TensorExpressions

Modules
	TensorComparison
	TensorMathOperations
	TensorExpressionOptimizations

Functions
template<class F , class T0 , class T1 , std::enable_if_t< AreProperTensors< T0, T1 >::value &&!FunctorHas< IsTensorOperation, F >::value, int > = 0>
constexpr auto	Dune::ACFem::Tensor::operate (Expressions::DontOptimize, F &&f, T0 &&t0, T1 &&t1)
	Generate a binary tensor expression.
template<class F , class T , std::enable_if_t< IsTensor< T >::value, int > = 0>
auto	Dune::ACFem::Tensor::zero (F &&, T &&)
	Generate the canonical zero for tensors, given operation.
template<class T , std::enable_if_t< Tensor::IsTensor< T >::value, int > = 0>
auto	Dune::ACFem::Tensor::one (T &&)
	Generate the canonical scalar one for tensors.
template<std::size_t N, class T1 , class T2 , std::enable_if_t< AreProperTensors< T1, T2 >::value, int > = 0>
constexpr auto	Dune::ACFem::Tensor::contractInner (T1 &&t1, T2 &&t2, IndexConstant< N >=IndexConstant< N >{})
	Contraction over the #N inner dimensions. More...
template<class T1 , class T2 , std::enable_if_t< AreProperTensors< T1, T2 >::value, int > = 0>
auto	Dune::ACFem::Tensor::contractInner (T1 &&t1, T2 &&t2)
	Inner product w.r.t. More...
template<class T1 , class T2 , std::enable_if_t< AreProperTensors< T1, T2 >::value, int > = 0>
auto	Dune::ACFem::Tensor::outer (T1 &&t1, T2 &&t2)
	Outer tensor product.
template<class T , std::enable_if_t< IsProperTensor< T >::value, int > = 0>
constexpr auto	Dune::ACFem::Tensor::trace (T &&t)
	Trace is the contraction over all indices with the eye tensor.
template<class T1 , class T2 , std::enable_if_t< AreProperTensors< T1, T2 >::value, int > = 0>
auto	Dune::ACFem::Tensor::inner (T1 &&t1, T2 &&t2)
	"scalar product"
template<class Arg , std::enable_if_t< IsProperTensor< Arg >::value, int > = 0>
constexpr auto	Dune::ACFem::Tensor::frobenius2 (Arg &&arg)
	Square of Frobenius norm.
template<class T1 , class T2 , std::enable_if_t<(AreProperTensors< T1, T2 >::value &&TensorTraits< T1 >::rank > 0 &&TensorTraits< T2 >::rank > 0 &&TensorTraits< T1 >::template dim< TensorTraits< T1 >::rank - 1 >()==TensorTraits< T2 >::template dim< 0 >()), int > = 0>
auto	Dune::ACFem::Tensor::operator* (T1 &&t1, T2 &&t2)
	Multiplication of non-trivial tensors is Einstein-summation over the inner (right-most of the left and the left-most of the right) index if the dimension matches. More...
template<class T1 , class T2 , std::enable_if_t< AreProperTensors< T1, T2 >::value, int > = 0>
auto	Dune::ACFem::Tensor::operator& (T1 &&t1, T2 &&t2)
	Greedy contraction over all leading matching dimensions.
template<class T1 , class T2 , std::enable_if_t<(AreProperTensors< T1, T2 >::value &&TensorTraits< T2 >::rank==0), int > = 0>
auto	Dune::ACFem::Tensor::operator/ (T1 &&t1, T2 &&t2)
	Division is multiplication with inverse.
template<class T1 , class T2 , std::enable_if_t<(IsTensorOperand< T1 >::value &&IsTensorOperand< T2 >::value &&(IsTensor< T1 >::value||IsTensor< T2 >::value)), int > = 0>
T1 &	Dune::ACFem::Tensor::operator+= (T1 &t1, T2 &&t2)
	operator+=() with generic tensors.
template<class T1 , class T2 , std::enable_if_t<(IsTensorOperand< T1 >::value &&IsTensorOperand< T2 >::value &&(IsTensor< T1 >::value||IsTensor< T2 >::value)), int > = 0>
T1 &	Dune::ACFem::Tensor::operator-= (T1 &t1, T2 &&t2)
	operator-=() with generic tensors.
template<class T1 , class T2 , std::enable_if_t<(IsTensorOperand< T1 >::value &&IsTensorOperand< T2 >::value &&(IsTensor< T1 >::value||IsTensor< T2 >::value) &&TensorTraits< T2 >::rank==0), int > = 0>
T1 &	Dune::ACFem::Tensor::operator*= (T1 &t1, T2 &&t2)
	operator*=() with rank-0 tensors.
template<class F , class T , std::enable_if_t< IsProperTensor< T >::value &&!FunctorHas< IsTensorOperation, F >::value, int > = 0>
constexpr auto	Dune::ACFem::Tensor::operate (Expressions::DontOptimize, F &&f, T &&t)
	Generate a unary tensor expression. More...

Detailed Description

Function Documentation

contractInner() [1/2]

template<class T1 , class T2 , std::enable_if_t< AreProperTensors< T1, T2 >::value, int > = 0>

auto Dune::ACFem::Tensor::contractInner	(	T1 &&	t1,
		T2 &&	t2
	)

Inner product w.r.t.

to just the innermost index position.

contractInner() [2/2]

template<std::size_t N, class T1 , class T2 , std::enable_if_t< AreProperTensors< T1, T2 >::value, int > = 0>

constexpr auto Dune::ACFem::Tensor::contractInner ( T1 &&  t1, T2 &&  t2, IndexConstant< N >  = IndexConstant<N>{}  )

constexpr

Contraction over the #N inner dimensions.

Special cases:

• if N == 1 and T1 is a matrix and T2 a vector, then this is matrix-vector multiplication.
• if T1 and T2 are matrices, this will yield for N == 1 a matrix-matrix product

An attempt to call contractInner() with mis-matching dimensions is a compile-time error.

Note

Internally, this simply forwards to einsum().

Referenced by Dune::ACFem::EllipticEstimator< DiscreteFunctionSpace, Model, Norm >::estimateBoundary(), Dune::ACFem::ParabolicEulerEstimator< OldSolutionFunction, TimeProvider, ImplicitModel, ExplicitModel, Norm >::estimateBoundary(), Dune::ACFem::EllipticEstimator< DiscreteFunctionSpace, Model, Norm >::estimateIntersection(), Dune::ACFem::ParabolicEulerEstimator< OldSolutionFunction, TimeProvider, ImplicitModel, ExplicitModel, Norm >::estimateIntersection(), Dune::ACFem::ParabolicEulerEstimator< OldSolutionFunction, TimeProvider, ImplicitModel, ExplicitModel, Norm >::estimateProcessBoundary(), and Dune::ACFem::EllipticEstimator< DiscreteFunctionSpace, Model, Norm >::estimateProcessorBoundary().

operate()

template<class F , class T , std::enable_if_t< IsProperTensor< T >::value &&!FunctorHas< IsTensorOperation, F >::value, int > = 0>

constexpr auto Dune::ACFem::Tensor::operate ( Expressions::DontOptimize  , F &&  f, T &&  t  )

constexpr

Generate a unary tensor expression.

Parameters

t	The operand.
f	The operation functor.

operator*()

template<class T1 , class T2 , std::enable_if_t<(AreProperTensors< T1, T2 >::value &&TensorTraits< T1 >::rank > 0 &&TensorTraits< T2 >::rank > 0 &&TensorTraits< T1 >::template dim< TensorTraits< T1 >::rank - 1 >()==TensorTraits< T2 >::template dim< 0 >()), int > = 0>

auto Dune::ACFem::Tensor::operator*	(	T1 &&	t1,
		T2 &&	t2
	)

Multiplication of non-trivial tensors is Einstein-summation over the inner (right-most of the left and the left-most of the right) index if the dimension matches.

Multiplication of resp.

with scalars.