mm::RKExplicit< Scalar, num_stages > Class Template Reference

#include <RKExplicit_fwd.hpp>

Detailed Description

template<typename Scalar, int num_stages>
class mm::RKExplicit< Scalar, num_stages >

Class representing an explicit Runge-Kutta method.

Template Parameters

Scalar	type of scalars to use for calculations, e.g. double
num_stages	number of stages of the method

Usage example:

    std::function<Eigen::VectorXd(double, const Eigen::VectorXd&)> func =
            [](double, const Eigen::VectorXd& y) {
                return -y;
            };
    Eigen::VectorXd y0(1);
    y0 << 1.0;
    double tmax = 10.0;
    double dt = 0.1;
    auto integrator = integrators::Explicit::RK4().solve(func, 0.0, tmax, dt, y0);
    std::cout << integrator << std::endl;
    for (auto& step : integrator) {
        // You can use read write access to:
        step.value();
        step.time();
        // and check if this is the last step:
        step.is_last();
    }
 
    // Aditionally, one can iterate manually
    auto step = integrator.begin();
    while (step) {
        // do something with step
        ++step;
    }
    Eigen::VectorXd value = step.value();  // do something with value

Definition at line 32 of file RKExplicit_fwd.hpp.

Public Member Functions
	RKExplicit (const Eigen::Matrix< scalar_t, stages, 1 > &alpha, const Eigen::Matrix< scalar_t, stages, stages > &beta, const Eigen::Matrix< scalar_t, stages, 1 > &gamma)
	Construct a Runge-Kutta method with tableau \( \begin{array}{l|l} \alpha & \beta \\ \hline & \gamma^\mathsf{T} \end{array} \). More...
template<typename func_t >
Integrator< func_t >	solve (const func_t &func, scalar_t t0, scalar_t t_max, scalar_t dt, const Eigen::VectorXd &y0) const
	Returns a solver using this method. More...

Public Types
enum	{ stages = num_stages }
typedef Scalar	scalar_t
	Floating point type used in the computations. More...

Classes
class	Integrator
	Integrator class for RK methods. More...

Friends
template<typename Scalar2 , int num_steps2>
class	AdamsBashforth
	Implements Adams Bashforth multistep methods. More...
template<typename scalar_t , int stages>
std::ostream &	operator<< (std::ostream &os, const RKExplicit< scalar_t, stages > &)
	Output the method's tableau for debugging. More...

Private Member Functions
template<typename func_t >
Eigen::VectorXd	step (const func_t &func, scalar_t t, const Eigen::VectorXd &y, scalar_t dt) const
	Returns next value. More...

Private Attributes
Eigen::Matrix< scalar_t, stages, 1 >	alpha_
	Left row of the tableau. More...
Eigen::Matrix< scalar_t, stages, stages >	beta_
	Central matrix of the tableau. More...
Eigen::Matrix< scalar_t, stages, 1 >	gamma_
	Bottom row of the tableau. More...

Member Enumeration Documentation

anonymous enum

template<typename Scalar , int num_stages>

anonymous enum

Enumerator
stages	number of stages

Definition at line 35 of file RKExplicit_fwd.hpp.

Constructor & Destructor Documentation

RKExplicit()

template<typename Scalar , int num_stages>

mm::RKExplicit< Scalar, num_stages >::RKExplicit ( const Eigen::Matrix< scalar_t, stages, 1 > &  alpha, const Eigen::Matrix< scalar_t, stages, stages > &  beta, const Eigen::Matrix< scalar_t, stages, 1 > &  gamma  )

inline

Construct a Runge-Kutta method with tableau \( \begin{array}{l|l} \alpha & \beta \\ \hline & \gamma^\mathsf{T} \end{array} \).

Parameters

alpha	Vector of size stages.
beta	Matrix of size stages times stages. Only strictly lower triangular part is used.
gamma	Vector of size stages.

Definition at line 56 of file RKExplicit_fwd.hpp.

Member Function Documentation

solve()

template<typename Scalar , int num_stages>

template<typename func_t >

Integrator<func_t> mm::RKExplicit< Scalar, num_stages >::solve ( const func_t &  func, scalar_t  t0, scalar_t  t_max, scalar_t  dt, const Eigen::VectorXd &  y0  ) const

inline

Returns a solver using this method.

Parameters

func	Function to integrate.
t0	Start time.
t_max	End time.
dt	Time step.
y0	Initial value.

Warning

Last step might not finish exactly on t_max. The number of steps is calculated as std::ceil((t_max - t0)/dt).

Returns

A solver object.

Definition at line 204 of file RKExplicit_fwd.hpp.

step()

template<typename Scalar , int num_stages>

template<typename func_t >

Eigen::VectorXd mm::RKExplicit< Scalar, num_stages >::step ( const func_t &  func, scalar_t  t, const Eigen::VectorXd &  y, scalar_t  dt  ) const

inlineprivate

Returns next value.

Definition at line 212 of file RKExplicit_fwd.hpp.

Friends And Related Function Documentation

AdamsBashforth

template<typename Scalar , int num_stages>

template<typename Scalar2 , int num_steps2>

friend class AdamsBashforth

friend

Implements Adams Bashforth multistep methods.

Definition at line 230 of file RKExplicit_fwd.hpp.

operator<<

template<typename Scalar , int num_stages>

template<typename scalar_t , int stages>

std::ostream& operator<< ( std::ostream &  os, const RKExplicit< scalar_t, stages > &    )

friend

Output the method's tableau for debugging.

Member Data Documentation

alpha_

template<typename Scalar , int num_stages>

Eigen::Matrix<scalar_t, stages, 1> mm::RKExplicit< Scalar, num_stages >::alpha_

private

Left row of the tableau.

Definition at line 38 of file RKExplicit_fwd.hpp.

beta_

template<typename Scalar , int num_stages>

Eigen::Matrix<scalar_t, stages, stages> mm::RKExplicit< Scalar, num_stages >::beta_

private

Central matrix of the tableau.

Definition at line 39 of file RKExplicit_fwd.hpp.

gamma_

template<typename Scalar , int num_stages>

Eigen::Matrix<scalar_t, stages, 1> mm::RKExplicit< Scalar, num_stages >::gamma_

private

Bottom row of the tableau.

Definition at line 40 of file RKExplicit_fwd.hpp.

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

• include/medusa/bits/integrators/RKExplicit_fwd.hpp