Collection of several utilities. More...

Collaboration diagram for Utilities:

Classes
class	Ikarus::BasisHandler< PB >
	Wrapper class for a hierarchical basis constructed from a pre-basis. More...

class	Ikarus::DirichletValues< B, FC >
	Class for handling Dirichlet boundary conditions in Ikarus. More...

struct	Ikarus::FlatPreBasis< PreBasis >
	Transform a PreBasis into one with flat index-merging strategyThis utility takes a pre-basis and converts recursively all index-merging strategies into their flat analog, i.e. `BlockedInterleaved` is converted into `FlatInterleaved` and `BlockedLexicographic` is transformed into `FlatLexicographic`. More...

class	Ikarus::NonLinearOperator< TypeListOne, TypeListTwo >
	Represents a NonLinearOperator class for handling nonlinear operators. More...

struct	Ikarus::utils::SolverDefault
	Default functor for solving operations. More...

struct	Ikarus::utils::UpdateDefault
	Default functor for updating operations. More...

Macros
#define	MAKE_ENUM(type, ...)
	Macro to create an enumeration with a string conversion function.The macro creates an enum class with a BEGIN and END enumerator, and provides a constexpr toString function for string conversion. More...

Functions
template<typename Fun , typename... Vars, typename... Args, typename U , typename G , typename H >
void	Ikarus::utils::hessianN (const Fun &f, const autodiff::Wrt< Vars... > &wrt, const autodiff::At< Args... > &at, U &u, std::array< G, U::RowsAtCompileTime > &g, std::array< H, U::RowsAtCompileTime > &h)
	Computes the Hessian matrix for each parameter of a given function.The Hessian matrix represents the second-order partial derivatives of the function with respect to the specified variables. More...

std::tuple< Dune::Functions::Polynomial< double >, decltype(Eigen::seq(0, 0))>	Ikarus::utils::findLineSegment (const Eigen::VectorXd &x, const Eigen::VectorXd &y, int segmentSize)
	Find a linear segment in a set of data points. More...

template<class PreBasis >
decltype(auto)	Ikarus::flatPreBasis (const PreBasis &preBasis)
	Generator function for a flatted PreBasis. More...

template<int size, typename LV >
void	Ikarus::utils::obtainLagrangeGlobalNodePositions (const LV &localView, std::vector< Dune::FieldVector< double, size > > &lagrangeNodeGlobalCoords)
	A function to obtain the global positions of the nodes of an element with Lagrangian basis. More...

template<int size, typename Basis >
auto	Ikarus::utils::globalIndexFromGlobalPosition (const Basis &basis, const Dune::FieldVector< double, size > &pos)
	A helper function to obtain the global index from the global positions for a Lagrange node. More...

template<typename FE >
auto	Ikarus::utils::referenceElementSubEntityPositions (FE &fe, int codim)
	A function to obtain the local coordinates of subentities of an FiniteElement. More...

template<typename FE >
auto	Ikarus::utils::referenceElementVertexPositions (FE &fe)
	A function to obtain the local coordinates the vertices of an FiniteElement. More...

template<typename NonlinearOperator , typename UpdateType = typename NonlinearOperator::template ParameterValue<0>>
bool	Ikarus::utils::checkGradient (NonlinearOperator &nonLinOp, CheckFlags checkFlags=CheckFlags(), std::function< void(typename NonlinearOperator::template ParameterValue< 0 > &, const UpdateType &)> p_updateFunction=[](typename NonlinearOperator::template ParameterValue< 0 > &a, const UpdateType &b) { a+=b;})
	Checks the gradient of a nonlinear operator. More...

template<typename NonlinearOperator , typename UpdateType = typename NonlinearOperator::template ParameterValue<0>>
bool	Ikarus::utils::checkJacobian (NonlinearOperator &nonLinOp, CheckFlags checkFlags=CheckFlags(), std::function< void(typename NonlinearOperator::template ParameterValue< 0 > &, const UpdateType &)> p_updateFunction=[](typename NonlinearOperator::template ParameterValue< 0 > &a, const UpdateType &b) { a+=b;})
	Checks the Jacobian of a nonlinear operator. More...

template<typename NonlinearOperator , typename UpdateType = typename NonlinearOperator::template ParameterValue<0>>
bool	Ikarus::utils::checkHessian (NonlinearOperator &nonLinOp, CheckFlags checkFlags=CheckFlags(), std::function< void(typename NonlinearOperator::template ParameterValue< 0 > &, const UpdateType &)> p_updateFunction=[](typename NonlinearOperator::template ParameterValue< 0 > &a, const UpdateType &b) { a+=b;})
	Checks the Hessian of a nonlinear operator. More...

template<typename Derived >
auto	Ikarus::orthonormalizeMatrixColumns (const Eigen::MatrixBase< Derived > &A)
	Orthonormalizes all Matrix columns using Gram-Schmidt Orthogonalization. More...

template<typename ValueType >
auto	Ikarus::viewAsFlatEigenVector (Dune::BlockVector< ValueType > &blockedVector)
	View Dune::BlockVector as an Eigen::Vector. More...

template<typename ValueType >
auto	Ikarus::viewAsFlatEigenVector (const Dune::BlockVector< ValueType > &blockedVector)
	View const Dune::BlockVector as an Eigen::Vector. More...

template<typename ValueType >
auto	Ikarus::viewAsEigenMatrixAsDynFixed (Dune::BlockVector< ValueType > &blockedVector)
	View Dune::BlockVector as an Eigen::Matrix with dynamic rows and fixed columns depending on the size of the ValueType. More...

template<typename ValueType >
auto	Ikarus::viewAsEigenMatrixAsDynFixed (const Dune::BlockVector< ValueType > &blockedVector)
	Const view Dune::BlockVector as an Eigen::Matrix with dynamic rows and fixed columns depending on the size of the ValueType. More...

template<typename ValueType >
auto	Ikarus::viewAsEigenMatrixFixedDyn (Dune::BlockVector< ValueType > &blockedVector)
	View Dune::BlockVector as an Eigen::Matrix with fixed rows depending on the size of the ValueType and dynamic columns. More...

template<typename ValueType >
auto	Ikarus::viewAsEigenMatrixFixedDyn (const Dune::BlockVector< ValueType > &blockedVector)
	Const view Dune::BlockVector as an Eigen::Matrix with fixed rows depending on the size of the ValueType and dynamic columns. More...

template<typename Type > requires requires { Type::correctionSize; }
size_t	Ikarus::correctionSize (const Dune::BlockVector< Type > &a)
	Returns the total correction size of a block vector with a Manifold as the underlying type. More...

template<typename Type > requires requires { Type::valueSize; }
size_t	Ikarus::valueSize (const Dune::BlockVector< Type > &a)
	Returns the total value size of a block vector with a Manifold as the underlying type. More...

template<typename Type , typename Derived > requires (Ikarus::Concepts::AddAssignAble<Type, decltype(b.template segment<Type::correctionSize>(0))> and requires() { Type::correctionSize; })
Dune::BlockVector< Type > &	Ikarus::operator+= (Dune::BlockVector< Type > &a, const Eigen::MatrixBase< Derived > &b)
	Enables the += operator for Dune::BlockVector += Eigen::Vector. More...

template<typename Type , typename Derived > requires (Ikarus::Concepts::AddAssignAble<Type, decltype(b.template segment<Type::correctionSize>(0))> and requires() { Type::correctionSize; })
Dune::BlockVector< Type > &	Ikarus::operator-= (Dune::BlockVector< Type > &a, const Eigen::MatrixBase< Derived > &b)
	Enables the -= operator for Dune::BlockVector += Eigen::Vector. More...

template<typename... Types, typename Derived >
Dune::TupleVector< Types... > &	Ikarus::operator+= (Dune::TupleVector< Types... > &a, const Eigen::MatrixBase< Derived > &b)
	Enables the += operator for Dune::TupleVector += Eigen::Vector. More...

template<typename ManifoldPoint , typename Derived > requires (Ikarus::Concepts::AddAssignAble<ManifoldPoint, decltype(b.template segment<ManifoldPoint::valueSize>(0))> and requires() { ManifoldPoint::valueSize; })
Dune::BlockVector< ManifoldPoint > &	Ikarus::addInEmbedding (Dune::BlockVector< ManifoldPoint > &a, const Eigen::MatrixBase< Derived > &b)
	Enables the addition in the embedding space of a vector in the space M^n, where M is a manifold with the points of type ManifoldPoint. More...

template<typename Derived > requires (!std::floating_point<Derived>)
auto	Ikarus::norm (const Eigen::MatrixBase< Derived > &v)
	Adding free norm function to Eigen types. More...

auto	Ikarus::norm (const std::floating_point auto &v)
	Helper Free Function to have the same interface as for Eigen Vector Types. More...

template<typename Scalar , int size>
auto	Ikarus::operator* (const Eigen::DiagonalMatrix< Scalar, size > &a, const Eigen::DiagonalMatrix< Scalar, size > &b)
	Eigen::DiagonalMatrix Product Missing in Eigen. More...

template<typename Scalar , int size>
auto	Ikarus::operator+= (Eigen::DiagonalMatrix< Scalar, size > &a, const Eigen::DiagonalMatrix< Scalar, size > &b)
	In-place addition for Eigen::DiagonalMatrix. More...

template<typename Derived , typename Scalar , int size>
auto	Ikarus::operator+ (const Eigen::MatrixBase< Derived > &a, const Eigen::DiagonalMatrix< Scalar, size > &b)
	Eigen::Matrix + Eigen::DiagonalMatrix addition missing in Eigen. More...

template<typename Derived , typename Scalar , int size>
auto	Ikarus::operator+ (const Eigen::DiagonalMatrix< Scalar, size > &a, const Eigen::MatrixBase< Derived > &b)
	Eigen::DiagonalMatrix + Eigen::Matrix addition missing in Eigen. More...

template<typename Scalar , int size>
auto	Ikarus::operator- (const Eigen::DiagonalMatrix< Scalar, size > &a)
	Unary minus for Eigen::DiagonalMatrix. More...

template<typename Derived , typename Derived2 >
auto	Ikarus::operator+ (const Eigen::MatrixBase< Derived > &a, const Eigen::DiagonalWrapper< Derived2 > &b)
	Addition of Eigen::Matrix and Eigen::DiagonalWrapper. More...

template<typename Derived , typename Derived2 >
auto	Ikarus::operator+ (const Eigen::DiagonalWrapper< Derived > &a, const Eigen::MatrixBase< Derived2 > &b)
	Addition of Eigen::DiagonalWrapper and Eigen::Matrix. More...

template<typename Scalar , int size>
std::ostream &	Ikarus::operator<< (std::ostream &os, const Eigen::DiagonalMatrix< Scalar, size > &a)
	Output stream operator for Eigen::DiagonalMatrix. More...

template<typename Derived >
Derived	Ikarus::sym (const Eigen::MatrixBase< Derived > &A)
	Returns the symmetric part of a matrix. More...

template<typename Derived >
Derived	Ikarus::skew (const Eigen::MatrixBase< Derived > &A)
	Returns the skew part of a matrix. More...

template<typename Derived >
void	Ikarus::printForMaple (const Eigen::EigenBase< Derived > &A)
	Method to print the matrix in a format that can directly be copied to Maple. More...

template<typename FieldVectorT >
auto	Ikarus::createRandomVector (typename FieldVectorT::value_type lower=-1, typename FieldVectorT::value_type upper=1)
	Creates a random vector of the specified type within a given range. More...

template<typename ScalarType >
Eigen::Matrix< ScalarType, 3, 3 >	Ikarus::skew (const Eigen::Vector< ScalarType, 3 > &a)
	Create skew 3x3 matrix from 3d vector. More...

template<typename Derived , size_t sizeOfCondensedIndices>
auto	Ikarus::staticCondensation (const Eigen::MatrixBase< Derived > &E, const std::array< size_t, sizeOfCondensedIndices > &indices)
	Performs static condensation on a square matrix. More...

template<typename Derived , size_t sizeOfRemovedCols>
auto	Ikarus::removeCol (const Eigen::MatrixBase< Derived > &E, const std::array< size_t, sizeOfRemovedCols > &indices)
	Removes specified columns from a matrix. More...

template<typename ST , typename MaterialImpl >
auto	Ikarus::toVoigtAndMaybeReduce (const Eigen::Matrix< ST, 3, 3 > &E, const MaterialImpl &material, bool isStrain=true)
	Converts a 3x3 matrix to Voigt notation, possibly reducing it based on material properties. More...

template<typename M , typename Derived >
decltype(auto)	Ikarus::enlargeIfReduced (const Eigen::MatrixBase< Derived > &E)
	Enlarges a matrix if it reduced in the context of material laws, i.e., VanishingStress If the material is not reduced the untouched matrix is returned and rendering the function as a NoOp. More...

template<typename MessageType >
MessageType &	Ikarus::increment (MessageType &e)
	Increments the given enum value. More...

std::tuple< Dune::Functions::Polynomial< double >, double >	Ikarus::utils::polyfit (const Eigen::Ref< const Eigen::VectorXd > &x, const Eigen::Ref< const Eigen::VectorXd > &y, int deg)
	Fits a polynomial of a given degree to the given data points. More...

void	addBindingsToUtils ()

Variables
template<int dim>
constexpr auto	Ikarus::voigtNotationContainer = std::get<dim - 1>(Impl::voigtIndices)
	Container for Voigt notation indices based on dimension.1D: 0,0 2D: 0,0; 1,1; 0,1 3D: 0,0; 1,1; 2,2; 1,2; 0,2; 0,1. More...

Detailed Description

Macro Definition Documentation

◆ MAKE_ENUM

#define MAKE_ENUM	(	type,
		...
	)

Value:

  enum class type                           \
  {                                         \
    BEGIN,                                  \
    __VA_ARGS__,                            \
    END                                     \
  };                                        \
  constexpr std::string toString(type _e) { \
    using enum type;                        \
    switch (_e) {                           \
      ENUM_CASE(BEGIN)                      \
      FOR_EACH(ENUM_CASE, __VA_ARGS__)      \
      ENUM_CASE(END)                        \
    }                                       \
    __builtin_unreachable();                \
  }

Parameters

type	The name of the enum class.
...	Enumerators to be included between BEGIN and END.

Function Documentation

◆ addBindingsToUtils()

void addBindingsToUtils ( )

Converts a square 1x1, 2x2 or 3x3 matrix to a Voigt notation vector.

Parameters

E	Input matrix of size (size x size).
isStrain	Flag indicating whether the conversion is for strain (true) or not (false) (default is true)..

Returns: Vector with components in Voigt notation vector.

This function converts a square matrix to a Voigt notation vector, which contains the unique components of the input matrix.

The optional isStrain parameter allows the user to specify whether the conversion is intended for strain calculations. If isStrain is true, the off-diagonal components are multiplied by 2, providing the correct Voigt notation for symmetric strain tensors.

Converts a vector given in Voigt notation to a matrix.

Parameters

EVoigt	Voigt notation vector.
isStrain	Flag indicating whether the vector represents a strain (default is true).

Returns: Matrix corresponding to the vector in Voigt notation.

This function converts a vector given in Voigt notation to the corresponding matrix. The conversion depends on the size The parameter isStrain is used to determine the conversion factor for off-diagonal components, which need to be divided by 2 in the matrix representation if the quantity is a strain tensor.

The function requires that the size of the Voigt notation vector is valid (1, 3, or 6).

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◆ addInEmbedding()

template<typename ManifoldPoint , typename Derived >
requires (Ikarus::Concepts::AddAssignAble<ManifoldPoint, decltype(b.template segment<ManifoldPoint::valueSize>(0))> and requires() { ManifoldPoint::valueSize; })

Dune::BlockVector< ManifoldPoint > & Ikarus::addInEmbedding	(	Dune::BlockVector< ManifoldPoint > &	a,
		const Eigen::MatrixBase< Derived > &	b
	)

Template Parameters

ManifoldPoint	Manifold type.
Derived	ManifoldPoint of the input Eigen matrix.

Parameters

a	Input Dune::BlockVector.
b	Input Eigen::Matrix.

Returns: Reference to the modified Dune::BlockVector.

◆ checkGradient()

template<typename NonlinearOperator , typename UpdateType = typename NonlinearOperator::template ParameterValue<0>>

bool Ikarus::utils::checkGradient	(	NonlinearOperator &	nonLinOp,
		CheckFlags	checkFlags = `CheckFlags()`,
		std::function< void(typename NonlinearOperator::template ParameterValue< 0 > &, const UpdateType &)>	p_updateFunction = `[](typename NonlinearOperator::template ParameterValue<0>& a, const UpdateType& b) { a += b; }`
	)

The checkgradient function is inspired by http://sma.epfl.ch/~nboumal/book/ Chapter 4.8 and https://github.com/NicolasBoumal/manopt/blob/master/manopt/tools/checkdiff.m

Template Parameters

NonlinearOperator	Type of the nonlinear operator.
UpdateType	Type of the update.

Parameters

nonLinOp	The nonlinear operator.
checkFlags	Flags for the check.
p_updateFunction	Update function.

Returns: True if the check passed, false otherwise.

◆ checkHessian()

template<typename NonlinearOperator , typename UpdateType = typename NonlinearOperator::template ParameterValue<0>>

bool Ikarus::utils::checkHessian	(	NonlinearOperator &	nonLinOp,
		CheckFlags	checkFlags = `CheckFlags()`,
		std::function< void(typename NonlinearOperator::template ParameterValue< 0 > &, const UpdateType &)>	p_updateFunction = `[](typename NonlinearOperator::template ParameterValue<0>& a, const UpdateType& b) { a += b; }`
	)

The checkHessian function is inspired by http://sma.epfl.ch/~nboumal/book/ Chapter 6.8 and https://github.com/NicolasBoumal/manopt/blob/master/manopt/tools/checkhessian.m

Template Parameters

NonlinearOperator	Type of the nonlinear operator.
UpdateType	Type of the update.

Parameters

nonLinOp	The nonlinear operator.
checkFlags	Flags for the check.
p_updateFunction	Update function.

Returns: True if the check passed, false otherwise.

◆ checkJacobian()

template<typename NonlinearOperator , typename UpdateType = typename NonlinearOperator::template ParameterValue<0>>

bool Ikarus::utils::checkJacobian	(	NonlinearOperator &	nonLinOp,
		CheckFlags	checkFlags = `CheckFlags()`,
		std::function< void(typename NonlinearOperator::template ParameterValue< 0 > &, const UpdateType &)>	p_updateFunction = `[](typename NonlinearOperator::template ParameterValue<0>& a, const UpdateType& b) { a += b; }`
	)

The checkjacobian function is inspired by http://sma.epfl.ch/~nboumal/book/ Chapter 4.8 and https://github.com/NicolasBoumal/manopt/blob/master/manopt/tools/checkdiff.m

Template Parameters

NonlinearOperator	Type of the nonlinear operator.
UpdateType	Type of the update.

Parameters

nonLinOp	The nonlinear operator.
checkFlags	Flags for the check.
p_updateFunction	Update function.

Returns: True if the check passed, false otherwise.

◆ correctionSize()

template<typename Type >
requires requires { Type::correctionSize; }

size_t Ikarus::correctionSize ( const Dune::BlockVector< Type > & a )

Template Parameters

Type	Manifold type.

Parameters

a	Input Dune::BlockVector.

Returns: Total correction size.

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◆ createRandomVector()

template<typename FieldVectorT >

auto Ikarus::createRandomVector	(	typename FieldVectorT::value_type	lower = `-1`,
		typename FieldVectorT::value_type	upper = `1`
	)

Template Parameters

FieldVectorT The type of the vector.

Parameters

lower	The lower bound of the random values (default is -1).
upper	The upper bound of the random values (default is 1).

Returns: A random vector within the specified range.

◆ enlargeIfReduced()

template<typename M , typename Derived >

decltype(auto) Ikarus::enlargeIfReduced ( const Eigen::MatrixBase< Derived > & E )

Template Parameters

M	Type of the material.
Derived	Type of the input matrix.

Parameters

E	Input matrix.

Returns: auto Resulting matrix based on material properties.

This function takes an input matrix and, based on the material properties, either returns the original matrix (if it is not reduced) or enlarges the matrix by filling in the specified columns with zeros (if it is reduced).

◆ findLineSegment()

std::tuple< Dune::Functions::Polynomial< double >, decltype(Eigen::seq(0, 0))> Ikarus::utils::findLineSegment	(	const Eigen::VectorXd &	x,
		const Eigen::VectorXd &	y,
		int	segmentSize
	)

his function is inspired by the MATLAB code at: https://github.com/NicolasBoumal/manopt/blob/master/manopt/tools/identify_linear_piece.m It is designed to find the most linear segment in a set of data points

Parameters

x	The x-coordinates of the data points.
y	The y-coordinates of the data points.
segmentSize	The size of the line segment to be identified.

Returns: A tuple containing the polynomial representing the identified line segment and the indices of the data points in the segment.

◆ flatPreBasis()

template<class PreBasis >

decltype(auto) Ikarus::flatPreBasis ( const PreBasis & preBasis )

◆ globalIndexFromGlobalPosition()

template<int size, typename Basis >

auto Ikarus::utils::globalIndexFromGlobalPosition	(	const Basis &	basis,
		const Dune::FieldVector< double, size > &	pos
	)

Template Parameters

size	Size of the global nodal coordinate vector
Basis	Type of the basis.

Parameters

basis	The grid basis.
pos	Global position

Returns: Global index

◆ hessianN()

template<typename Fun , typename... Vars, typename... Args, typename U , typename G , typename H >

void Ikarus::utils::hessianN	(	const Fun &	f,
		const autodiff::Wrt< Vars... > &	wrt,
		const autodiff::At< Args... > &	at,
		U &	u,
		std::array< G, U::RowsAtCompileTime > &	g,
		std::array< H, U::RowsAtCompileTime > &	h
	)

Template Parameters

Fun	The type of the function to be differentiated.
Vars	The types of the variables with respect to which the Hessian is computed.
Args	The types of the arguments passed to the function.
U	The type representing the result of the function evaluation.
G	The type representing the gradient of the function.
H	The type representing the Hessian matrix.

Parameters

f	The function to be differentiated.
wrt	The variables with respect to which the Hessian is computed.
at	The values at which the Hessian is evaluated.
u	The result of the function evaluation.
g	The gradient of the function.
h	The Hessian matrix (output).

◆ increment()

template<typename MessageType >

MessageType & Ikarus::increment ( MessageType & e )

Template Parameters

MessageType The enum type.

Parameters

e	The enum value to increment.

Returns: The incremented enum value.

Exceptions

Dune::RangeError if trying to increment MessageType::END.

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◆ norm() [1/2]

template<typename Derived >
requires (!std::floating_point<Derived>)

auto Ikarus::norm ( const Eigen::MatrixBase< Derived > & v )

Template Parameters

Derived Type of the input Eigen matrix.

Parameters

v	Input Eigen matrix.

Returns: Norm of the matrix.

◆ norm() [2/2]

auto Ikarus::norm ( const std::floating_point auto & v )

Parameters

v	Input scalar.

Returns: Absolute value of the scalar.

◆ obtainLagrangeGlobalNodePositions()

template<int size, typename LV >

void Ikarus::utils::obtainLagrangeGlobalNodePositions	(	const LV &	localView,
		std::vector< Dune::FieldVector< double, size > > &	lagrangeNodeGlobalCoords
	)

Template Parameters

size	Size of the global nodal coordinate vector
LV	Type of the local view

Parameters

localView	Local view bounded to an element
lagrangeNodeGlobalCoords	A vector of global nodal coordinates to be updated

◆ operator*()

template<typename Scalar , int size>

auto Ikarus::operator*	(	const Eigen::DiagonalMatrix< Scalar, size > &	a,
		const Eigen::DiagonalMatrix< Scalar, size > &	b
	)

Template Parameters

Scalar	Scalar type.
size	Size of the diagonal matrix.

Parameters

a	Input DiagonalMatrix.
b	Input DiagonalMatrix.

Returns: Product of the two DiagonalMatrices.

◆ operator+() [1/4]

template<typename Derived , typename Scalar , int size>

auto Ikarus::operator+	(	const Eigen::DiagonalMatrix< Scalar, size > &	a,
		const Eigen::MatrixBase< Derived > &	b
	)

Template Parameters

Derived	Type of the input Eigen matrix.
Scalar	Scalar type.
size	Size of the diagonal matrix.

Parameters

a	Input DiagonalMatrix.
b	Input Eigen matrix.

Returns: Sum of the DiagonalMatrix and Eigen matrix.

◆ operator+() [2/4]

template<typename Derived , typename Derived2 >

auto Ikarus::operator+	(	const Eigen::DiagonalWrapper< Derived > &	a,
		const Eigen::MatrixBase< Derived2 > &	b
	)

Template Parameters

Derived	Type of the input Eigen DiagonalWrapper.
Derived2	Type of the input Eigen matrix.

Parameters

a	Input Eigen DiagonalWrapper.
b	Input Eigen matrix.

Returns: Sum of DiagonalWrapper and Eigen matrix.

◆ operator+() [3/4]

template<typename Derived , typename Scalar , int size>

auto Ikarus::operator+	(	const Eigen::MatrixBase< Derived > &	a,
		const Eigen::DiagonalMatrix< Scalar, size > &	b
	)

Template Parameters

Derived	Type of the input Eigen matrix.
Scalar	Scalar type.
size	Size of the diagonal matrix.

Parameters

a	Input Eigen matrix.
b	Input DiagonalMatrix.

Returns: Sum of the Eigen matrix and DiagonalMatrix.

◆ operator+() [4/4]

template<typename Derived , typename Derived2 >

auto Ikarus::operator+	(	const Eigen::MatrixBase< Derived > &	a,
		const Eigen::DiagonalWrapper< Derived2 > &	b
	)

Template Parameters

Derived	Type of the input Eigen matrix.
Derived2	Type of the input Eigen DiagonalWrapper.

Parameters

a	Input Eigen matrix.
b	Input Eigen DiagonalWrapper.

Returns: Sum of Eigen matrix and DiagonalWrapper.

◆ operator+=() [1/3]

template<typename Type , typename Derived >
requires (Ikarus::Concepts::AddAssignAble<Type, decltype(b.template segment<Type::correctionSize>(0))> and requires() { Type::correctionSize; })

Dune::BlockVector< Type > & Ikarus::operator+=	(	Dune::BlockVector< Type > &	a,
		const Eigen::MatrixBase< Derived > &	b
	)

Template Parameters

Type	Manifold type.
Derived	Type of the input Eigen matrix.

Parameters

a	Input Dune::BlockVector.
b	Input Eigen::Matrix.

Returns: Reference to the modified Dune::BlockVector.

◆ operator+=() [2/3]

template<typename... Types, typename Derived >

Dune::TupleVector< Types... > & Ikarus::operator+=	(	Dune::TupleVector< Types... > &	a,
		const Eigen::MatrixBase< Derived > &	b
	)

Template Parameters

Types	Types of the elements in the TupleVector.
Derived	Type of the input Eigen matrix.

Parameters

a	Input Dune::TupleVector.
b	Input Eigen::Matrix.

Returns: Reference to the modified Dune::TupleVector.

◆ operator+=() [3/3]

template<typename Scalar , int size>

auto Ikarus::operator+=	(	Eigen::DiagonalMatrix< Scalar, size > &	a,
		const Eigen::DiagonalMatrix< Scalar, size > &	b
	)

Template Parameters

Scalar	Scalar type.
size	Size of the diagonal matrix.

Parameters

a	Input DiagonalMatrix.
b	Input DiagonalMatrix.

Returns: Reference to the modified DiagonalMatrix.

◆ operator-()

template<typename Scalar , int size>

auto Ikarus::operator- ( const Eigen::DiagonalMatrix< Scalar, size > & a )

Template Parameters

Scalar	Scalar type.
size	Size of the diagonal matrix.

Parameters

a	Input DiagonalMatrix.

Returns: Negation of the DiagonalMatrix.

◆ operator-=()

template<typename Type , typename Derived >
requires (Ikarus::Concepts::AddAssignAble<Type, decltype(b.template segment<Type::correctionSize>(0))> and requires() { Type::correctionSize; })

Dune::BlockVector< Type > & Ikarus::operator-=	(	Dune::BlockVector< Type > &	a,
		const Eigen::MatrixBase< Derived > &	b
	)

Template Parameters

Type	Manifold type.
Derived	Type of the input Eigen matrix.

Parameters

a	Input Dune::BlockVector.
b	Input Eigen::Matrix.

Returns: Reference to the modified Dune::BlockVector.

◆ operator<<()

template<typename Scalar , int size>

std::ostream & Ikarus::operator<<	(	std::ostream &	os,
		const Eigen::DiagonalMatrix< Scalar, size > &	a
	)

Template Parameters

Scalar	Scalar type.
size	Size of the diagonal matrix.

Parameters

os	Output stream.
a	Input DiagonalMatrix.

Returns: Reference to the output stream.

◆ orthonormalizeMatrixColumns()

template<typename Derived >

auto Ikarus::orthonormalizeMatrixColumns ( const Eigen::MatrixBase< Derived > & A )

Template Parameters

Derived Type of the input matrix.

Parameters

A	The input matrix.

Returns: Eigen Matrix with orthonormalized columns.

◆ polyfit()

std::tuple< Dune::Functions::Polynomial< double >, double > Ikarus::utils::polyfit	(	const Eigen::Ref< const Eigen::VectorXd > &	x,
		const Eigen::Ref< const Eigen::VectorXd > &	y,
		int	deg
	)

Parameters

x	The input vector of x-coordinates.
y	The input vector of y-coordinates.
deg	The degree of the polynomial to fit.

Returns: std::tuple<Dune::Functions::Polynomial<double>, double> A tuple containing the fitted polynomial and the least square error.

◆ printForMaple()

template<typename Derived >

void Ikarus::printForMaple ( const Eigen::EigenBase< Derived > & A )

Template Parameters

Derived The derived type of the matrix.

Parameters

A	The input matrix.

◆ referenceElementSubEntityPositions()

template<typename FE >

auto Ikarus::utils::referenceElementSubEntityPositions	(	FE &	fe,
		int	codim
	)

Template Parameters

FE	Type of the finite element

Parameters

fe	finite element
codim	codim of requested subentity

Returns: view over the position of the subenties

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◆ referenceElementVertexPositions()

template<typename FE >

auto Ikarus::utils::referenceElementVertexPositions ( FE & fe )

Template Parameters

FE	Type of the finite element

Parameters

fe	finite element

Returns

◆ removeCol()

template<typename Derived , size_t sizeOfRemovedCols>

auto Ikarus::removeCol	(	const Eigen::MatrixBase< Derived > &	E,
		const std::array< size_t, sizeOfRemovedCols > &	indices
	)

Template Parameters

Derived	Type of the matrix.
sizeOfRemovedCols	Size of the columns to be removed.

Parameters

E	Input matrix.
indices	Array of column indices to be removed.

Returns: Resulting matrix after removing specified columns.

This function removes specified columns from a matrix. It computes the remaining columns after removing the specified indices and returns the resulting matrix.

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◆ skew() [1/2]

template<typename Derived >

Derived Ikarus::skew ( const Eigen::MatrixBase< Derived > & A )

Template Parameters

Derived Type of the input Eigen matrix.

Parameters

A	Input Eigen matrix.

Returns: Skew part of the matrix.

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◆ skew() [2/2]

template<typename ScalarType >

Eigen::Matrix< ScalarType, 3, 3 > Ikarus::skew ( const Eigen::Vector< ScalarType, 3 > & a )

Template Parameters

ScalarType The type of the coordinates in the vector.

Parameters

a	The vector.

Returns: The skew matrix.

◆ staticCondensation()

template<typename Derived , size_t sizeOfCondensedIndices>

auto Ikarus::staticCondensation	(	const Eigen::MatrixBase< Derived > &	E,
		const std::array< size_t, sizeOfCondensedIndices > &	indices
	)

Template Parameters

Derived	Type of the matrix.
sizeOfCondensedIndices	Size of the condensed indices.

Parameters

E	Input matrix.
indices	Array of indices to be condensed.

Returns: Resulting matrix after static condensation.

This function performs static condensation on a square matrix. It removes the specified indices from the matrix, computes the remaining submatrices (K11, K12, K22), and returns the result of the static condensation.

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◆ sym()

template<typename Derived >

Derived Ikarus::sym ( const Eigen::MatrixBase< Derived > & A )

Template Parameters

Derived Type of the input Eigen matrix.

Parameters

A	Input Eigen matrix.

Returns: Symmetric part of the matrix.

◆ toVoigtAndMaybeReduce()

template<typename ST , typename MaterialImpl >

auto Ikarus::toVoigtAndMaybeReduce	(	const Eigen::Matrix< ST, 3, 3 > &	E,
		const MaterialImpl &	material,
		bool	isStrain = `true`
	)

Template Parameters

ST	Scalar type of the matrix.
MaterialImpl	Type of the material implementation.

Parameters

E	Input 3x3 matrix.
material	Reference to the material implementation.
isStrain	Flag indicating if the matrix represents strain (default is true).

Returns: Resulting matrix in Voigt notation.

This function converts a 3x3 matrix to its Voigt notation. If the material is not reduced, the full Voigt notation is returned. Otherwise, the specified columns (based on material properties, such as VanishingStress) are removed, and the reduced Voigt notation is returned.

◆ valueSize()

template<typename Type >
requires requires { Type::valueSize; }

size_t Ikarus::valueSize ( const Dune::BlockVector< Type > & a )

Template Parameters

Type	Manifold type.

Parameters

a	Input Dune::BlockVector.

Returns: Total value size.

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◆ viewAsEigenMatrixAsDynFixed() [1/2]

template<typename ValueType >

auto Ikarus::viewAsEigenMatrixAsDynFixed ( const Dune::BlockVector< ValueType > & blockedVector )

Template Parameters

ValueType Type of the elements in the BlockVector.

Parameters

blockedVector Input Dune::BlockVector.

Returns: Eigen::Map of the BlockVector as a dynamic Eigen::Matrix (const version).

◆ viewAsEigenMatrixAsDynFixed() [2/2]

template<typename ValueType >

auto Ikarus::viewAsEigenMatrixAsDynFixed ( Dune::BlockVector< ValueType > & blockedVector )

Template Parameters

ValueType Type of the elements in the BlockVector.

Parameters

blockedVector Input Dune::BlockVector.

Returns: Eigen::Map of the BlockVector as a dynamic Eigen::Matrix.

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◆ viewAsEigenMatrixFixedDyn() [1/2]

template<typename ValueType >

auto Ikarus::viewAsEigenMatrixFixedDyn ( const Dune::BlockVector< ValueType > & blockedVector )

Template Parameters

ValueType Type of the elements in the BlockVector.

Parameters

blockedVector Input Dune::BlockVector.

Returns: Eigen::Map of the BlockVector as a fixed-size Eigen::Matrix with dynamic columns (const version).

◆ viewAsEigenMatrixFixedDyn() [2/2]

template<typename ValueType >

auto Ikarus::viewAsEigenMatrixFixedDyn ( Dune::BlockVector< ValueType > & blockedVector )

Template Parameters

ValueType Type of the elements in the BlockVector.

Parameters

blockedVector Input Dune::BlockVector.

Returns: Eigen::Map of the BlockVector as a fixed-size Eigen::Matrix with dynamic columns.

◆ viewAsFlatEigenVector() [1/2]

template<typename ValueType >

auto Ikarus::viewAsFlatEigenVector ( const Dune::BlockVector< ValueType > & blockedVector )

Template Parameters

ValueType Type of the elements in the BlockVector.

Parameters

blockedVector Input Dune::BlockVector.

Returns: Eigen::Map of the BlockVector as a flat Eigen::Vector (const version).

◆ viewAsFlatEigenVector() [2/2]

template<typename ValueType >

auto Ikarus::viewAsFlatEigenVector ( Dune::BlockVector< ValueType > & blockedVector )

Template Parameters

ValueType Type of the elements in the BlockVector.

Parameters

blockedVector Input Dune::BlockVector.

Returns: Eigen::Map of the BlockVector as a flat Eigen::Vector.

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Variable Documentation

◆ voigtNotationContainer

template<int dim>

constexpr auto Ikarus::voigtNotationContainer = std::get<dim - 1>(Impl::voigtIndices)

constexpr

Template Parameters

dim	The dimension for which Voigt indices are needed.

Classes

Macros

Functions

Variables

Detailed Description

Macro Definition Documentation

◆ MAKE_ENUM

Function Documentation

◆ addBindingsToUtils()

◆ addInEmbedding()

◆ checkGradient()

◆ checkHessian()

◆ checkJacobian()

◆ correctionSize()

◆ createRandomVector()

◆ enlargeIfReduced()

◆ findLineSegment()

◆ flatPreBasis()

◆ globalIndexFromGlobalPosition()

◆ hessianN()

◆ increment()

◆ norm() [1/2]

◆ norm() [2/2]

◆ obtainLagrangeGlobalNodePositions()

◆ operator*()

◆ operator+() [1/4]

◆ operator+() [2/4]

◆ operator+() [3/4]

◆ operator+() [4/4]

◆ operator+=() [1/3]

◆ operator+=() [2/3]

◆ operator+=() [3/3]

◆ operator-()

◆ operator-=()

◆ operator<<()

◆ orthonormalizeMatrixColumns()

◆ polyfit()

◆ printForMaple()

◆ referenceElementSubEntityPositions()

◆ referenceElementVertexPositions()

◆ removeCol()

◆ skew() [1/2]

◆ skew() [2/2]

◆ staticCondensation()

◆ sym()

◆ toVoigtAndMaybeReduce()

◆ valueSize()

◆ viewAsEigenMatrixAsDynFixed() [1/2]

◆ viewAsEigenMatrixAsDynFixed() [2/2]

◆ viewAsEigenMatrixFixedDyn() [1/2]

◆ viewAsEigenMatrixFixedDyn() [2/2]

◆ viewAsFlatEigenVector() [1/2]

◆ viewAsFlatEigenVector() [2/2]

Variable Documentation

◆ voigtNotationContainer