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

#include <Linear.hxx>

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

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

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

using	MatrixE = typename Explicit<N, M>::MatrixJF

using	MatrixA = typename Explicit<N, M>::MatrixJF

using	VectorB = typename Explicit<N, M>::VectorF

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

Public Types inherited from Sandals::Explicit< N, 0 >
using	Pointer

using	VectorF

using	MatrixJF

using	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
	Linear ()

	Linear (std::string t_name)

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

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

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

VectorF	f (VectorF const &x, Real t) const override

MatrixJF	Jf_x (VectorF const &, Real t) const override

virtual MatrixE	E (Real t) const =0

virtual MatrixA	A (Real t) const =0

virtual VectorB	b (Real t) const =0

Public Member Functions inherited from Sandals::Explicit< N, 0 >
	Explicit ()

	Explicit (std::string t_name)

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

Private Attributes
Eigen::FullPivLU< MatrixE >	m_lu

Additional Inherited Members
Protected Member Functions inherited from Sandals::Explicit< N, 0 >
	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 = 0>
class Sandals::Linear< N, M >

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

Template Parameters

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

Member Typedef Documentation

◆ MatrixA

template<Integer N, Integer M = 0>

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

Templetized matrix type.

◆ MatrixE

template<Integer N, Integer M = 0>

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

Templetized matrix type.

◆ MatrixJF

template<Integer N, Integer M = 0>

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

Templetized matrix type.

◆ Pointer

template<Integer N, Integer M = 0>

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

Shared pointer to a semi-explicit ODE/DAE system.

◆ Type

template<Integer N, Integer M = 0>

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

System type enumeration.

◆ VectorB

template<Integer N, Integer M = 0>

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

Templetized vector type.

◆ VectorF

template<Integer N, Integer M = 0>

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

Templetized vector type.

Constructor & Destructor Documentation

◆ Linear() [1/2]

template<Integer N, Integer M = 0>

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

inline

Class constructor for the linear ODE/DAE system.

◆ Linear() [2/2]

template<Integer N, Integer M = 0>

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

inline

Class constructor for the linear ODE/DAE system.

Parameters

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

Member Function Documentation

◆ A()

template<Integer N, Integer M = 0>

virtual MatrixA Sandals::Linear< N, M >::A ( Real t ) const

pure virtual

Evaluate the linear ODE/DAE system matrix $\mathbf{A}(t)$ .

Parameters

[in] t Independent variable (or time) $t$ .

Returns: The system function $\mathbf{A}(t)$ .

◆ b()

template<Integer N, Integer M = 0>

virtual VectorB Sandals::Linear< N, M >::b ( Real t ) const

pure virtual

Evaluate the linear ODE/DAE system vector $\mathbf{b}(t)$ .

Parameters

[in] t Independent variable (or time) $t$ .

Returns: The system function $\mathbf{b}(t)$ .

◆ E()

template<Integer N, Integer M = 0>

virtual MatrixE Sandals::Linear< N, M >::E ( Real t ) const

pure virtual

Evaluate the linear ODE/DAE system mass matrix $\mathbf{E}(t)$ .

Parameters

[in] t Independent variable (or time) $t$ .

Returns: The system function $\mathbf{E}(t)$ .

◆ F()

template<Integer N, Integer M = 0>

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

inlineoverridevirtual

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

$\mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t) = \mathbf{E}(t) \mathbf{x}^{\prime} - \mathbf{A}(t) \mathbf{x} - \mathbf{b}(t)$

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

Reimplemented from Sandals::Explicit< N, 0 >.

◆ f()

template<Integer N, Integer M = 0>

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

inlineoverridevirtual

Evaluate the explicit ODE/DAE system function $\mathbf{f}(\mathbf{x}, t)$ as

$\mathbf{f}(\mathbf{x}, t) = \mathbf{E}(t)^{-1}(\mathbf{A}(t)\mathbf{x} + \mathbf{b}(t))$

Parameters

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

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

Implements Sandals::Explicit< N, 0 >.

◆ JF_x()

template<Integer N, Integer M = 0>

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

inlineoverridevirtual

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

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

Parameters

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

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

Reimplemented from Sandals::Explicit< N, 0 >.

◆ Jf_x()

template<Integer N, Integer M = 0>

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

inlineoverridevirtual

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

$\mathbf{Jf}_{\mathbf{x}}(\mathbf{x}, t) = \displaystyle\frac{\partial\mathbf{f}( \mathbf{x}, t)}{\partial\mathbf{x}} = \mathbf{E}(t)^{-1} \mathbf{A}(t) \text{.}$

Parameters

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

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

Implements Sandals::Explicit< N, 0 >.

◆ JF_x_dot()

template<Integer N, Integer M = 0>

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

inlineoverridevirtual

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

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

Parameters

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

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

Reimplemented from Sandals::Explicit< N, 0 >.

Member Data Documentation

◆ m_lu

template<Integer N, Integer M = 0>

Eigen::FullPivLU<MatrixE> Sandals::Linear< N, M >::m_lu

private

LU decomposition.

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

include/Sandals/System/Linear.hxx

Public Types

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ MatrixA

◆ MatrixE

◆ MatrixJF

◆ Pointer

◆ Type

◆ VectorB

◆ VectorF

Constructor & Destructor Documentation

◆ Linear() [1/2]

◆ Linear() [2/2]

Member Function Documentation

◆ A()

◆ b()

◆ E()

◆ F()

◆ f()

◆ JF_x()

◆ Jf_x()

◆ JF_x_dot()

Member Data Documentation

◆ m_lu