Class container for the system of implicit ODEs/DAEs. More...

#include <Implicit.hxx>

Inherited by Sandals::Explicit< N, 0 >, and Sandals::Explicit< N, M >.

Public Types
using	Type = enum class Type : Integer {IMPLICIT=0, EXPLICIT=1, SEMIEXPLICIT=1}

using	Pointer = std::shared_ptr<Implicit<N, M>>

using	VectorF = Eigen::Vector<Real, N>

using	MatrixJF = Eigen::Matrix<Real, N, N>

using	VectorH = Eigen::Vector<Real, M>

using	MatrixJH = Eigen::Matrix<Real, M, N>

Public Member Functions
	Implicit ()

	Implicit (std::string t_name)

virtual	~Implicit ()

Type	type () const

bool	is_implicit () const

bool	is_explicit () const

bool	is_semiexplicit () const

std::string &	name ()

std::string const &	name () const

Integer	equations_number () const

Integer	invariants_number () const

virtual VectorF	F (VectorF const &x, VectorF const &x_dot, Real t) const =0

virtual MatrixJF	JF_x (VectorF const &x, VectorF const &x_dot, Real t) const =0

virtual MatrixJF	JF_x_dot (VectorF const &x, VectorF const &x_dot, Real t) const =0

virtual VectorH	h (VectorF const &x, Real t) const =0

virtual MatrixJH	Jh_x (VectorF const &x, Real t) const =0

virtual bool	in_domain (VectorF const &x, Real t) const =0

VectorF	F_reverse (VectorF const &x, VectorF const &x_dot, Real t) const

MatrixJF	JF_x_reverse (VectorF const &x, VectorF const &x_dot, Real t) const

MatrixJF	JF_x_dot_reverse (VectorF const &x, VectorF const &x_dot, Real t) const

Protected Member Functions
	Implicit (Type t_type, std::string t_name)

Private Attributes
Type	m_type {Type::IMPLICIT}

std::string	m_name

Detailed Description

template<Integer N, Integer M>
class Sandals::Implicit< N, M >

Class container for the system of inplicit ordinary differential equations (ODEs) or differential algebraic equations (DAEs) of the type \( \mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t) = \mathbf{0} \), with invariants manifold \( \mathbf{h}(\mathbf{x}, t) = \mathbf{0} \).

Template Parameters

N	The dimension of the implicit ODE system.
M	The dimension of the invariants manifold.

Member Typedef Documentation

◆ MatrixJF

template<Integer N, Integer M>

using Sandals::Implicit< N, M >::MatrixJF = Eigen::Matrix<Real, N, N>

Templetized matrix type.

◆ MatrixJH

template<Integer N, Integer M>

using Sandals::Implicit< N, M >::MatrixJH = Eigen::Matrix<Real, M, N>

Templetized matrix type.

◆ Pointer

template<Integer N, Integer M>

using Sandals::Implicit< N, M >::Pointer = std::shared_ptr<Implicit<N, M>>

Shared pointer to an implicit ODE system.

◆ Type

template<Integer N, Integer M>

using Sandals::Implicit< N, M >::Type = enum class Type : Integer {IMPLICIT=0, EXPLICIT=1, SEMIEXPLICIT=1}

System type enumeration.

◆ VectorF

template<Integer N, Integer M>

using Sandals::Implicit< N, M >::VectorF = Eigen::Vector<Real, N>

Templetized vector type.

◆ VectorH

template<Integer N, Integer M>

using Sandals::Implicit< N, M >::VectorH = Eigen::Vector<Real, M>

Templetized vector type.

Constructor & Destructor Documentation

◆ Implicit() [1/3]

template<Integer N, Integer M>

Sandals::Implicit< N, M >::Implicit	(	Type	t_type,
		std::string	t_name )

inlineprotected

Class constructor for an implicit ODE/DAE system.

Parameters

[in]	t_type	The type of the implicit ODE/DAE system.
[in]	t_name	The name of the implicit ODE/DAE system.

◆ Implicit() [2/3]

template<Integer N, Integer M>

Sandals::Implicit< N, M >::Implicit ( )

inline

Class constructor for an implicit ODE/DAE system.

◆ Implicit() [3/3]

template<Integer N, Integer M>

Sandals::Implicit< N, M >::Implicit ( std::string t_name )

inline

Class constructor for an implicit ODE/DAE system.

Parameters

[in] t_name The name of the implicit ODE/DAE system.

◆ ~Implicit()

template<Integer N, Integer M>

virtual Sandals::Implicit< N, M >::~Implicit ( )

inlinevirtual

Class destructor for an implicit ODE/DAE system.

Member Function Documentation

◆ equations_number()

template<Integer N, Integer M>

Integer Sandals::Implicit< N, M >::equations_number ( ) const

inline

Get the number of equations of the ODE/DAE system.

Returns: The number of equations of the ODE/DAE system.

◆ F()

template<Integer N, Integer M>

virtual VectorF Sandals::Implicit< N, M >::F	(	VectorF const &	x,
		VectorF const &	x_dot,
		Real	t ) const

pure virtual

Evaluate the ODE/DAE system \( \mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t) \).

Parameters

[in]	x	States \( \mathbf{x} \).
[in]	x_dot	States derivative \( \mathbf{x}^{\prime} \).
[in]	t	Independent variable (or time) \( t \).

Returns: The system function \( \mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t) \).

Implemented in Sandals::Explicit< N, M >, Sandals::Explicit< N, 0 >, Sandals::Linear< N, M >, and Sandals::SemiExplicit< N, M >.

◆ F_reverse()

template<Integer N, Integer M>

VectorF Sandals::Implicit< N, M >::F_reverse	(	VectorF const &	x,
		VectorF const &	x_dot,
		Real	t ) const

inline

Time reversal of the implicit ODE system function \( \mathbf{F}(\mathbf{x}, \mathbf{x}^{ \prime}, t) = -\mathbf{F}(\mathbf{x}, -\mathbf{x}^{\prime}, -t) \).

Parameters

[in]	x	States \( \mathbf{x} \).
[in]	x_dot	States derivative \( \mathbf{x}^{\prime} \).
[in]	t	Independent variable (or time) \( t \).

Returns: The time-reversed system function \( \mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, -t) \).

◆ h()

template<Integer N, Integer M>

virtual VectorH Sandals::Implicit< N, M >::h	(	VectorF const &	x,
		Real	t ) const

pure virtual

Evaluate the ODE/DAE system invariants \( \mathbf{h}(\mathbf{x}, t) \).

Parameters

[in]	x	States \( \mathbf{x} \).
[in]	t	Independent variable (or time) \( t \).

Returns: The system invariants \( \mathbf{h}(\mathbf{x}, t) \).

◆ in_domain()

template<Integer N, Integer M>

virtual bool Sandals::Implicit< N, M >::in_domain	(	VectorF const &	x,
		Real	t ) const

pure virtual

Return true if the values \( \mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t) \) is in the domain of the ODE/DAE system.

Parameters

[in]	x	States \( \mathbf{x} \).
[in]	t	Independent variable (or time) \( t \).

Returns: True if \( \mathbf{F}(\mathbf{x}, t) \) is in the domain of the ODE/DAE system.

◆ invariants_number()

template<Integer N, Integer M>

Integer Sandals::Implicit< N, M >::invariants_number ( ) const

inline

Get the number of invariants of the ODE/DAE system.

Returns: The number of invariants of the ODE/DAE system.

◆ is_explicit()

template<Integer N, Integer M>

bool Sandals::Implicit< N, M >::is_explicit ( ) const

inline

Check if the ODE/DAE system is explicit.

Returns: True if the ODE/DAE system is explicit, false otherwise.

◆ is_implicit()

template<Integer N, Integer M>

bool Sandals::Implicit< N, M >::is_implicit ( ) const

inline

Check if the ODE/DAE system is implicit.

Returns: True if the ODE/DAE system is implicit, false otherwise.

◆ is_semiexplicit()

template<Integer N, Integer M>

bool Sandals::Implicit< N, M >::is_semiexplicit ( ) const

inline

Check if the ODE/DAE system is semi-explicit.

Returns: True if the ODE/DAE system is semi-explicit, false otherwise.

◆ JF_x()

template<Integer N, Integer M>

virtual MatrixJF Sandals::Implicit< N, M >::JF_x	(	VectorF const &	x,
		VectorF const &	x_dot,
		Real	t ) const

pure virtual

Evaluate the Jacobian of the ODE/DAE system function \( \mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t) \) with respect to the states \( \mathbf{x} \)

\[\mathbf{JF}_{\mathbf{x}}(\mathbf{x}, \mathbf{x}^{\prime}, t) = \displaystyle\frac{ \partial\mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t)}{\partial\mathbf{x}} \text{.} \]

Parameters

[in]	x	States \( \mathbf{x} \).
[in]	x_dot	States derivative \( \mathbf{x}^{\prime} \).
[in]	t	Independent variable (or time) \( t \).

Returns: The Jacobian \( \mathbf{JF}_{\mathbf{x}}(\mathbf{x}, \mathbf{x}^{\prime}, t) \).

Implemented in Sandals::Explicit< N, M >, Sandals::Explicit< N, 0 >, Sandals::Linear< N, M >, and Sandals::SemiExplicit< N, M >.

◆ JF_x_dot()

template<Integer N, Integer M>

virtual MatrixJF Sandals::Implicit< N, M >::JF_x_dot	(	VectorF const &	x,
		VectorF const &	x_dot,
		Real	t ) const

pure virtual

Evaluate the Jacobian of the ODE/DAE system function \( \mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t) \) with respect to the states derivative \( \mathbf{x}^{\prime} \)

\[\mathbf{JF}_{\mathbf{x}^{\prime}}(\mathbf{x}, \mathbf{x}^{\prime}, t) = \displaystyle \frac{\partial\mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t)}{\partial\mathbf{x}^{\prime}} \text{.} \]

Parameters

[in]	x	States \( \mathbf{x} \).
[in]	x_dot	States derivative \( \mathbf{x}^{\prime} \).
[in]	t	Independent variable (or time) \( t \).

Returns: The Jacobian \( \mathbf{JF}_{\mathbf{x}^{\prime}}(\mathbf{x}, \mathbf{x}^{\prime}, t) \).

Implemented in Sandals::Explicit< N, M >, Sandals::Explicit< N, 0 >, Sandals::Linear< N, M >, and Sandals::SemiExplicit< N, M >.

◆ JF_x_dot_reverse()

template<Integer N, Integer M>

MatrixJF Sandals::Implicit< N, M >::JF_x_dot_reverse	(	VectorF const &	x,
		VectorF const &	x_dot,
		Real	t ) const

inline

Time reversal of the Jacobian of the implicit ODE system function \( \mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t) \) with respect to the states derivative \( \mathbf{x}^{\prime} = -\mathbf{JF}_{\mathbf{x}^{\prime}}(\mathbf{x}, -\mathbf{x}^{\prime}, -t) \).

Parameters

[in]	x	States \( \mathbf{x} \).
[in]	x_dot	States derivative \( \mathbf{x}^{\prime} \).
[in]	t	Independent variable (or time) \( t \).

Returns: The time-reversed Jacobian \( \mathbf{JF}_{\mathbf{x}^{\prime}}(\mathbf{x}, -\mathbf{x}^{ \prime}, -t) \).

◆ JF_x_reverse()

template<Integer N, Integer M>

MatrixJF Sandals::Implicit< N, M >::JF_x_reverse	(	VectorF const &	x,
		VectorF const &	x_dot,
		Real	t ) const

inline

Time reversal of the Jacobian of the implicit ODE system function \( \mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t) \) with respect to the states \( \mathbf{x} = -\mathbf{JF}_{\mathbf{x}} (\mathbf{x}, -\mathbf{x}^{\prime}, -t) \).

Parameters

[in]	x	States \( \mathbf{x} \).
[in]	x_dot	States derivative \( \mathbf{x}^{\prime} \).
[in]	t	Independent variable (or time) \( t \).

Returns: The time-reversed Jacobian \( \mathbf{JF}_{\mathbf{x}}(\mathbf{x}, -\mathbf{x}^{\prime}, -t) \).

◆ Jh_x()

template<Integer N, Integer M>

virtual MatrixJH Sandals::Implicit< N, M >::Jh_x	(	VectorF const &	x,
		Real	t ) const

pure virtual

Evaluate the Jacobian of the ODE/DAE system invariants \( \mathbf{h}(\mathbf{x}, t) \) with respect to the states \( \mathbf{x} \)

\[\mathbf{Jh}_{\mathbf{x}}(\mathbf{x} t) = \displaystyle\frac{\partial\mathbf{h}(\mathbf{x}, t)}{\partial\mathbf{x}} \text{.} \]

Parameters

[in]	x	States \( \mathbf{x} \).
[in]	t	Independent variable (or time) \( t \).

Returns: The Jacobian \( \mathbf{Jh}_{\mathbf{x}}(\mathbf{x}, \mathbf{x}^{\prime}, t) \).

◆ name() [1/2]

template<Integer N, Integer M>

std::string & Sandals::Implicit< N, M >::name ( )

inline

Get the ODE/DAE system name reference.

Returns: The ODE/DAE system name reference.

◆ name() [2/2]

template<Integer N, Integer M>

std::string const & Sandals::Implicit< N, M >::name ( ) const

inline

Get the ODE/DAE system name const reference.

Returns: The ODE/DAE system name const reference.

◆ type()

template<Integer N, Integer M>

Type Sandals::Implicit< N, M >::type ( ) const

inline

Get the enumeration type of the ODE/DAE system.

Returns: The enumeration type of the ODE/DAE system.

Member Data Documentation

◆ m_name

template<Integer N, Integer M>

std::string Sandals::Implicit< N, M >::m_name

private

Name of the ODE/DAE system.

◆ m_type

template<Integer N, Integer M>

Type Sandals::Implicit< N, M >::m_type {Type::IMPLICIT}

private

ODE/DAE system type.

The documentation for this class was generated from the following file:

include/Sandals/System/Implicit.hxx

Public Types

Public Member Functions

Protected Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ MatrixJF

◆ MatrixJH

◆ Pointer

◆ Type

◆ VectorF

◆ VectorH

Constructor & Destructor Documentation

◆ Implicit() [1/3]

◆ Implicit() [2/3]

◆ Implicit() [3/3]

◆ ~Implicit()

Member Function Documentation

◆ equations_number()

◆ F()

◆ F_reverse()

◆ h()

◆ in_domain()

◆ invariants_number()

◆ is_explicit()

◆ is_implicit()

◆ is_semiexplicit()

◆ JF_x()

◆ JF_x_dot()

◆ JF_x_dot_reverse()

◆ JF_x_reverse()

◆ Jh_x()

◆ name() [1/2]

◆ name() [2/2]

◆ type()

Member Data Documentation

◆ m_name

◆ m_type