|
| using | Pointer = std::shared_ptr<SemiExplicit<Real, N, M>> |
| using | VectorF = typename Explicit<Real, N, M>::VectorF |
| using | MatrixJF = typename Explicit<Real, N, M>::MatrixJF |
| using | MatrixE = typename Explicit<Real, N, M>::MatrixJF |
| using | MatrixA = typename Explicit<Real, N, M>::MatrixJF |
| using | VectorB = typename Explicit<Real, N, M>::VectorF |
| using | Type = typename Explicit<Real, N, M>::Type |
| Public Types inherited from Sandals::Explicit< Real, N, 0 > |
| using | Pointer |
| using | VectorF |
| using | MatrixJF |
| using | Type |
| Public Types inherited from Sandals::Implicit< Real, N, M > |
| using | Type |
| using | Pointer |
| using | VectorF |
| using | MatrixJF |
| using | VectorH |
| using | MatrixJH |
|
| | 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< Real, N, 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< Real, N, M > |
| virtual | ~Implicit () |
| Type | type () const |
| bool | is_implicit () const |
| bool | is_explicit () const |
| bool | is_semiexplicit () const |
| std::string & | name () |
| 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 |
template<typename Real,
Integer N,
Integer M = 0>
class Sandals::Linear< Real, 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
-
| Real | The scalar number type. |
| N | The dimension of the semi-explicit ODE system. |
| M | The dimension of the invariants manifold. |
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< 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 \( \mathbf{x} \)
\[\mathbf{JF}_{\mathbf{x}}(\mathbf{x}, \mathbf{x}^{\prime}, t) =
\displaystyle\frac{\partial\mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t)}{\partial\mathbf{x}} =
-\mathbf{A}(t) \text{.}
\]
- 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< Real, N, 0 >.
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< 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 \( \mathbf{x}^{\prime} \)
\[\mathbf{JF}_{\mathbf{x}^{\prime}}(\mathbf{x}, \mathbf{x}^{\prime}, t) = \displaystyle
\frac{\partial\mathbf{F}(\mathbf{x}, \mathbf{x}^{\prime}, t)}{\partial\mathbf{x}^{\prime}} =
\mathbf{E}(t) \text{.}
\]
- 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< Real, N, 0 >.
1.14.0