NAME

       tensor4 - d-dimensional physical fourth-order tensor (rheolef-7.2)

DESCRIPTION

       The tensor4 class defines a d^4 array with floating coefficients. This class is suitable
       for defining fourth-order tensors, i.e. field(2) with d^4 matrix values at each physical
       position.

       It is represented as a fourth-dimensional array of coordinates. The coordinate indexes
       start at zero and finishes at d-1, e.g. a(0,0,0,0), a(0,0,0,1), ..., a(2,2,2,2).

       The default constructor set all components to zero:

           tensor4 a;

        The standard linear algebra is supported.

IMPLEMENTATION

       This documentation has been generated from file fem/geo_element/tensor4.h

       The tensor4 class is simply an alias to the tensor4_basic class

       typedef tensor4_basic<Float> tensor4;

       The tensor4_basic class is a template class with the floating type as parameter:

       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);

         tensor4_basic (const std::initializer_list<std::initializer_list<
                              std::initializer_list<std::initializer_list<T> > > >& il);

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

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

       };

       The norm and contracted product with a second-order tensor is provided, together with the
       dexp fuinction, that represents the derivative of the tensor matrix function.

       template <class T>
       T norm (const tensor4_basic<T>& a) { return sqrt(norm2(a)); }

       template <class T>
       T norm2 (const tensor4_basic<T>&);

       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>&);

       template <class T>
       tensor4_basic<T> dexp (const tensor_basic<T>& a, size_t d = 3);

AUTHOR

       Pierre  Saramito  <Pierre.Saramito@imag.fr>

COPYRIGHT

       Copyright   (C)  2000-2018  Pierre  Saramito  <Pierre.Saramito@imag.fr> GPLv3+: GNU GPL
       version 3 or later  <http://gnu.org/licenses/gpl.html>.  This  is  free  software:  you
       are free to change and redistribute it.  There is NO WARRANTY, to the extent permitted by
       law.