Sandals::SemiExplicit< N, M > Class Template Reference

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

#include <SemiExplicit.hxx>

Inherits Sandals::Explicit< N, 0 >.

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	MatrixA = typename Explicit<N, M>::MatrixJF
using	TensorTA = typename std::vector<MatrixJF>
using	VectorB = typename Explicit<N, M>::VectorF
using	MatrixJB = typename Explicit<N, M>::MatrixJF
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
	SemiExplicit ()
	SemiExplicit (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 &x_dot, Real t) const override
MatrixJF	JF_x_dot (VectorF const &x, VectorF const &, Real t) const override
VectorF	f (VectorF const &x, Real t) const override
MatrixJF	Jf_x (VectorF const &x, VectorF const &x_dot, Real t) const
MatrixJF	Jf_x (VectorF const &x, Real t) const override
virtual MatrixA	A (VectorF const &x, Real t) const =0
virtual TensorTA	TA_x (VectorF const &x, Real t) const =0
virtual VectorB	b (VectorF const &x, Real t) const =0
virtual MatrixJB	Jb_x (VectorF const &x, 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< MatrixA >	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::SemiExplicit< N, M >

Class container for the system of semi-explicit ordinary differential equations (ODEs) or differential algebraic equations (DAEs)of the type \( \mathbf{A}(\mathbf{x}, t) \mathbf{x}^{\prime} = \mathbf{b}(\mathbf{x}, t) \), 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::SemiExplicit< N, M >::MatrixA = typename Explicit<N, M>::MatrixJF

Templetized matrix type.

MatrixJB

template<Integer N, Integer M = 0>

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

Templetized vector type.

MatrixJF

template<Integer N, Integer M = 0>

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

Templetized matrix type.

Pointer

template<Integer N, Integer M = 0>

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

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

TensorTA

template<Integer N, Integer M = 0>

using Sandals::SemiExplicit< N, M >::TensorTA = typename std::vector<MatrixJF>

Templetized matrix type.

Type

template<Integer N, Integer M = 0>

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

System type enumeration.

VectorB

template<Integer N, Integer M = 0>

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

Templetized vector type.

VectorF

template<Integer N, Integer M = 0>

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

Templetized vector type.

Constructor & Destructor Documentation

SemiExplicit() [1/2]

template<Integer N, Integer M = 0>

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

inline

Class constructor for the semi-explicit ODE/DAE system.

SemiExplicit() [2/2]

template<Integer N, Integer M = 0>

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

inline

Class constructor for the semi-explicit ODE/DAE system.

Parameters

[in]

t_name

The name of the semi-explicit ODE/DAE system.

Member Function Documentation

A()

template<Integer N, Integer M = 0>

virtual MatrixA Sandals::SemiExplicit< N, M >::A ( VectorF const & x, Real t ) const

pure virtual

Evaluate the semi-explicit ODE/DAE system mass matrix \( \mathbf{A}(\mathbf{x}, t) \).

Parameters

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

Returns

The system function \( \mathbf{A}(\mathbf{x}, t) \).

b()

template<Integer N, Integer M = 0>

virtual VectorB Sandals::SemiExplicit< N, M >::b ( VectorF const & x, Real t ) const

pure virtual

Evaluate the semi-explicit ODE/DAE system right-hand-side function \( \mathbf{b}(\mathbf{x}, t) \).

Parameters

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

Returns

The system function \( \mathbf{b}(\mathbf{x}, t) \).

F()

template<Integer N, Integer M = 0>

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

inlineoverridevirtual

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

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

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

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

f()

template<Integer N, Integer M = 0>

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

inlineoverridevirtual

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

\[\mathbf{f}(\mathbf{x}, t) = \mathbf{A}(\mathbf{x}, t)^{-1} \mathbf{b}(\mathbf{x}, t) \text{.} \]

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 >.

Jb_x()

template<Integer N, Integer M = 0>

virtual MatrixJB Sandals::SemiExplicit< N, M >::Jb_x ( VectorF const & x, Real t ) const

pure virtual

Evaluate the Jacobian of the semi-explicit ODE/DAE system right-hand-side function \( \mathbf{b} (\mathbf{x}, t) \) with respect to the states \( \mathbf{x} \)

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

Parameters

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

Returns

The Jacobian \( \mathbf{Jb}_{\mathbf{x}}(\mathbf{x}, t) \).

JF_x()

template<Integer N, Integer M = 0>

MatrixJF Sandals::SemiExplicit< N, M >::JF_x ( VectorF const & x, VectorF const & x_dot, 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 \( \mathbf{x} \)

\[\mathbf{JF}_{\mathbf{x}}(\mathbf{x}, \mathbf{x}^{\prime}, t) = \displaystyle\frac{\partial\mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t)}{\partial\mathbf{x}} = -\displaystyle\frac{\partial\mathbf{f}(\mathbf{x}, \mathbf{x}^{\prime}, t)}{\partial\mathbf{x}} = -\mathbf{Jf}_{\mathbf{x}}(\mathbf{x}, t) = -\mathbf{A}(\mathbf{x}, t)^{-1}(\mathbf{Jb}_{ \mathbf{x}}(\mathbf{x}, t) - \mathbf{TA}_{\mathbf{x}}(\mathbf{x}, t) \mathbf{x}^\prime) \text{.} \]

Parameters

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

Returns

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

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

Jf_x() [1/2]

template<Integer N, Integer M = 0>

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

inlineoverridevirtual

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

\[\mathbf{Jf}_{\mathbf{x}}(\mathbf{x}, t) = \displaystyle\frac{\partial\mathbf{f}( \mathbf{x}, t)}{\partial\mathbf{x}} = \mathbf{A}(\mathbf{x}, t)^{-1}( \mathbf{Jb}_{\mathbf{x}} (\mathbf{x}, t) - \mathbf{TA}_{\mathbf{x}}(\mathbf{x}, t) \mathbf{f}(\mathbf{x}, t)) \text{.} \]

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() [2/2]

template<Integer N, Integer M = 0>

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

inline

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

\[\mathbf{Jf}_{\mathbf{x}}(\mathbf{x}, \mathbf{x}^\prime, t) = \displaystyle\frac{\partial \mathbf{f}(\mathbf{x}, t)}{\partial\mathbf{x}} = \mathbf{A}(\mathbf{x}, t)^{-1}(\mathbf{Jb}_{ \mathbf{x}}(\mathbf{x}, t) - \mathbf{TA}_{\mathbf{x}}(\mathbf{x}, t) \mathbf{x}^\prime) \text{.} \]

Parameters

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

Returns

The Jacobian \( \mathbf{Jf}_{\mathbf{x}}(\mathbf{x}, \mathbf{x}^\prime, t) \).

JF_x_dot()

template<Integer N, Integer M = 0>

MatrixJF Sandals::SemiExplicit< N, M >::JF_x_dot ( VectorF const & x, 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 \( \mathbf{x}^{\prime} \)

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

Parameters

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

Returns

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

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

TA_x()

template<Integer N, Integer M = 0>

virtual TensorTA Sandals::SemiExplicit< N, M >::TA_x ( VectorF const & x, Real t ) const

pure virtual

Evaluate the tensor of the semi-explicit ODE/DAE system mass matrix \( \mathbf{A}(\mathbf{x}, t) \) with respect to the states \( \mathbf{x} \)

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

Parameters

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

Returns

The Jacobian \( \mathbf{TA}_{\mathbf{x}}(\mathbf{x}, t) \).

Member Data Documentation

m_lu

template<Integer N, Integer M = 0>

Eigen::FullPivLU<MatrixA> Sandals::SemiExplicit< N, M >::m_lu

mutableprivate

LU decomposition.

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

• include/Sandals/System/SemiExplicit.hxx