libMesh::TypeNTensor< N, T > Class Template Reference

This class will eventually define a rank-N tensor in LIBMESH_DIM dimensional space of type T. More...

#include <tensor_tools.h>

Public Types
typedef tuple_of< N, unsigned int >	index_type
	Helper typedef for generic index programming. More...

Public Member Functions
	TypeNTensor ()
	TypeNTensor (const T &)
	TypeNTensor (const TypeVector< T > &)
	TypeNTensor (const TypeTensor< T > &)
	TypeNTensor (const TypeNTensor< N, T > &)
TypeNTensor &	operator= (const TypeNTensor< N, T > &)
	operator TypeVector< T > () const
	operator VectorValue< T > () const
	operator TypeTensor< T > () const
	operator TensorValue< T > () const
	~TypeNTensor ()=default
	Destructor. More...
const TypeNTensor< N-1, T >	slice (const unsigned int) const
TypeNTensor< N-1, T >	slice (const unsigned int)
template<typename Scalar >
boostcopy::enable_if_c< ScalarTraits< Scalar >::value, TypeNTensor & >::type	operator= (const Scalar &libmesh_dbg_var(p))
template<typename T2 >
TypeNTensor< N, typename CompareTypes< T, T2 >::supertype >	operator+ (const TypeNTensor< N, T2 > &) const
	Add two tensors. More...
template<typename T2 >
const TypeNTensor< N, T > &	operator+= (const TypeNTensor< N, T2 > &)
	Add to this tensor. More...
template<typename T2 >
TypeNTensor< N, typename CompareTypes< T, T2 >::supertype >	operator- (const TypeNTensor< N, T2 > &) const
	Subtract two tensors. More...
template<typename T2 >
const TypeNTensor< N, T > &	operator-= (const TypeNTensor< N, T2 > &)
	Subtract from this tensor. More...
TypeNTensor< N, T >	operator- () const
template<typename Scalar >
boostcopy::enable_if_c< ScalarTraits< Scalar >::value, TypeNTensor< N, typename CompareTypes< T, Scalar >::supertype > >::type	operator* (const Scalar) const
	Multiply every entry of a tensor by a number. More...
template<typename Scalar >
const TypeNTensor< N, T > &	operator*= (const Scalar)
	Multiply every entry of this tensor by a number. More...
template<typename Scalar >
boostcopy::enable_if_c< ScalarTraits< Scalar >::value, TypeNTensor< N, typename CompareTypes< T, Scalar >::supertype > >::type	operator/ (const Scalar) const
	Divide every entry of a tensor by a number. More...
const TypeNTensor< N, T > &	operator/= (const T)
	Divide every entry of this tensor by a number. More...
template<typename T2 >
CompareTypes< T, T2 >::supertype	contract (const TypeNTensor< N, T2 > &) const
	Multiply 2 tensors together to return a scalar, i.e. More...
auto	norm () const -> decltype(std::norm(T()))
auto	norm_sq () const -> decltype(std::norm(T()))
void	zero ()
	Set all entries of the tensor to 0. More...
bool	operator== (const TypeNTensor< N, T > &) const
bool	operator< (const TypeNTensor< N, T > &) const
bool	operator> (const TypeNTensor< N, T > &) const
void	print (std::ostream &) const
	Do a formatted print of this tensor to a stream which defaults to libMesh::out. More...
template<typename T2 >
void	add_scaled (const TypeNTensor< N, T2 > &, const T &)
	Add a scaled type N tensor to this type N tensor without creating a temporary. More...

Public Attributes
std::vector< T >	_coords
	The coordinates of the TypeNTensor. More...

Static Private Member Functions
static constexpr int	int_pow (int b, int e)

Friends
std::ostream &	operator<< (std::ostream &os, const TypeNTensor< N, T > &t)
	Does a formatted print (as above) but supports the syntax: More...

Detailed Description

template<unsigned int N, typename T>
class libMesh::TypeNTensor< N, T >

This class will eventually define a rank-N tensor in LIBMESH_DIM dimensional space of type T.

Right now it defines a shim to allow for rank-independent code to compile (but not give correct results) in the case of vector-valued elements and second derivatives.

Author

Roy Stogner

Date

2012

Definition at line 38 of file tensor_tools.h.

Member Typedef Documentation

index_type

template<unsigned int N, typename T>

typedef tuple_of<N, unsigned int> libMesh::TypeNTensor< N, T >::index_type

Helper typedef for generic index programming.

Definition at line 54 of file type_n_tensor.h.

Constructor & Destructor Documentation

TypeNTensor() [1/5]

template<unsigned int N, typename T>

libMesh::TypeNTensor< N, T >::TypeNTensor ( )

inline

Definition at line 56 of file type_n_tensor.h.

: _coords(std::vector<T>(int_pow(LIBMESH_DIM, N))) {}

TypeNTensor() [2/5]

template<unsigned int N, typename T>

libMesh::TypeNTensor< N, T >::TypeNTensor ( const T &  )

inline

Definition at line 58 of file type_n_tensor.h.

: _coords(std::vector<T>(int_pow(LIBMESH_DIM, N))) {}

TypeNTensor() [3/5]

template<unsigned int N, typename T>

libMesh::TypeNTensor< N, T >::TypeNTensor ( const TypeVector< T > &  )

inline

Definition at line 60 of file type_n_tensor.h.

: _coords(std::vector<T>(int_pow(LIBMESH_DIM, N))) {}

TypeNTensor() [4/5]

template<unsigned int N, typename T>

libMesh::TypeNTensor< N, T >::TypeNTensor ( const TypeTensor< T > &  )

inline

Definition at line 62 of file type_n_tensor.h.

: _coords(std::vector<T>(int_pow(LIBMESH_DIM, N))) {}

TypeNTensor() [5/5]

template<unsigned int N, typename T>

libMesh::TypeNTensor< N, T >::TypeNTensor ( const TypeNTensor< N, T > &  )

inline

Definition at line 64 of file type_n_tensor.h.

: _coords(std::vector<T>(int_pow(LIBMESH_DIM, N))) {}

~TypeNTensor()

template<unsigned int N, typename T>

libMesh::TypeNTensor< N, T >::~TypeNTensor ( )

default

Destructor.

Member Function Documentation

add_scaled()

template<unsigned int N, typename T >

template<typename T2 >

void libMesh::TypeNTensor< N, T >::add_scaled ( const TypeNTensor< N, T2 > &  p, const T &  factor  )

inline

Add a scaled type N tensor to this type N tensor without creating a temporary.

Definition at line 312 of file type_n_tensor.h.

{
  unsigned int size = int_pow(LIBMESH_DIM, N);
  for (unsigned int i = 0; i < size ; i++)
    _coords[i] += factor*p._coords[i];
}

contract()

template<unsigned int N, typename T>

template<typename T2 >

CompareTypes<T,T2>::supertype libMesh::TypeNTensor< N, T >::contract ( const TypeNTensor< N, T2 > &  ) const

inline

Multiply 2 tensors together to return a scalar, i.e.

\( \sum_{ij} A_{ij} B_{ij} \) The tensors may contain different numeric types. Also known as the "double inner product" or "double dot product" of tensors.

Returns

The scalar-valued result, this tensor is unchanged.

Definition at line 211 of file type_n_tensor.h.

Referenced by libMesh::TensorTools::inner_product().

  {
    libmesh_not_implemented();
    return 0;
  }

int_pow()

template<unsigned int N, typename T>

static constexpr int libMesh::TypeNTensor< N, T >::int_pow ( int  b, int  e  )

inlinestaticprivate

Definition at line 302 of file type_n_tensor.h.

  {
    return (e == 0) ? 1 : b * int_pow(b, e - 1);
  }

norm()

template<unsigned int N, typename T>

auto libMesh::TypeNTensor< N, T >::norm ( ) const -> decltype(std::norm(T()))

inline

Returns

The Frobenius norm of the tensor, i.e. the square-root of the sum of the elements squared.

Definition at line 221 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return 0.;
  }

norm_sq()

template<unsigned int N, typename T>

auto libMesh::TypeNTensor< N, T >::norm_sq ( ) const -> decltype(std::norm(T()))

inline

Returns

The Frobenius norm of the tensor squared, i.e. the sum of the entry magnitudes squared.

Definition at line 231 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return 0.;
  }

operator TensorValue< T >()

template<unsigned int N, typename T>

libMesh::TypeNTensor< N, T >::operator TensorValue< T > ( ) const

inline

Definition at line 72 of file type_n_tensor.h.

{ libmesh_not_implemented(); return 0; }

operator TypeTensor< T >()

template<unsigned int N, typename T>

libMesh::TypeNTensor< N, T >::operator TypeTensor< T > ( ) const

inline

Definition at line 71 of file type_n_tensor.h.

{ libmesh_not_implemented(); return 0; }

operator TypeVector< T >()

template<unsigned int N, typename T>

libMesh::TypeNTensor< N, T >::operator TypeVector< T > ( ) const

inline

Definition at line 68 of file type_n_tensor.h.

{ libmesh_not_implemented(); return 0; }

operator VectorValue< T >()

template<unsigned int N, typename T>

libMesh::TypeNTensor< N, T >::operator VectorValue< T > ( ) const

inline

Definition at line 69 of file type_n_tensor.h.

{ libmesh_not_implemented(); return 0; }

operator*()

template<unsigned int N, typename T>

template<typename Scalar >

boostcopy::enable_if_c< ScalarTraits<Scalar>::value, TypeNTensor<N,typename CompareTypes<T, Scalar>::supertype> >::type libMesh::TypeNTensor< N, T >::operator* ( const Scalar  ) const

inline

Multiply every entry of a tensor by a number.

Definition at line 162 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return TypeNTensor<N,typename CompareTypes<T, Scalar>::supertype>();
  }

operator*=()

template<unsigned int N, typename T>

template<typename Scalar >

const TypeNTensor<N,T>& libMesh::TypeNTensor< N, T >::operator*= ( const Scalar  )

inline

Multiply every entry of this tensor by a number.

Definition at line 172 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return *this;
  }

operator+()

template<unsigned int N, typename T>

template<typename T2 >

TypeNTensor<N,typename CompareTypes<T, T2>::supertype> libMesh::TypeNTensor< N, T >::operator+ ( const TypeNTensor< N, T2 > &  ) const

inline

Add two tensors.

Definition at line 109 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return TypeNTensor<N,typename CompareTypes<T,T2>::supertype>();
  }

operator+=()

template<unsigned int N, typename T>

template<typename T2 >

const TypeNTensor<N,T>& libMesh::TypeNTensor< N, T >::operator+= ( const TypeNTensor< N, T2 > &  )

inline

Add to this tensor.

Definition at line 119 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return *this;
  }

operator-() [1/2]

template<unsigned int N, typename T>

template<typename T2 >

TypeNTensor<N,typename CompareTypes<T, T2>::supertype> libMesh::TypeNTensor< N, T >::operator- ( const TypeNTensor< N, T2 > &  ) const

inline

Subtract two tensors.

Definition at line 130 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return TypeNTensor<N,typename CompareTypes<T,T2>::supertype>();
  }

operator-() [2/2]

template<unsigned int N, typename T>

TypeNTensor<N,T> libMesh::TypeNTensor< N, T >::operator- ( ) const

inline

Returns

The negative of a tensor.

Definition at line 149 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return *this;
  }

operator-=()

template<unsigned int N, typename T>

template<typename T2 >

const TypeNTensor<N,T>& libMesh::TypeNTensor< N, T >::operator-= ( const TypeNTensor< N, T2 > &  )

inline

Subtract from this tensor.

Definition at line 140 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return *this;
  }

operator/()

template<unsigned int N, typename T>

template<typename Scalar >

boostcopy::enable_if_c< ScalarTraits<Scalar>::value, TypeNTensor<N,typename CompareTypes<T, Scalar>::supertype> >::type libMesh::TypeNTensor< N, T >::operator/ ( const Scalar  ) const

inline

Divide every entry of a tensor by a number.

Definition at line 185 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return *this;
  }

operator/=()

template<unsigned int N, typename T>

const TypeNTensor<N,T>& libMesh::TypeNTensor< N, T >::operator/= ( const T  )

inline

Divide every entry of this tensor by a number.

Definition at line 194 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return *this;
  }

operator<()

template<unsigned int N, typename T>

bool libMesh::TypeNTensor< N, T >::operator< ( const TypeNTensor< N, T > &  ) const

inline

Returns

true if this tensor is "less" than another.

Useful for sorting.

Definition at line 256 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return false;
  }

operator=() [1/2]

template<unsigned int N, typename T>

TypeNTensor& libMesh::TypeNTensor< N, T >::operator= ( const TypeNTensor< N, T > &  )

inline

Definition at line 66 of file type_n_tensor.h.

{ libmesh_not_implemented(); return *this; }

operator=() [2/2]

template<unsigned int N, typename T>

template<typename Scalar >

boostcopy::enable_if_c< ScalarTraits<Scalar>::value, TypeNTensor &>::type libMesh::TypeNTensor< N, T >::operator= ( const Scalar &  libmesh_dbg_varp )

inline

Definition at line 101 of file type_n_tensor.h.

References libMesh::TypeNTensor< N, T >::zero().

  { libmesh_assert_equal_to (p, Scalar(0)); this->zero(); return *this; }

operator==()

template<unsigned int N, typename T>

bool libMesh::TypeNTensor< N, T >::operator== ( const TypeNTensor< N, T > &  ) const

inline

Returns

true if two tensors are equal, false otherwise.

Definition at line 245 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return true;
  }

operator>()

template<unsigned int N, typename T>

bool libMesh::TypeNTensor< N, T >::operator> ( const TypeNTensor< N, T > &  ) const

inline

Returns

true if this tensor is "greater" than another.

Definition at line 265 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return false;
  }

print()

template<unsigned int N, typename T>

void libMesh::TypeNTensor< N, T >::print ( std::ostream &  ) const

inline

Do a formatted print of this tensor to a stream which defaults to libMesh::out.

Definition at line 275 of file type_n_tensor.h.

{}

slice() [1/2]

template<unsigned int N, typename T>

const TypeNTensor<N-1,T> libMesh::TypeNTensor< N, T >::slice ( const unsigned  int ) const

inline

Returns

A proxy for the \( i^{th} \) slice of the tensor.

Definition at line 82 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return TypeNTensor<N-1,T>();
  }

slice() [2/2]

template<unsigned int N, typename T>

TypeNTensor<N-1,T> libMesh::TypeNTensor< N, T >::slice ( const unsigned  int )

inline

Returns

A writable proxy for the \( i^{th} \) slice of the tensor.

Definition at line 91 of file type_n_tensor.h.

  {
    libmesh_not_implemented();
    return TypeNTensor<N-1,T>();
  }

zero()

template<unsigned int N, typename T>

void libMesh::TypeNTensor< N, T >::zero ( )

inline

Set all entries of the tensor to 0.

Definition at line 240 of file type_n_tensor.h.

Referenced by libMesh::TypeNTensor< N, T >::operator=().

{ libmesh_not_implemented(); }

Friends And Related Function Documentation

operator<<

template<unsigned int N, typename T>

std::ostream& operator<< ( std::ostream &  os, const TypeNTensor< N, T > &  t  )

friend

Does a formatted print (as above) but supports the syntax:

std::cout << t << std::endl;

Definition at line 283 of file type_n_tensor.h.

  {
    t.print(os);
    return os;
  }

Member Data Documentation

_coords

template<unsigned int N, typename T>

std::vector<T> libMesh::TypeNTensor< N, T >::_coords

The coordinates of the TypeNTensor.

Definition at line 299 of file type_n_tensor.h.

---

The documentation for this class was generated from the following files:

• include/numerics/tensor_tools.h
• include/numerics/type_n_tensor.h