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tensor3

d-dimensional physical third-order tensor

# Description

The tensor3 class defines a d*d*d array with floating coefficients. This class is suitable for defining third-order tensors, i.e. field with d*d*d matrix values at each physical position.

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

The default constructor set all components to zero:

        tensor3 a;

The linear algebra with scalars and tensor is supported.

# Implementation

This documentation has been generated from file fem/geo_element/tensor3.h

The tensor3 class is simply an alias to the tensor3_basic class

typedef tensor3_basic<Float> tensor3;

The tensor3_basic class is a template class with the floating type as parameter:

template<class T>
class tensor3_basic {
public:
typedef size_t size_type;
typedef T element_type;
typedef T float_type;
// allocators:
tensor3_basic (const T& init_val = 0);
tensor3_basic (const tensor3_basic<T>& a);
// affectation:
tensor3_basic<T>& operator= (const tensor3_basic<T>& a);
tensor3_basic<T>& operator= (const T& val);
// accessors:
T& operator()(size_type i, size_type j, size_type k);
const T& operator()(size_type i, size_type j, size_type k) const;
// algebra
tensor3_basic<T> operator* (const T& k) const;
tensor3_basic<T> operator/ (const T& k) const;
tensor_basic<T> operator* (const point_basic<T>& v) const;
tensor3_basic<T> operator* (const tensor_basic<T>& b) const;
tensor3_basic<T> operator+ (const tensor3_basic<T>& b) const;
tensor3_basic<T> operator- (const tensor3_basic<T>& b) const;
tensor3_basic<T>& operator+= (const tensor3_basic<T>&);
tensor3_basic<T>& operator-= (const tensor3_basic<T>&);
tensor3_basic<T>& operator*= (const T& k);
tensor3_basic<T>& operator/= (const T& k) { return operator*= (1./k); }
// inputs/outputs:
std::ostream& put (std::ostream& s, size_type d = 3) const;
std::istream& get (std::istream&);
};