---
name: "tensor3"
section: "2rheolef"
platform: "linux"
package: "librheolef-dev"
version: "7.2-4"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/tensor3"
---

# tensor3(2rheolef)

d-dimensional physical third-order tensor (rheolef-7.2)

## NAME

tensor3 - d-dimensional physical third-order tensor (rheolef-7.2)

## 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(2)** 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(2)** 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&);
```

```
};
```

## 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.**