---
name: "tensor4"
section: "2rheolef"
platform: "linux"
package: "librheolef-dev"
version: "7.2-4"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/tensor4"
---

# tensor4(2rheolef)

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

## 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.**