diagonalmatrix.hh

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// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
// SPDX-FileCopyrightInfo: Copyright © DUNE Project contributors, see file LICENSE.md in module root
// SPDX-License-Identifier: LicenseRef-GPL-2.0-only-with-DUNE-exception
#ifndef DUNE_DIAGONAL_MATRIX_HH
#define DUNE_DIAGONAL_MATRIX_HH
 
#include <algorithm>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstddef>
#include <initializer_list>
#include <iostream>
#include <memory>
 
#include <dune/common/boundschecking.hh>
#include <dune/common/densematrix.hh>
#include <dune/common/dynmatrix.hh>
#include <dune/common/exceptions.hh>
#include <dune/common/fmatrix.hh>
#include <dune/common/ftraits.hh>
#include <dune/common/fvector.hh>
#include <dune/common/genericiterator.hh>
#include <dune/common/matrixconcepts.hh>
#include <dune/common/typetraits.hh>
 
 
namespace Dune {
 
  template< class K, int n > class DiagonalRowVectorConst;
  template< class K, int n > class DiagonalRowVector;
  template< class DiagonalMatrixType > class DiagonalMatrixWrapper;
  template< class C, class T, class R> class ContainerWrapperIterator;
 
  template<class K, int n>
  class DiagonalMatrix
  {
    template<class, int> friend class DiagonalMatrix;
    typedef DiagonalMatrixWrapper< DiagonalMatrix<K,n> > WrapperType;
 
  public:
    //===== type definitions and constants
 
    typedef K value_type;
    typedef value_type field_type;
 
    typedef K block_type;
 
    typedef std::size_t size_type;
 
    constexpr static int blocklevel = 1;
 
    typedef DiagonalRowVector<K,n> row_type;
    typedef row_type reference;
    typedef row_type row_reference;
    typedef DiagonalRowVectorConst<K,n> const_row_type;
    typedef const_row_type const_reference;
    typedef const_row_type const_row_reference;
 
    constexpr static int rows = n;
    constexpr static int cols = n;
 
    //==== size
 
    static constexpr size_type size ()
    {
      return rows;
    }
 
    //===== constructors
 
    constexpr DiagonalMatrix() = default;
 
    DiagonalMatrix (const K& k)
      : diag_(k)
    {}
 
    DiagonalMatrix (const FieldVector<K,n>& diag)
      : diag_(diag)
    {}
 
    DiagonalMatrix (std::initializer_list<K> const &l)
    {
      std::copy_n(l.begin(), std::min<std::size_t>(rows, l.size()),
                 diag_.begin());
    }
 
    template <class OtherK>
    DiagonalMatrix (const DiagonalMatrix<OtherK,n>& other)
      : diag_(other.diag_)
    {}
 
    DiagonalMatrix& operator= (const K& k)
    {
      diag_ = k;
      return *this;
    }
 
    template <class OtherK>
    DiagonalMatrix& operator= (const DiagonalMatrix<OtherK,n>& other)
    {
      diag_ = other.diag_;
      return *this;
    }
 
    bool identical(const DiagonalMatrix<K,n>& other) const
    {
      return (this==&other);
    }
 
    DiagonalMatrix<K, n> transposed() const
    {
      return *this;
    }
 
    //===== iterator interface to rows of the matrix
    typedef ContainerWrapperIterator<const WrapperType, reference, reference> Iterator;
    typedef Iterator iterator;
    typedef Iterator RowIterator;
    typedef typename row_type::Iterator ColIterator;
 
    Iterator begin ()
    {
      return Iterator(WrapperType(this),0);
    }
 
    Iterator end ()
    {
      return Iterator(WrapperType(this),n);
    }
 
    Iterator beforeEnd ()
    {
      return Iterator(WrapperType(this),n-1);
    }
 
    Iterator beforeBegin ()
    {
      return Iterator(WrapperType(this),-1);
    }
 
 
    typedef ContainerWrapperIterator<const WrapperType, const_reference, const_reference> ConstIterator;
    typedef ConstIterator const_iterator;
    typedef ConstIterator ConstRowIterator;
    typedef typename const_row_type::ConstIterator ConstColIterator;
 
    ConstIterator begin () const
    {
      return ConstIterator(WrapperType(this),0);
    }
 
    ConstIterator end () const
    {
      return ConstIterator(WrapperType(this),n);
    }
 
    ConstIterator beforeEnd() const
    {
      return ConstIterator(WrapperType(this),n-1);
    }
 
    ConstIterator beforeBegin () const
    {
      return ConstIterator(WrapperType(this),-1);
    }
 
 
 
    //===== vector space arithmetic
 
    DiagonalMatrix& operator+= (const DiagonalMatrix& y)
    {
      diag_ += y.diag_;
      return *this;
    }
 
    DiagonalMatrix& operator-= (const DiagonalMatrix& y)
    {
      diag_ -= y.diag_;
      return *this;
    }
 
    DiagonalMatrix& operator+= (const K& k)
    {
      diag_ += k;
      return *this;
    }
 
    DiagonalMatrix& operator-= (const K& k)
    {
      diag_ -= k;
      return *this;
    }
 
    DiagonalMatrix& operator*= (const K& k)
    {
      diag_ *= k;
      return *this;
    }
 
    DiagonalMatrix& operator/= (const K& k)
    {
      diag_ /= k;
      return *this;
    }
 
    //===== comparison ops
 
    bool operator==(const DiagonalMatrix& other) const
    {
      return diag_==other.diagonal();
    }
 
    bool operator!=(const DiagonalMatrix& other) const
    {
      return diag_!=other.diagonal();
    }
 
 
    //===== linear maps
 
    template<class X, class Y>
    void mv (const X& x, Y& y) const
    {
#ifdef DUNE_FMatrix_WITH_CHECKING
      if (x.N()!=M()) DUNE_THROW(FMatrixError,"index out of range");
      if (y.N()!=N()) DUNE_THROW(FMatrixError,"index out of range");
#endif
      for (size_type i=0; i<n; ++i)
        y[i] = diag_[i] * x[i];
    }
 
    template<class X, class Y>
    void mtv (const X& x, Y& y) const
    {
      mv(x, y);
    }
 
    template<class X, class Y>
    void umv (const X& x, Y& y) const
    {
#ifdef DUNE_FMatrix_WITH_CHECKING
      if (x.N()!=M()) DUNE_THROW(FMatrixError,"index out of range");
      if (y.N()!=N()) DUNE_THROW(FMatrixError,"index out of range");
#endif
      for (size_type i=0; i<n; ++i)
        y[i] += diag_[i] * x[i];
    }
 
    template<class X, class Y>
    void umtv (const X& x, Y& y) const
    {
#ifdef DUNE_FMatrix_WITH_CHECKING
      if (x.N()!=N()) DUNE_THROW(FMatrixError,"index out of range");
      if (y.N()!=M()) DUNE_THROW(FMatrixError,"index out of range");
#endif
      for (size_type i=0; i<n; ++i)
        y[i] += diag_[i] * x[i];
    }
 
    template<class X, class Y>
    void umhv (const X& x, Y& y) const
    {
#ifdef DUNE_FMatrix_WITH_CHECKING
      if (x.N()!=N()) DUNE_THROW(FMatrixError,"index out of range");
      if (y.N()!=M()) DUNE_THROW(FMatrixError,"index out of range");
#endif
      for (size_type i=0; i<n; i++)
        y[i] += conjugateComplex(diag_[i])*x[i];
    }
 
    template<class X, class Y>
    void mmv (const X& x, Y& y) const
    {
#ifdef DUNE_FMatrix_WITH_CHECKING
      if (x.N()!=M()) DUNE_THROW(FMatrixError,"index out of range");
      if (y.N()!=N()) DUNE_THROW(FMatrixError,"index out of range");
#endif
      for (size_type i=0; i<n; ++i)
        y[i] -= diag_[i] * x[i];
    }
 
    template<class X, class Y>
    void mmtv (const X& x, Y& y) const
    {
#ifdef DUNE_FMatrix_WITH_CHECKING
      if (x.N()!=N()) DUNE_THROW(FMatrixError,"index out of range");
      if (y.N()!=M()) DUNE_THROW(FMatrixError,"index out of range");
#endif
      for (size_type i=0; i<n; ++i)
        y[i] -= diag_[i] * x[i];
    }
 
    template<class X, class Y>
    void mmhv (const X& x, Y& y) const
    {
#ifdef DUNE_FMatrix_WITH_CHECKING
      if (x.N()!=N()) DUNE_THROW(FMatrixError,"index out of range");
      if (y.N()!=M()) DUNE_THROW(FMatrixError,"index out of range");
#endif
      for (size_type i=0; i<n; i++)
        y[i] -= conjugateComplex(diag_[i])*x[i];
    }
 
    template<class X, class Y>
    void usmv (const typename FieldTraits<Y>::field_type & alpha,
      const X& x, Y& y) const
    {
#ifdef DUNE_FMatrix_WITH_CHECKING
      if (x.N()!=M()) DUNE_THROW(FMatrixError,"index out of range");
      if (y.N()!=N()) DUNE_THROW(FMatrixError,"index out of range");
#endif
      for (size_type i=0; i<n; i++)
        y[i] += alpha * diag_[i] * x[i];
    }
 
    template<class X, class Y>
    void usmtv (const typename FieldTraits<Y>::field_type & alpha,
      const X& x, Y& y) const
    {
#ifdef DUNE_FMatrix_WITH_CHECKING
      if (x.N()!=N()) DUNE_THROW(FMatrixError,"index out of range");
      if (y.N()!=M()) DUNE_THROW(FMatrixError,"index out of range");
#endif
      for (size_type i=0; i<n; i++)
        y[i] += alpha * diag_[i] * x[i];
    }
 
    template<class X, class Y>
    void usmhv (const typename FieldTraits<Y>::field_type & alpha,
      const X& x, Y& y) const
    {
#ifdef DUNE_FMatrix_WITH_CHECKING
      if (x.N()!=N()) DUNE_THROW(FMatrixError,"index out of range");
      if (y.N()!=M()) DUNE_THROW(FMatrixError,"index out of range");
#endif
      for (size_type i=0; i<n; i++)
        y[i] += alpha * conjugateComplex(diag_[i]) * x[i];
    }
 
    //===== norms
 
    double frobenius_norm () const
    {
      return diag_.two_norm();
    }
 
    double frobenius_norm2 () const
    {
      return diag_.two_norm2();
    }
 
    double infinity_norm () const
    {
      return diag_.infinity_norm();
    }
 
    double infinity_norm_real () const
    {
      return diag_.infinity_norm_real();
    }
 
 
 
    //===== solve
 
    template<class V>
    void solve (V& x, const V& b) const
    {
      for (int i=0; i<n; i++)
        x[i] = b[i]/diag_[i];
    }
 
    void invert()
    {
      using real_type = typename FieldTraits<K>::real_type;
      for (int i=0; i<n; i++)
        diag_[i] = real_type(1.0)/diag_[i];
    }
 
    K determinant () const
    {
      K det = diag_[0];
      for (int i=1; i<n; i++)
        det *= diag_[i];
      return det;
    }
 
 
 
    //===== matrix-matrix multiplication
 
    template <class OtherScalar>
    friend auto operator* ( const DiagonalMatrix& matrixA,
                            const DiagonalMatrix<OtherScalar, n>& matrixB)
    {
      auto result = DiagonalMatrix<typename PromotionTraits<K,OtherScalar>::PromotedType, n>{};
      for(int i=0; i<n; ++i)
        result.diagonal(i) = matrixA.diagonal(i)*matrixB.diagonal(i);
      return result;
    }
 
    template <class OtherMatrix,
      std::enable_if_t<(Impl::IsDenseMatrix<OtherMatrix>::value), int> = 0,
      std::enable_if_t<(not Impl::IsFieldMatrix<OtherMatrix>::value), int> = 0>
    friend auto operator* ( const DiagonalMatrix& matrixA,
                            const OtherMatrix& matrixB)
    {
      using OtherField = typename FieldTraits<OtherMatrix>::field_type;
      using F = typename PromotionTraits<field_type, OtherField>::PromotedType;
 
      auto result = [&]{
        if constexpr (Impl::IsStaticSizeMatrix_v<OtherMatrix>) {
          static_assert(n == OtherMatrix::rows);
          return FieldMatrix<F, n, OtherMatrix::cols>{};
        } else {
          assert(n == matrixB.N());
          return DynamicMatrix<F>{n,matrixB.M()};
        }
      }();
 
      for (int i = 0; i < result.N(); ++i)
        for (int j = 0; j < result.M(); ++j)
          result[i][j] = matrixA.diagonal(i) * matrixB[i][j];
      return result;
    }
 
    //===== sizes
 
    static constexpr size_type N ()
    {
      return n;
    }
 
    static constexpr size_type M ()
    {
      return n;
    }
 
 
 
    //===== query
 
    bool exists (size_type i, size_type j) const
    {
      DUNE_ASSERT_BOUNDS(i >= 0 && i < n);
      DUNE_ASSERT_BOUNDS(j >= 0 && j < n);
      return i==j;
    }
 
 
 
    friend std::ostream& operator<< (std::ostream& s, const DiagonalMatrix<K,n>& a)
    {
      for (size_type i=0; i<n; i++) {
        for (size_type j=0; j<n; j++)
          s << ((i==j) ? a.diag_[i] : 0) << " ";
        s << std::endl;
      }
      return s;
    }
 
    reference operator[](size_type i)
    {
      return reference(const_cast<K*>(&diag_[i]), i);
    }
 
    const_reference operator[](size_type i) const
    {
      return const_reference(const_cast<K*>(&diag_[i]), i);
    }
 
    const K& diagonal(size_type i) const
    {
      return diag_[i];
    }
 
    K& diagonal(size_type i)
    {
      return diag_[i];
    }
 
    const FieldVector<K,n>& diagonal() const
    {
      return diag_;
    }
 
    FieldVector<K,n>& diagonal()
    {
      return diag_;
    }
 
  private:
 
    // the data, a FieldVector storing the diagonal
    FieldVector<K,n> diag_;
  };
 
  template< class K, int n >
  struct FieldTraits< DiagonalMatrix<K,n> >
  {
    typedef typename FieldTraits<K>::field_type field_type;
    typedef typename FieldTraits<K>::real_type real_type;
  };
 
 
#ifndef DOXYGEN // hide specialization
  template< class K >
  class DiagonalMatrix<K, 1> : public FieldMatrix<K, 1, 1>
  {
    typedef FieldMatrix<K,1,1> Base;
  public:
    typedef typename Base::size_type size_type;
 
    constexpr static int blocklevel = 1;
 
    typedef typename Base::row_type row_type;
 
    typedef typename Base::row_reference row_reference;
    typedef typename Base::const_row_reference const_row_reference;
 
    constexpr static int rows = 1;
    constexpr static int cols = 1;
 
 
    constexpr DiagonalMatrix() = default;
 
    DiagonalMatrix(const K& scalar)
    {
      (*this)[0][0] = scalar;
    }
 
    template <class OtherK>
    DiagonalMatrix(const DiagonalMatrix<OtherK,1>& other)
      : Base(FieldMatrix<OtherK,1,1>(other))
    {}
 
    const K& diagonal(size_type) const
    {
      return (*this)[0][0];
    }
 
    K& diagonal(size_type)
    {
      return (*this)[0][0];
    }
 
    const FieldVector<K,1>& diagonal() const
    {
      return (*this)[0];
    }
 
    FieldVector<K,1>& diagonal()
    {
      return (*this)[0];
    }
 
    DiagonalMatrix<K, 1> transposed() const
    {
      return *this;
    }
 
    template <class OtherScalar>
    friend auto operator* ( const DiagonalMatrix& matrixA,
                            const DiagonalMatrix<OtherScalar, 1>& matrixB)
    {
      return DiagonalMatrix<typename PromotionTraits<K,OtherScalar>::PromotedType, 1>{matrixA.diagonal(0)*matrixB.diagonal(0)};
    }
 
    template <class OtherMatrix,
      std::enable_if_t<(Impl::IsDenseMatrix<OtherMatrix>::value), int> = 0,
      std::enable_if_t<(not Impl::IsFieldMatrix<OtherMatrix>::value), int> = 0>
    friend auto operator* ( const DiagonalMatrix& matrixA,
                            const OtherMatrix& matrixB)
    {
      using OtherField = typename FieldTraits<OtherMatrix>::field_type;
      using F = typename PromotionTraits<K, OtherField>::PromotedType;
 
      auto result = [&]{
        if constexpr (Impl::IsStaticSizeMatrix_v<OtherMatrix>) {
          static_assert(1 == OtherMatrix::rows);
          return FieldMatrix<F, 1, OtherMatrix::cols>{};
        } else {
          assert(1 == matrixB.N());
          return DynamicMatrix<F>{1,matrixB.M()};
        }
      }();
 
      for (int i = 0; i < result.N(); ++i)
        for (int j = 0; j < result.M(); ++j)
          result[i][j] = matrixA.diagonal(i) * matrixB[i][j];
      return result;
    }
 
  };
#endif
 
 
  template<class DiagonalMatrixType>
  class DiagonalMatrixWrapper
  {
    typedef typename DiagonalMatrixType::reference reference;
    typedef typename DiagonalMatrixType::const_reference const_reference;
    typedef typename DiagonalMatrixType::field_type K;
    typedef DiagonalRowVector<K, DiagonalMatrixType::rows> row_type;
    typedef std::size_t size_type;
    typedef DiagonalMatrixWrapper< DiagonalMatrixType> MyType;
 
    friend class ContainerWrapperIterator<const MyType, reference, reference>;
    friend class ContainerWrapperIterator<const MyType, const_reference, const_reference>;
 
  public:
 
    DiagonalMatrixWrapper() :
      mat_(0)
    {}
 
    DiagonalMatrixWrapper(const DiagonalMatrixType* mat) :
      mat_(const_cast<DiagonalMatrixType*>(mat))
    {}
 
    size_type realIndex(int i) const
    {
      return i;
    }
 
    row_type* pointer(int i) const
    {
      row_ = row_type(&(mat_->diagonal(i)), i);
      return &row_;
    }
 
    bool identical(const DiagonalMatrixWrapper& other) const
    {
      return mat_==other.mat_;
    }
 
  private:
 
    mutable DiagonalMatrixType* mat_;
    mutable row_type row_;
  };
 
  template< class K, int n >
  class DiagonalRowVectorConst
  {
    template<class DiagonalMatrixType>
    friend class DiagonalMatrixWrapper;
    friend class ContainerWrapperIterator<DiagonalRowVectorConst<K,n>, const K, const K&>;
 
  public:
    // remember size of vector
    constexpr static int dimension = n;
 
    // standard constructor and everything is sufficient ...
 
    //===== type definitions and constants
 
    typedef K field_type;
 
    typedef K block_type;
 
    typedef std::size_t size_type;
 
    constexpr static int blocklevel = 1;
 
    constexpr static int size = n;
 
    DiagonalRowVectorConst() :
      p_(0),
      row_(0)
    {}
 
    explicit DiagonalRowVectorConst (K* p, int col) :
      p_(p),
      row_(col)
    {}
 
    //===== access to components
 
    const K& operator[] ([[maybe_unused]] size_type i) const
    {
      DUNE_ASSERT_BOUNDS(i == row_);
      return *p_;
    }
 
    // check if row is identical to other row (not only identical values)
    // since this is a proxy class we need to check equality of the stored pointer
    bool identical(const DiagonalRowVectorConst<K,n>& other) const
    {
      return ((p_ == other.p_)and (row_ == other.row_));
    }
 
    typedef ContainerWrapperIterator<DiagonalRowVectorConst<K,n>, const K, const K&> ConstIterator;
    typedef ConstIterator const_iterator;
 
    ConstIterator begin () const
    {
      return ConstIterator(*this,0);
    }
 
    ConstIterator end () const
    {
      return ConstIterator(*this,1);
    }
 
    ConstIterator beforeEnd() const
    {
      return ConstIterator(*this,0);
    }
 
    ConstIterator beforeBegin () const
    {
      return ConstIterator(*this,-1);
    }
 
    bool operator== (const DiagonalRowVectorConst& y) const
    {
      return ((p_==y.p_)and (row_==y.row_));
    }
 
    //===== sizes
 
    size_type N () const
    {
      return n;
    }
 
    size_type dim () const
    {
      return n;
    }
 
    size_type rowIndex() const
    {
      return row_;
    }
 
    const K& diagonal() const
    {
      return *p_;
    }
 
  protected:
 
    size_type realIndex([[maybe_unused]] int i) const
    {
      return rowIndex();
    }
 
    K* pointer([[maybe_unused]] size_type i) const
    {
      return const_cast<K*>(p_);
    }
 
    DiagonalRowVectorConst* operator&()
    {
      return this;
    }
 
    // the data, very simply a pointer to the diagonal value and the row number
    K* p_;
    size_type row_;
  };
 
  template< class K, int n >
  class DiagonalRowVector : public DiagonalRowVectorConst<K,n>
  {
    template<class DiagonalMatrixType>
    friend class DiagonalMatrixWrapper;
    friend class ContainerWrapperIterator<DiagonalRowVector<K,n>, K, K&>;
 
  public:
    // standard constructor and everything is sufficient ...
 
    //===== type definitions and constants
 
    typedef K field_type;
 
    typedef K block_type;
 
    typedef std::size_t size_type;
 
    DiagonalRowVector() : DiagonalRowVectorConst<K,n>()
    {}
 
    explicit DiagonalRowVector (K* p, int col) : DiagonalRowVectorConst<K,n>(p, col)
    {}
 
    //===== assignment from scalar
    DiagonalRowVector& operator= (const K& k)
    {
      *p_ = k;
      return *this;
    }
 
    //===== access to components
 
    K& operator[] ([[maybe_unused]] size_type i)
    {
      DUNE_ASSERT_BOUNDS(i == row_);
      return *p_;
    }
 
    typedef ContainerWrapperIterator<DiagonalRowVector<K,n>, K, K&> Iterator;
    typedef Iterator iterator;
 
    Iterator begin ()
    {
      return Iterator(*this, 0);
    }
 
    Iterator end ()
    {
      return Iterator(*this, 1);
    }
 
    Iterator beforeEnd ()
    {
      return Iterator(*this, 0);
    }
 
    Iterator beforeBegin ()
    {
      return Iterator(*this, -1);
    }
 
    typedef ContainerWrapperIterator<DiagonalRowVectorConst<K,n>, const K, const K&> ConstIterator;
    typedef ConstIterator const_iterator;
 
    using DiagonalRowVectorConst<K,n>::identical;
    using DiagonalRowVectorConst<K,n>::operator[];
    using DiagonalRowVectorConst<K,n>::operator==;
    using DiagonalRowVectorConst<K,n>::begin;
    using DiagonalRowVectorConst<K,n>::end;
    using DiagonalRowVectorConst<K,n>::beforeEnd;
    using DiagonalRowVectorConst<K,n>::beforeBegin;
    using DiagonalRowVectorConst<K,n>::N;
    using DiagonalRowVectorConst<K,n>::dim;
    using DiagonalRowVectorConst<K,n>::rowIndex;
    using DiagonalRowVectorConst<K,n>::diagonal;
 
  protected:
 
    DiagonalRowVector* operator&()
    {
      return this;
    }
 
  private:
 
    using DiagonalRowVectorConst<K,n>::p_;
    using DiagonalRowVectorConst<K,n>::row_;
  };
 
 
  // implement type traits
  template<class K, int n>
  struct const_reference< DiagonalRowVector<K,n> >
  {
    typedef DiagonalRowVectorConst<K,n> type;
  };
 
  template<class K, int n>
  struct const_reference< DiagonalRowVectorConst<K,n> >
  {
    typedef DiagonalRowVectorConst<K,n> type;
  };
 
  template<class K, int n>
  struct mutable_reference< DiagonalRowVector<K,n> >
  {
    typedef DiagonalRowVector<K,n> type;
  };
 
  template<class K, int n>
  struct mutable_reference< DiagonalRowVectorConst<K,n> >
  {
    typedef DiagonalRowVector<K,n> type;
  };
 
 
 
  template<class CW, class T, class R>
  class ContainerWrapperIterator : public BidirectionalIteratorFacade<ContainerWrapperIterator<CW,T,R>,T, R, int>
  {
    typedef typename std::remove_const<CW>::type NonConstCW;
 
    friend class ContainerWrapperIterator<CW, typename mutable_reference<T>::type, typename mutable_reference<R>::type>;
    friend class ContainerWrapperIterator<CW, typename const_reference<T>::type, typename const_reference<R>::type>;
 
    typedef ContainerWrapperIterator<CW, typename mutable_reference<T>::type, typename mutable_reference<R>::type> MyType;
    typedef ContainerWrapperIterator<CW, typename const_reference<T>::type, typename const_reference<R>::type> MyConstType;
 
  public:
 
    // Constructors needed by the facade iterators.
    ContainerWrapperIterator() :
      containerWrapper_(),
      position_(0)
    {}
 
    ContainerWrapperIterator(CW containerWrapper, int position) :
      containerWrapper_(containerWrapper),
      position_(position)
    {}
 
    template<class OtherContainerWrapperIteratorType>
    ContainerWrapperIterator(OtherContainerWrapperIteratorType& other) :
      containerWrapper_(other.containerWrapper_),
      position_(other.position_)
    {}
 
    ContainerWrapperIterator(const MyType& other) :
      containerWrapper_(other.containerWrapper_),
      position_(other.position_)
    {}
 
    ContainerWrapperIterator(const MyConstType& other) :
      containerWrapper_(other.containerWrapper_),
      position_(other.position_)
    {}
 
    template<class OtherContainerWrapperIteratorType>
    ContainerWrapperIterator& operator=(OtherContainerWrapperIteratorType& other)
    {
      containerWrapper_ = other.containerWrapper_;
      position_ = other.position_;
      return *this;
    }
 
    // This operator is needed since we can not get the address of the
    // temporary object returned by dereference
    T* operator->() const
    {
      return containerWrapper_.pointer(position_);
    }
 
    // Methods needed by the forward iterator
    bool equals(const MyType& other) const
    {
      return position_ == other.position_ && containerWrapper_.identical(other.containerWrapper_);
    }
 
    bool equals(const MyConstType& other) const
    {
      return position_ == other.position_ && containerWrapper_.identical(other.containerWrapper_);
    }
 
    R dereference() const
    {
      return *containerWrapper_.pointer(position_);
    }
 
    void increment()
    {
      ++position_;
    }
 
    // Additional function needed by BidirectionalIterator
    void decrement()
    {
      --position_;
    }
 
    // Additional function needed by RandomAccessIterator
    R elementAt(int i) const
    {
      return *containerWrapper_.pointer(position_+i);
    }
 
    void advance(int n)
    {
      position_=position_+n;
    }
 
    template<class OtherContainerWrapperIteratorType>
    std::ptrdiff_t distanceTo(OtherContainerWrapperIteratorType& other) const
    {
      assert(containerWrapper_.identical(other));
      return other.position_ - position_;
    }
 
    std::ptrdiff_t index() const
    {
      return containerWrapper_.realIndex(position_);
    }
 
  private:
    NonConstCW containerWrapper_;
    size_t position_;
  };
 
  template <class DenseMatrix, class field, int N>
  struct DenseMatrixAssigner<DenseMatrix, DiagonalMatrix<field, N>> {
    static void apply(DenseMatrix& denseMatrix,
                      DiagonalMatrix<field, N> const& rhs) {
#ifdef DUNE_CHECK_BOUNDS
      if (denseMatrix.M() != N || denseMatrix.N() != N)
        DUNE_THROW(Dune::RangeError, "Incompatible matrix dimensions in assignment.");
#endif // DUNE_CHECK_BOUNDS
 
      denseMatrix = field(0);
      for (int i = 0; i < N; ++i)
        denseMatrix[i][i] = rhs.diagonal()[i];
    }
  };
  /* @} */
} // end namespace
#endif