|
| | 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 |
template<typename Real,
Integer N,
Integer M = 0>
class Sandals::Implicit< Real, N, M >
Class container for the system of implicit 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
-
| Real | The scalar number type. |
| N | The dimension of the implicit ODE system. |
| M | The dimension of the invariants manifold. |
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< Real, N, M >, Sandals::Explicit< Real, N, 0 >, Sandals::Explicit< Real, N, M >, Sandals::ImplicitWrapper< Real, N, M >, Sandals::Linear< Real, N, M >, Sandals::Linear< Real, N, 0 >, Sandals::SemiExplicit< Real, N, M >, and Sandals::SemiExplicit< Real, N, 0 >.
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.
Implemented in Sandals::ExplicitWrapper< Real, N, M >, Sandals::ImplicitWrapper< Real, N, M >, Sandals::LinearWrapper< Real, N, M >, and Sandals::SemiExplicitWrapper< Real, N, M >.
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< Real, N, M >, Sandals::Explicit< Real, N, 0 >, Sandals::Explicit< Real, N, M >, Sandals::ImplicitWrapper< Real, N, M >, Sandals::Linear< Real, N, M >, Sandals::Linear< Real, N, 0 >, Sandals::SemiExplicit< Real, N, M >, and Sandals::SemiExplicit< Real, N, 0 >.
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< Real, N, M >, Sandals::Explicit< Real, N, 0 >, Sandals::Explicit< Real, N, M >, Sandals::ImplicitWrapper< Real, N, M >, Sandals::Linear< Real, N, M >, Sandals::Linear< Real, N, 0 >, Sandals::SemiExplicit< Real, N, M >, and Sandals::SemiExplicit< Real, N, 0 >.
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 \( \mathbf{Jh}_{\mathbf{x}}(\mathbf{x}, t) \).
Implemented in Sandals::ExplicitWrapper< Real, N, M >, Sandals::ImplicitWrapper< Real, N, M >, Sandals::LinearWrapper< Real, N, M >, and Sandals::SemiExplicitWrapper< Real, N, M >.
1.14.0