size Number of entries to copy.
      * @throws NullArgumentException if {@code d} is {@code null}.
      * @throws NumberIsTooLargeException if the size of {@code d} is less
      * than {@code pos + size}.
      */
     public ArrayFieldVector(T[] d, int pos, int size)
             throws NullArgumentException, NumberIsTooLargeException {
         NullArgumentException.check(d);
         if (d.length < pos + size) {
             throw new NumberIsTooLargeException(pos + size, d.length, true);
         }
         field = d[0].getField();
         data = MathArrays.buildArray(field, size);
         System.arraycopy(d, pos, data, 0, size);
     }
 
     /**
      * Construct a vector from part of a array.
      *
      * @param field Field to which the elements belong.
      * @param d Array.
      * @param pos Position of the first entry.
      * @param size Number of entries to copy.
      * @throws NullArgumentException if {@code d} is {@code null}.
      * @throws NumberIsTooLargeException if the size of {@code d} is less
      * than {@code pos + size}.
      */
     public ArrayFieldVector(Field<T> field, T[] d, int pos, int size)
             throws NullArgumentException, NumberIsTooLargeException {
         NullArgumentException.check(d);
         if (d.length < pos + size) {
             throw new NumberIsTooLargeException(pos + size, d.length, true);
         }
         this.field = field;
         data = MathArrays.buildArray(field, size);
         System.arraycopy(d, pos, data, 0, size);
     }
 
     /**
      * Construct a vector from another vector, using a deep copy.
      *
      * @param v Vector to copy.
      * @throws NullArgumentException if {@code v} is {@code null}.
      */
     public ArrayFieldVector(FieldVector<T> v)
             throws NullArgumentException {
         NullArgumentException.check(v);
         field = v.getField();
         data = MathArrays.buildArray(field, v.getDimension());
         for (int i = 0; i < data.length; ++i) {
             data[i] = v.getEntry(i);
         }
     }
 
     /**
      * Construct a vector from another vector, using a deep copy.
      *
      * @param v Vector to copy.
      * @throws NullArgumentException if {@code v} is {@code null}.
      */
     public ArrayFieldVector(ArrayFieldVector<T> v)
             throws NullArgumentException {
         NullArgumentException.check(v);
         field = v.getField();
         data = v.data.clone();
     }
 
     /**
      * Construct a vector from another vector.
      *
      * @param v Vector to copy.
      * @param deep If {@code true} perform a deep copy, otherwise perform
      * a shallow copy
      * @throws NullArgumentException if {@code v} is {@code null}.
      */
     public ArrayFieldVector(ArrayFieldVector<T> v, boolean deep)
             throws NullArgumentException {
         NullArgumentException.check(v);
         field = v.getField();
         data = deep ? v.data.clone() : v.data;
     }
 
     /**
      * Construct a vector by appending one vector to another vector.
      *
      * @param v1 First vector (will be put in front of the new vector).
      * @param v2 Second vector (will be put at back of the new vector).
      * @throws NullArgumentException if {@code v1} or {@code v2} is
      * {@code null}.
      * @since 3.2
      */
     public ArrayFieldVector(FieldVector<T> v1, FieldVector<T> v2)
             throws NullArgumentException {
         NullArgumentException.check(v1);
         NullArgumentException.check(v2);
         field = v1.getField();
         final T[] v1Data =
                 (v1 instanceof ArrayFieldVector) ? ((ArrayFieldVector<T>) v1).data : v1.toArray();
         final T[] v2Data =
                 (v2 instanceof ArrayFieldVector) ? ((ArrayFieldVector<T>) v2).data : v2.toArray();
         data = MathArrays.buildArray(field, v1Data.length + v2Data.length);
         System.arraycopy(v1Data, 0, data, 0, v1Data.length);
         System.arraycopy(v2Data, 0, data, v1Data.length, v2Data.length);
     }
 
     /**
      * Construct a vector by appending one vector to another vector.
      *
      * @param v1 First vector (will be put in front of the new vector).
      * @param v2 Second vector (will be put at back of the new vector).
      * @throws NullArgumentException if {@code v1} or {@code v2} is
      * {@code null}.
      * @since 3.2
      */
     public ArrayFieldVector(FieldVector<T> v1, T[] v2)
             throws NullArgumentException {
         NullArgumentException.check(v1);
         NullArgumentException.check(v2);
         field = v1.getField();
         final T[] v1Data =
                 (v1 instanceof ArrayFieldVector) ? ((ArrayFieldVector<T>) v1).data : v1.toArray();
         data = MathArrays.buildArray(field, v1Data.length + v2.length);
         System.arraycopy(v1Data, 0, data, 0, v1Data.length);
         System.arraycopy(v2, 0, data, v1Data.length, v2.length);
     }
 
     /**
      * Construct a vector by appending one vector to another vector.
      *
      * @param v1 First vector (will be put in front of the new vector).
      * @param v2 Second vector (will be put at back of the new vector).
      * @throws NullArgumentException if {@code v1} or {@code v2} is
      * {@code null}.
      * @since 3.2
      */
     public ArrayFieldVector(T[] v1, FieldVector<T> v2)
             throws NullArgumentException {
         NullArgumentException.check(v1);
         NullArgumentException.check(v2);
         field = v2.getField();
         final T[] v2Data =
                 (v2 instanceof ArrayFieldVector) ? ((ArrayFieldVector<T>) v2).data : v2.toArray();
         data = MathArrays.buildArray(field, v1.length + v2Data.length);
         System.arraycopy(v1, 0, data, 0, v1.length);
         System.arraycopy(v2Data, 0, data, v1.length, v2Data.length);
     }
 
     /**
      * Construct a vector by appending one vector to another vector.
      * This constructor needs at least one non-empty array to retrieve
      * the field from its first element. This implies it cannot build
      * 0 length vectors. To build vectors from any size, one should
      * use the {@link #ArrayFieldVector(Field, FieldElement[], FieldElement[])}
      * constructor.
      *
      * @param v1 First vector (will be put in front of the new vector).
      * @param v2 Second vector (will be put at back of the new vector).
      * @throws NullArgumentException if {@code v1} or {@code v2} is
      * {@code null}.
      * @throws ZeroException if both arrays are empty.
      * @see #ArrayFieldVector(Field, FieldElement[], FieldElement[])
      */
     public ArrayFieldVector(T[] v1, T[] v2)
             throws NullArgumentException, ZeroException {
         NullArgumentException.check(v1);
         NullArgumentException.check(v2);
         if (v1.length + v2.length == 0) {
             throw new ZeroException(LocalizedFormats.VECTOR_MUST_HAVE_AT_LEAST_ONE_ELEMENT);
         }
         data = MathArrays.buildArray(v1[0].getField(), v1.length + v2.length);
         System.arraycopy(v1, 0, data, 0, v1.length);
         System.arraycopy(v2, 0, data, v1.length, v2.length);
         field = data[0].getField();
     }
 
     /**
      * Construct a vector by appending one vector to another vector.
      *
      * @param field Field to which the elements belong.
      * @param v1 First vector (will be put in front of the new vector).
      * @param v2 Second vector (will be put at back of the new vector).
      * @throws NullArgumentException if {@code v1} or {@code v2} is
      * {@code null}.
      * @throws ZeroException if both arrays are empty.
      * @see #ArrayFieldVector(FieldElement[], FieldElement[])
      */
     public ArrayFieldVector(Field<T> field, T[] v1, T[] v2)
             throws NullArgumentException, ZeroException {
         NullArgumentException.check(v1);
         NullArgumentException.check(v2);
         if (v1.length + v2.length == 0) {
             throw new ZeroException(LocalizedFormats.VECTOR_MUST_HAVE_AT_LEAST_ONE_ELEMENT);
         }
         data = MathArrays.buildArray(field, v1.length + v2.length);
         System.arraycopy(v1, 0, data, 0, v1.length);
         System.arraycopy(v2, 0, data, v1.length, v2.length);
         this.field = field;
     }
 
     /** {@inheritDoc} */
     @Override
     public Field<T> getField() {
         return field;
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> copy() {
         return new ArrayFieldVector<>(this, true);
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> add(FieldVector<T> v)
         throws DimensionMismatchException {
         if (v instanceof ArrayFieldVector) {
             return add((ArrayFieldVector<T>) v);
         }
 
         checkVectorDimensions(v);
         T[] out = MathArrays.buildArray(field, data.length);
         for (int i = 0; i < data.length; i++) {
             out[i] = data[i].add(v.getEntry(i));
         }
         return new ArrayFieldVector<>(field, out, false);
     }
 
     /**
      * Compute the sum of {@code this} and {@code v}.
      * @param v vector to be added
      * @return {@code this + v}
      * @throws DimensionMismatchException if {@code v} is not the same size as
      * {@code this}
      */
     public ArrayFieldVector<T> add(ArrayFieldVector<T> v)
         throws DimensionMismatchException {
         checkVectorDimensions(v.data.length);
         T[] out = MathArrays.buildArray(field, data.length);
         for (int i = 0; i < data.length; i++) {
             out[i] = data[i].add(v.data[i]);
         }
         return new ArrayFieldVector<>(field, out, false);
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> subtract(FieldVector<T> v)
         throws DimensionMismatchException {
         if (v instanceof ArrayFieldVector) {
             return subtract((ArrayFieldVector<T>) v);
         }
 
         checkVectorDimensions(v);
         T[] out = MathArrays.buildArray(field, data.length);
         for (int i = 0; i < data.length; i++) {
             out[i] = data[i].subtract(v.getEntry(i));
         }
         return new ArrayFieldVector<>(field, out, false);
     }
 
     /**
      * Compute {@code this} minus {@code v}.
      * @param v vector to be subtracted
      * @return {@code this - v}
      * @throws DimensionMismatchException if {@code v} is not the same size as
      * {@code this}
      */
     public ArrayFieldVector<T> subtract(ArrayFieldVector<T> v)
         throws DimensionMismatchException {
         checkVectorDimensions(v.data.length);
         T[] out = MathArrays.buildArray(field, data.length);
         for (int i = 0; i < data.length; i++) {
             out[i] = data[i].subtract(v.data[i]);
         }
         return new ArrayFieldVector<>(field, out, false);
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> mapAdd(T d) throws NullArgumentException {
         T[] out = MathArrays.buildArray(field, data.length);
         for (int i = 0; i < data.length; i++) {
             out[i] = data[i].add(d);
         }
         return new ArrayFieldVector<>(field, out, false);
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> mapAddToSelf(T d) throws NullArgumentException {
         for (int i = 0; i < data.length; i++) {
             data[i] = data[i].add(d);
         }
         return this;
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> mapSubtract(T d) throws NullArgumentException {
         T[] out = MathArrays.buildArray(field, data.length);
         for (int i = 0; i < data.length; i++) {
             out[i] = data[i].subtract(d);
         }
         return new ArrayFieldVector<>(field, out, false);
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> mapSubtractToSelf(T d) throws NullArgumentException {
         for (int i = 0; i < data.length; i++) {
             data[i] = data[i].subtract(d);
         }
         return this;
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> mapMultiply(T d) throws NullArgumentException {
         T[] out = MathArrays.buildArray(field, data.length);
         for (int i = 0; i < data.length; i++) {
             out[i] = data[i].multiply(d);
         }
         return new ArrayFieldVector<>(field, out, false);
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> mapMultiplyToSelf(T d) throws NullArgumentException {
         for (int i = 0; i < data.length; i++) {
             data[i] = data[i].multiply(d);
         }
         return this;
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> mapDivide(T d)
         throws NullArgumentException, MathArithmeticException {
         NullArgumentException.check(d);
         T[] out = MathArrays.buildArray(field, data.length);
         for (int i = 0; i < data.length; i++) {
             out[i] = data[i].divide(d);
         }
         return new ArrayFieldVector<>(field, out, false);
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> mapDivideToSelf(T d)
         throws NullArgumentException, MathArithmeticException {
         NullArgumentException.check(d);
         for (int i = 0; i < data.length; i++) {
             data[i] = data[i].divide(d);
         }
         return this;
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> mapInv() throws MathArithmeticException {
         T[] out = MathArrays.buildArray(field, data.length);
         final T one = field.getOne();
         for (int i = 0; i < data.length; i++) {
             try {
                 out[i] = one.divide(data[i]);
             } catch (final MathArithmeticException e) {
                 throw new MathArithmeticException(LocalizedFormats.INDEX, i);
             }
         }
         return new ArrayFieldVector<>(field, out, false);
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> mapInvToSelf() throws MathArithmeticException {
         final T one = field.getOne();
         for (int i = 0; i < data.length; i++) {
             try {
                 data[i] = one.divide(data[i]);
             } catch (final MathArithmeticException e) {
                 throw new MathArithmeticException(LocalizedFormats.INDEX, i);
             }
         }
         return this;
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> ebeMultiply(FieldVector<T> v)
         throws DimensionMismatchException {
         if (v instanceof ArrayFieldVector) {
             return ebeMultiply((ArrayFieldVector<T>) v);
         }
 
         checkVectorDimensions(v);
         T[] out = MathArrays.buildArray(field, data.length);
         for (int i = 0; i < data.length; i++) {
             out[i] = data[i].multiply(v.getEntry(i));
         }
         return new ArrayFieldVector<>(field, out, false);
     }
 
     /**
      * Element-by-element multiplication.
      * @param v vector by which instance elements must be multiplied
      * @return a vector containing {@code this[i] * v[i]} for all {@code i}
      * @throws DimensionMismatchException if {@code v} is not the same size as
      * {@code this}
      */
     public ArrayFieldVector<T> ebeMultiply(ArrayFieldVector<T> v)
         throws DimensionMismatchException {
         checkVectorDimensions(v.data.length);
         T[] out = MathArrays.buildArray(field, data.length);
         for (int i = 0; i < data.length; i++) {
             out[i] = data[i].multiply(v.data[i]);
         }
         return new ArrayFieldVector<>(field, out, false);
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> ebeDivide(FieldVector<T> v)
         throws DimensionMismatchException, MathArithmeticException {
         if (v instanceof ArrayFieldVector) {
             return ebeDivide((ArrayFieldVector<T>) v);
         }
 
         checkVectorDimensions(v);
         T[] out = MathArrays.buildArray(field, data.length);
         for (int i = 0; i < data.length; i++) {
             try {
                 out[i] = data[i].divide(v.getEntry(i));
             } catch (final MathArithmeticException e) {
                 throw new MathArithmeticException(LocalizedFormats.INDEX, i);
             }
         }
         return new ArrayFieldVector<>(field, out, false);
     }
 
     /**
      * Element-by-element division.
      * @param v vector by which instance elements must be divided
      * @return a vector containing {@code this[i] / v[i]} for all {@code i}
      * @throws DimensionMismatchException if {@code v} is not the same size as
      * {@code this}
      * @throws MathArithmeticException if one entry of {@code v} is zero.
      */
     public ArrayFieldVector<T> ebeDivide(ArrayFieldVector<T> v)
         throws DimensionMismatchException, MathArithmeticException {
         checkVectorDimensions(v.data.length);
         T[] out = MathArrays.buildArray(field, data.length);
         for (int i = 0; i < data.length; i++) {
             try {
                 out[i] = data[i].divide(v.data[i]);
             } catch (final MathArithmeticException e) {
                 throw new MathArithmeticException(LocalizedFormats.INDEX, i);
             }
         }
         return new ArrayFieldVector<>(field, out, false);
     }
 
     /**
      * Returns a reference to the underlying data array.
      * <p>Does not make a fresh copy of the underlying data.</p>
      * @return array of entries
      */
     public T[] getDataRef() {
         return data;
     }
 
     /** {@inheritDoc} */
     @Override
     public T dotProduct(FieldVector<T> v)
         throws DimensionMismatchException {
         if (v instanceof ArrayFieldVector) {
             return dotProduct((ArrayFieldVector<T>) v);
         }
 
         checkVectorDimensions(v);
         T dot = field.getZero();
         for (int i = 0; i < data.length; i++) {
             dot = dot.add(data[i].multiply(v.getEntry(i)));
         }
         return dot;
     }
 
     /**
      * Compute the dot product.
      * @param v vector with which dot product should be computed
      * @return the scalar dot product of {@code this} and {@code v}
      * @throws DimensionMismatchException if {@code v} is not the same size as
      * {@code this}
      */
     public T dotProduct(ArrayFieldVector<T> v)
         throws DimensionMismatchException {
         checkVectorDimensions(v.data.length);
         T dot = field.getZero();
         for (int i = 0; i < data.length; i++) {
             dot = dot.add(data[i].multiply(v.data[i]));
         }
         return dot;
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> projection(FieldVector<T> v)
         throws DimensionMismatchException, MathArithmeticException {
         return v.mapMultiply(dotProduct(v).divide(v.dotProduct(v)));
     }
 
     /** Find the orthogonal projection of this vector onto another vector.
      * @param v vector onto which {@code this} must be projected
      * @return projection of {@code this} onto {@code v}
      * @throws DimensionMismatchException if {@code v} is not the same size as
      * {@code this}
      * @throws MathArithmeticException if {@code v} is the null vector.
      */
     public ArrayFieldVector<T> projection(ArrayFieldVector<T> v)
         throws DimensionMismatchException, MathArithmeticException {
         return (ArrayFieldVector<T>) v.mapMultiply(dotProduct(v).divide(v.dotProduct(v)));
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldMatrix<T> outerProduct(FieldVector<T> v) {
         if (v instanceof ArrayFieldVector) {
             return outerProduct((ArrayFieldVector<T>) v);
         }
 
         final int m = data.length;
         final int n = v.getDimension();
         final FieldMatrix<T> out = new Array2DRowFieldMatrix<>(field, m, n);
         for (int i = 0; i < m; i++) {
             for (int j = 0; j < n; j++) {
                 out.setEntry(i, j, data[i].multiply(v.getEntry(j)));
             }
         }
         return out;
     }
 
     /**
      * Compute the outer product.
      * @param v vector with which outer product should be computed
      * @return the matrix outer product between instance and v
      */
     public FieldMatrix<T> outerProduct(ArrayFieldVector<T> v) {
         final int m = data.length;
         final int n = v.data.length;
         final FieldMatrix<T> out = new Array2DRowFieldMatrix<>(field, m, n);
         for (int i = 0; i < m; i++) {
             for (int j = 0; j < n; j++) {
                 out.setEntry(i, j, data[i].multiply(v.data[j]));
             }
         }
         return out;
     }
 
     /** {@inheritDoc} */
     @Override
     public T getEntry(int index) {
         return data[index];
     }
 
     /** {@inheritDoc} */
     @Override
     public int getDimension() {
         return data.length;
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> append(FieldVector<T> v) {
         if (v instanceof ArrayFieldVector) {
             return append((ArrayFieldVector<T>) v);
         }
 
         return new ArrayFieldVector<>(this,new ArrayFieldVector<>(v));
     }
 
     /**
      * Construct a vector by appending a vector to this vector.
      * @param v vector to append to this one.
      * @return a new vector
      */
     public ArrayFieldVector<T> append(ArrayFieldVector<T> v) {
         return new ArrayFieldVector<>(this, v);
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> append(T in) {
         final T[] out = MathArrays.buildArray(field, data.length + 1);
         System.arraycopy(data, 0, out, 0, data.length);
         out[data.length] = in;
         return new ArrayFieldVector<>(field, out, false);
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldVector<T> getSubVector(int index, int n)
         throws OutOfRangeException, NotPositiveException {
         if (n < 0) {
             throw new NotPositiveException(LocalizedFormats.NUMBER_OF_ELEMENTS_SHOULD_BE_POSITIVE, n);
         }
         ArrayFieldVector<T> out = new ArrayFieldVector<>(field, n);
         try {
             System.arraycopy(data, index, out.data, 0, n);
         } catch (IndexOutOfBoundsException e) {
             checkIndex(index);
             checkIndex(index + n - 1);
         }
         return out;
     }
 
     /** {@inheritDoc} */
     @Override
     public void setEntry(int index, T value) {
         try {
             data[index] = value;
         } catch (IndexOutOfBoundsException e) {
             checkIndex(index);
         }
     }
 
     /** {@inheritDoc} */
     @Override
     public void setSubVector(int index, FieldVector<T> v) throws OutOfRangeException {
         try {
             if (v instanceof ArrayFieldVector) {
                 set(index, (ArrayFieldVector<T>) v);
             } else {
                 for (int i = index; i < index + v.getDimension(); ++i) {
                     data[i] = v.getEntry(i-index);
                 }
             }
         } catch (IndexOutOfBoundsException e) {
             checkIndex(index);
             checkIndex(index + v.getDimension() - 1);
         }
     }
 
     /**
      * Set a set of consecutive elements.
      *
      * @param index index of first element to be set.
      * @param v vector containing the values to set.
      * @throws OutOfRangeException if the index is invalid.
      */
     public void set(int index, ArrayFieldVector<T> v) throws OutOfRangeException {
         try {
             System.arraycopy(v.data, 0, data, index, v.data.length);
         } catch (IndexOutOfBoundsException e) {
             checkIndex(index);
             checkIndex(index + v.data.length - 1);
         }
     }
 
     /** {@inheritDoc} */
     @Override
     public void set(T value) {
         Arrays.fill(data, value);
     }
 
     /** {@inheritDoc} */
     @Override
     public T[] toArray(){
         return data.clone();
     }
 
     /**
      * Check if instance and specified vectors have the same dimension.
      * @param v vector to compare instance with
      * @exception DimensionMismatchException if the vectors do not
      * have the same dimensions
      */
     protected void checkVectorDimensions(FieldVector<T> v)
         throws DimensionMismatchException {
         checkVectorDimensions(v.getDimension());
     }
 
     /**
      * Check if instance dimension is equal to some expected value.
      *
      * @param n Expected dimension.
      * @throws DimensionMismatchException if the dimension is not equal to the
      * size of {@code this} vector.
      */
     protected void checkVectorDimensions(int n)
         throws DimensionMismatchException {
         if (data.length != n) {
             throw new DimensionMismatchException(data.length, n);
         }
     }
 
     /**
      * Visits (but does not alter) all entries of this vector in default order
      * (increasing index).
      *
      * @param visitor the visitor to be used to process the entries of this
      * vector
      * @return the value returned by {@link FieldVectorPreservingVisitor#end()}
      * at the end of the walk
      * @since 3.3
      */
     public T walkInDefaultOrder(final FieldVectorPreservingVisitor<T> visitor) {
         final int dim = getDimension();
         visitor.start(dim, 0, dim - 1);
         for (int i = 0; i < dim; i++) {
             visitor.visit(i, getEntry(i));
         }
         return visitor.end();
     }
 
     /**
      * Visits (but does not alter) some entries of this vector in default order
      * (increasing index).
      *
      * @param visitor visitor to be used to process the entries of this vector
      * @param start the index of the first entry to be visited
      * @param end the index of the last entry to be visited (inclusive)
      * @return the value returned by {@link FieldVectorPreservingVisitor#end()}
      * at the end of the walk
      * @throws NumberIsTooSmallException if {@code end < start}.
      * @throws OutOfRangeException if the indices are not valid.
      * @since 3.3
      */
     public T walkInDefaultOrder(final FieldVectorPreservingVisitor<T> visitor,
                                 final int start, final int end)
         throws NumberIsTooSmallException, OutOfRangeException {
         checkIndices(start, end);
         visitor.start(getDimension(), start, end);
         for (int i = start; i <= end; i++) {
             visitor.visit(i, getEntry(i));
         }
         return visitor.end();
     }
 
     /**
      * Visits (but does not alter) all entries of this vector in optimized
      * order. The order in which the entries are visited is selected so as to
      * lead to the most efficient implementation; it might depend on the
      * concrete implementation of this abstract class.
      *
      * @param visitor the visitor to be used to process the entries of this
      * vector
      * @return the value returned by {@link FieldVectorPreservingVisitor#end()}
      * at the end of the walk
      * @since 3.3
      */
     public T walkInOptimizedOrder(final FieldVectorPreservingVisitor<T> visitor) {
         return walkInDefaultOrder(visitor);
     }
 
     /**
      * Visits (but does not alter) some entries of this vector in optimized
      * order. The order in which the entries are visited is selected so as to
      * lead to the most efficient implementation; it might depend on the
      * concrete implementation of this abstract class.
      *
      * @param visitor visitor to be used to process the entries of this vector
      * @param start the index of the first entry to be visited
      * @param end the index of the last entry to be visited (inclusive)
      * @return the value returned by {@link FieldVectorPreservingVisitor#end()}
      * at the end of the walk
      * @throws NumberIsTooSmallException if {@code end < start}.
      * @throws OutOfRangeException if the indices are not valid.
      * @since 3.3
      */
     public T walkInOptimizedOrder(final FieldVectorPreservingVisitor<T> visitor,
                                   final int start, final int end)
         throws NumberIsTooSmallException, OutOfRangeException {
         return walkInDefaultOrder(visitor, start, end);
     }
 
     /**
      * Visits (and possibly alters) all entries of this vector in default order
      * (increasing index).
      *
      * @param visitor the visitor to be used to process and modify the entries
      * of this vector
      * @return the value returned by {@link FieldVectorChangingVisitor#end()}
      * at the end of the walk
      * @since 3.3
      */
     public T walkInDefaultOrder(final FieldVectorChangingVisitor<T> visitor) {
         final int dim = getDimension();
         visitor.start(dim, 0, dim - 1);
         for (int i = 0; i < dim; i++) {
             setEntry(i, visitor.visit(i, getEntry(i)));
         }
         return visitor.end();
     }
 
     /**
      * Visits (and possibly alters) some entries of this vector in default order
      * (increasing index).
      *
      * @param visitor visitor to be used to process the entries of this vector
      * @param start the index of the first entry to be visited
      * @param end the index of the last entry to be visited (inclusive)
      * @return the value returned by {@link FieldVectorChangingVisitor#end()}
      * at the end of the walk
      * @throws NumberIsTooSmallException if {@code end < start}.
      * @throws OutOfRangeException if the indices are not valid.
      * @since 3.3
      */
     public T walkInDefaultOrder(final FieldVectorChangingVisitor<T> visitor,
                                 final int start, final int end)
         throws NumberIsTooSmallException, OutOfRangeException {
         checkIndices(start, end);
         visitor.start(getDimension(), start, end);
         for (int i = start; i <= end; i++) {
             setEntry(i, visitor.visit(i, getEntry(i)));
         }
         return visitor.end();
     }
 
     /**
      * Visits (and possibly alters) all entries of this vector in optimized
      * order. The order in which the entries are visited is selected so as to
      * lead to the most efficient implementation; it might depend on the
      * concrete implementation of this abstract class.
      *
      * @param visitor the visitor to be used to process the entries of this
      * vector
      * @return the value returned by {@link FieldVectorChangingVisitor#end()}
      * at the end of the walk
      * @since 3.3
      */
     public T walkInOptimizedOrder(final FieldVectorChangingVisitor<T> visitor) {
         return walkInDefaultOrder(visitor);
     }
 
     /**
      * Visits (and possibly change) some entries of this vector in optimized
      * order. The order in which the entries are visited is selected so as to
      * lead to the most efficient implementation; it might depend on the
      * concrete implementation of this abstract class.
      *
      * @param visitor visitor to be used to process the entries of this vector
      * @param start the index of the first entry to be visited
      * @param end the index of the last entry to be visited (inclusive)
      * @return the value returned by {@link FieldVectorChangingVisitor#end()}
      * at the end of the walk
      * @throws NumberIsTooSmallException if {@code end < start}.
      * @throws OutOfRangeException if the indices are not valid.
      * @since 3.3
      */
     public T walkInOptimizedOrder(final FieldVectorChangingVisitor<T> visitor,
                                   final int start, final int end)
         throws NumberIsTooSmallException, OutOfRangeException {
         return walkInDefaultOrder(visitor, start, end);
     }
 
     /**
      * Test for the equality of two vectors.
      *
      * @param other Object to test for equality.
      * @return {@code true} if two vector objects are equal, {@code false}
      * otherwise.
      */
     @Override
     public boolean equals(Object other) {
         if (this == other) {
             return true;
         }
         if (other == null) {
             return false;
         }
 
         if (!(other instanceof FieldVector)) {
             return false;
         }
 
         FieldVector rhs = (FieldVector) other;
         if (data.length != rhs.getDimension()) {
             return false;
         }
 
         for (int i = 0; i < data.length; ++i) {
             if (!data[i].equals(rhs.getEntry(i))) {
                 return false;
             }
         }
         return true;
     }
 
     /**
      * Get a hashCode for the real vector.
      * <p>All NaN values have the same hash code.</p>
      * @return a hash code value for this object
      */
     @Override
     public int hashCode() {
         int h = 3542;
         for (final T a : data) {
             h ^= a.hashCode();
         }
         return h;
     }
 
     /**
      * Check if an index is valid.
      *
      * @param index Index to check.
      * @exception OutOfRangeException if the index is not valid.
      */
     private void checkIndex(final int index) throws OutOfRangeException {
         if (index < 0 || index >= getDimension()) {
             throw new OutOfRangeException(LocalizedFormats.INDEX,
                                           index, 0, getDimension() - 1);
         }
     }
 
     /**
      * Checks that the indices of a subvector are valid.
      *
      * @param start the index of the first entry of the subvector
      * @param end the index of the last entry of the subvector (inclusive)
      * @throws OutOfRangeException if {@code start} of {@code end} are not valid
      * @throws NumberIsTooSmallException if {@code end < start}
      * @since 3.3
      */
     private void checkIndices(final int start, final int end)
         throws NumberIsTooSmallException, OutOfRangeException {
         final int dim = getDimension();
         if (start < 0 || start >= dim) {
             throw new OutOfRangeException(LocalizedFormats.INDEX, start, 0,
                                           dim - 1);
         }
         if (end < 0 || end >= dim) {
             throw new OutOfRangeException(LocalizedFormats.INDEX, end, 0,
                                           dim - 1);
         }
         if (end < start) {
             throw new NumberIsTooSmallException(LocalizedFormats.INITIAL_ROW_AFTER_FINAL_ROW,
                                                 end, start, false);
         }
     }
 }