deal.II/lac/vector.h

// ---------------------------------------------------------------------
//
// Copyright (C) 1999 - 2020 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE.md at
// the top level directory of deal.II.
//
// ---------------------------------------------------------------------

#ifndef dealii_vector_h
#define dealii_vector_h


#include <deal.II/base/config.h>

#include <deal.II/base/aligned_vector.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/index_set.h>
#include <deal.II/base/subscriptor.h>

#include <deal.II/differentiation/ad/ad_number_traits.h>

#include <deal.II/lac/vector_operation.h>
#include <deal.II/lac/vector_type_traits.h>

#include <boost/serialization/split_member.hpp>

#include <algorithm>
#include <initializer_list>
#include <iosfwd>
#include <iterator>
#include <vector>

DEAL_II_NAMESPACE_OPEN


// Forward declarations
#ifndef DOXYGEN
#  ifdef DEAL_II_WITH_PETSC
namespace PETScWrappers
{
  class VectorBase;
}
#  endif

#  ifdef DEAL_II_WITH_TRILINOS
namespace TrilinosWrappers
{
  namespace MPI
  {
    class Vector;
  }
} // namespace TrilinosWrappers
#  endif

template <typename number>
class LAPACKFullMatrix;

template <typename>
class BlockVector;

namespace parallel
{
  namespace internal
  {
    class TBBPartitioner;
  }
} // namespace parallel
#endif


/*! @addtogroup Vectors
 *@{
 */

/**
 * A class that represents a vector of numerical elements. As for the
 * other classes, in the
 * @ref Vectors
 * group, this class has a substantial
 * number of member functions. These include:
 * - functions that initialize the vector or change its size;
 * - functions that compute properties of the vector, such as a variety of
 *   norms;
 * - functions that allow reading from or writing to individual elements of the
 *   vector;
 * - functions that implement algebraic operations for vectors, such as
 *   addition of vectors; and
 * - functions that allow inputting and outputting the data stored by vectors.
 *
 * In contrast to the C++ standard library class `std::vector`, this class
 * intends to implement not simply an array that allows access to its elements,
 * but indeed a vector that is a member of the mathematical concept of a
 * "vector space" suitable for numerical computations.
 *
 * @note Instantiations for this template are provided for <tt>@<float@>,
 * @<double@>, @<std::complex@<float@>@>, @<std::complex@<double@>@></tt>;
 * others can be generated in application programs (see the section on
 * @ref Instantiations
 * in the manual).
 */
template <typename Number>
class Vector : public Subscriptor
{
public:
  // The assertion in vector.templates.h for whether or not a number is
  // finite is not compatible for AD number types.
  static_assert(
    !Differentiation::AD::is_ad_number<Number>::value,
    "The Vector class does not support auto-differentiable numbers.");

  /**
   * Declare standard types used in all containers. These types parallel those
   * in the <tt>C++</tt> standard libraries <tt>vector<...></tt> class.
   */
  using value_type      = Number;
  using pointer         = value_type *;
  using const_pointer   = const value_type *;
  using iterator        = value_type *;
  using const_iterator  = const value_type *;
  using reference       = value_type &;
  using const_reference = const value_type &;
  using size_type       = types::global_dof_index;

  /**
   * Declare a type that has holds real-valued numbers with the same precision
   * as the template argument to this class. If the template argument of this
   * class is a real data type, then real_type equals the template argument.
   * If the template argument is a std::complex type then real_type equals the
   * type underlying the complex numbers.
   *
   * This alias is used to represent the return type of norms.
   */
  using real_type = typename numbers::NumberTraits<Number>::real_type;

  /**
   * @name Basic object handling
   */
  //@{
  /**
   * Constructor. Create a vector of dimension zero.
   */
  Vector();

  /**
   * Copy constructor. Sets the dimension to that of the given vector, and
   * copies all elements.
   *
   * We would like to make this constructor explicit, but standard containers
   * insist on using it implicitly.
   *
   * @dealiiOperationIsMultithreaded
   */
  Vector(const Vector<Number> &v);

  /**
   * Move constructor. Creates a new vector by stealing the internal data of
   * the vector @p v.
   */
  Vector(Vector<Number> &&v) noexcept = default;

  /**
   * Copy constructor taking a vector of another data type.
   *
   * This constructor will fail to compile if
   * there is no conversion path from @p OtherNumber to @p Number. You may
   * lose accuracy when copying to a vector with data elements with
   * less accuracy.
   */
  template <typename OtherNumber>
  explicit Vector(const Vector<OtherNumber> &v);

  /**
   * Copy constructor taking an object of type `std::initializer_list`. This
   * constructor can be used to initialize a vector using a brace-enclosed
   * list of numbers, such as in the following example:
   * @code
   *   Vector<double> v({1,2,3});
   * @endcode
   * This creates a vector of size 3, whose (double precision) elements have
   * values 1.0, 2.0, and 3.0.
   *
   * This constructor will fail to compile if
   * there is no conversion path from @p OtherNumber to @p Number. You may
   * lose accuracy when copying to a vector with data elements with
   * less accuracy.
   */
  template <typename OtherNumber>
  explicit Vector(const std::initializer_list<OtherNumber> &v);

#ifdef DEAL_II_WITH_PETSC
  /**
   * Another copy constructor: copy the values from a PETSc vector class. This
   * copy constructor is only available if PETSc was detected during
   * configuration time.
   *
   * Note that due to the communication model used in MPI, this operation can
   * only succeed if all processes do it at the same time when <code>v</code>
   * is a distributed vector: It is not possible for only one process to
   * obtain a copy of a parallel vector while the other jobs do something
   * else.
   */
  explicit Vector(const PETScWrappers::VectorBase &v);
#endif

#ifdef DEAL_II_WITH_TRILINOS
  /**
   * Another copy constructor: copy the values from a Trilinos wrapper vector.
   * This copy constructor is only available if Trilinos was detected during
   * configuration time.
   *
   * @note Due to the communication model used in MPI, this operation can
   * only succeed if all processes that have knowledge of @p v
   * (i.e. those given by <code>v.get_mpi_communicator()</code>) do it at
   * the same time. This means that unless you use a split MPI communicator
   * then it is not normally possible for only one or a subset of processes
   * to obtain a copy of a parallel vector while the other jobs do something
   * else. In other words, calling this function is a 'collective operation'
   * that needs to be executed by all MPI processes that jointly share @p v.
   */
  explicit Vector(const TrilinosWrappers::MPI::Vector &v);
#endif

  /**
   * Constructor. Set dimension to @p n and initialize all elements with zero.
   *
   * The constructor is made explicit to avoid accidents like this:
   * <tt>v=0;</tt>. Presumably, the user wants to set every element of the
   * vector to zero, but instead, what happens is this call:
   * <tt>v=Vector@<number@>(0);</tt>, i.e. the vector is replaced by one of
   * length zero.
   */
  explicit Vector(const size_type n);

  /**
   * Initialize the vector with a given range of values pointed to by the
   * iterators. This function is there in analogy to the @p std::vector class.
   */
  template <typename InputIterator>
  Vector(const InputIterator first, const InputIterator last);

  /**
   * Destructor, deallocates memory. Made virtual to allow for derived classes
   * to behave properly.
   */
  virtual ~Vector() override = default;

  /**
   * This function does nothing but exists for compatibility with the parallel
   * vector classes.
   *
   * For the parallel vector wrapper class, this function compresses the
   * underlying representation of the vector, i.e. flushes the buffers of the
   * vector object if it has any. This function is necessary after writing
   * into a vector element-by-element and before anything else can be done on
   * it.
   *
   * However, for the implementation of this class, it is immaterial and thus
   * an empty function.
   */
  void
  compress(::dealii::VectorOperation::values operation =
             ::dealii::VectorOperation::unknown) const;

  /**
   * Change the dimension of the vector to @p N. The reserved memory for this
   * vector remains unchanged if possible, to make things faster; this may
   * waste some memory, so keep this in mind.  However, if <tt>N==0</tt> all
   * memory is freed, i.e. if you want to resize the vector and release the
   * memory not needed, you have to first call <tt>reinit(0)</tt> and then
   * <tt>reinit(N)</tt>. This cited behaviour is analogous to that of the
   * standard library containers.
   *
   * If @p omit_zeroing_entries is false, the vector is filled by zeros.
   * Otherwise, the elements are left an unspecified state.
   *
   * This function is virtual in order to allow for derived classes to handle
   * memory separately.
   */
  virtual void
  reinit(const size_type N, const bool omit_zeroing_entries = false);

  /**
   * Same as above, but will preserve the values of vector upon resizing.
   * If we new size is bigger, we will have
   * \f[
   * \mathbf V \rightarrow
   * \left(
   * \begin{array}{c}
   * \mathbf V   \\
   * \mathbf 0
   * \end{array}
   * \right)
   * \f]
   * whereas if the desired size is smaller, then
   * \f[
   * \left(
   * \begin{array}{c}
   * \mathbf V_1   \\
   * \mathbf V_2
   * \end{array}
   * \right)
   * \rightarrow \mathbf V_1
   * \f]
   */
  void
  grow_or_shrink(const size_type N);

  /**
   * Apply <a href="https://en.wikipedia.org/wiki/Givens_rotation">Givens
   * rotation</a>
   * @p csr (a triplet of cosine, sine and radius, see
   * Utilities::LinearAlgebra::givens_rotation())
   * to the vector in the plane spanned by the @p i'th and @p k'th unit vectors.
   */
  void
  apply_givens_rotation(const std::array<Number, 3> &csr,
                        const size_type              i,
                        const size_type              k);

  /**
   * Change the dimension to that of the vector @p V. The same applies as for
   * the other @p reinit function.
   *
   * The elements of @p V are not copied, i.e.  this function is the same as
   * calling <tt>reinit (V.size(), omit_zeroing_entries)</tt>.
   */
  template <typename Number2>
  void
  reinit(const Vector<Number2> &V, const bool omit_zeroing_entries = false);

  /**
   * Swap the contents of this vector and the other vector @p v. One could do
   * this operation with a temporary variable and copying over the data
   * elements, but this function is significantly more efficient since it only
   * swaps the pointers to the data of the two vectors and therefore does not
   * need to allocate temporary storage and move data around.
   *
   * This function is analogous to the @p swap function of all C++
   * standard containers. Also, there is a global function <tt>swap(u,v)</tt>
   * that simply calls <tt>u.swap(v)</tt>, again in analogy to standard
   * functions.
   *
   * This function is virtual in order to allow for derived classes to handle
   * memory separately.
   */
  virtual void
  swap(Vector<Number> &v);

  /**
   * Set all components of the vector to the given number @p s.
   *
   * Since the semantics of assigning a scalar to a vector are not immediately
   * clear, this operator should really only be used if you want to set the
   * entire vector to zero. This allows the intuitive notation <tt>v=0</tt>.
   * Assigning other values is deprecated and may be disallowed in the future.
   *
   * @dealiiOperationIsMultithreaded
   */
  Vector<Number> &
  operator=(const Number s);

  /**
   * Copy the given vector. Resize the present vector if necessary.
   *
   * @dealiiOperationIsMultithreaded
   */
  Vector<Number> &
  operator=(const Vector<Number> &v);

  /**
   * Move the given vector. This operator replaces the present vector with
   * the internal data of the vector @p v and resets @p v to the state it would
   * have after being newly default-constructed.
   */
  Vector<Number> &
  operator=(Vector<Number> &&v) noexcept = default;

  /**
   * Copy the given vector. Resize the present vector if necessary.
   *
   * @dealiiOperationIsMultithreaded
   */
  template <typename Number2>
  Vector<Number> &
  operator=(const Vector<Number2> &v);

  /**
   * Copy operator for assigning a block vector to a regular vector.
   */
  Vector<Number> &
  operator=(const BlockVector<Number> &v);

#ifdef DEAL_II_WITH_PETSC
  /**
   * Another copy operator: copy the values from a PETSc wrapper vector
   * class. This operator is only available if PETSc was detected during
   * configuration time.
   *
   * Note that due to the communication model used in MPI, this operation can
   * only succeed if all processes do it at the same time when <code>v</code>
   * is a distributed vector: It is not possible for only one process to
   * obtain a copy of a parallel vector while the other jobs do something
   * else.
   */
  Vector<Number> &
  operator=(const PETScWrappers::VectorBase &v);
#endif


#ifdef DEAL_II_WITH_TRILINOS
  /**
   * Another copy operator: copy the values from a (sequential or parallel,
   * depending on the underlying compiler) Trilinos wrapper vector class. This
   * operator is only available if Trilinos was detected during configuration
   * time.
   *
   * @note Due to the communication model used in MPI, this operation can
   * only succeed if all processes that have knowledge of @p v
   * (i.e. those given by <code>v.get_mpi_communicator()</code>) do it at
   * the same time. This means that unless you use a split MPI communicator
   * then it is not normally possible for only one or a subset of processes
   * to obtain a copy of a parallel vector while the other jobs do something
   * else. In other words, calling this function is a 'collective operation'
   * that needs to be executed by all MPI processes that jointly share @p v.
   */
  Vector<Number> &
  operator=(const TrilinosWrappers::MPI::Vector &v);
#endif

  /**
   * Test for equality. This function assumes that the present vector and the
   * one to compare with have the same size already, since comparing vectors
   * of different sizes makes not much sense anyway.
   */
  template <typename Number2>
  bool
  operator==(const Vector<Number2> &v) const;

  /**
   * Test for inequality. This function assumes that the present vector and
   * the one to compare with have the same size already, since comparing
   * vectors of different sizes makes not much sense anyway.
   */
  template <typename Number2>
  bool
  operator!=(const Vector<Number2> &v) const;

  //@}


  /**
   * @name Scalar products, norms and related operations
   */
  //@{

  /**
   * Return the scalar product of two vectors.  The return type is the
   * underlying type of @p this vector, so the return type and the accuracy
   * with which it the result is computed depend on the order of the arguments
   * of this vector.
   *
   * For complex vectors, the scalar product is implemented as
   * $\left<v,w\right>=\sum_i v_i \bar{w_i}$.
   *
   * @dealiiOperationIsMultithreaded The algorithm uses pairwise summation
   * with the same order of summation in every run, which gives fully
   * repeatable results from one run to another.
   */
  template <typename Number2>
  Number operator*(const Vector<Number2> &V) const;

  /**
   * Return the square of the $l_2$-norm.
   *
   * @dealiiOperationIsMultithreaded The algorithm uses pairwise summation
   * with the same order of summation in every run, which gives fully
   * repeatable results from one run to another.
   */
  real_type
  norm_sqr() const;

  /**
   * Mean value of the elements of this vector.
   *
   * @dealiiOperationIsMultithreaded The algorithm uses pairwise summation
   * with the same order of summation in every run, which gives fully
   * repeatable results from one run to another.
   */
  Number
  mean_value() const;

  /**
   * $l_1$-norm of the vector. The sum of the absolute values.
   *
   * @dealiiOperationIsMultithreaded The algorithm uses pairwise summation
   * with the same order of summation in every run, which gives fully
   * repeatable results from one run to another.
   */
  real_type
  l1_norm() const;

  /**
   * $l_2$-norm of the vector. The square root of the sum of the squares of
   * the elements.
   *
   * @dealiiOperationIsMultithreaded The algorithm uses pairwise summation
   * with the same order of summation in every run, which gives fully
   * repeatable results from one run to another.
   */
  real_type
  l2_norm() const;

  /**
   * $l_p$-norm of the vector. The pth root of the sum of the pth powers of
   * the absolute values of the elements.
   *
   * @dealiiOperationIsMultithreaded The algorithm uses pairwise summation
   * with the same order of summation in every run, which gives fully
   * repeatable results from one run to another.
   */
  real_type
  lp_norm(const real_type p) const;

  /**
   * Maximum absolute value of the elements.
   */
  real_type
  linfty_norm() const;

  /**
   * Performs a combined operation of a vector addition and a subsequent inner
   * product, returning the value of the inner product. In other words, the
   * result of this function is the same as if the user called
   * @code
   * this->add(a, V);
   * return_value = *this * W;
   * @endcode
   *
   * The reason this function exists is that this operation involves less
   * memory transfer than calling the two functions separately. This method
   * only needs to load three vectors, @p this, @p V, @p W, whereas calling
   * separate methods means to load the calling vector @p this twice. Since
   * most vector operations are memory transfer limited, this reduces the time
   * by 25\% (or 50\% if @p W equals @p this).
   *
   * For complex-valued vectors, the scalar product in the second step is
   * implemented as
   * $\left<v,w\right>=\sum_i v_i \bar{w_i}$.
   *
   * @dealiiOperationIsMultithreaded The algorithm uses pairwise summation
   * with the same order of summation in every run, which gives fully
   * repeatable results from one run to another.
   */
  Number
  add_and_dot(const Number a, const Vector<Number> &V, const Vector<Number> &W);

  //@}


  /**
   * @name Data access
   */
  //@{

  /**
   * Return a pointer to the underlying data buffer.
   */
  pointer
  data();

  /**
   * Return a const pointer to the underlying data buffer.
   */
  const_pointer
  data() const;

  /**
   * Make the @p Vector class a bit like the <tt>vector<></tt> class of the
   * C++ standard library by returning iterators to the start and end of the
   * elements of this vector.
   */
  iterator
  begin();

  /**
   * Return constant iterator to the start of the vectors.
   */
  const_iterator
  begin() const;

  /**
   * Return an iterator pointing to the element past the end of the array.
   */
  iterator
  end();

  /**
   * Return a constant iterator pointing to the element past the end of the
   * array.
   */
  const_iterator
  end() const;

  /**
   * Access the value of the @p ith component.
   */
  Number
  operator()(const size_type i) const;

  /**
   * Access the @p ith component as a writeable reference.
   */
  Number &
  operator()(const size_type i);

  /**
   * Access the value of the @p ith component.
   *
   * Exactly the same as operator().
   */
  Number operator[](const size_type i) const;

  /**
   * Access the @p ith component as a writeable reference.
   *
   * Exactly the same as operator().
   */
  Number &operator[](const size_type i);

  /**
   * Instead of getting individual elements of a vector via operator(),
   * this function allows getting a whole set of elements at once. The
   * indices of the elements to be read are stated in the first argument, the
   * corresponding values are returned in the second.
   *
   * If the current vector is called @p v, then this function is the equivalent
   * to the code
   * @code
   *   for (unsigned int i = 0; i < indices.size(); ++i)
   *     values[i] = v[indices[i]];
   * @endcode
   *
   * @pre The sizes of the @p indices and @p values arrays must be identical.
   */
  template <typename OtherNumber>
  void
  extract_subvector_to(const std::vector<size_type> &indices,
                       std::vector<OtherNumber> &    values) const;

  /**
   * Instead of getting individual elements of a vector via operator(),
   * this function allows getting a whole set of elements at once. In
   * contrast to the previous function, this function obtains the
   * indices of the elements by dereferencing all elements of the iterator
   * range provided by the first two arguments, and puts the vector
   * values into memory locations obtained by dereferencing a range
   * of iterators starting at the location pointed to by the third
   * argument.
   *
   * If the current vector is called @p v, then this function is the equivalent
   * to the code
   * @code
   *   ForwardIterator indices_p = indices_begin;
   *   OutputIterator  values_p  = values_begin;
   *   while (indices_p != indices_end)
   *     {
   *       *values_p = v[*indices_p];
   *       ++indices_p;
   *       ++values_p;
   *     }
   * @endcode
   *
   * @pre It must be possible to write into as many memory locations
   *   starting at @p values_begin as there are iterators between
   *   @p indices_begin and @p indices_end.
   */
  template <typename ForwardIterator, typename OutputIterator>
  void
  extract_subvector_to(ForwardIterator       indices_begin,
                       const ForwardIterator indices_end,
                       OutputIterator        values_begin) const;
  //@}


  /**
   * @name Modification of vectors
   */
  //@{

  /**
   * Add the given vector to the present one.
   *
   * @dealiiOperationIsMultithreaded
   */
  Vector<Number> &
  operator+=(const Vector<Number> &V);

  /**
   * Subtract the given vector from the present one.
   *
   * @dealiiOperationIsMultithreaded
   */
  Vector<Number> &
  operator-=(const Vector<Number> &V);

  /**
   * A collective add operation: This function adds a whole set of values
   * stored in @p values to the vector components specified by @p indices.
   */
  template <typename OtherNumber>
  void
  add(const std::vector<size_type> &  indices,
      const std::vector<OtherNumber> &values);

  /**
   * This is a second collective add operation. As a difference, this function
   * takes a deal.II vector of values.
   */
  template <typename OtherNumber>
  void
  add(const std::vector<size_type> &indices, const Vector<OtherNumber> &values);

  /**
   * Take an address where <tt>n_elements</tt> are stored contiguously and add
   * them into the vector. Handles all cases which are not covered by the
   * other two <tt>add()</tt> functions above.
   */
  template <typename OtherNumber>
  void
  add(const size_type    n_elements,
      const size_type *  indices,
      const OtherNumber *values);

  /**
   * Addition of @p s to all components. Note that @p s is a scalar and not a
   * vector.
   *
   * @dealiiOperationIsMultithreaded
   */
  void
  add(const Number s);

  /**
   * Multiple addition of scaled vectors, i.e. <tt>*this += a*V+b*W</tt>.
   *
   * @dealiiOperationIsMultithreaded
   */
  void
  add(const Number          a,
      const Vector<Number> &V,
      const Number          b,
      const Vector<Number> &W);

  /**
   * Simple addition of a multiple of a vector, i.e. <tt>*this += a*V</tt>.
   *
   * @dealiiOperationIsMultithreaded
   */
  void
  add(const Number a, const Vector<Number> &V);

  /**
   * Scaling and simple vector addition, i.e.  <tt>*this = s*(*this)+V</tt>.
   *
   * @dealiiOperationIsMultithreaded
   */
  void
  sadd(const Number s, const Vector<Number> &V);

  /**
   * Scaling and simple addition, i.e.  <tt>*this = s*(*this)+a*V</tt>.
   *
   * @dealiiOperationIsMultithreaded
   */
  void
  sadd(const Number s, const Number a, const Vector<Number> &V);

  /**
   * Scale each element of the vector by a constant value.
   *
   * @dealiiOperationIsMultithreaded
   */
  Vector<Number> &
  operator*=(const Number factor);

  /**
   * Scale each element of the vector by the inverse of the given value.
   *
   * @dealiiOperationIsMultithreaded
   */
  Vector<Number> &
  operator/=(const Number factor);

  /**
   * Scale each element of this vector by the corresponding element in the
   * argument. This function is mostly meant to simulate multiplication (and
   * immediate re-assignment) by a diagonal scaling matrix.
   *
   * @dealiiOperationIsMultithreaded
   */
  void
  scale(const Vector<Number> &scaling_factors);

  /**
   * Scale each element of this vector by the corresponding element in the
   * argument. This function is mostly meant to simulate multiplication (and
   * immediate re-assignment) by a diagonal scaling matrix.
   */
  template <typename Number2>
  void
  scale(const Vector<Number2> &scaling_factors);

  /**
   * Assignment <tt>*this = a*u</tt>.
   *
   * @dealiiOperationIsMultithreaded
   */
  void
  equ(const Number a, const Vector<Number> &u);

  /**
   * Assignment <tt>*this = a*u</tt>.
   */
  template <typename Number2>
  void
  equ(const Number a, const Vector<Number2> &u);

  /**
   * This function does nothing but exists for compatibility with the @p
   * parallel vector classes (e.g., LinearAlgebra::distributed::Vector class).
   */
  void
  update_ghost_values() const;
  //@}


  /**
   * @name Input and output
   */
  //@{
  /**
   * Print to a stream. @p precision denotes the desired precision with which
   * values shall be printed, @p scientific whether scientific notation shall
   * be used. If @p across is @p true then the vector is printed in a line,
   * while if @p false then the elements are printed on a separate line each.
   */
  void
  print(std::ostream &     out,
        const unsigned int precision  = 3,
        const bool         scientific = true,
        const bool         across     = true) const;

  /**
   * Write the vector en bloc to a file. This is done in a binary mode, so the
   * output is neither readable by humans nor (probably) by other computers
   * using a different operating system or number format.
   */
  void
  block_write(std::ostream &out) const;

  /**
   * Read a vector en block from a file. This is done using the inverse
   * operations to the above function, so it is reasonably fast because the
   * bitstream is not interpreted.
   *
   * The vector is resized if necessary.
   *
   * A primitive form of error checking is performed which will recognize the
   * bluntest attempts to interpret some data as a vector stored bitwise to a
   * file, but not more.
   */
  void
  block_read(std::istream &in);

  /**
   * Write the data of this object to a stream for the purpose of
   * serialization.
   */
  template <class Archive>
  void
  save(Archive &ar, const unsigned int version) const;

  /**
   * Read the data of this object from a stream for the purpose of
   * serialization.
   */
  template <class Archive>
  void
  load(Archive &ar, const unsigned int version);

#ifdef DOXYGEN
  /**
   * Write and read the data of this object from a stream for the purpose
   * of serialization.
   */
  template <class Archive>
  void
  serialize(Archive &archive, const unsigned int version);
#else
  // This macro defines the serialize() method that is compatible with
  // the templated save() and load() method that have been implemented.
  BOOST_SERIALIZATION_SPLIT_MEMBER()
#endif

  /**
   * @}
   */

  /**
   * @name Information about the object
   */
  //@{

  /**
   * Return true if the given global index is in the local range of this
   * processor.  Since this is not a distributed vector the method always
   * returns true.
   */
  bool
  in_local_range(const size_type global_index) const;

  /**
   * Return an index set that describes which elements of this vector are
   * owned by the current processor. Note that this index set does not include
   * elements this vector may store locally as ghost elements but that are in
   * fact owned by another processor. As a consequence, the index sets
   * returned on different processors if this is a distributed vector will
   * form disjoint sets that add up to the complete index set. Obviously, if a
   * vector is created on only one processor, then the result would satisfy
   * @code
   *   vec.locally_owned_elements() == complete_index_set (vec.size())
   * @endcode
   *
   * Since the current data type does not support parallel data storage across
   * different processors, the returned index set is the complete index set.
   */
  IndexSet
  locally_owned_elements() const;

  /**
   * Return dimension of the vector.
   */
  size_type
  size() const;

  /**
   * Return whether the vector contains only elements with value zero. This
   * function is mainly for internal consistency checks and should seldom be
   * used when not in debug mode since it uses quite some time.
   */
  bool
  all_zero() const;

  /**
   * Return @p true if the vector has no negative entries, i.e. all entries
   * are zero or positive. This function is used, for example, to check
   * whether refinement indicators are really all positive (or zero).
   *
   * The function obviously only makes sense if the template argument of this
   * class is a real type. If it is a complex type, then an exception is
   * thrown.
   */
  bool
  is_non_negative() const;

  /**
   * Determine an estimate for the memory consumption (in bytes) of this
   * object.
   */
  std::size_t
  memory_consumption() const;

  /**
   * This function exists for compatibility with the @p
   * parallel vector classes (e.g., LinearAlgebra::distributed::Vector class).
   * Always returns false since this implementation is serial.
   */
  bool
  has_ghost_elements() const;
  //@}

private:
  /**
   * Array of elements owned by this vector.
   */
  AlignedVector<Number> values;

  /**
   * Convenience function used at the end of initialization or
   * reinitialization. Resets (if necessary) the loop partitioner to the
   * correct state, based on its current state and the length of the vector.
   */
  void
  maybe_reset_thread_partitioner();

  /**
   * Actual implementation of the reinit functions.
   */
  void
  do_reinit(const size_type new_size,
            const bool      omit_zeroing_entries,
            const bool      reset_partitioner);

  /**
   * For parallel loops with TBB, this member variable stores the affinity
   * information of loops.
   */
  mutable std::shared_ptr<parallel::internal::TBBPartitioner>
    thread_loop_partitioner;

  // Make all other vector types friends.
  template <typename Number2>
  friend class Vector;
};

/*@}*/
/*----------------------- Inline functions ----------------------------------*/


#ifndef DOXYGEN


//------------------------ declarations for explicit specializations
template <>
Vector<int>::real_type
Vector<int>::lp_norm(const real_type) const;


//------------------------ inline functions

template <typename Number>
inline Vector<Number>::Vector()
{
  // virtual functions called in constructors and destructors never use the
  // override in a derived class
  // for clarity be explicit on which function is called
  Vector<Number>::reinit(0);
}


template <typename Number>
template <typename OtherNumber>
Vector<Number>::Vector(const std::initializer_list<OtherNumber> &v)
  : Vector(v.begin(), v.end())
{}


template <typename Number>
template <typename InputIterator>
Vector<Number>::Vector(const InputIterator first, const InputIterator last)
{
  // allocate memory. do not initialize it, as we will copy over to it in a
  // second
  reinit(std::distance(first, last), true);
  std::copy(first, last, begin());
}


template <typename Number>
inline Vector<Number>::Vector(const size_type n)
{
  // virtual functions called in constructors and destructors never use the
  // override in a derived class
  // for clarity be explicit on which function is called
  Vector<Number>::reinit(n, false);
}


template <typename Number>
inline typename Vector<Number>::size_type
Vector<Number>::size() const
{
  return values.size();
}


template <typename Number>
inline bool
Vector<Number>::in_local_range(const size_type) const
{
  return true;
}


template <typename Number>
inline typename Vector<Number>::pointer
Vector<Number>::data()
{
  return values.data();
}


template <typename Number>
inline typename Vector<Number>::const_pointer
Vector<Number>::data() const
{
  return values.data();
}


template <typename Number>
inline typename Vector<Number>::iterator
Vector<Number>::begin()
{
  return values.begin();
}


template <typename Number>
inline typename Vector<Number>::const_iterator
Vector<Number>::begin() const
{
  return values.begin();
}


template <typename Number>
inline typename Vector<Number>::iterator
Vector<Number>::end()
{
  return values.end();
}


template <typename Number>
inline typename Vector<Number>::const_iterator
Vector<Number>::end() const
{
  return values.end();
}


template <typename Number>
inline Number
Vector<Number>::operator()(const size_type i) const
{
  AssertIndexRange(i, size());
  return values[i];
}


template <typename Number>
inline Number &
Vector<Number>::operator()(const size_type i)
{
  AssertIndexRange(i, size());
  return values[i];
}


template <typename Number>
inline Number Vector<Number>::operator[](const size_type i) const
{
  return operator()(i);
}


template <typename Number>
inline Number &Vector<Number>::operator[](const size_type i)
{
  return operator()(i);
}


template <typename Number>
template <typename OtherNumber>
inline void
Vector<Number>::extract_subvector_to(const std::vector<size_type> &indices,
                                     std::vector<OtherNumber> &    values) const
{
  for (size_type i = 0; i < indices.size(); ++i)
    values[i] = operator()(indices[i]);
}


template <typename Number>
template <typename ForwardIterator, typename OutputIterator>
inline void
Vector<Number>::extract_subvector_to(ForwardIterator       indices_begin,
                                     const ForwardIterator indices_end,
                                     OutputIterator        values_begin) const
{
  while (indices_begin != indices_end)
    {
      *values_begin = operator()(*indices_begin);
      indices_begin++;
      values_begin++;
    }
}


template <typename Number>
inline Vector<Number> &
Vector<Number>::operator/=(const Number factor)
{
  AssertIsFinite(factor);
  Assert(factor != Number(0.), ExcZero());

  this->operator*=(Number(1.) / factor);
  return *this;
}


template <typename Number>
template <typename OtherNumber>
inline void
Vector<Number>::add(const std::vector<size_type> &  indices,
                    const std::vector<OtherNumber> &values)
{
  Assert(indices.size() == values.size(),
         ExcDimensionMismatch(indices.size(), values.size()));
  add(indices.size(), indices.data(), values.data());
}


template <typename Number>
template <typename OtherNumber>
inline void
Vector<Number>::add(const std::vector<size_type> &indices,
                    const Vector<OtherNumber> &   values)
{
  Assert(indices.size() == values.size(),
         ExcDimensionMismatch(indices.size(), values.size()));
  add(indices.size(), indices.data(), values.values.begin());
}


template <typename Number>
template <typename OtherNumber>
inline void
Vector<Number>::add(const size_type    n_indices,
                    const size_type *  indices,
                    const OtherNumber *values)
{
  for (size_type i = 0; i < n_indices; ++i)
    {
      AssertIndexRange(indices[i], size());
      Assert(
        numbers::is_finite(values[i]),
        ExcMessage(
          "The given value is not finite but either infinite or Not A Number (NaN)"));

      this->values[indices[i]] += values[i];
    }
}


template <typename Number>
template <typename Number2>
inline bool
Vector<Number>::operator!=(const Vector<Number2> &v) const
{
  return !(*this == v);
}


template <typename Number>
inline void Vector<Number>::compress(::dealii::VectorOperation::values) const
{}


template <typename Number>
inline bool
Vector<Number>::has_ghost_elements() const
{
  return false;
}

template <typename Number>
inline void
Vector<Number>::update_ghost_values() const
{}


// Moved from vector.templates.h as an inline function by Luca Heltai
// on 2009/04/12 to prevent strange compiling errors, after making
// swap virtual.
template <typename Number>
inline void
Vector<Number>::swap(Vector<Number> &v)
{
  values.swap(v.values);
  std::swap(thread_loop_partitioner, v.thread_loop_partitioner);
}


template <typename Number>
template <class Archive>
inline void
Vector<Number>::save(Archive &ar, const unsigned int) const
{
  // forward to serialization function in the base class.
  ar &static_cast<const Subscriptor &>(*this);
  ar &values;
}


template <typename Number>
template <class Archive>
inline void
Vector<Number>::load(Archive &ar, const unsigned int)
{
  // the load stuff again from the archive
  ar &static_cast<Subscriptor &>(*this);
  ar &values;
  maybe_reset_thread_partitioner();
}

#endif


/*! @addtogroup Vectors
 *@{
 */


/**
 * Global function @p swap which overloads the default implementation of the
 * C++ standard library which uses a temporary object. The function simply
 * exchanges the data of the two vectors.
 *
 * @relatesalso Vector
 */
template <typename Number>
inline void
swap(Vector<Number> &u, Vector<Number> &v)
{
  u.swap(v);
}


/**
 * Output operator writing a vector to a stream. This operator outputs the
 * elements of the vector one by one, with a space between entries. Each entry
 * is formatted according to the flags set on the output stream.
 *
 * @relatesalso Vector
 */
template <typename number>
inline std::ostream &
operator<<(std::ostream &out, const Vector<number> &v)
{
  Assert(v.size() != 0, ExcEmptyObject());
  AssertThrow(out, ExcIO());

  for (typename Vector<number>::size_type i = 0; i < v.size() - 1; ++i)
    out << v(i) << ' ';
  out << v(v.size() - 1);

  AssertThrow(out, ExcIO());

  return out;
}

/*@}*/


/**
 * Declare dealii::Vector< Number > as serial vector.
 *
 * @relatesalso Vector
 */
template <typename Number>
struct is_serial_vector<Vector<Number>> : std::true_type
{};


DEAL_II_NAMESPACE_CLOSE

#endif