.TH "tensor4" 2rheolef "Sat Mar 13 2021" "Version 7.1" "rheolef" \" -*- nroff -*-
.ad l
.nh
.SH NAME
tensor4 \- d-dimensional physical fourth-order tensor (rheolef-7\&.1)
.PP
.SH "DESCRIPTION"
.PP
The \fCtensor4\fP class defines a \fCd^4\fP array with floating coefficients\&. This class is suitable for defining fourth-order tensors, i\&.e\&. \fBfield(2)\fP with \fCd^4\fP matrix values at each physical position\&.
.PP
It is represented as a fourth-dimensional array of coordinates\&. The coordinate indexes start at zero and finishes at \fCd-1\fP, e\&.g\&. \fCa(0,0,0,0)\fP, \fCa(0,0,0,1)\fP, \&.\&.\&., \fCa(2,2,2,2)\fP\&.
.PP
The default constructor set all components to zero: 
.PP
.nf
    tensor4 a;

.fi
.PP
 The standard linear algebra is supported\&.
.SH "IMPLEMENTATION"
.PP
This documentation has been generated from file fem/geo_element/tensor4\&.h
.PP
The \fCtensor4\fP class is simply an alias to the \fC\fBtensor4_basic\fP\fP class
.PP
.PP
.nf
typedef tensor4_basic<Float> tensor4;
.fi
.PP
 The \fC\fBtensor4_basic\fP\fP class is a template class with the floating type as parameter:
.PP
.PP
.nf
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;
.fi
.PP
.PP
.nf
};
.fi
.PP
\fB\fP
.RS 4
.RE
.PP
The norm and contracted product with a second-order tensor is provided, together with the \fCdexp\fP fuinction, that represents the derivative of the tensor matrix function\&.
.PP
.PP
.nf
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);
.fi
.PP

.SH AUTHOR
Pierre  Saramito  <Pierre.Saramito@imag.fr>
.SH 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.