chunk_sparse_matrix.h

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// ------------------------------------------------------------------------
//
// SPDX-License-Identifier: LGPL-2.1-or-later
// Copyright (C) 2008 - 2023 by the deal.II authors
//
// This file is part of the deal.II library.
//
// Part of the source code is dual licensed under Apache-2.0 WITH
// LLVM-exception OR LGPL-2.1-or-later. Detailed license information
// governing the source code and code contributions can be found in
// LICENSE.md and CONTRIBUTING.md at the top level directory of deal.II.
//
// ------------------------------------------------------------------------
 
#ifndef dealii_chunk_sparse_matrix_h
#define dealii_chunk_sparse_matrix_h
 
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/enable_observer_pointer.h>
#include <deal.II/base/observer_pointer.h>
 
#include <deal.II/lac/chunk_sparsity_pattern.h>
#include <deal.II/lac/exceptions.h>
#include <deal.II/lac/identity_matrix.h>
 
#include <iterator>
#include <memory>
 
 
DEAL_II_NAMESPACE_OPEN
 
// Forward declarations
#ifndef DOXYGEN
template <typename number>
class Vector;
template <typename number>
class FullMatrix;
#endif
 
namespace ChunkSparseMatrixIterators
{
  // forward declaration
  template <typename number, bool Constness>
  class Iterator;
 
  template <typename number, bool Constness>
  class Accessor : public ChunkSparsityPatternIterators::Accessor
  {
  public:
    number
    value() const;
 
    number &
    value();
 
    const ChunkSparseMatrix<number> &
    get_matrix() const;
  };
 
 
 
  template <typename number>
  class Accessor<number, true> : public ChunkSparsityPatternIterators::Accessor
  {
  public:
    using MatrixType = const ChunkSparseMatrix<number>;
 
    Accessor(MatrixType *matrix, const unsigned int row);
 
    Accessor(MatrixType *matrix);
 
    Accessor(const ChunkSparseMatrixIterators::Accessor<number, false> &a);
 
    number
    value() const;
 
    const MatrixType &
    get_matrix() const;
 
  private:
    MatrixType *matrix;
 
    using ChunkSparsityPatternIterators::Accessor::advance;
 
    // Make iterator class a friend.
    template <typename, bool>
    friend class Iterator;
  };
 
 
  template <typename number>
  class Accessor<number, false> : public ChunkSparsityPatternIterators::Accessor
  {
  private:
    class Reference
    {
    public:
      Reference(const Accessor *accessor, const bool dummy);
 
      operator number() const;
 
      const Reference &
      operator=(const number n) const;
 
      const Reference &
      operator+=(const number n) const;
 
      const Reference &
      operator-=(const number n) const;
 
      const Reference &
      operator*=(const number n) const;
 
      const Reference &
      operator/=(const number n) const;
 
    private:
      const Accessor *accessor;
    };
 
  public:
    using MatrixType = ChunkSparseMatrix<number>;
 
    Accessor(MatrixType *matrix, const unsigned int row);
 
    Accessor(MatrixType *matrix);
 
    Reference
    value() const;
 
    MatrixType &
    get_matrix() const;
 
  private:
    MatrixType *matrix;
 
    using ChunkSparsityPatternIterators::Accessor::advance;
 
    // Make iterator class a friend.
    template <typename, bool>
    friend class Iterator;
  };
 
 
 
  template <typename number, bool Constness>
  class Iterator
  {
  public:
    using MatrixType = typename Accessor<number, Constness>::MatrixType;
 
    using value_type = const Accessor<number, Constness> &;
 
    using difference_type = types::global_dof_index;
 
    Iterator(MatrixType *matrix, const unsigned int row);
 
    Iterator(MatrixType *matrix);
 
    Iterator(const ChunkSparseMatrixIterators::Iterator<number, false> &i);
 
    Iterator &
    operator++();
 
    Iterator
    operator++(int);
 
    const Accessor<number, Constness> &
    operator*() const;
 
    const Accessor<number, Constness> *
    operator->() const;
 
    bool
    operator==(const Iterator &) const;
 
    bool
    operator!=(const Iterator &) const;
 
    bool
    operator<(const Iterator &) const;
 
    bool
    operator>(const Iterator &) const;
 
    int
    operator-(const Iterator &p) const;
 
    Iterator
    operator+(const unsigned int n) const;
 
  private:
    Accessor<number, Constness> accessor;
  };
 
} // namespace ChunkSparseMatrixIterators
 
DEAL_II_NAMESPACE_CLOSE
 
namespace std
{
  template <typename number, bool Constness>
  struct iterator_traits<
    ::ChunkSparseMatrixIterators::Iterator<number, Constness>>
  {
    using iterator_category = forward_iterator_tag;
    using value_type        = typename ::ChunkSparseMatrixIterators::
      Iterator<number, Constness>::value_type;
    using difference_type = typename ::ChunkSparseMatrixIterators::
      Iterator<number, Constness>::difference_type;
  };
} // namespace std
 
DEAL_II_NAMESPACE_OPEN
 
 
 
template <typename number>
class ChunkSparseMatrix : public virtual EnableObserverPointer
{
public:
  using size_type = types::global_dof_index;
 
  using value_type = number;
 
  using real_type = typename numbers::NumberTraits<number>::real_type;
 
  using const_iterator = ChunkSparseMatrixIterators::Iterator<number, true>;
 
  using iterator = ChunkSparseMatrixIterators::Iterator<number, false>;
 
  struct Traits
  {
    static const bool zero_addition_can_be_elided = true;
  };
 
  ChunkSparseMatrix();
 
  ChunkSparseMatrix(const ChunkSparseMatrix &);
 
  explicit ChunkSparseMatrix(const ChunkSparsityPattern &sparsity);
 
  ChunkSparseMatrix(const ChunkSparsityPattern &sparsity,
                    const IdentityMatrix       &id);
 
  virtual ~ChunkSparseMatrix() override;
 
  ChunkSparseMatrix<number> &
  operator=(const ChunkSparseMatrix<number> &);
 
  ChunkSparseMatrix<number> &
  operator=(const IdentityMatrix &id);
 
  ChunkSparseMatrix &
  operator=(const double d);
 
  virtual void
  reinit(const ChunkSparsityPattern &sparsity);
 
  virtual void
  clear();
  bool
  empty() const;
 
  size_type
  m() const;
 
  size_type
  n() const;
 
  size_type
  n_nonzero_elements() const;
 
  size_type
  n_actually_nonzero_elements() const;
 
  const ChunkSparsityPattern &
  get_sparsity_pattern() const;
 
  std::size_t
  memory_consumption() const;
 
  void
  set(const size_type i, const size_type j, const number value);
 
  void
  add(const size_type i, const size_type j, const number value);
 
  template <typename number2>
  void
  add(const size_type  row,
      const size_type  n_cols,
      const size_type *col_indices,
      const number2   *values,
      const bool       elide_zero_values      = true,
      const bool       col_indices_are_sorted = false);
 
  ChunkSparseMatrix &
  operator*=(const number factor);
 
  ChunkSparseMatrix &
  operator/=(const number factor);
 
  void
  symmetrize();
 
  template <typename somenumber>
  ChunkSparseMatrix<number> &
  copy_from(const ChunkSparseMatrix<somenumber> &source);
 
  template <typename ForwardIterator>
  void
  copy_from(const ForwardIterator begin, const ForwardIterator end);
 
  template <typename somenumber>
  void
  copy_from(const FullMatrix<somenumber> &matrix);
 
  template <typename somenumber>
  void
  add(const number factor, const ChunkSparseMatrix<somenumber> &matrix);
 
  number
  operator()(const size_type i, const size_type j) const;
 
  number
  el(const size_type i, const size_type j) const;
 
  number
  diag_element(const size_type i) const;
 
  void
  extract_row_copy(const size_type row,
                   const size_type array_length,
                   size_type      &row_length,
                   size_type      *column_indices,
                   number         *values) const;
 
  template <class OutVector, class InVector>
  void
  vmult(OutVector &dst, const InVector &src) const;
 
  template <class OutVector, class InVector>
  void
  Tvmult(OutVector &dst, const InVector &src) const;
 
  template <class OutVector, class InVector>
  void
  vmult_add(OutVector &dst, const InVector &src) const;
 
  template <class OutVector, class InVector>
  void
  Tvmult_add(OutVector &dst, const InVector &src) const;
 
  template <typename somenumber>
  somenumber
  matrix_norm_square(const Vector<somenumber> &v) const;
 
  template <typename somenumber>
  somenumber
  matrix_scalar_product(const Vector<somenumber> &u,
                        const Vector<somenumber> &v) const;
  template <typename somenumber>
  somenumber
  residual(Vector<somenumber>       &dst,
           const Vector<somenumber> &x,
           const Vector<somenumber> &b) const;
 
  real_type
  l1_norm() const;
 
  real_type
  linfty_norm() const;
 
  real_type
  frobenius_norm() const;
  template <typename somenumber>
  void
  precondition_Jacobi(Vector<somenumber>       &dst,
                      const Vector<somenumber> &src,
                      const number              omega = 1.) const;
 
  template <typename somenumber>
  void
  precondition_SSOR(Vector<somenumber>       &dst,
                    const Vector<somenumber> &src,
                    const number              om = 1.) const;
 
  template <typename somenumber>
  void
  precondition_SOR(Vector<somenumber>       &dst,
                   const Vector<somenumber> &src,
                   const number              om = 1.) const;
 
  template <typename somenumber>
  void
  precondition_TSOR(Vector<somenumber>       &dst,
                    const Vector<somenumber> &src,
                    const number              om = 1.) const;
 
  template <typename somenumber>
  void
  SSOR(Vector<somenumber> &v, const number omega = 1.) const;
 
  template <typename somenumber>
  void
  SOR(Vector<somenumber> &v, const number om = 1.) const;
 
  template <typename somenumber>
  void
  TSOR(Vector<somenumber> &v, const number om = 1.) const;
 
  template <typename somenumber>
  void
  PSOR(Vector<somenumber>           &v,
       const std::vector<size_type> &permutation,
       const std::vector<size_type> &inverse_permutation,
       const number                  om = 1.) const;
 
  template <typename somenumber>
  void
  TPSOR(Vector<somenumber>           &v,
        const std::vector<size_type> &permutation,
        const std::vector<size_type> &inverse_permutation,
        const number                  om = 1.) const;
 
  template <typename somenumber>
  void
  SOR_step(Vector<somenumber>       &v,
           const Vector<somenumber> &b,
           const number              om = 1.) const;
 
  template <typename somenumber>
  void
  TSOR_step(Vector<somenumber>       &v,
            const Vector<somenumber> &b,
            const number              om = 1.) const;
 
  template <typename somenumber>
  void
  SSOR_step(Vector<somenumber>       &v,
            const Vector<somenumber> &b,
            const number              om = 1.) const;
  const_iterator
  begin() const;
 
  const_iterator
  end() const;
 
  iterator
  begin();
 
  iterator
  end();
 
  const_iterator
  begin(const unsigned int r) const;
 
  const_iterator
  end(const unsigned int r) const;
 
  iterator
  begin(const unsigned int r);
 
  iterator
  end(const unsigned int r);
  void
  print(std::ostream &out) const;
 
  void
  print_formatted(std::ostream      &out,
                  const unsigned int precision   = 3,
                  const bool         scientific  = true,
                  const unsigned int width       = 0,
                  const char        *zero_string = " ",
                  const double       denominator = 1.,
                  const char        *separator   = " ") const;
 
  void
  print_pattern(std::ostream &out, const double threshold = 0.) const;
 
  void
  block_write(std::ostream &out) const;
 
  void
  block_read(std::istream &in);
  DeclException2(ExcInvalidIndex,
                 int,
                 int,
                 << "You are trying to access the matrix entry with index <"
                 << arg1 << ',' << arg2
                 << ">, but this entry does not exist in the sparsity pattern "
                    "of this matrix."
                    "\n\n"
                    "The most common cause for this problem is that you used "
                    "a method to build the sparsity pattern that did not "
                    "(completely) take into account all of the entries you "
                    "will later try to write into. An example would be "
                    "building a sparsity pattern that does not include "
                    "the entries you will write into due to constraints "
                    "on degrees of freedom such as hanging nodes or periodic "
                    "boundary conditions. In such cases, building the "
                    "sparsity pattern will succeed, but you will get errors "
                    "such as the current one at one point or other when "
                    "trying to write into the entries of the matrix.");
  DeclException0(ExcDifferentChunkSparsityPatterns);
  DeclException2(ExcIteratorRange,
                 int,
                 int,
                 << "The iterators denote a range of " << arg1
                 << " elements, but the given number of rows was " << arg2);
  DeclExceptionMsg(ExcSourceEqualsDestination,
                   "You are attempting an operation on two vectors that "
                   "are the same object, but the operation requires that the "
                   "two objects are in fact different.");
private:
  ObserverPointer<const ChunkSparsityPattern, ChunkSparseMatrix<number>> cols;
 
  std::unique_ptr<number[]> val;
 
  size_type max_len;
 
  size_type
  compute_location(const size_type i, const size_type j) const;
 
  // make all other sparse matrices friends
  template <typename somenumber>
  friend class ChunkSparseMatrix;
 
  // Also give access to internal details to the iterator/accessor classes.
  template <typename, bool>
  friend class ChunkSparseMatrixIterators::Iterator;
  template <typename, bool>
  friend class ChunkSparseMatrixIterators::Accessor;
};
 
#ifndef DOXYGEN
/*---------------------- Inline functions -----------------------------------*/
 
 
 
template <typename number>
inline typename ChunkSparseMatrix<number>::size_type
ChunkSparseMatrix<number>::m() const
{
  Assert(cols != nullptr, ExcNeedsSparsityPattern());
  return cols->rows;
}
 
 
template <typename number>
inline typename ChunkSparseMatrix<number>::size_type
ChunkSparseMatrix<number>::n() const
{
  Assert(cols != nullptr, ExcNeedsSparsityPattern());
  return cols->cols;
}
 
 
 
template <typename number>
inline const ChunkSparsityPattern &
ChunkSparseMatrix<number>::get_sparsity_pattern() const
{
  Assert(cols != nullptr, ExcNeedsSparsityPattern());
  return *cols;
}
 
 
 
template <typename number>
inline typename ChunkSparseMatrix<number>::size_type
ChunkSparseMatrix<number>::compute_location(const size_type i,
                                            const size_type j) const
{
  const size_type chunk_size = cols->get_chunk_size();
  const size_type chunk_index =
    cols->sparsity_pattern(i / chunk_size, j / chunk_size);
 
  if (chunk_index == ChunkSparsityPattern::invalid_entry)
    return ChunkSparsityPattern::invalid_entry;
  else
    {
      return (chunk_index * chunk_size * chunk_size +
              (i % chunk_size) * chunk_size + (j % chunk_size));
    }
}
 
 
template <typename number>
inline void
ChunkSparseMatrix<number>::set(const size_type i,
                               const size_type j,
                               const number    value)
{
  AssertIsFinite(value);
 
  Assert(cols != nullptr, ExcNeedsSparsityPattern());
  // it is allowed to set elements of the matrix that are not part of the
  // sparsity pattern, if the value to which we set it is zero
  const size_type index = compute_location(i, j);
  Assert((index != SparsityPattern::invalid_entry) || (value == 0.),
         ExcInvalidIndex(i, j));
 
  if (index != SparsityPattern::invalid_entry)
    val[index] = value;
}
 
 
 
template <typename number>
inline void
ChunkSparseMatrix<number>::add(const size_type i,
                               const size_type j,
                               const number    value)
{
  AssertIsFinite(value);
 
  Assert(cols != nullptr, ExcNeedsSparsityPattern());
 
  if (std::abs(value) != 0.)
    {
      const size_type index = compute_location(i, j);
      Assert((index != ChunkSparsityPattern::invalid_entry),
             ExcInvalidIndex(i, j));
 
      val[index] += value;
    }
}
 
 
 
template <typename number>
template <typename number2>
inline void
ChunkSparseMatrix<number>::add(const size_type  row,
                               const size_type  n_cols,
                               const size_type *col_indices,
                               const number2   *values,
                               const bool /*elide_zero_values*/,
                               const bool /*col_indices_are_sorted*/)
{
  // TODO: could be done more efficiently...
  for (size_type col = 0; col < n_cols; ++col)
    add(row, col_indices[col], static_cast<number>(values[col]));
}
 
 
 
template <typename number>
inline ChunkSparseMatrix<number> &
ChunkSparseMatrix<number>::operator*=(const number factor)
{
  Assert(cols != nullptr, ExcNeedsSparsityPattern());
  Assert(val != nullptr, ExcNotInitialized());
 
  const size_type chunk_size = cols->get_chunk_size();
 
  // multiply all elements of the matrix with the given factor. this includes
  // the padding elements in chunks that overlap the boundaries of the actual
  // matrix -- but since multiplication with a number does not violate the
  // invariant of keeping these elements at zero nothing can happen
  number             *val_ptr = val.get();
  const number *const end_ptr =
    val.get() +
    cols->sparsity_pattern.n_nonzero_elements() * chunk_size * chunk_size;
  while (val_ptr != end_ptr)
    *val_ptr++ *= factor;
 
  return *this;
}
 
 
 
template <typename number>
inline ChunkSparseMatrix<number> &
ChunkSparseMatrix<number>::operator/=(const number factor)
{
  Assert(cols != nullptr, ExcNeedsSparsityPattern());
  Assert(val != nullptr, ExcNotInitialized());
  Assert(std::abs(factor) != 0, ExcDivideByZero());
 
  const number factor_inv = 1. / factor;
 
  const size_type chunk_size = cols->get_chunk_size();
 
  // multiply all elements of the matrix with the given factor. this includes
  // the padding elements in chunks that overlap the boundaries of the actual
  // matrix -- but since multiplication with a number does not violate the
  // invariant of keeping these elements at zero nothing can happen
  number             *val_ptr = val.get();
  const number *const end_ptr =
    val.get() +
    cols->sparsity_pattern.n_nonzero_elements() * chunk_size * chunk_size;
 
  while (val_ptr != end_ptr)
    *val_ptr++ *= factor_inv;
 
  return *this;
}
 
 
 
template <typename number>
inline number
ChunkSparseMatrix<number>::operator()(const size_type i,
                                      const size_type j) const
{
  Assert(cols != nullptr, ExcNeedsSparsityPattern());
  AssertThrow(compute_location(i, j) != SparsityPattern::invalid_entry,
              ExcInvalidIndex(i, j));
  return val[compute_location(i, j)];
}
 
 
 
template <typename number>
inline number
ChunkSparseMatrix<number>::el(const size_type i, const size_type j) const
{
  Assert(cols != nullptr, ExcNeedsSparsityPattern());
  const size_type index = compute_location(i, j);
 
  if (index != ChunkSparsityPattern::invalid_entry)
    return val[index];
  else
    return 0;
}
 
 
 
template <typename number>
inline number
ChunkSparseMatrix<number>::diag_element(const size_type i) const
{
  Assert(cols != nullptr, ExcNeedsSparsityPattern());
  Assert(m() == n(), ExcNotQuadratic());
  AssertIndexRange(i, m());
 
  // Use that the first element in each row of a quadratic matrix is the main
  // diagonal of the chunk sparsity pattern
  const size_type chunk_size = cols->get_chunk_size();
  return val[cols->sparsity_pattern.rowstart[i / chunk_size] * chunk_size *
               chunk_size +
             (i % chunk_size) * chunk_size + (i % chunk_size)];
}
 
 
 
template <typename number>
template <typename ForwardIterator>
inline void
ChunkSparseMatrix<number>::copy_from(const ForwardIterator begin,
                                     const ForwardIterator end)
{
  Assert(static_cast<size_type>(std::distance(begin, end)) == m(),
         ExcIteratorRange(std::distance(begin, end), m()));
 
  // for use in the inner loop, we define an alias to the type of the inner
  // iterators
  using inner_iterator =
    typename std::iterator_traits<ForwardIterator>::value_type::const_iterator;
  size_type row = 0;
  for (ForwardIterator i = begin; i != end; ++i, ++row)
    {
      const inner_iterator end_of_row = i->end();
      for (inner_iterator j = i->begin(); j != end_of_row; ++j)
        // write entries
        set(row, j->first, j->second);
    }
}
 
 
 
//---------------------------------------------------------------------------
 
 
namespace ChunkSparseMatrixIterators
{
  template <typename number>
  inline Accessor<number, true>::Accessor(const MatrixType  *matrix,
                                          const unsigned int row)
    : ChunkSparsityPatternIterators::Accessor(&matrix->get_sparsity_pattern(),
                                              row)
    , matrix(matrix)
  {}
 
 
 
  template <typename number>
  inline Accessor<number, true>::Accessor(const MatrixType *matrix)
    : ChunkSparsityPatternIterators::Accessor(&matrix->get_sparsity_pattern())
    , matrix(matrix)
  {}
 
 
 
  template <typename number>
  inline Accessor<number, true>::Accessor(
    const ChunkSparseMatrixIterators::Accessor<number, false> &a)
    : ChunkSparsityPatternIterators::Accessor(a)
    , matrix(&a.get_matrix())
  {}
 
 
 
  template <typename number>
  inline number
  Accessor<number, true>::value() const
  {
    const unsigned int chunk_size =
      matrix->get_sparsity_pattern().get_chunk_size();
    return matrix->val[reduced_index() * chunk_size * chunk_size +
                       chunk_row * chunk_size + chunk_col];
  }
 
 
 
  template <typename number>
  inline const typename Accessor<number, true>::MatrixType &
  Accessor<number, true>::get_matrix() const
  {
    return *matrix;
  }
 
 
 
  template <typename number>
  inline Accessor<number, false>::Reference::Reference(const Accessor *accessor,
                                                       const bool)
    : accessor(accessor)
  {}
 
 
  template <typename number>
  inline Accessor<number, false>::Reference::operator number() const
  {
    const unsigned int chunk_size =
      accessor->matrix->get_sparsity_pattern().get_chunk_size();
    return accessor->matrix
      ->val[accessor->reduced_index() * chunk_size * chunk_size +
            accessor->chunk_row * chunk_size + accessor->chunk_col];
  }
 
 
 
  template <typename number>
  inline const typename Accessor<number, false>::Reference &
  Accessor<number, false>::Reference::operator=(const number n) const
  {
    const unsigned int chunk_size =
      accessor->matrix->get_sparsity_pattern().get_chunk_size();
    accessor->matrix
      ->val[accessor->reduced_index() * chunk_size * chunk_size +
            accessor->chunk_row * chunk_size + accessor->chunk_col] = n;
    return *this;
  }
 
 
 
  template <typename number>
  inline const typename Accessor<number, false>::Reference &
  Accessor<number, false>::Reference::operator+=(const number n) const
  {
    const unsigned int chunk_size =
      accessor->matrix->get_sparsity_pattern().get_chunk_size();
    accessor->matrix
      ->val[accessor->reduced_index() * chunk_size * chunk_size +
            accessor->chunk_row * chunk_size + accessor->chunk_col] += n;
    return *this;
  }
 
 
 
  template <typename number>
  inline const typename Accessor<number, false>::Reference &
  Accessor<number, false>::Reference::operator-=(const number n) const
  {
    const unsigned int chunk_size =
      accessor->matrix->get_sparsity_pattern().get_chunk_size();
    accessor->matrix
      ->val[accessor->reduced_index() * chunk_size * chunk_size +
            accessor->chunk_row * chunk_size + accessor->chunk_col] -= n;
    return *this;
  }
 
 
 
  template <typename number>
  inline const typename Accessor<number, false>::Reference &
  Accessor<number, false>::Reference::operator*=(const number n) const
  {
    const unsigned int chunk_size =
      accessor->matrix->get_sparsity_pattern().get_chunk_size();
    accessor->matrix
      ->val[accessor->reduced_index() * chunk_size * chunk_size +
            accessor->chunk_row * chunk_size + accessor->chunk_col] *= n;
    return *this;
  }
 
 
 
  template <typename number>
  inline const typename Accessor<number, false>::Reference &
  Accessor<number, false>::Reference::operator/=(const number n) const
  {
    const unsigned int chunk_size =
      accessor->matrix->get_sparsity_pattern().get_chunk_size();
    accessor->matrix
      ->val[accessor->reduced_index() * chunk_size * chunk_size +
            accessor->chunk_row * chunk_size + accessor->chunk_col] /= n;
    return *this;
  }
 
 
 
  template <typename number>
  inline Accessor<number, false>::Accessor(MatrixType        *matrix,
                                           const unsigned int row)
    : ChunkSparsityPatternIterators::Accessor(&matrix->get_sparsity_pattern(),
                                              row)
    , matrix(matrix)
  {}
 
 
 
  template <typename number>
  inline Accessor<number, false>::Accessor(MatrixType *matrix)
    : ChunkSparsityPatternIterators::Accessor(&matrix->get_sparsity_pattern())
    , matrix(matrix)
  {}
 
 
 
  template <typename number>
  inline typename Accessor<number, false>::Reference
  Accessor<number, false>::value() const
  {
    return Reference(this, true);
  }
 
 
 
  template <typename number>
  inline typename Accessor<number, false>::MatrixType &
  Accessor<number, false>::get_matrix() const
  {
    return *matrix;
  }
 
 
 
  template <typename number, bool Constness>
  inline Iterator<number, Constness>::Iterator(MatrixType        *matrix,
                                               const unsigned int row)
    : accessor(matrix, row)
  {}
 
 
 
  template <typename number, bool Constness>
  inline Iterator<number, Constness>::Iterator(MatrixType *matrix)
    : accessor(matrix)
  {}
 
 
 
  template <typename number, bool Constness>
  inline Iterator<number, Constness>::Iterator(
    const ChunkSparseMatrixIterators::Iterator<number, false> &i)
    : accessor(*i)
  {}
 
 
 
  template <typename number, bool Constness>
  inline Iterator<number, Constness> &
  Iterator<number, Constness>::operator++()
  {
    accessor.advance();
    return *this;
  }
 
 
  template <typename number, bool Constness>
  inline Iterator<number, Constness>
  Iterator<number, Constness>::operator++(int)
  {
    const Iterator iter = *this;
    accessor.advance();
    return iter;
  }
 
 
  template <typename number, bool Constness>
  inline const Accessor<number, Constness> &
  Iterator<number, Constness>::operator*() const
  {
    return accessor;
  }
 
 
  template <typename number, bool Constness>
  inline const Accessor<number, Constness> *
  Iterator<number, Constness>::operator->() const
  {
    return &accessor;
  }
 
 
  template <typename number, bool Constness>
  inline bool
  Iterator<number, Constness>::operator==(const Iterator &other) const
  {
    return (accessor == other.accessor);
  }
 
 
  template <typename number, bool Constness>
  inline bool
  Iterator<number, Constness>::operator!=(const Iterator &other) const
  {
    return !(*this == other);
  }
 
 
  template <typename number, bool Constness>
  inline bool
  Iterator<number, Constness>::operator<(const Iterator &other) const
  {
    Assert(&accessor.get_matrix() == &other.accessor.get_matrix(),
           ExcInternalError());
 
    return (accessor < other.accessor);
  }
 
 
  template <typename number, bool Constness>
  inline bool
  Iterator<number, Constness>::operator>(const Iterator &other) const
  {
    return (other < *this);
  }
 
 
  template <typename number, bool Constness>
  inline int
  Iterator<number, Constness>::operator-(const Iterator &other) const
  {
    Assert(&accessor.get_matrix() == &other.accessor.get_matrix(),
           ExcInternalError());
 
    // TODO: can be optimized
    int difference = 0;
    if (*this < other)
      {
        Iterator copy = *this;
        while (copy != other)
          {
            ++copy;
            --difference;
          }
      }
    else
      {
        Iterator copy = other;
        while (copy != *this)
          {
            ++copy;
            ++difference;
          }
      }
    return difference;
  }
 
 
 
  template <typename number, bool Constness>
  inline Iterator<number, Constness>
  Iterator<number, Constness>::operator+(const unsigned int n) const
  {
    Iterator x = *this;
    for (unsigned int i = 0; i < n; ++i)
      ++x;
 
    return x;
  }
 
} // namespace ChunkSparseMatrixIterators
 
 
 
template <typename number>
inline typename ChunkSparseMatrix<number>::const_iterator
ChunkSparseMatrix<number>::begin() const
{
  return const_iterator(this, 0);
}
 
 
template <typename number>
inline typename ChunkSparseMatrix<number>::const_iterator
ChunkSparseMatrix<number>::end() const
{
  return const_iterator(this);
}
 
 
template <typename number>
inline typename ChunkSparseMatrix<number>::iterator
ChunkSparseMatrix<number>::begin()
{
  return iterator(this, 0);
}
 
 
template <typename number>
inline typename ChunkSparseMatrix<number>::iterator
ChunkSparseMatrix<number>::end()
{
  return iterator(this);
}
 
 
template <typename number>
inline typename ChunkSparseMatrix<number>::const_iterator
ChunkSparseMatrix<number>::begin(const unsigned int r) const
{
  AssertIndexRange(r, m());
  return const_iterator(this, r);
}
 
 
 
template <typename number>
inline typename ChunkSparseMatrix<number>::const_iterator
ChunkSparseMatrix<number>::end(const unsigned int r) const
{
  AssertIndexRange(r, m());
  return const_iterator(this, r + 1);
}
 
 
 
template <typename number>
inline typename ChunkSparseMatrix<number>::iterator
ChunkSparseMatrix<number>::begin(const unsigned int r)
{
  AssertIndexRange(r, m());
  return iterator(this, r);
}
 
 
 
template <typename number>
inline typename ChunkSparseMatrix<number>::iterator
ChunkSparseMatrix<number>::end(const unsigned int r)
{
  AssertIndexRange(r, m());
  return iterator(this, r + 1);
}
 
 
 
#endif // DOXYGEN
 
DEAL_II_NAMESPACE_CLOSE
 
#endif