Domi_MDArray.hpp

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#ifndef DOMI_MDARRAY_HPP
#define DOMI_MDARRAY_HPP

// Standard includes
#include <cstdarg>

// Teuchos includes
#include "Teuchos_Array.hpp"

// Domi includes
#include "Domi_ConfigDefs.hpp"
#include "Domi_Utils.hpp"
#include "Domi_MDIterator.hpp"
#include "Domi_MDRevIterator.hpp"
#include "Domi_MDArrayView.hpp"

namespace Domi
{

// I put these non-member template functions here for the same reason
// that Ross did the same thing for the Teuchos::Array class.  See
// Teuchos_Array.hpp for details.
template< typename T > class MDArray;

template< typename T >
bool operator==(const MDArray< T > & a1,
                const MDArray< T > & a2);

template< typename T >
bool operator==(const MDArray< T > & a1,
                const MDArrayView< T > & a2);

template< typename T >
bool operator==(const MDArrayView< T > & a1,
                const MDArray< T > & a2);

template< typename T >
bool operator!=(const MDArray< T > & a1,
                const MDArray< T > & a2);

template< typename T >
bool operator!=(const MDArray< T > & a1,
                const MDArrayView< T > & a2);

template< typename T >
bool operator!=(const MDArrayView< T > & a1,
                const MDArray< T > & a2);

template< typename T >
void swap(MDArray< T > & a1, MDArray< T > & a2);

template< typename T >
class MDArray
{
public:


  typedef T value_type;

  typedef T* pointer;

  typedef const T* const_pointer;

  typedef T& reference;

  typedef const T& const_reference;



  inline MDArray();

  inline MDArray(const Teuchos::ArrayView< dim_type > & dims);

  inline MDArray(const Teuchos::ArrayView< dim_type > & dims,
         const T & value,
         const Layout layout = DEFAULT_ORDER);

  inline MDArray(const Teuchos::ArrayView< dim_type > & dims,
         const Layout layout,
         const T & value = value_type());

  inline MDArray(const MDArray< T > & source);

  MDArray(const MDArrayView< T > & source);

  ~MDArray();



  inline int numDims() const;

  inline const Teuchos::Array< dim_type > & dimensions() const;

  inline dim_type dimension(int axis) const;

  inline size_type size() const;

  inline const Teuchos::Array< size_type > & strides() const;

  inline const Teuchos::Array< T > & array() const;

  inline const Layout layout() const;



  friend class MDIterator< MDArray< T > >;
  friend class MDIterator< MDArray< const T > >;
  friend class MDRevIterator< MDArray< T > >;
  friend class MDRevIterator< MDArray< const T > >;

  typedef MDIterator< MDArray< T > >          iterator;
  typedef MDIterator< MDArray< const T > >    const_iterator;
  typedef MDRevIterator< MDArray< T > >       reverse_iterator;
  typedef MDRevIterator< MDArray< const T > > const_reverse_iterator;

  iterator begin();

  iterator end();

  const_iterator begin() const;

  const_iterator end() const;

  const_iterator cbegin() const;

  const_iterator cend() const;

  reverse_iterator rbegin();

  reverse_iterator rend();

  const_reverse_iterator crbegin() const;

  const_reverse_iterator crend() const;



  MDArrayView< T > mdArrayView();

  const MDArrayView< T > mdArrayView() const;

  MDArrayView< const T > mdArrayViewConst();

  const MDArrayView< const T > mdArrayViewConst() const;

#ifndef SWIG

  inline operator MDArrayView< T >() const;

  inline operator MDArrayView< const T >() const;
#endif



  MDArrayView< T > operator[](dim_type i);

  const MDArrayView< T > operator[](dim_type i) const;

  MDArrayView< T > operator[](Slice s);

  const MDArrayView< T > operator[](Slice s) const;

  inline MDArrayView< T > operator()();

  inline const MDArrayView< T > operator()() const;



  inline T & operator()(dim_type i);

  inline T & operator()(dim_type i, dim_type j);

  inline T & operator()(dim_type i, dim_type j, dim_type k);

  inline T & operator()(dim_type i, dim_type j, dim_type k, dim_type m);

  inline T & operator()(dim_type i, dim_type j, dim_type k, dim_type m,
                        dim_type n);

  inline T & operator()(dim_type i, dim_type j, dim_type k, dim_type m,
                        dim_type n, dim_type p, ...);

  inline const T & operator()(dim_type i) const;

  inline const T & operator()(dim_type i, dim_type j) const;

  inline const T & operator()(dim_type i, dim_type j, dim_type k) const;

  inline const T & operator()(dim_type i, dim_type j, dim_type k,
                              dim_type m) const;

  inline const T & operator()(dim_type i, dim_type j, dim_type k,
                              dim_type m, dim_type n) const;

  inline const T & operator()(dim_type i, dim_type j, dim_type k,
                              dim_type m, dim_type n, dim_type p, ...) const;



  void assign(const T & value);

  T & at(dim_type i, ...);

  const T & at(dim_type i, ...) const;

  inline size_type capacity() const;

  void clear();

  inline bool empty() const;

  inline size_type max_size() const;

  void resize(const Teuchos::ArrayView< dim_type > & dims);

  void swap(MDArray<T> & a);

  inline static bool hasBoundsChecking();

  std::string toString() const;

  inline const T * getRawPtr() const;

  inline T * getRawPtr();


  // These operators are declared as friends so that the compiler will
  // do automatic type conversion.


  template< typename T2 >
  friend bool operator==(const MDArray< T2 > & a1,
                         const MDArray< T2 > & a2);

  template< typename T2 >
  friend bool operator==(const MDArray< T2 > & a1,
                         const MDArrayView< T2 > & a2);

  template< typename T2 >
  friend bool operator==(const MDArrayView< T2 > & a1,
                         const MDArray< T2 > & a2);

  template< typename T2 >
  friend bool operator!=(const MDArray< T2 > & a1,
                         const MDArray< T2 > & a2);

  template< typename T2 >
  friend bool operator!=(const MDArray< T2 > & a1,
                         const MDArrayView< T2 > & a2);

  template< typename T2 >
  friend bool operator!=(const MDArrayView< T2 > & a1,
                         const MDArray< T2 > & a2);

  template< typename T2 >
  friend std::ostream & operator<<(std::ostream & os,
                                   const MDArray< T2 > & a);

  template< typename T2 >
  friend void swap(MDArray< T2 > & a1,
                   MDArray< T2 > & a2);


private:
  Teuchos::Array< dim_type >  _dimensions;
  Teuchos::Array< size_type > _strides;
  Teuchos::Array< T >         _array;
  Layout                      _layout;
  pointer                     _ptr;

  // Used for array bounds checking
  void assertAxis(int axis) const;

  // Used for array bounds checking
  void assertIndex(dim_type i, int axis) const;
};

// Implementations //

template< typename T >
MDArray< T >::MDArray() :
  _dimensions(Teuchos::tuple< dim_type >(0)),
  _strides(Teuchos::tuple< size_type >(1)),
  _array(),
  _layout(DEFAULT_ORDER),
  _ptr()
{
}


template< typename T >
MDArray< T >::MDArray(const Teuchos::ArrayView< dim_type > & dims) :
  _dimensions(dims),
  _strides(computeStrides< size_type, dim_type >(dims, DEFAULT_ORDER)),
  _array(computeSize(dims)),
  _layout(DEFAULT_ORDER),
  _ptr(_array.getRawPtr())
{
}


template< typename T >
MDArray< T >::MDArray(const Teuchos::ArrayView< dim_type > & dims,
              const T & value,
              const Layout layout) :
  _dimensions(dims),
  _strides(computeStrides< size_type, dim_type >(dims, layout)),
  _array(computeSize(dims), value),
  _layout(layout),
  _ptr(_array.getRawPtr())
{
}


template< typename T >
MDArray< T >::MDArray(const Teuchos::ArrayView< dim_type > & dims,
              const Layout layout,
              const T & value) :
  _dimensions(dims),
  _strides(computeStrides< size_type, dim_type >(dims, layout)),
  _array(computeSize(dims), value),
  _layout(layout),
  _ptr(_array.getRawPtr())
{
}


template< typename T >
MDArray< T >::MDArray(const MDArray< T > & source) :
  _dimensions(source._dimensions),
  _strides(source._strides),
  _array(source._array),
  _layout(source._layout),
  _ptr(_array.getRawPtr())
{
}


template< typename T >
MDArray< T >::MDArray(const MDArrayView< T > & source) :
  _dimensions(source.dimensions()),
  _strides(computeStrides< size_type, dim_type >(source.dimensions(),
                                                 source.layout())),
  _array(computeSize(source.dimensions())),
  _layout(source.layout()),
  _ptr(_array.getRawPtr())
{
  // Copy the values from the MDArrayView to the MDArray
  iterator thisit = begin();
  typename MDArrayView< T >::const_iterator srcit = source.cbegin();
  for ( ; srcit != source.cend(); ++thisit, ++srcit)
  {
    *thisit = *srcit;
  }
}


template< typename T >
MDArray< T >::~MDArray()
{
}


template< typename T >
int
MDArray< T >::numDims() const
{
  return _dimensions.size();
}


template< typename T >
const Teuchos::Array< dim_type > &
MDArray< T >::dimensions() const
{
  return _dimensions;
}


template< typename T >
dim_type
MDArray< T >::dimension(int axis) const
{
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
  assertAxis(axis);
#endif
  return _dimensions[axis];
}


template< typename T >
size_type
MDArray< T >::size() const
{
  return _array.size();
}


template< typename T >
const Teuchos::Array< size_type > &
MDArray< T >::strides() const
{
  return _strides;
}


template< typename T >
const Teuchos::Array< T > &
MDArray< T >::array() const
{
  return _array;
}


template< typename T >
const Layout
MDArray< T >::layout() const
{
  return _layout;
}


template< typename T >
typename MDArray< T >::iterator
MDArray< T >::begin()
{
  return iterator(*this);
}


template< typename T >
typename MDArray< T >::iterator
MDArray< T >::end()
{
  // Return the iterator corresponding to the last element
  return iterator(*this, true);
}


template< typename T >
typename MDArray< T >::const_iterator
MDArray< T >::begin() const
{
  return const_iterator(*this);
}


template< typename T >
typename MDArray< T >::const_iterator
MDArray< T >::end() const
{
  // Return the iterator corresponding to the last element
  return const_iterator(*this, true);
}


template< typename T >
typename MDArray< T >::const_iterator
MDArray< T >::cbegin() const
{
  return const_iterator(*this);
}


template< typename T >
typename MDArray< T >::const_iterator
MDArray< T >::cend() const
{
  // Return the iterator corresponding to the last element
  return const_iterator(*this, true);
}


template< typename T >
typename MDArray< T >::reverse_iterator
MDArray< T >::rbegin()
{
  return reverse_iterator(*this);
}


template< typename T >
typename MDArray< T >::reverse_iterator
MDArray< T >::rend()
{
  // Return the reverse_iterator corresponding to the last element
  return reverse_iterator(*this, true);
}


template< typename T >
typename MDArray< T >::const_reverse_iterator
MDArray< T >::crbegin() const
{
  return const_reverse_iterator(*this);
}


template< typename T >
typename MDArray< T >::const_reverse_iterator
MDArray< T >::crend() const
{
  // Return the reverse_iterator corresponding to the last element
  return const_reverse_iterator(*this, true);
}


template< typename T >
MDArrayView< T >
MDArray< T >::mdArrayView()
{
  return MDArrayView< T >(_array(), _dimensions, _layout);
}


template< typename T >
const MDArrayView< T >
MDArray< T >::mdArrayView() const
{
  Teuchos::ArrayView< T > array(const_cast< T* >(_array.getRawPtr()),
                                _array.size());
  Teuchos::Array< dim_type > dims(_dimensions);
  return MDArrayView< T >(array, dims(), _layout);
}


template< typename T >
MDArrayView< const T >
MDArray< T >::mdArrayViewConst()
{
  return MDArrayView< const T >(_array, _dimensions(), _layout);
}


template< typename T >
const MDArrayView< const T >
MDArray< T >::mdArrayViewConst() const
{
  return MDArrayView< const T >(_array, _dimensions(), _layout);
}


#ifndef SWIG
template< typename T >
MDArray< T >::operator MDArrayView< T >() const
{
  return mdArrayView();
}


template< typename T >
MDArray< T >::operator MDArrayView< const T >() const
{
  return mdArrayViewConst();
}
#endif


template< typename T >
MDArrayView< T >
MDArray< T >::operator[](dim_type i)
{
  // Note: array bounds checking, if active, will be performed by the
  // MDArrayView class
  return mdArrayView()[i];
}


template< typename T >
const MDArrayView< T >
MDArray< T >::operator[](dim_type i) const
{
  // Note: array bounds checking, if active, will be performed by the
  // MDArrayView class
  return mdArrayView()[i];
}


template< typename T >
MDArrayView< T >
MDArray< T >::operator[](Slice s)
{
  // Note: Slices produce safe indexes
  return mdArrayView()[s];
}


template< typename T >
const MDArrayView< T >
MDArray< T >::operator[](Slice s) const
{
  // Note: Slices produce safe indexes
  return mdArrayView()[s];
}


template< typename T >
MDArrayView< T >
MDArray< T >::operator()()
{
  return mdArrayView();
}


template< typename T >
const MDArrayView< T >
MDArray< T >::operator()() const
{
  return mdArrayView();
}


template< typename T >
T &
MDArray< T >::operator()(dim_type i)
{
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
  TEUCHOS_TEST_FOR_EXCEPTION(
    (_dimensions.size() != 1), RangeError,
    "Attempt to access " << _dimensions.size() << "D array with 1 index"
    );
  assertIndex(i, 0);
#endif
  return _ptr[i * _strides[0]];
}


template< typename T >
T &
MDArray< T >::operator()(dim_type i,
                         dim_type j)
{
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
  TEUCHOS_TEST_FOR_EXCEPTION(
    (_dimensions.size() != 2), RangeError,
    "Attempt to access " << _dimensions.size() << "D array with 2 indexes"
    );
  assertIndex(i, 0);
  assertIndex(j, 1);
#endif
  return _ptr[i * _strides[0] + j * _strides[1]];
}


template< typename T >
T &
MDArray< T >::operator()(dim_type i,
                         dim_type j,
                         dim_type k)
{
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
  TEUCHOS_TEST_FOR_EXCEPTION(
    (_dimensions.size() != 3), RangeError,
    "Attempt to access " << _dimensions.size() << "D array with 3 indexes"
    );
  assertIndex(i, 0);
  assertIndex(j, 1);
  assertIndex(k, 2);
#endif
  return _ptr[i * _strides[0] + j * _strides[1] + k * _strides[2]];
}


template< typename T >
T &
MDArray< T >::operator()(dim_type i,
                         dim_type j,
                         dim_type k,
                         dim_type m)
{
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
  TEUCHOS_TEST_FOR_EXCEPTION(
    (_dimensions.size() != 4), RangeError,
    "Attempt to access " << _dimensions.size() << "D array with 4 indexes"
    );
  assertIndex(i, 0);
  assertIndex(j, 1);
  assertIndex(k, 2);
  assertIndex(m, 3);
#endif
  return _ptr[i * _strides[0] + j * _strides[1] + k * _strides[2] +
              m * _strides[3]];
}


template< typename T >
T &
MDArray< T >::operator()(dim_type i,
                         dim_type j,
                         dim_type k,
                         dim_type m,
                         dim_type n)
{
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
  TEUCHOS_TEST_FOR_EXCEPTION(
    (_dimensions.size() != 5), RangeError,
    "Attempt to access " << _dimensions.size() << "D array with 5 indexes"
    );
  assertIndex(i, 0);
  assertIndex(j, 1);
  assertIndex(k, 2);
  assertIndex(m, 3);
  assertIndex(n, 4);
#endif
  return _ptr[i * _strides[0] + j * _strides[1] + k * _strides[2] +
              m * _strides[3] + n * _strides[4]];
}


template< typename T >
T &
MDArray< T >::operator()(dim_type i,
                         dim_type j,
                         dim_type k,
                         dim_type m,
                         dim_type n,
                         dim_type p,
                         ...)
{
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
  TEUCHOS_TEST_FOR_EXCEPTION(
    (_dimensions.size() < 6), RangeError,
    "Attempt to access " << _dimensions.size() << "D array with too many indexes"
    );
  assertIndex(i, 0);
  assertIndex(j, 1);
  assertIndex(k, 2);
  assertIndex(m, 3);
  assertIndex(n, 4);
  assertIndex(p, 5);
#endif
  va_list indexes;
  size_type offset = i * _strides[0] + j * _strides[1] + k * _strides[2] +
                     m * _strides[3] + n * _strides[4] + p * _strides[5];
  va_start(indexes, p);
  for (int axis = 6; axis < _dimensions.size(); axis++)
  {
    dim_type q = va_arg(indexes, dim_type);
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
    assertIndex(q, axis);
#endif
    offset += q * _strides[axis];
  }
  va_end(indexes);
  return _ptr[offset];
}


template< typename T >
const T &
MDArray< T >::operator()(dim_type i) const
{
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
  TEUCHOS_TEST_FOR_EXCEPTION(
    (_dimensions.size() != 1), RangeError,
    "Attempt to access " << _dimensions.size() << "D array with 1 index"
    );
  assertIndex(i, 0);
#endif
  return _ptr[i * _strides[0]];
}


template< typename T >
const T &
MDArray< T >::operator()(dim_type i,
                         dim_type j) const
{
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
  TEUCHOS_TEST_FOR_EXCEPTION(
    (_dimensions.size() != 2), RangeError,
    "Attempt to access " << _dimensions.size() << "D array with 2 indexes"
    );
  assertIndex(i, 0);
  assertIndex(j, 1);
#endif
  return _ptr[i * _strides[0] + j * _strides[1]];
}


template< typename T >
const T &
MDArray< T >::operator()(dim_type i,
                         dim_type j,
                         dim_type k) const
{
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
  TEUCHOS_TEST_FOR_EXCEPTION(
    (_dimensions.size() != 3), RangeError,
    "Attempt to access " << _dimensions.size() << "D array with 3 indexes"
    );
  assertIndex(i, 0);
  assertIndex(j, 1);
  assertIndex(k, 2);
#endif
  return _ptr[i * _strides[0] + j * _strides[1] + k * _strides[2]];
}


template< typename T >
const T &
MDArray< T >::operator()(dim_type i,
                         dim_type j,
                         dim_type k,
                         dim_type m) const
{
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
  TEUCHOS_TEST_FOR_EXCEPTION(
    (_dimensions.size() != 4), RangeError,
    "Attempt to access " << _dimensions.size() << "D array with 4 indexes"
    );
  assertIndex(i, 0);
  assertIndex(j, 1);
  assertIndex(k, 2);
  assertIndex(m, 3);
#endif
  return _ptr[i * _strides[0] + j * _strides[1] + k * _strides[2] +
              m * _strides[3]];
}


template< typename T >
const T &
MDArray< T >::operator()(dim_type i,
                         dim_type j,
                         dim_type k,
                         dim_type m,
                         dim_type n) const
{
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
  TEUCHOS_TEST_FOR_EXCEPTION(
    (_dimensions.size() != 5), RangeError,
    "Attempt to access " << _dimensions.size() << "D array with 5 indexes"
    );
  assertIndex(i, 0);
  assertIndex(j, 1);
  assertIndex(k, 2);
  assertIndex(m, 3);
  assertIndex(n, 4);
#endif
  return _ptr[i * _strides[0] + j * _strides[1] + k * _strides[2] +
              m * _strides[3] + n * _strides[4]];
}


template< typename T >
const T &
MDArray< T >::operator()(dim_type i,
                         dim_type j,
                         dim_type k,
                         dim_type m,
                         dim_type n,
                         dim_type p,
                         ...) const
{
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
  TEUCHOS_TEST_FOR_EXCEPTION(
    (_dimensions.size() < 6), RangeError,
    "Attempt to access " << _dimensions.size() << "D array with too many indexes"
    );
  assertIndex(i, 0);
  assertIndex(j, 1);
  assertIndex(k, 2);
  assertIndex(m, 3);
  assertIndex(n, 4);
  assertIndex(p, 5);
#endif
  va_list indexes;
  size_type offset = i * _strides[0] + j * _strides[1] + k * _strides[2] +
                     m * _strides[3] + n * _strides[4] + p * _strides[5];
  va_start(indexes, p);
  for (int axis = 6; axis < _dimensions.size(); axis++)
  {
    dim_type q = va_arg(indexes, dim_type);
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
    assertIndex(q, axis);
#endif
    offset += q * _strides[axis];
  }
  va_end(indexes);
  return _ptr[offset];
}


template< typename T >
void
MDArray< T >::assign(const T & value)
{
  for (iterator it = begin(); it != end(); ++it)
    *it = value;
}


template< typename T >
T &
MDArray< T >::at(dim_type i, ...)
{
  assertIndex(i, 0);
  va_list indexes;
  size_type offset = i * _strides[0];
  va_start(indexes, i);
  for (int axis = 1; axis < _dimensions.size(); axis++)
  {
    dim_type j = va_arg(indexes, dim_type);
    assertIndex(j, axis);
    offset += j * _strides[axis];
  }
  va_end(indexes);
  return _ptr[offset];
}


template< typename T >
const T &
MDArray< T >::at(dim_type i, ...) const
{
  assertIndex(i, 0);
  va_list indexes;
  size_type offset = i * _strides[0];
  va_start(indexes, i);
  for (int axis = 1; axis < _dimensions.size(); axis++)
  {
    dim_type j = va_arg(indexes, dim_type);
    assertIndex(j, axis);
    offset += j * _strides[axis];
  }
  va_end(indexes);
  return _ptr[offset];
}


template< typename T >
size_type
MDArray< T >::capacity() const
{
  return _array.capacity();
}


template< typename T >
void
MDArray< T >::clear()
{
  _dimensions.resize(1);
  _dimensions[0] = 0;
  _strides.resize(1);
  _strides[0] = 1;
  _array.clear();
  _ptr = _array.getRawPtr();
}


template< typename T >
bool
MDArray< T >::empty() const
{
  return _array.empty();
}


template< typename T >
size_type
MDArray< T >::max_size() const
{
  return _array.max_size();
}


template< typename T >
void
MDArray< T >::resize(const Teuchos::ArrayView< dim_type > & dims)
{
  _dimensions.assign(dims.begin(), dims.end());
  _strides = computeStrides< size_type, dim_type >(dims, _layout);
  _array.resize(computeSize(dims));
  _ptr = _array.getRawPtr();
}


template< typename T >
void
MDArray< T >::swap(MDArray<T> & a)
{
  // Use Teuchos::swap() to swap the dimensions, strides and
  // underlying array
  Teuchos::swap(_dimensions, a._dimensions);
  Teuchos::swap(_strides,    a._strides   );
  Teuchos::swap(_array,      a._array     );
  // Perform a raw swap of the storage order
  Layout tmp = _layout;
  _layout    = a._layout;
  a._layout  = tmp;
  // Make sure the pointers are correct
  _ptr   = _array.getRawPtr();
  a._ptr = a._array.getRawPtr();
}


template< typename T >
bool
MDArray< T >::hasBoundsChecking()
{
#ifdef HAVE_DOMI_ARRAY_BOUNDSCHECK
  return true;
#else
  return false;
#endif
}


template< typename T >
std::string
MDArray< T >::toString() const
{
  return mdArrayView().toString();
}


template< typename T >
const T *
MDArray< T >::getRawPtr() const
{
  return _array.getRawPtr();
}


template< typename T >
T *
MDArray< T >::getRawPtr()
{
  return _array.getRawPtr();
}


template< typename T >
bool operator==(const MDArray< T > & a1, const MDArray< T > & a2)
{
  return (a1() == a2());
}


template< typename T >
bool operator==(const MDArray< T > & a1, const MDArrayView< T > & a2)
{
  return (a1() == a2);
}


template< typename T >
bool operator==(const MDArrayView< T > & a1, const MDArray< T > & a2)
{
  return (a1 == a2());
}


template< typename T >
bool operator!=(const MDArray< T > & a1, const MDArray< T > & a2)
{
  return not (a1 == a2);
}


template< typename T >
bool operator!=(const MDArray< T > & a1, const MDArrayView< T > & a2)
{
  return (a1() != a2);
}


template< typename T >
bool operator!=(const MDArrayView< T > & a1, const MDArray< T > & a2)
{
  return (a1 != a2());
}


template< typename T >
std::ostream & operator<<(std::ostream & os, const MDArray< T > & a)
{
  os << a.toString();
  return os;
}


template< typename T >
void swap(MDArray< T > & a1, MDArray< T > & a2)
{
  a1.swap(a2);
}

// Private implementations //

template< typename T >
void
MDArray< T >::assertAxis(int axis) const
{
  TEUCHOS_TEST_FOR_EXCEPTION(
    !(0 <= axis && axis < _dimensions.size()),
    RangeError,
    "MDArray<T>::assertAxis(axis=" << axis << "): out of range "
    << "axis in [0, " << _dimensions.size() << ")"
    );
}


template< typename T >
void
MDArray< T >::assertIndex(dim_type i, int axis) const
{
  TEUCHOS_TEST_FOR_EXCEPTION(
    !(0 <= i && i < _dimensions[axis]), RangeError,
    "MDArray<T>::assertIndex(i=" << i << ",axis=" << axis << "): out of range "
    << "i in [0, " << _dimensions[axis] << ")"
    );
}

}  // end namespace Domi

#endif