Main namespace of the RFFGen library. More...

Classes
struct	Constant
	Wrap a constant. More...

struct	Identity
	Identity mapping . More...

struct	Variable
	Independent variable. Can be uniquely identified by its id. More...

struct	Base
	Base class for functions satisfying FunctionConcept. Required for enabling the operators in generate.hh. More...

class	OutOfDomainException
	Exception for scalar function arguments that are outside the domain of the function. More...

class	NonSymmetricMatrixException
	Exception for non-symmetric matrices if symmetric matrices are required. More...

struct	Zero
	Specialize this struct for your matrix type if a zero matrix cannot be generated via Matrix(0.). More...

struct	Zero< Matrix, void_t< Checks::TryCallToFill< Matrix > > >
	Specialization for the case that a matrix can be set to zero by calling the member function fill(0). More...

Typedefs
template<class F , bool arithmeticArgument = false>
using	Finalize = Detail::FinalizeImpl< F, arithmeticArgument, Checks::hasVariable< F >() >
	Finish function definition. More...

template<class F , int id>
using	Variable_t = typename VariableDetail::VariableType< F, id >::type
	Get underlying type of variable with index id.

template<class... Types>
using	void_t = typename Detail::voider< Types...>::type
	Most fascinating type ever. Is always void.

Functions
template<class Arg >
auto	constRef (const Arg &x)
	Generate a constant function that stores its argument as constant reference. More...

template<class Arg >
auto	constant (const Arg &x)
	Wrap a constant. More...

template<class F >
auto	finalize (const F &f)
	Finish function definition. More...

template<class F >
auto	finalize_scalar (const F &f)
	Finish function definition. More...

template<class F , class G , class = std::enable_if_t< std::is_base_of<Base,F>::value \|\| std::is_base_of<Base,G>::value >>
auto	operator+ (const F &f, const G &g)
	overload of "+"-operator for the generation of functions. More...

template<class F , class G , class = std::enable_if_t< std::is_base_of<Base,F>::value \|\| std::is_base_of<Base,G>::value >>
auto	operator* (const F &f, const G &g)
	overload of "*"-operator for the generation of functions. More...

template<class F , class = std::enable_if_t< std::is_base_of<Base,F>::value >>
auto	operator^ (const F &f, int k)
	overload of "^"-operator for the generation of functions. More...

template<class F , class G , class = std::enable_if_t<std::is_base_of<Base,F>::value && std::is_base_of<Base,G>::value>>
auto	operator<< (const F &f, const G &g)
	overload of "<<"-operator for chaining functions and to $f \circ g$ . More...

template<class F , class T , class = std::enable_if_t<std::is_convertible<T,decltype(std::declval<F>().d0())>::value && std::is_base_of<Base,F>::value>>
auto	operator- (const F &f, const T &t)
	overload of "-"-operator for the generation of functions. Here the second argument is a constant that is wrapped in to an object of type Constant. More...

template<class F , class T , class = std::enable_if_t<std::is_convertible<T,decltype(std::declval<F>().d0())>::value && std::is_base_of<Base,F>::value>>
auto	operator- (const T &t, const F &f)
	overload of "-"-operator for the generation of functions. Here the first argument is a constant that is wrapped in to an object of type Constant. More...

template<class Arg >
auto	identity (const Arg &x)
	Construct Identity<Arg>(x).

template<int id, class T >
Variable< T, id >	variable (const T &t)
	Generate variable from input type.

template<class Inflation , class Compression , class Matrix >
auto	volumetricPenalty (double d0, double d1, const Matrix &A)
	Create volumetric penalty function composed of a penalty for inflation and one for compression.

template<class Matrix >
auto	volumetricQuadAndLog (double d0, double d1, const Matrix &A)
	Create the volumetric penalty function $d_0 j^2 + d_1 \log(j),\ j=\det(A)$ .

template<class Matrix >
auto	volumetricHartmannNeff (double d0, double d1, const Matrix &A)
	Create the volumetric penalty function $d_0 j^5 + d_1 j^{-5},\ j=\det(A)$ .

template<class Matrix >
auto	yieldSurface (double beta, double offset, Matrix sigma=LinearAlgebra::unitMatrix< Matrix >())
	Yield surface $\frac{\beta}{3}\iota_1(\sigma) + J_2(\sigma)-offset$ , where $\iota_1$ is the first principal and is the second deviatoric invariant.

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	incompressibleMooneyRivlin (double c0, double c1, const Matrix &F)
	Generate an "incompressible" Mooney-Rivlin material law $W(F)=c_0\iota_1(F^T F) + c_1\iota_2(F^T F)$ , where $\iota_1$ is the first and $\iota_2$ the second principal matrix invariant.

template<class InflationPenalty , class CompressionPenalty , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	compressibleMooneyRivlin (double c0, double c1, double d0, double d1, const Matrix &F)
	Generate a compressible Mooney-Rivlin material law $W(F)=c_0\iota_1(F^T F) + c_1\iota_2(F^T F) + d_0\Gamma_\mathrm{In}(\det(F))+d_1\Gamma_\mathrm{Co}(\det(F))$ , where $\iota_1$ is the first and $\iota_2$ the second principal matrix invariant.

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	incompressibleNeoHooke (double c, const Matrix &F)
	Generate an "incompressible" neo-Hookean material law $W(F)=c\iota_1(F^T F)$ , where $\iota_1$ is the first principal matrix invariant .

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	modifiedIncompressibleNeoHooke (double c, const Matrix &F)
	Generate an "incompressible" neo-Hookean material law $W(F)=c\bar\iota_1(F^T F)$ , where $\bar\iota_1$ is the modified first principal matrix invariant.

template<class InflationPenalty , class CompressionPenalty , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	compressibleNeoHooke (double c, double d0, double d1, const Matrix &F)
	Generate a compressible neo-Hookean material law $W(F)=c\iota_1(F^T F)+d_0\Gamma_\mathrm{In}(\det(F))+d_1\Gamma_\mathrm{Co}(\det(F))$ , where $\iota_1$ is the first principal matrix invariant.

template<class InflationPenalty , class CompressionPenalty , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	modifiedCompressibleNeoHooke (double c, double d0, double d1, const Matrix &F)
	Generate a compressible neo-Hookean material law $W(F)=c\bar\iota_1(F^T F)+d_0\Gamma_\mathrm{In}(\det(F))+d_1\Gamma_\mathrm{Co}(\det(F))$ , where $\bar\iota_1$ is the modified first principal matrix invariant.

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	incompressibleAdiposeTissue_SommerHolzapfel (double cCells, double k1, double k2, double kappa, const Matrix &M, const Matrix &F)
	Model for adipose tissue of Sommer et al.: Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery. Acta Biomater., 9:9036-9048, 2013. More...

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	incompressibleAdiposeTissue_SommerHolzapfel (const Matrix &M, const Matrix &F)
	Model for adipose tissue of Sommer et al.: Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery. Acta Biomater., 9:9036-9048, 2013. More...

template<class Inflation , class Compression , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	compressibleAdiposeTissue_SommerHolzapfel (double cCells, double k1, double k2, double kappa, double d0, double d1, const Matrix &M, const Matrix &F)
	Compressible version of the model for adipose tissue of Sommer et al.: Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery. Acta Biomater., 9:9036-9048, 2013. More...

template<class Inflation , class Compression , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	compressibleAdiposeTissue_SommerHolzapfel (double d0, double d1, const Matrix &M, const Matrix &F)
	Compressible version of the model for adipose tissue of Sommer et al.: Multiaxial mechanical properties and constitutive modeling of human adipose tissue: A basis for preoperative simulations in plastic and reconstructive surgery. Acta Biomater., 9:9036-9048, 2013. Material parameters are taken from the same publication, Table 2, i.e. $c_\mathrm{Cells}=0.15 (\,\mathrm{kPa})$ , $k_1=0.8 (\,\mathrm{kPa})$ , and $\kappa=0.09$ . More...

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	incompressibleMuscleTissue_Martins (double c, double b, double A, double a, const Matrix &M, const Matrix &F)
	Incompressible version of the model for muscle tissue of Martins et al.: A numerical model of passive and active bahevaior of skeletal muscles. Comp. Meth. Appl. Mech. Eng. 151:419-433, 1998. More...

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	incompressibleMuscleTissue_Martins (const Matrix &M, const Matrix &F)
	Incompressible version of the model for muscle tissue of Martins et al.: A numerical model of passive and active bahevaior of skeletal muscles. Comp. Meth. Appl. Mech. Eng. 151:419-433, 1998. More...

template<class Inflation , class Compression , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	compressibleMuscleTissue_Martins (double c, double b, double A, double a, double d0, double d1, const Matrix &M, const Matrix &F)
	Compressible version of the model for muscle tissue of Martins et al.: A numerical model of passive and active bahevaior of skeletal muscles. Comp. Meth. Appl. Mech. Eng. 151:419-433, 1998. More...

template<class Inflation , class Compression , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	compressibleMuscleTissue_Martins (double d0, double d1, const Matrix &M, const Matrix &F)
	Compressible version of the model for muscle tissue of Martins et al.: A numerical model of passive and active bahevaior of skeletal muscles. Comp. Meth. Appl. Mech. Eng. 151:419-433, 1998. More...

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	incompressibleSkin_Hendriks (double c0, double c1, const Matrix &F)
	Model for skin tissue of Hendriks: Mechanical behavior of human epidermal and dermal layers in vivo. PhD thesis, Technische Universiteit Eindhoven, 2005. More...

template<class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	incompressibleSkin_Hendriks (const Matrix &F)
	Model for skin tissue of Hendriks: Mechanical behavior of human epidermal and dermal layers in vivo. PhD thesis, Technische Universiteit Eindhoven, 2005. More...

template<class InflationPenalty , class CompressionPenalty , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	compressibleSkin_Hendriks (double c0, double c1, double d0, double d1, const Matrix &F)
	Compressible version of the model for skin tissue of Hendriks: Mechanical behavior of human epidermal and dermal layers in vivo. PhD thesis, Technische Universiteit Eindhoven, 2005. More...

template<class InflationPenalty , class CompressionPenalty , class Matrix , int offset = LinearAlgebra::dimension<Matrix>()>
auto	compressibleSkin_Hendriks (double d0, double d1, const Matrix &F)
	Compressible version of the model for skin tissue of Hendriks: Mechanical behavior of human epidermal and dermal layers in vivo. PhD thesis, Technische Universiteit Eindhoven, 2005. More...

template<class Arg , class = std::enable_if_t< !std::is_base_of<Base,Arg>() && !std::is_arithmetic<Arg>() >, class = std::enable_if_t< !Checks::summation<Arg>() && Checks::inPlaceSummation<Arg>() >>
auto	operator+ (Arg x, const Arg &y)
	Defines operator+ if not yet defined and in-place summation (operator+=()) is supported.

template<class Arg , class ScalarArg , class = std::enable_if_t< std::is_arithmetic<ScalarArg>::value >, class = std::enable_if_t< !std::is_base_of<Base,Arg>() && !std::is_arithmetic<Arg>() >, class = std::enable_if_t< !Checks::multiplicationWithArithmeticFromLeft<Arg,ScalarArg>() && Checks::inPlaceMultiplicationWithArithmetic<Arg,ScalarArg>() >>
auto	operator* (ScalarArg a, Arg x)
	Defines operator* for multiplication with built-in arithmetic types from the left if undefined and in-place multiplication (operator*=()) is supported.

template<class Arg , class ScalarArg , class = std::enable_if_t< std::is_arithmetic<ScalarArg>::value >, class = std::enable_if_t< !std::is_base_of<Base,Arg>() && !std::is_arithmetic<Arg>::value>, class = std::enable_if_t< !Checks::multiplicationWithArithmeticFromRight<Arg,ScalarArg>() && Checks::inPlaceMultiplicationWithArithmetic<Arg,ScalarArg>() >>
auto	operator* (Arg x, ScalarArg a)
	Defines operator* for multiplication with built-in arithmetic types from the right if undefined and in-place multiplication (operator*=()) is supported.

template<class Arg1 , class Arg2 , class = std::enable_if_t< !std::is_base_of<Arg1,Base>() && !std::is_base_of<Arg2,Base>() >, class = std::enable_if_t< !std::is_arithmetic<Arg1>() && !std::is_arithmetic<Arg2>() >, class = std::enable_if_t< !Checks::multiplication<Arg1,Arg2>() && Checks::inPlaceMultiplication<Arg1,Arg2>() >>
auto	operator* (Arg1 x, const Arg2 &y)
	Defines operator* for multiplication of non-arithmetic types if undefined and in-place multiplication (operator*=()) is supported.

template<class Arg1 , class Arg2 , class = std::enable_if_t< !std::is_base_of<Arg1,Base>() && !std::is_base_of<Arg2,Base>() >, class = std::enable_if_t< !std::is_arithmetic<Arg1>() && !std::is_arithmetic<Arg2>() >, class = std::enable_if_t< !Checks::multiplication<Arg1,Arg2>() && !Checks::inPlaceMultiplication<Arg1,Arg2>() >, class = std::enable_if_t< Checks::callToRightMultiply<Arg1,Arg2>() >>
auto	operator* (Arg1 x, const Arg2 &y)
	Defines operator* for multiplication of non-arithmetic types if undefined and in-place multiplication is provided in terms of the member function rightmultiplyany() (such as for Dune::FieldMatrix).

template<class Matrix , class = std::enable_if_t<Checks::isConstantSizeMatrix<Matrix>()>>
Matrix	addTransposed (Matrix &A)
	Overwrites with . More...

template<class Matrix , class = std::enable_if_t<!Checks::isConstantSizeMatrix<Matrix>()>, class = std::enable_if_t<Checks::isDynamicMatrix<Matrix>()>>
Matrix	addTransposed (Matrix &A)
	Overwrites with . More...

template<class Matrix , class = std::enable_if_t<Checks::isConstantSizeMatrix<Matrix>()>>
Matrix	zero ()

template<class Matrix , class = std::enable_if_t<!Checks::isConstantSizeMatrix<Matrix>()>>
constexpr Matrix	zero (int rows, int cols)

Detailed Description

Main namespace of the RFFGen library.

See Also: MathematicalOperations; CMath

Typedef Documentation

template<class F , bool arithmeticArgument = false>

using RFFGen::Finalize = typedef Detail::FinalizeImpl< F , arithmeticArgument , Checks::hasVariable<F>() >

Finish function definition.

Adds the definition of possibly undefined vanishing higher order derivatives.

Function Documentation

template<class Matrix , class = std::enable_if_t<Checks::isConstantSizeMatrix<Matrix>()>>

Matrix RFFGen::addTransposed ( Matrix & A )

Overwrites $A$ with $A+A^T$ .

Returns

template<class Matrix , class = std::enable_if_t<!Checks::isConstantSizeMatrix<Matrix>()>, class = std::enable_if_t<Checks::isDynamicMatrix<Matrix>()>>

Matrix RFFGen::addTransposed ( Matrix & A )

Overwrites $A$ with $A+A^T$ .

Returns

template<class Arg >

auto RFFGen::constant ( const Arg & x )

Wrap a constant.

Returns: Constant<Arg>(x)

template<class Arg >

auto RFFGen::constRef ( const Arg & x )

Generate a constant function that stores its argument as constant reference.

This admits to use variable constant arguments, i.e. parameters that we want to study.

template<class F >

auto RFFGen::finalize ( const F & f )

Finish function definition.

Adds the definition of possibly undefined vanishing higher order derivatives.

template<class F >

auto RFFGen::finalize_scalar ( const F & f )

Finish function definition.

Adds the definition of possibly undefined vanishing higher order derivatives.

template<class F , class G , class = std::enable_if_t< std::is_base_of<Base,F>::value || std::is_base_of<Base,G>::value >>

auto RFFGen::operator*	(	const F &	f,
		const G &	g
	)

overload of "*"-operator for the generation of functions.