Classes
struct	DecrementRank

struct	DecrementRank< TensorValue< T > >

struct	DecrementRank< TypeNTensor< N, T > >

struct	DecrementRank< TypeTensor< T > >

struct	DecrementRank< TypeVector< T > >

struct	DecrementRank< VectorValue< T > >

struct	IncrementRank

struct	IncrementRank< TensorValue< T > >

struct	IncrementRank< TypeNTensor< N, T > >

struct	IncrementRank< TypeTensor< T > >

struct	IncrementRank< TypeVector< T > >

struct	IncrementRank< VectorValue< T > >

struct	MakeBaseNumber

struct	MakeBaseNumber< T, typename std::enable_if< ScalarTraits< T >::value >::type >

struct	MakeBaseNumber< Wrapper< T >, typename std::enable_if< MathWrapperTraits< Wrapper< T > >::value >::type >

struct	MakeNumber

struct	MakeNumber< std::complex< T > >

struct	MakeNumber< TensorValue< T > >

struct	MakeNumber< TypeNTensor< N, T > >

struct	MakeNumber< TypeTensor< T > >

struct	MakeNumber< TypeVector< T > >

struct	MakeNumber< VectorValue< T > >

struct	MakeReal

struct	MakeReal< std::complex< T > >

struct	MakeReal< TensorValue< T > >

struct	MakeReal< TypeNTensor< N, T > >

struct	MakeReal< TypeTensor< T > >

struct	MakeReal< TypeVector< T > >

struct	MakeReal< VectorValue< T > >

struct	MathWrapperTraits
	This helper structure is used to determine whether a template class is one of our mathematical structures, like TypeVector, TypeTensor and their descendents. More...

struct	MathWrapperTraits< TensorValue< T > >

struct	MathWrapperTraits< TypeNTensor< N, T > >

struct	MathWrapperTraits< TypeTensor< T > >

struct	MathWrapperTraits< TypeVector< T > >

struct	MathWrapperTraits< VectorValue< T > >

struct	TensorTraits

struct	TensorTraits< T, typename std::enable_if< ScalarTraits< T >::value >::type >

struct	TensorTraits< TensorValue< T > >

struct	TensorTraits< TypeNTensor< N, T > >

struct	TensorTraits< TypeTensor< T > >

struct	TensorTraits< TypeVector< T > >

struct	TensorTraits< VectorValue< T > >

Functions
template<typename T , typename T2 >
std::enable_if< ScalarTraits< T >::value &&ScalarTraits< T2 >::value, typenameCompareTypes< T, T2 >::supertype >::type	inner_product (const T &a, const T2 &b)

template<typename T , typename T2 >
CompareTypes< T, T2 >::supertype	inner_product (const TypeVector< T > &a, const TypeVector< T2 > &b)

template<typename T , typename T2 >
CompareTypes< T, T2 >::supertype	inner_product (const TypeTensor< T > &a, const TypeTensor< T2 > &b)

template<unsigned int N, typename T , typename T2 >
CompareTypes< T, T2 >::supertype	inner_product (const TypeNTensor< N, T > &a, const TypeNTensor< N, T2 > &b)

template<typename T >
auto	norm (const T &a)

template<typename T >
T	norm (std::complex< T > a)

template<typename T >
auto	norm (const TypeVector< T > &a) -> decltype(TensorTools::norm(T()))

template<typename T >
auto	norm (const VectorValue< T > &a) -> decltype(TensorTools::norm(T()))

template<typename T >
auto	norm (const TypeTensor< T > &a) -> decltype(TensorTools::norm(T()))

template<typename T >
auto	norm (const TensorValue< T > &a) -> decltype(TensorTools::norm(T()))

template<typename T >
auto	norm_sq (const T &a)

template<typename T >
T	norm_sq (std::complex< T > a)

template<typename T >
auto	norm_sq (const TypeVector< T > &a)

template<typename T >
auto	norm_sq (const VectorValue< T > &a)

template<typename T >
auto	norm_sq (const TypeTensor< T > &a)

template<typename T >
auto	norm_sq (const TensorValue< T > &a)

template<typename T >
bool	is_zero (const T &a)

Number	curl_from_grad (const VectorValue< Number > &)

VectorValue< Number >	curl_from_grad (const TensorValue< Number > &grad)
	Computes the curl of a vector given the gradient of that vector.

TensorValue< Number >	curl_from_grad (const TypeNTensor< 3, Number > &grad)

Number	div_from_grad (const VectorValue< Number > &grad)
	Dummy. Divergence of a scalar not defined, but is needed for ExactSolution to compile.

Number	div_from_grad (const TensorValue< Number > &grad)
	Computes the divergence of a vector given the gradient of that vector.

VectorValue< Number >	div_from_grad (const TypeNTensor< 3, Number > &grad)

Function Documentation

◆ curl_from_grad() [1/3]

VectorValue< Number > libMesh::TensorTools::curl_from_grad ( const TensorValue< Number > & grad )

Computes the curl of a vector given the gradient of that vector.

Definition at line 33 of file tensor_tools.C.

{
  const Number duz_dy = grad(2,1);
  const Number duy_dz = grad(1,2);
  const Number dux_dz = grad(0,2);
  const Number duz_dx = grad(2,0);
  const Number duy_dx = grad(1,0);
  const Number dux_dy = grad(0,1);
 
  return VectorValue<Number>(duz_dy - duy_dz,
                             dux_dz - duz_dx,
                             duy_dx - dux_dy);
}

◆ curl_from_grad() [2/3]

TensorValue< Number > libMesh::TensorTools::curl_from_grad ( const TypeNTensor< 3, Number > & grad )

Place holder needed for ExactSolution to compile. Will compute the curl of a tensor given the gradient of that tensor.

Definition at line 48 of file tensor_tools.C.

{
  libmesh_not_implemented();
}

◆ curl_from_grad() [3/3]

Number libMesh::TensorTools::curl_from_grad ( const VectorValue< Number > & )

Definition at line 28 of file tensor_tools.C.

{
  libmesh_error_msg("Operation not defined for scalar quantities.");
}

Referenced by libMesh::ExactSolution::_compute_error().

◆ div_from_grad() [1/3]

Number libMesh::TensorTools::div_from_grad ( const TensorValue< Number > & grad )

Computes the divergence of a vector given the gradient of that vector.

Definition at line 59 of file tensor_tools.C.

{
  const Number dux_dx = grad(0,0);
  const Number duy_dy = grad(1,1);
  const Number duz_dz = grad(2,2);
 
  return dux_dx + duy_dy + duz_dz;
}

◆ div_from_grad() [2/3]

VectorValue< Number > libMesh::TensorTools::div_from_grad ( const TypeNTensor< 3, Number > & grad )

Place holder needed for ExactSolution to compile. Will compute the divergence of a tensor given the gradient of that tensor.

Definition at line 69 of file tensor_tools.C.

{
  libmesh_not_implemented();
}

◆ div_from_grad() [3/3]

Number libMesh::TensorTools::div_from_grad ( const VectorValue< Number > & grad )

Dummy. Divergence of a scalar not defined, but is needed for ExactSolution to compile.

Definition at line 54 of file tensor_tools.C.

{
  libmesh_error_msg("Operation not defined for scalar quantities.");
}

Referenced by libMesh::ExactSolution::_compute_error().

◆ inner_product() [1/4]

template<typename T , typename T2 >

std::enable_if< ScalarTraits< T >::value &&ScalarTraits< T2 >::value, typenameCompareTypes< T, T2 >::supertype >::type libMesh::TensorTools::inner_product	(	const T &	a,
		const T2 &	b
	)

inline

Definition at line 51 of file tensor_tools.h.

52{ return a * b; }

b

static const Real b

Definition disjoint_neighbor_test.C:24

References b.

Referenced by libMesh::FEGenericBase< OutputType >::coarsened_dof_values(), libMesh::FEGenericBase< OutputType >::compute_periodic_constraints(), libMesh::FEGenericBase< OutputType >::compute_proj_constraints(), and libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::SubProjector::construct_projection().

◆ inner_product() [2/4]

template<unsigned int N, typename T , typename T2 >

CompareTypes< T, T2 >::supertype libMesh::TensorTools::inner_product	(	const TypeNTensor< N, T > &	a,
		const TypeNTensor< N, T2 > &	b
	)

inline

Definition at line 69 of file tensor_tools.h.

70{ return a.contract(b); }

libMesh::TypeNTensor::contract

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

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

Definition type_n_tensor.h:211

References b, and libMesh::TypeNTensor< N, T >::contract().

◆ inner_product() [3/4]

template<typename T , typename T2 >

CompareTypes< T, T2 >::supertype libMesh::TensorTools::inner_product	(	const TypeTensor< T > &	a,
		const TypeTensor< T2 > &	b
	)

inline

Definition at line 63 of file tensor_tools.h.

64{ return a.contract(b); }

libMesh::TypeTensor::contract

CompareTypes< T, T2 >::supertype contract(const TypeTensor< T2 > &) const

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

Definition type_tensor.h:1275

References b, and libMesh::TypeTensor< T >::contract().

◆ inner_product() [4/4]

template<typename T , typename T2 >

CompareTypes< T, T2 >::supertype libMesh::TensorTools::inner_product	(	const TypeVector< T > &	a,
		const TypeVector< T2 > &	b
	)

inline

Definition at line 57 of file tensor_tools.h.

58{ return a * b; }

References b.

◆ is_zero()

template<typename T >

bool libMesh::TensorTools::is_zero ( const T & a )

inline

Definition at line 134 of file tensor_tools.h.

134{ return a.is_zero();}

◆ norm() [1/6]

template<typename T >

auto libMesh::TensorTools::norm ( const T & a )

inline

Definition at line 74 of file tensor_tools.h.

75{ using std::abs; return abs(a); }

Referenced by norm_sq(), and norm_sq().

◆ norm() [2/6]

template<typename T >

auto libMesh::TensorTools::norm ( const TensorValue< T > & a ) -> decltype(TensorTools::norm(T()))

inline

Definition at line 98 of file tensor_tools.h.

99{using std::sqrt; return sqrt(a.norm_sq());}

libMesh::TypeTensor::norm_sq

auto norm_sq() const

Definition type_tensor.h:1356

◆ norm() [3/6]

template<typename T >

auto libMesh::TensorTools::norm ( const TypeTensor< T > & a ) -> decltype(TensorTools::norm(T()))

inline

Definition at line 93 of file tensor_tools.h.

94{using std::sqrt; return sqrt(a.norm_sq());}

◆ norm() [4/6]

template<typename T >

auto libMesh::TensorTools::norm ( const TypeVector< T > & a ) -> decltype(TensorTools::norm(T()))

inline

Definition at line 83 of file tensor_tools.h.

84{using std::sqrt; return sqrt(a.norm_sq());}

libMesh::TypeVector::norm_sq

auto norm_sq() const

Definition type_vector.h:928

◆ norm() [5/6]

template<typename T >

auto libMesh::TensorTools::norm ( const VectorValue< T > & a ) -> decltype(TensorTools::norm(T()))

inline

Definition at line 88 of file tensor_tools.h.

89{using std::sqrt; return sqrt(a.norm_sq());}

◆ norm() [6/6]

template<typename T >

T libMesh::TensorTools::norm ( std::complex< T > a )

inline

Definition at line 79 of file tensor_tools.h.

79{ using std::abs; return abs(a); }

◆ norm_sq() [1/6]

template<typename T >

auto libMesh::TensorTools::norm_sq ( const T & a )

inline

Definition at line 104 of file tensor_tools.h.

105{ using std::norm; return norm(a); }

libMesh::TensorTools::norm

auto norm(const T &a)

Definition tensor_tools.h:74

std::norm

auto norm(const libMesh::TypeVector< T > &vector) -> decltype(std::norm(T()))

Definition type_vector.h:1301

References std::norm(), and norm().

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::DiscontinuityMeasure::boundary_side_integration(), libMesh::KellyErrorEstimator::boundary_side_integration(), libMesh::ExactErrorEstimator::find_squared_element_error(), libMesh::DiscontinuityMeasure::internal_side_integration(), libMesh::LaplacianErrorEstimator::internal_side_integration(), libMesh::KellyErrorEstimator::internal_side_integration(), libMesh::DenseSubVector< T >::l2_norm(), libMesh::DenseVector< T >::l2_norm(), libMesh::DistributedVector< T >::l2_norm(), libMesh::DenseSubVector< T >::linfty_norm(), libMesh::DenseVector< T >::linfty_norm(), libMesh::TypeTensor< T >::norm_sq(), libMesh::TypeVector< T >::norm_sq(), libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), and libMesh::HPCoarsenTest::select_refinement().

◆ norm_sq() [2/6]

template<typename T >

auto libMesh::TensorTools::norm_sq ( const TensorValue< T > & a )

inline

Definition at line 128 of file tensor_tools.h.

129{return a.norm_sq();}

References libMesh::TypeTensor< T >::norm_sq().

◆ norm_sq() [3/6]

template<typename T >

auto libMesh::TensorTools::norm_sq ( const TypeTensor< T > & a )

inline

Definition at line 123 of file tensor_tools.h.

124{return a.norm_sq();}

References libMesh::TypeTensor< T >::norm_sq().

◆ norm_sq() [4/6]

template<typename T >

auto libMesh::TensorTools::norm_sq ( const TypeVector< T > & a )

inline

Definition at line 113 of file tensor_tools.h.

114{return a.norm_sq();}

References libMesh::TypeVector< T >::norm_sq().

◆ norm_sq() [5/6]

template<typename T >

auto libMesh::TensorTools::norm_sq ( const VectorValue< T > & a )

inline

Definition at line 118 of file tensor_tools.h.

119{return a.norm_sq();}

References libMesh::TypeVector< T >::norm_sq().

◆ norm_sq() [6/6]

template<typename T >

T libMesh::TensorTools::norm_sq ( std::complex< T > a )

inline

Definition at line 109 of file tensor_tools.h.

109{ using std::norm; return norm(a); }

References std::norm(), and norm().

Classes

Functions

Function Documentation

◆ curl_from_grad() [1/3]

◆ curl_from_grad() [2/3]

◆ curl_from_grad() [3/3]

◆ div_from_grad() [1/3]

◆ div_from_grad() [2/3]

◆ div_from_grad() [3/3]

◆ inner_product() [1/4]

◆ inner_product() [2/4]

◆ inner_product() [3/4]

◆ inner_product() [4/4]

◆ is_zero()

◆ norm() [1/6]

◆ norm() [2/6]

◆ norm() [3/6]

◆ norm() [4/6]

◆ norm() [5/6]

◆ norm() [6/6]

◆ norm_sq() [1/6]

◆ norm_sq() [2/6]

◆ norm_sq() [3/6]

◆ norm_sq() [4/6]

◆ norm_sq() [5/6]

◆ norm_sq() [6/6]