Class container for the system of explicit ODEs. More...

#include <Explicit.hxx>

Public Types
using	Pointer = std::shared_ptr<Explicit<N, M>>

using	VectorF = typename Implicit<N, M>::VectorF

using	MatrixJF = typename Implicit<N, M>::MatrixJF

using	Type = typename Implicit<N, M>::Type

Public Types inherited from Sandals::Implicit< N, M >
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
	Explicit ()

	Explicit (std::string t_name)

VectorF	F (VectorF const &x, VectorF const &x_dot, Real t) const override

MatrixJF	JF_x (VectorF const &x, VectorF const &, Real t) const override

MatrixJF	JF_x_dot (VectorF const &, VectorF const &, Real) const override

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

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

VectorF	f_reverse (VectorF const &x, Real t) const

MatrixJF	Jf_x_reverse (VectorF const &x, Real t) const

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

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

MatrixJF	JF_x_dot_reverse (VectorF const &, VectorF const &, Real) const

Public Member Functions inherited from Sandals::Implicit< N, M >
	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 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
	Explicit (Type t_type, std::string t_name)

Protected Member Functions inherited from Sandals::Implicit< N, M >
	Implicit (Type t_type, std::string t_name)

Detailed Description

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

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

Template Parameters

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

Member Typedef Documentation

◆ MatrixJF

template<Integer N, Integer M>

using Sandals::Explicit< N, M >::MatrixJF = typename Implicit<N, M>::MatrixJF

Templetized matrix type.

◆ Pointer

template<Integer N, Integer M>

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

Shared pointer to an explicit ODE system.

◆ Type

template<Integer N, Integer M>

using Sandals::Explicit< N, M >::Type = typename Implicit<N, M>::Type

System type enumeration.

◆ VectorF

template<Integer N, Integer M>

using Sandals::Explicit< N, M >::VectorF = typename Implicit<N, M>::VectorF

Templetized vector type.

Constructor & Destructor Documentation

◆ Explicit() [1/3]

template<Integer N, Integer M>

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

inlineprotected

Class constructor for an explicit ODE/DAE system.

Parameters

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

◆ Explicit() [2/3]

template<Integer N, Integer M>

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

inline

Class constructor for the explicit ODE system.

◆ Explicit() [3/3]

template<Integer N, Integer M>

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

inline

Class constructor for the explicit ODE system.

Parameters

[in] t_name The name of the explicit ODE system.

Member Function Documentation

◆ F()

template<Integer N, Integer M>

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

inlineoverridevirtual

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

\[\mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t) = \mathbf{x}^{\prime} - \mathbf{f}(\mathbf{x}, t) \text{.} \]

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 \( \mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t) \).

Implements Sandals::Implicit< N, M >.

Reimplemented in Sandals::Linear< N, M >, and Sandals::SemiExplicit< N, M >.

◆ f()

template<Integer N, Integer M>

virtual VectorF Sandals::Explicit< N, M >::f	(	VectorF const &	x,
		Real	t ) const

pure virtual

Evaluate the explicit ODE system function \( \mathbf{f}(\mathbf{x}, t) \).

Parameters

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

Returns: The system function \( \mathbf{f}(\mathbf{x}, t) \).

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

◆ F_reverse()

template<Integer N, Integer M>

VectorF Sandals::Explicit< 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 \( \mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, -t) \).

◆ f_reverse()

template<Integer N, Integer M>

VectorF Sandals::Explicit< N, M >::f_reverse	(	VectorF const &	x,
		Real	t ) const

inline

Time reversal of the explicit ODE system function \( \mathbf{f}(\mathbf{x}, t) = -\mathbf{f}( \mathbf{x}, -t) \).

Parameters

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

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

◆ JF_x()

template<Integer N, Integer M>

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

inlineoverridevirtual

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

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

Parameters

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

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

Implements Sandals::Implicit< N, M >.

Reimplemented in Sandals::Linear< N, M >, and Sandals::SemiExplicit< N, M >.

◆ Jf_x()

template<Integer N, Integer M>

virtual MatrixJF Sandals::Explicit< N, M >::Jf_x	(	VectorF const &	x,
		Real	t ) const

pure virtual

Evaluate the Jacobian of the explicit ODE system function \( \mathbf{f}(\mathbf{x}, t) \) with respect to the states \( \mathbf{x} \)

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

Parameters

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

Returns: The Jacobian \( \mathbf{Jf}_{\mathbf{x}}(\mathbf{x}, t) \).

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

◆ JF_x_dot()

template<Integer N, Integer M>

MatrixJF Sandals::Explicit< N, M >::JF_x_dot	(	VectorF const &	,
		VectorF const &	,
		Real	) const

inlineoverridevirtual

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

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

Parameters

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

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

Implements Sandals::Implicit< N, M >.

Reimplemented in Sandals::Linear< N, M >, and Sandals::SemiExplicit< N, M >.

◆ JF_x_dot_reverse()

template<Integer N, Integer M>

MatrixJF Sandals::Explicit< N, M >::JF_x_dot_reverse	(	VectorF const &	,
		VectorF const &	,
		Real	) 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::Explicit< N, M >::JF_x_reverse	(	VectorF const &	x,
		VectorF const &	,
		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 \( \mathbf{JF}_{\mathbf{x}}(\mathbf{x}, -\mathbf{x}^{\prime}, -t) \).

◆ Jf_x_reverse()

template<Integer N, Integer M>

MatrixJF Sandals::Explicit< N, M >::Jf_x_reverse	(	VectorF const &	x,
		Real	t ) const

inline

Time reversal of the Jacobian of the explicit ODE system function \( \mathbf{f}(\mathbf{x}, t) \) with respect to the states \( \mathbf{x} = -\mathbf{Jf}_{\mathbf{x}}(\mathbf{x}, -t) \).

Parameters

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

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

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

include/Sandals/System/Explicit.hxx

Public Types

Public Member Functions

Protected Member Functions

Detailed Description

Member Typedef Documentation

◆ MatrixJF

◆ Pointer

◆ Type

◆ VectorF

Constructor & Destructor Documentation

◆ Explicit() [1/3]

◆ Explicit() [2/3]

◆ Explicit() [3/3]

Member Function Documentation

◆ F()

◆ f()

◆ F_reverse()

◆ f_reverse()

◆ JF_x()

◆ Jf_x()

◆ JF_x_dot()

◆ JF_x_dot_reverse()

◆ JF_x_reverse()

◆ Jf_x_reverse()