#include <deal.II/base/tensor.h>

Public Types
using	real_type = typename numbers::NumberTraits< Number >::real_type

using	value_type = Number

using	array_type = Number

using	tensor_type = Number

Public Member Functions
constexpr	Tensor ()

template<typename OtherNumber >
constexpr	Tensor (const Tensor< 0, dim, OtherNumber > &initializer)

template<typename OtherNumber >
constexpr	Tensor (const OtherNumber &initializer)

Number *	begin_raw ()

const Number *	begin_raw () const

Number *	end_raw ()

const Number *	end_raw () const

constexpr	operator Number & ()

constexpr	operator const Number & () const

template<typename OtherNumber >
constexpr Tensor &	operator= (const Tensor< 0, dim, OtherNumber > &rhs)

template<typename OtherNumber >
constexpr Tensor &	operator= (const OtherNumber &d)

template<typename OtherNumber >
constexpr bool	operator== (const Tensor< 0, dim, OtherNumber > &rhs) const

template<typename OtherNumber >
constexpr bool	operator!= (const Tensor< 0, dim, OtherNumber > &rhs) const

template<typename OtherNumber >
constexpr Tensor &	operator+= (const Tensor< 0, dim, OtherNumber > &rhs)

template<typename OtherNumber >
constexpr Tensor &	operator-= (const Tensor< 0, dim, OtherNumber > &rhs)

template<typename OtherNumber >
constexpr Tensor &	operator*= (const OtherNumber &factor)

template<typename OtherNumber >
constexpr Tensor &	operator/= (const OtherNumber &factor)

constexpr Tensor	operator- () const

constexpr void	clear ()

real_type	norm () const

constexpr real_type	norm_square () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Static Public Attributes
static constexpr unsigned int	dimension = dim

static constexpr unsigned int	rank = 0

static constexpr unsigned int	n_independent_components = 1

Private Member Functions
template<typename OtherNumber >
void	unroll_recursion (Vector< OtherNumber > &result, unsigned int &start_index) const

Private Attributes
Number	value

Friends
template<int , int , typename >
class	Tensor

Detailed Description

template<int dim, typename Number>
class Tensor< 0, dim, Number >

This class is a specialized version of the Tensor<rank,dim,Number> class. It handles tensors of rank zero, i.e. scalars. The second template argument dim is ignored.

This class exists because in some cases we want to construct objects of type Tensor<spacedim-dim,dim,Number>, which should expand to scalars, vectors, matrices, etc, depending on the values of the template arguments dim and spacedim. We therefore need a class that acts as a scalar (i.e. Number) for all purposes but is part of the Tensor template family.

Template Parameters

dim An integer that denotes the dimension of the space in which this tensor operates. This of course equals the number of coordinates that identify a point and rank-1 tensor. Since the current object is a rank-0 tensor (a scalar), this template argument has no meaning for this class.

Number The data type in which the tensor elements are to be stored. This will, in almost all cases, simply be the default double, but there are cases where one may want to store elements in a different (and always scalar) type. It can be used to base tensors on float or complex numbers or any other data type that implements basic arithmetic operations. Another example would be a type that allows for Automatic Differentiation (see, for example, the Sacado type used in step-33) and thereby can generate analytic (spatial) derivatives of a function that takes a tensor as argument.

Author: Wolfgang Bangerth, 2009, Matthias Maier, 2015

Definition at line 93 of file tensor.h.

Member Typedef Documentation

◆ real_type

template<int dim, typename Number >

using Tensor< 0, dim, Number >::real_type = typename numbers::NumberTraits<Number>::real_type

Declare a type that has holds real-valued numbers with the same precision as the template argument to this class. For std::complex<number>, this corresponds to type number, and it is equal to Number for all other cases. See also the respective field in Vector<Number>.

This alias is used to represent the return type of norms.

Definition at line 127 of file tensor.h.

◆ value_type

template<int dim, typename Number >

using Tensor< 0, dim, Number >::value_type = Number

Type of objects encapsulated by this container and returned by operator[](). This is a scalar number type for a rank 0 tensor.

Definition at line 133 of file tensor.h.

◆ array_type

template<int dim, typename Number >

using Tensor< 0, dim, Number >::array_type = Number

Declare an array type which can be used to initialize an object of this type statically. In case of a tensor of rank 0 this is just the scalar number type Number.

Definition at line 140 of file tensor.h.

◆ tensor_type

template<int dim, typename Number >

using Tensor< 0, dim, Number >::tensor_type = Number

Internal type declaration that is used to specialize the return type of operator[]() for Tensor<1,dim,Number>

Definition at line 352 of file tensor.h.

Constructor & Destructor Documentation

◆ Tensor() [1/3]

template<int dim, typename Number >

constexpr Tensor< 0, dim, Number >::Tensor ( )

constexpr

Constructor. Set to zero.

Note: This function can also be used in CUDA device code.

◆ Tensor() [2/3]

template<int dim, typename Number >

template<typename OtherNumber >

constexpr Tensor< 0, dim, Number >::Tensor ( const Tensor< 0, dim, OtherNumber > & initializer )

constexpr

Constructor from tensors with different underlying scalar type. This obviously requires that the OtherNumber type is convertible to Number.

Note: This function can also be used in CUDA device code.

◆ Tensor() [3/3]

template<int dim, typename Number >

template<typename OtherNumber >

constexpr Tensor< 0, dim, Number >::Tensor ( const OtherNumber & initializer )

constexpr

Constructor, where the data is copied from a C-style array.

Note: This function can also be used in CUDA device code.

Member Function Documentation

◆ begin_raw() [1/2]

template<int dim, typename Number >

Number* Tensor< 0, dim, Number >::begin_raw ( )

Return a pointer to the first element of the underlying storage.

◆ begin_raw() [2/2]

template<int dim, typename Number >

const Number* Tensor< 0, dim, Number >::begin_raw ( ) const

Return a const pointer to the first element of the underlying storage.

◆ end_raw() [1/2]

template<int dim, typename Number >

Number* Tensor< 0, dim, Number >::end_raw ( )

Return a pointer to the element past the end of the underlying storage.

◆ end_raw() [2/2]

template<int dim, typename Number >

const Number* Tensor< 0, dim, Number >::end_raw ( ) const

Return a const pointer to the element past the end of the underlying storage.

◆ operator Number &()

template<int dim, typename Number >

constexpr Tensor< 0, dim, Number >::operator Number & ( )

constexpr

Return a reference to the encapsulated Number object. Since rank-0 tensors are scalars, this is a natural operation.

This is the non-const conversion operator that returns a writable reference.

Note: This function can also be used in CUDA device code.

◆ operator const Number &()

template<int dim, typename Number >

constexpr Tensor< 0, dim, Number >::operator const Number & ( ) const

constexpr

Return a reference to the encapsulated Number object. Since rank-0 tensors are scalars, this is a natural operation.

This is the const conversion operator that returns a read-only reference.

Note: This function can also be used in CUDA device code.

◆ operator=() [1/2]

template<int dim, typename Number >

template<typename OtherNumber >

constexpr Tensor& Tensor< 0, dim, Number >::operator= ( const Tensor< 0, dim, OtherNumber > & rhs )

constexpr

Assignment from tensors with different underlying scalar type. This obviously requires that the OtherNumber type is convertible to Number.

Note: This function can also be used in CUDA device code.

◆ operator=() [2/2]

template<int dim, typename Number >

template<typename OtherNumber >

constexpr Tensor& Tensor< 0, dim, Number >::operator= ( const OtherNumber & d )

constexpr

This operator assigns a scalar to a tensor. This obviously requires that the OtherNumber type is convertible to Number.

Note: This function can also be used in CUDA device code.

◆ operator==()

template<int dim, typename Number >

template<typename OtherNumber >

constexpr bool Tensor< 0, dim, Number >::operator== ( const Tensor< 0, dim, OtherNumber > & rhs ) const

constexpr

Test for equality of two tensors.

◆ operator!=()

template<int dim, typename Number >

template<typename OtherNumber >

constexpr bool Tensor< 0, dim, Number >::operator!= ( const Tensor< 0, dim, OtherNumber > & rhs ) const

constexpr

Test for inequality of two tensors.

◆ operator+=()

template<int dim, typename Number >

template<typename OtherNumber >

constexpr Tensor& Tensor< 0, dim, Number >::operator+= ( const Tensor< 0, dim, OtherNumber > & rhs )

constexpr

Add another scalar.

Note: This function can also be used in CUDA device code.

◆ operator-=()

template<int dim, typename Number >

template<typename OtherNumber >

constexpr Tensor& Tensor< 0, dim, Number >::operator-= ( const Tensor< 0, dim, OtherNumber > & rhs )

constexpr

Subtract another scalar.

Note: This function can also be used in CUDA device code.

◆ operator*=()

template<int dim, typename Number >

template<typename OtherNumber >

constexpr Tensor& Tensor< 0, dim, Number >::operator*= ( const OtherNumber & factor )

constexpr

Multiply the scalar with a factor.

Note: This function can also be used in CUDA device code.

◆ operator/=()

template<int dim, typename Number >

template<typename OtherNumber >

constexpr Tensor& Tensor< 0, dim, Number >::operator/= ( const OtherNumber & factor )

constexpr

Divide the scalar by factor.

Note: This function can also be used in CUDA device code.

◆ operator-()

template<int dim, typename Number >

constexpr Tensor Tensor< 0, dim, Number >::operator- ( ) const

constexpr

Tensor with inverted entries.

Note: This function can also be used in CUDA device code.

◆ clear()

template<int dim, typename Number >

constexpr void Tensor< 0, dim, Number >::clear ( )

constexpr

Reset all values to zero.

Note that this is partly inconsistent with the semantics of the clear() member functions of the standard library containers and of several other classes within deal.II, which not only reset the values of stored elements to zero, but release all memory and return the object into a virginial state. However, since the size of objects of the present type is determined by its template parameters, resizing is not an option, and indeed the state where all elements have a zero value is the state right after construction of such an object.

◆ norm()

template<int dim, typename Number >

real_type Tensor< 0, dim, Number >::norm ( ) const

Return the Frobenius-norm of a tensor, i.e. the square root of the sum of the absolute squares of all entries. For the present case of rank-1 tensors, this equals the usual l₂ norm of the vector.

◆ norm_square()

template<int dim, typename Number >

constexpr real_type Tensor< 0, dim, Number >::norm_square ( ) const

constexpr

Return the square of the Frobenius-norm of a tensor, i.e. the sum of the absolute squares of all entries.

Note: This function can also be used in CUDA device code.

◆ serialize()

template<int dim, typename Number >

template<class Archive >

void Tensor< 0, dim, Number >::serialize	(	Archive &	ar,
		const unsigned int	version
	)

Read or write the data of this object to or from a stream for the purpose of serialization

◆ unroll_recursion()

template<int dim, typename Number >

template<typename OtherNumber >

void Tensor< 0, dim, Number >::unroll_recursion	(	Vector< OtherNumber > &	result,
		unsigned int &	start_index
	)		const

private

Internal helper function for unroll.

Friends And Related Function Documentation

◆ Tensor

template<int dim, typename Number >

template<int , int , typename >

friend class Tensor

friend

Definition at line 370 of file tensor.h.

Member Data Documentation

◆ dimension

template<int dim, typename Number >

constexpr unsigned int Tensor< 0, dim, Number >::dimension = dim

staticconstexpr

Provide a way to get the dimension of an object without explicit knowledge of it's data type. Implementation is this way instead of providing a function dimension() because now it is possible to get the dimension at compile time without the expansion and preevaluation of an inlined function; the compiler may therefore produce more efficient code and you may use this value to declare other data types.

Definition at line 107 of file tensor.h.

◆ rank

template<int dim, typename Number >

constexpr unsigned int Tensor< 0, dim, Number >::rank = 0

staticconstexpr

Publish the rank of this tensor to the outside world.

Definition at line 112 of file tensor.h.

◆ n_independent_components

template<int dim, typename Number >

constexpr unsigned int Tensor< 0, dim, Number >::n_independent_components = 1

staticconstexpr

Number of independent components of a tensor of rank 0.

Definition at line 117 of file tensor.h.

◆ value

template<int dim, typename Number >

Number Tensor< 0, dim, Number >::value

private

The value of this scalar object.

Definition at line 358 of file tensor.h.

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

include/deal.II/base/tensor.h

Public Types

Public Member Functions

Static Public Attributes

Private Member Functions

Private Attributes

Friends

Detailed Description

template<int dim, typename Number> class Tensor< 0, dim, Number >

Member Typedef Documentation

◆ real_type

◆ value_type

◆ array_type

◆ tensor_type

Constructor & Destructor Documentation

◆ Tensor() [1/3]

◆ Tensor() [2/3]

◆ Tensor() [3/3]

Member Function Documentation

◆ begin_raw() [1/2]

◆ begin_raw() [2/2]

◆ end_raw() [1/2]

◆ end_raw() [2/2]

◆ operator Number &()

◆ operator const Number &()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator!=()

◆ operator+=()

◆ operator-=()

◆ operator*=()

◆ operator/=()

◆ operator-()

◆ clear()

◆ norm()

◆ norm_square()

◆ serialize()

◆ unroll_recursion()

Friends And Related Function Documentation

◆ Tensor

Member Data Documentation

◆ dimension

◆ rank

◆ n_independent_components

◆ value

template<int dim, typename Number>
class Tensor< 0, dim, Number >