EigenMatrix Namespace Reference

Classes
struct	d2MCoefficients
struct	d2MImpl
struct	EigenMatrixImp
struct	Fdd4MImpl
struct	FirstMatrixDirectiveImpl
struct	GetDiffDiffMatImpl
struct	GetDiffDiffMatImpl< E, C, T1, FTensor::Tensor2_symmetric< VT2, DimT2 > >
struct	GetDiffMatImpl
struct	GetMatImpl
struct	ReconstructMatImpl
struct	SecondMatrixDirectiveImpl

Typedefs
template<typename T , int Dim>
using	Val = const FTensor::Tensor1< T, Dim >
template<typename T , int Dim>
using	Vec = const FTensor::Tensor2< T, Dim, Dim >
template<typename T >
using	Fun = boost::function< T(const T)>
template<int N>
using	Number = FTensor::Number< N >

Functions
template<typename T , int Dim>
FTensor::Tensor2_symmetric< double, Dim >	getMatImpl (Val< T, Dim > &t_val, Vec< T, Dim > &t_vec, Fun< double > f)
template<typename T , int Dim>
FTensor::Ddg< double, Dim, Dim >	getDiffMatImpl (Val< T, Dim > &t_val, Vec< T, Dim > &t_vec, Fun< double > f, Fun< double > d_f, const int nb)
template<typename T , typename S , int Dim>
FTensor::Ddg< double, Dim, Dim >	getDiffDiffMatImpl (Val< T, Dim > &t_val, Vec< T, Dim > &t_vec, Fun< double > f, Fun< double > d_f, Fun< double > dd_f, S &t_S, const int nb)
FTensor::Tensor2_symmetric< double, 3 >	getMat (Val< double, 3 > &t_val, Vec< double, 3 > &t_vec, Fun< double > f)
	Get the Mat object. More...
FTensor::Tensor2_symmetric< double, 3 >	getMat (Val< FTensor::PackPtr< double *, 1 >, 3 > &t_val, Vec< FTensor::PackPtr< double *, 1 >, 3 > &t_vec, Fun< double > f)
	Get the Mat object. More...
FTensor::Ddg< double, 3, 3 >	getDiffMat (Val< double, 3 > &t_val, Vec< double, 3 > &t_vec, Fun< double > f, Fun< double > d_f, const int nb)
	Get the Diff Mat object. More...
FTensor::Ddg< double, 3, 3 >	getDiffMat (Val< FTensor::PackPtr< double *, 1 >, 3 > &t_val, Vec< FTensor::PackPtr< double *, 1 >, 3 > &t_vec, Fun< double > f, Fun< double > d_f, const int nb)
	Get the Diff Mat object. More...
FTensor::Ddg< double, 3, 3 >	getDiffDiffMat (Val< double, 3 > &t_val, Vec< double, 3 > &t_vec, Fun< double > f, Fun< double > d_f, Fun< double > dd_f, FTensor::Tensor2< double, 3, 3 > &t_S, const int nb)
FTensor::Ddg< double, 3, 3 >	getDiffDiffMat (Val< FTensor::PackPtr< double *, 1 >, 3 > &t_val, Vec< FTensor::PackPtr< double *, 1 >, 3 > &t_vec, Fun< double > f, Fun< double > d_f, Fun< double > dd_f, FTensor::Tensor2< double, 3, 3 > &t_S, const int nb)
FTensor::Ddg< double, 3, 3 >	getDiffDiffMat (Val< double, 3 > &t_val, Vec< double, 3 > &t_vec, Fun< double > f, Fun< double > d_f, Fun< double > dd_f, FTensor::Tensor2_symmetric< double, 3 > &t_S, const int nb)
	Get the Diff Diff Mat object. More...
FTensor::Ddg< double, 3, 3 >	getDiffDiffMat (Val< FTensor::PackPtr< double *, 1 >, 3 > &t_val, Vec< FTensor::PackPtr< double *, 1 >, 3 > &t_vec, Fun< double > f, Fun< double > d_f, Fun< double > dd_f, FTensor::Tensor2_symmetric< double, 3 > &t_S, const int nb)
FTensor::Tensor2_symmetric< double, 2 >	getMat (Val< double, 2 > &t_val, Vec< double, 2 > &t_vec, Fun< double > f)
	Get the Mat object. More...
FTensor::Ddg< double, 2, 2 >	getDiffMat (Val< double, 2 > &t_val, Vec< double, 2 > &t_vec, Fun< double > f, Fun< double > d_f, const int nb)
	Get the Diff Mat object. More...
FTensor::Ddg< double, 2, 2 >	getDiffDiffMat (Val< double, 2 > &t_val, Vec< double, 2 > &t_vec, Fun< double > f, Fun< double > d_f, Fun< double > dd_f, FTensor::Tensor2< double, 2, 2 > &t_S, const int nb)
FTensor::Ddg< double, 2, 2 >	getDiffDiffMat (Val< double, 2 > &t_val, Vec< double, 2 > &t_vec, Fun< double > f, Fun< double > d_f, Fun< double > dd_f, FTensor::Tensor2_symmetric< double, 2 > &t_S, const int nb)
template<int N1, int N2, int Dim>
auto	get_sym_index (const Number< N1 > &, const Number< N2 > &, const Number< Dim > &)
auto	get_sym_index (const int N1, const int N2, const int Dim)
template<int N1, int N2, int Dim>
auto	get_nodiag_index (const Number< N1 > &, const Number< N2 > &, const Number< Dim > &)
auto	get_nodiag_index (const int N1, const int N2, int Dim)

Typedef Documentation

Fun

template<typename T >

using EigenMatrix::Fun = typedef boost::function<T(const T)>

Definition at line 67 of file MatrixFunction.hpp.

Number

template<int N>

using EigenMatrix::Number = typedef FTensor::Number<N>

Definition at line 55 of file MatrixFunctionTemplate.hpp.

Val

template<typename T , int Dim>

using EigenMatrix::Val = typedef const FTensor::Tensor1<T, Dim>

Definition at line 65 of file MatrixFunction.hpp.

Vec

template<typename T , int Dim>

using EigenMatrix::Vec = typedef const FTensor::Tensor2<T, Dim, Dim>

Examples

ADOLCPlasticity.hpp, analytical_nonlinear_poisson.cpp, analytical_poisson.cpp, analytical_poisson_field_split.cpp, AuxPoissonFunctions.hpp, cell_forces.cpp, dynamic_first_order_con_law.cpp, elasticity.cpp, elasticity_mixed_formulation.cpp, EshelbianPlasticity.cpp, free_surface.cpp, heat_equation.cpp, HookeElement.cpp, MagneticElement.hpp, mesh_smoothing.cpp, minimal_surface_area.cpp, NavierStokesElement.cpp, nonlinear_dynamics.cpp, nonlinear_elastic.cpp, plastic.cpp, PoissonOperators.hpp, Remodeling.cpp, Remodeling.hpp, simple_elasticity.cpp, simple_interface.cpp, test_cache_on_entities.cpp, testing_jacobian_of_hook_element.cpp, testing_jacobian_of_hook_scaled_with_density_element.cpp, and UnsaturatedFlow.hpp.

Definition at line 66 of file MatrixFunction.hpp.

Function Documentation

get_nodiag_index() [1/2]

auto EigenMatrix::get_nodiag_index ( const int  N1, const int  N2, int  Dim  )

inline

Definition at line 83 of file MatrixFunctionTemplate.hpp.

                                                                  {
  if (N2 > N1)
    return (Dim - 1) * N1 + N2 - 1;
  else
    return (Dim - 1) * N1 + N2;
}

get_nodiag_index() [2/2]

template<int N1, int N2, int Dim>

auto EigenMatrix::get_nodiag_index ( const Number< N1 > &  , const Number< N2 > &  , const Number< Dim > &    )

inline

Definition at line 74 of file MatrixFunctionTemplate.hpp.

                                        {
  static_assert(N1 != N2, "Bad index");
  if constexpr (N2 > N1)
    return (Dim - 1) * N1 + N2 - 1;
  else
    return (Dim - 1) * N1 + N2;
}

get_sym_index() [1/2]

auto EigenMatrix::get_sym_index ( const int  N1, const int  N2, const int  Dim  )

inline

Definition at line 66 of file MatrixFunctionTemplate.hpp.

                                                                     {
  if (N1 > N2)
    return N1 + (N2 * (2 * Dim - N2 - 1)) / 2;
  else
    return N2 + (N1 * (2 * Dim - N1 - 1)) / 2;
}

get_sym_index() [2/2]

template<int N1, int N2, int Dim>

auto EigenMatrix::get_sym_index ( const Number< N1 > &  , const Number< N2 > &  , const Number< Dim > &    )

inline

Definition at line 58 of file MatrixFunctionTemplate.hpp.

                                        {
  if constexpr (N1 > N2)
    return N1 + (N2 * (2 * Dim - N2 - 1)) / 2;
  else
    return N2 + (N1 * (2 * Dim - N1 - 1)) / 2;
}

getDiffDiffMat() [1/6]

FTensor::Ddg< double, 2, 2 > EigenMatrix::getDiffDiffMat	(	Val< double, 2 > &	t_val,
		Vec< double, 2 > &	t_vec,
		Fun< double >	f,
		Fun< double >	d_f,
		Fun< double >	dd_f,
		FTensor::Tensor2< double, 2, 2 > &	t_S,
		const int	nb
	)

Definition at line 127 of file MatrixFunction.cpp.

                                                        {
  return getDiffDiffMatImpl<double, FTensor::Tensor2<double, 2, 2>, 2>(
      t_val, t_vec, f, d_f, dd_f, t_S, nb);
}

getDiffDiffMat() [2/6]

FTensor::Ddg< double, 2, 2 > EigenMatrix::getDiffDiffMat	(	Val< double, 2 > &	t_val,
		Vec< double, 2 > &	t_vec,
		Fun< double >	f,
		Fun< double >	d_f,
		Fun< double >	dd_f,
		FTensor::Tensor2_symmetric< double, 2 > &	t_S,
		const int	nb
	)

Definition at line 137 of file MatrixFunction.cpp.

                                                                       {
  return getDiffDiffMatImpl<double, FTensor::Tensor2_symmetric<double, 2>, 2>(
      t_val, t_vec, f, d_f, dd_f, t_S, nb);
}

getDiffDiffMat() [3/6]

FTensor::Ddg< double, 3, 3 > EigenMatrix::getDiffDiffMat	(	Val< double, 3 > &	t_val,
		Vec< double, 3 > &	t_vec,
		Fun< double >	f,
		Fun< double >	d_f,
		Fun< double >	dd_f,
		FTensor::Tensor2< double, 3, 3 > &	t_S,
		const int	nb
	)

Examples

HenckyOps.hpp, and matrix_function.cpp.

Definition at line 78 of file MatrixFunction.cpp.

                                                        {
  return getDiffDiffMatImpl<double, FTensor::Tensor2<double, 3, 3>, 3>(
      t_val, t_vec, f, d_f, dd_f, t_S, nb);
}

getDiffDiffMat() [4/6]

FTensor::Ddg< double, 3, 3 > EigenMatrix::getDiffDiffMat	(	Val< double, 3 > &	t_val,
		Vec< double, 3 > &	t_vec,
		Fun< double >	f,
		Fun< double >	d_f,
		Fun< double >	dd_f,
		FTensor::Tensor2_symmetric< double, 3 > &	t_S,
		const int	nb
	)

Get the Diff Diff Mat object.

\[ LS_{klmn} = S_{ij} \frac{\partial^2 B_{ij}}{\partial A_{kl} \partial A_{mn} } \]

Note

Eigen vector are in rows.

Parameters

t_val	eigen values
t_vec	eigen vectors
f	function
d_f	directive of function
dd_f	second directive of function
t_S	S tensor
nb	number of nonzero eigen values

Returns

FTensor::Ddg<double, 3, 3>

Definition at line 98 of file MatrixFunction.cpp.

                                                                       {
  return getDiffDiffMatImpl<double, FTensor::Tensor2_symmetric<double, 3>, 3>(
      t_val, t_vec, f, d_f, dd_f, t_S, nb);
}

getDiffDiffMat() [5/6]

FTensor::Ddg< double, 3, 3 > EigenMatrix::getDiffDiffMat	(	Val< FTensor::PackPtr< double *, 1 >, 3 > &	t_val,
		Vec< FTensor::PackPtr< double *, 1 >, 3 > &	t_vec,
		Fun< double >	f,
		Fun< double >	d_f,
		Fun< double >	dd_f,
		FTensor::Tensor2< double, 3, 3 > &	t_S,
		const int	nb
	)

Definition at line 88 of file MatrixFunction.cpp.

                                                                {
  return getDiffDiffMatImpl<FTensor::PackPtr<double *, 1>,
                            FTensor::Tensor2<double, 3, 3>, 3>(
      t_val, t_vec, f, d_f, dd_f, t_S, nb);
}

getDiffDiffMat() [6/6]

FTensor::Ddg< double, 3, 3 > EigenMatrix::getDiffDiffMat	(	Val< FTensor::PackPtr< double *, 1 >, 3 > &	t_val,
		Vec< FTensor::PackPtr< double *, 1 >, 3 > &	t_vec,
		Fun< double >	f,
		Fun< double >	d_f,
		Fun< double >	dd_f,
		FTensor::Tensor2_symmetric< double, 3 > &	t_S,
		const int	nb
	)

Definition at line 106 of file MatrixFunction.cpp.

                                                                       {
  return getDiffDiffMatImpl<FTensor::PackPtr<double *, 1>,
                            FTensor::Tensor2_symmetric<double, 3>, 3>(
      t_val, t_vec, f, d_f, dd_f, t_S, nb);
}

getDiffDiffMatImpl()

template<typename T , typename S , int Dim>

FTensor::Ddg<double, Dim, Dim> EigenMatrix::getDiffDiffMatImpl	(	Val< T, Dim > &	t_val,
		Vec< T, Dim > &	t_vec,
		Fun< double >	f,
		Fun< double >	d_f,
		Fun< double >	dd_f,
		S &	t_S,
		const int	nb
	)

Definition at line 35 of file MatrixFunction.cpp.

                                                                            {
  switch (nb) {
  case 1:
    return EigenMatrixImp<T, T, 1, Dim>(t_val, t_vec)
        .getDiffDiffMat(f, d_f, dd_f, t_S);
  case 2:
    return EigenMatrixImp<T, T, 2, Dim>(t_val, t_vec)
        .getDiffDiffMat(f, d_f, dd_f, t_S);
  case 3:
    break;
  default:
    THROW_MESSAGE("third parameter should be 1,2 or 3");
  }
  return EigenMatrixImp<T, T, 3, Dim>(t_val, t_vec)
      .getDiffDiffMat(f, d_f, dd_f, t_S);
};

getDiffMat() [1/3]

FTensor::Ddg< double, 2, 2 > EigenMatrix::getDiffMat	(	Val< double, 2 > &	t_val,
		Vec< double, 2 > &	t_vec,
		Fun< double >	f,
		Fun< double >	d_f,
		const int	nb
	)

Get the Diff Mat object.

\[ P_{ijkl} = \frac{\partial B_{ij}}{\partial A_{kl}} \]

Note

Eiegn vetore are in rows.

Parameters

t_val	eigen values
t_vec	eigen vector
f	function
d_f	directive of function
nb	number of nonequal eigen valuse

Returns

FTensor::Ddg<double, 3, 3>

Definition at line 121 of file MatrixFunction.cpp.

                                                                     {
  return getDiffMatImpl<double, 2>(t_val, t_vec, f, d_f, nb);
}

getDiffMat() [2/3]

FTensor::Ddg< double, 3, 3 > EigenMatrix::getDiffMat	(	Val< double, 3 > &	t_val,
		Vec< double, 3 > &	t_vec,
		Fun< double >	f,
		Fun< double >	d_f,
		const int	nb
	)

Get the Diff Mat object.

\[ P_{ijkl} = \frac{\partial B_{ij}}{\partial A_{kl}} \]

Note

Eiegn vetore are in rows.

Parameters

t_val	eigen values
t_vec	eigen vector
f	function
d_f	directive of function
nb	number of nonequal eigen valuse

Returns

FTensor::Ddg<double, 3, 3>

Examples

EshelbianOperators.cpp, HenckyOps.hpp, and matrix_function.cpp.

Definition at line 64 of file MatrixFunction.cpp.

                                                                     {
  return getDiffMatImpl<double, 3>(t_val, t_vec, f, d_f, nb);
}

getDiffMat() [3/3]

FTensor::Ddg< double, 3, 3 > EigenMatrix::getDiffMat	(	Val< FTensor::PackPtr< double *, 1 >, 3 > &	t_val,
		Vec< FTensor::PackPtr< double *, 1 >, 3 > &	t_vec,
		Fun< double >	f,
		Fun< double >	d_f,
		const int	nb
	)

Get the Diff Mat object.

\[ P_{ijkl} = \frac{\partial B_{ij}}{\partial A_{kl}} \]

Note

Eiegn vetore are in rows.

Parameters

t_val	eigen values
t_vec	eigen vector
f	function
d_f	directive of function
nb	number of nonequal eigen valuse

Returns

FTensor::Ddg<double, 3, 3>

Definition at line 71 of file MatrixFunction.cpp.

                                          {
  return getDiffMatImpl<FTensor::PackPtr<double *, 1>, 3>(t_val, t_vec, f, d_f,
                                                          nb);
}

getDiffMatImpl()

template<typename T , int Dim>

FTensor::Ddg<double, Dim, Dim> EigenMatrix::getDiffMatImpl	(	Val< T, Dim > &	t_val,
		Vec< T, Dim > &	t_vec,
		Fun< double >	f,
		Fun< double >	d_f,
		const int	nb
	)

Definition at line 17 of file MatrixFunction.cpp.

                                                                             {
  switch (nb) {
  case 1:
    return EigenMatrixImp<T, T, 1, Dim>(t_val, t_vec).getDiffMat(f, d_f);
  case 2:
    return EigenMatrixImp<T, T, 2, Dim>(t_val, t_vec).getDiffMat(f, d_f);
  case 3:
    break;
  default:
    THROW_MESSAGE("third parameter should be 1,2 or 3");
  }
  return EigenMatrixImp<T, T, 3, Dim>(t_val, t_vec).getDiffMat(f, d_f);
};

getMat() [1/3]

FTensor::Tensor2_symmetric< double, 2 > EigenMatrix::getMat	(	Val< double, 2 > &	t_val,
		Vec< double, 2 > &	t_vec,
		Fun< double >	f
	)

Get the Mat object.

\[ \mathbf{B} = f(\mathbf{A}) \]

\[ B_{ij} = \sum_{a}^d f(\lambda^a) n^a_i n^a_j \]

where \(a\) is eigen value number.

Parameters

t_val	eigen values
t_vec	eigen vector
f	function

Returns

FTensor::Tensor2_symmetric<double, 3>

Definition at line 115 of file MatrixFunction.cpp.

                                                            {
  return getMatImpl<double, 2>(t_val, t_vec, f);
}

getMat() [2/3]

FTensor::Tensor2_symmetric< double, 3 > EigenMatrix::getMat	(	Val< double, 3 > &	t_val,
		Vec< double, 3 > &	t_vec,
		Fun< double >	f
	)

Get the Mat object.

\[ \mathbf{B} = f(\mathbf{A}) \]

\[ B_{ij} = \sum_{a}^d f(\lambda^a) n^a_i n^a_j \]

where \(a\) is eigen value number.

Parameters

t_val	eigen values
t_vec	eigen vector
f	function

Returns

FTensor::Tensor2_symmetric<double, 3>

Examples

EshelbianOperators.cpp, HenckyOps.hpp, and matrix_function.cpp.

Definition at line 53 of file MatrixFunction.cpp.

                                                                                   {
  return getMatImpl<double, 3>(t_val, t_vec, f);
}

getMat() [3/3]

FTensor::Tensor2_symmetric< double, 3 > EigenMatrix::getMat	(	Val< FTensor::PackPtr< double *, 1 >, 3 > &	t_val,
		Vec< FTensor::PackPtr< double *, 1 >, 3 > &	t_vec,
		Fun< double >	f
	)

Get the Mat object.

\[ \mathbf{B} = f(\mathbf{A}) \]

\[ B_{ij} = \sum_{a}^d f(\lambda^a) n^a_i n^a_j \]

where \(a\) is eigen value number.

Parameters

t_val	eigen values
t_vec	eigen vector
f	function

Returns

FTensor::Tensor2_symmetric<double, 3>

Definition at line 59 of file MatrixFunction.cpp.

                                                                  {
  return getMatImpl<FTensor::PackPtr<double *, 1>, 3>(t_val, t_vec, f);
}

getMatImpl()

template<typename T , int Dim>

FTensor::Tensor2_symmetric<double, Dim> EigenMatrix::getMatImpl	(	Val< T, Dim > &	t_val,
		Vec< T, Dim > &	t_vec,
		Fun< double >	f
	)

Definition at line 12 of file MatrixFunction.cpp.

                                                                  {
  return EigenMatrixImp<T, T, 3, Dim>(t_val, t_vec).getMat(f);
}