NAME

       tensor4 - a fouth order tensor

SYNOPSYS

       The  tensor4  class  defines  a  fourth  tensor where indices varie from zero to 2 (aka 3D
       physical space).

IMPLEMENTATION

       template<class T>
       class tensor4_basic {
       public:

         typedef size_t size_type;
         typedef T      element_type;
         typedef T      float_type;

       // allocators:

         tensor4_basic ();
         explicit tensor4_basic (const T& init_val);
         tensor4_basic (const tensor4_basic<T>& a);
         static tensor4_basic<T> eye (size_type d = 3);

       #ifdef _RHEOLEF_HAVE_STD_INITIALIZER_LIST
               tensor4_basic (const std::initializer_list<std::initializer_list<
                                    std::initializer_list<std::initializer_list<T> > > >& il);
       #endif // _RHEOLEF_HAVE_STD_INITIALIZER_LIST

       // affectation:

         tensor4_basic<T>& operator= (const tensor4_basic<T>& a);
         tensor4_basic<T>& operator= (const T& val);

       // accessors:

         T&       operator()(size_type i, size_type j, size_type k, size_type l);
         const T& operator()(size_type i, size_type j, size_type k, size_type l) const;

         tensor_basic<T>&  operator()(size_type i, size_type j);
         const tensor_basic<T>& operator()(size_type i, size_type j) const;

       // algebra:

         tensor4_basic<T>& operator*= (const T& k);
         tensor4_basic<T>& operator/= (const T& k) { return operator*= (1./k); }
         tensor4_basic<T>  operator* (const T& k) const;
         tensor4_basic<T>  operator/ (const T& k) const;
         tensor4_basic<T>  operator+ (const tensor4_basic<T>& b) const;
         tensor4_basic<T>  operator- (const tensor4_basic<T>& b) const;

       // io:
         std::ostream& put (std::ostream& out, size_type d=3) const;

       // data:
       protected:
         tensor_basic<tensor_basic<T> > _x;
       };
       typedef tensor4_basic<Float> tensor4;

       // nonlinear algebra:
       template <class T>
       T norm2 (const tensor4_basic<T>&);
       template <class T>
       T norm (const tensor4_basic<T>& a) { return sqrt(norm2(a)); }
       template <class T>
       tensor4_basic<T> dexp (const tensor_basic<T>& a, size_t d = 3);

       // algebra:
       template <class T>
       tensor_basic<T> ddot (const tensor4_basic<T>&, const tensor_basic<T>&);
       template <class T>
       tensor_basic<T> ddot (const tensor_basic<T>&, const tensor4_basic<T>&);