Drake
RungeKutta3Integrator< T > Class Template Referencefinal

A third-order Runge Kutta integrator with a third order error estimate. More...

#include <drake/systems/analysis/runge_kutta3_integrator.h>

Inheritance diagram for RungeKutta3Integrator< T >:
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Collaboration diagram for RungeKutta3Integrator< T >:
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## Public Member Functions

~RungeKutta3Integrator () override=default

RungeKutta3Integrator (const System< T > &system, Context< T > *context=nullptr)

bool supports_error_estimation () const override
The integrator supports error estimation. More...

int get_error_estimate_order () const override
This integrator provides third order error estimates. More...

Does not allow copy, move, or assignment
RungeKutta3Integrator (const RungeKutta3Integrator &)=delete

RungeKutta3Integratoroperator= (const RungeKutta3Integrator &)=delete

RungeKutta3Integrator (RungeKutta3Integrator &&)=delete

RungeKutta3Integratoroperator= (RungeKutta3Integrator &&)=delete

Public Member Functions inherited from IntegratorBase< T >
IntegratorBase (const System< T > &system, Context< T > *context=nullptr)
Maintains references to the system being integrated and the context used to specify the initial conditions for that system (if any). More...

virtual ~IntegratorBase ()=default
Destructor. More...

void set_fixed_step_mode (bool flag)
Sets an integrator with error control to fixed step mode. More...

bool get_fixed_step_mode () const
Gets whether an integrator is running in fixed step mode. More...

void set_target_accuracy (double accuracy)
Request that the integrator attempt to achieve a particular accuracy for the continuous portions of the simulation. More...

double get_target_accuracy () const
Gets the target accuracy. More...

double get_accuracy_in_use () const
Gets the accuracy in use by the integrator. More...

void set_maximum_step_size (const T &max_step_size)
Sets the maximum step size that may be taken by this integrator. More...

const T & get_maximum_step_size () const
Gets the maximum step size that may be taken by this integrator. More...

void Reset ()
Resets the integrator to initial values, i.e., default construction values. More...

void Initialize ()
An integrator must be initialized before being used. More...

void request_initial_step_size_target (const T &step_size)
Request that the first attempted integration step have a particular size. More...

const T & get_initial_step_size_target () const
Gets the target size of the first integration step. More...

StepResult IntegrateAtMost (const T &publish_dt, const T &update_dt, const T &boundary_dt)
Integrates the system forward in time by a single step with step size subject to integration error tolerances (assuming that the integrator supports error estimation). More...

double get_stretch_factor () const
Gets the stretch factor (> 1), which is multiplied by the maximum (typically user-designated) integration step size to obtain the amount that the integrator is able to stretch the maximum time step toward hitting an upcoming publish or update event in IntegrateAtMost(). More...

void IntegrateWithMultipleSteps (const T &dt)
Stepping function for integrators operating outside of Simulator that advances the continuous state exactly by dt. More...

void IntegrateWithSingleFixedStep (const T &dt)
Stepping function for integrators operating outside of Simulator that advances the continuous state exactly by dt and using a single fixed step. More...

const T & get_ideal_next_step_size () const
Return the step size the integrator would like to take next, based primarily on the integrator's accuracy prediction. More...

const Context< T > & get_context () const
Returns a const reference to the internally-maintained Context holding the most recent state in the trajectory. More...

Context< T > * get_mutable_context ()
Returns a mutable pointer to the internally-maintained Context holding the most recent state in the trajectory. More...

void reset_context (Context< T > *context)
Replace the pointer to the internally-maintained Context with a different one. More...

const System< T > & get_system () const
Gets a constant reference to the system that is being integrated (and was provided to the constructor of the integrator). More...

bool is_initialized () const
Indicates whether the integrator has been initialized. More...

const T & get_previous_integration_step_size () const
Gets the size of the last (previous) integration step. More...

const ContinuousState< T > * get_error_estimate () const
Gets the error estimate (used only for integrators that support error estimation). More...

IntegratorBase (const IntegratorBase &)=delete

IntegratorBaseoperator= (const IntegratorBase &)=delete

IntegratorBase (IntegratorBase &&)=delete

IntegratorBaseoperator= (IntegratorBase &&)=delete

void set_requested_minimum_step_size (const T &min_step_size)
Sets the requested minimum step size h_min that may be taken by this integrator. More...

const T & get_requested_minimum_step_size () const
Gets the requested minimum step size h_min for this integrator. More...

void set_throw_on_minimum_step_size_violation (bool throws)
Sets whether the integrator should throw a std::runtime_error exception when the integrator's step size selection algorithm determines that it must take a step smaller than the minimum step size (for, e.g., purposes of error control). More...

bool get_throw_on_minimum_step_size_violation () const
Reports the current setting of the throw_on_minimum_step_size_violation flag. More...

get_working_minimum_step_size () const
Gets the current value of the working minimum step size h_work(t) for this integrator, which may vary with the current time t as stored in the integrator's context. More...

void ResetStatistics ()
Forget accumulated statistics. More...

int64_t get_num_substep_failures () const
Gets the number of failed sub-steps (implying one or more step size reductions was required to permit solving the necessary nonlinear system of equations). More...

int64_t get_num_step_shrinkages_from_substep_failures () const
Gets the number of step size shrinkages due to sub-step failures (e.g., integrator convergence failures) since the last call to ResetStatistics() or Initialize(). More...

int64_t get_num_step_shrinkages_from_error_control () const
Gets the number of step size shrinkages due to failure to meet targeted error tolerances, since the last call to ResetStatistics or Initialize(). More...

int64_t get_num_derivative_evaluations () const
Returns the number of ODE function evaluations (calls to CalcTimeDerivatives()) since the last call to ResetStatistics() or Initialize(). More...

const T & get_actual_initial_step_size_taken () const
The actual size of the successful first step. More...

const T & get_smallest_adapted_step_size_taken () const
The size of the smallest step taken as the result of a controlled integration step adjustment since the last Initialize() or ResetStatistics() call. More...

const T & get_largest_step_size_taken () const
The size of the largest step taken since the last Initialize() or ResetStatistics() call. More...

int64_t get_num_steps_taken () const
The number of integration steps taken since the last Initialize() or ResetStatistics() call. More...

const Eigen::VectorXd & get_generalized_state_weight_vector () const
Gets the weighting vector (equivalent to a diagonal matrix) applied to weighting both generalized coordinate and velocity state variable errors, as described in the group documentation. More...

Eigen::VectorBlock< Eigen::VectorXd > get_mutable_generalized_state_weight_vector ()
Gets a mutable weighting vector (equivalent to a diagonal matrix) applied to weighting both generalized coordinate and velocity state variable errors, as described in the group documentation. More...

const Eigen::VectorXd & get_misc_state_weight_vector () const
Gets the weighting vector (equivalent to a diagonal matrix) for weighting errors in miscellaneous continuous state variables z. More...

Eigen::VectorBlock< Eigen::VectorXd > get_mutable_misc_state_weight_vector ()
Gets a mutable weighting vector (equivalent to a diagonal matrix) for weighting errors in miscellaneous continuous state variables z. More...

Public Types inherited from IntegratorBase< T >
enum  StepResult {
kReachedPublishTime = 1, kReachedZeroCrossing = 2, kReachedUpdateTime = 3, kTimeHasAdvanced = 4,
kReachedBoundaryTime = 5, kReachedStepLimit = 6
}
Status returned by StepOnceAtMost(). More...

Protected Member Functions inherited from IntegratorBase< T >
virtual void DoResetStatistics ()
Resets any statistics particular to a specific integrator. More...

void CalcTimeDerivatives (const Context< T > &context, ContinuousState< T > *dxdt)
Evaluates the derivative function (and updates call statistics). More...

template<typename U >
void CalcTimeDerivatives (const System< U > &system, const Context< U > &context, ContinuousState< U > *dxdt)
Evaluates the derivative function (and updates call statistics). More...

void set_accuracy_in_use (double accuracy)
Sets the working ("in use") accuracy for this integrator. More...

void InitializeAccuracy (double default_accuracy, double loosest_accuracy, double max_step_fraction)
Generic code for validating (and resetting, if need be) the integrator working accuracy for error controlled integrators. More...

bool StepOnceErrorControlledAtMost (const T &dt_max)
Default code for advancing the continuous state of the system by a single step of dt_max (or smaller, depending on error control). More...

CalcStateChangeNorm (const ContinuousState< T > &dx_state) const
Computes the infinity norm of a change in continuous state. More...

std::pair< bool, T > CalcAdjustedStepSize (const T &err, const T &attempted_step_size, bool *at_minimum_step_size) const
Calculates adjusted integrator step sizes toward keeping state variables within error bounds on the next integration step. More...

virtual void DoReset ()
Derived classes can override this method to perform routines when Reset() is called. More...

ContinuousState< T > * get_mutable_error_estimate ()
Gets an error estimate of the state variables recorded by the last call to StepOnceFixedSize(). More...

void set_actual_initial_step_size_taken (const T &dt)

Sets the size of the smallest-step-taken statistic as the result of a controlled integration step adjustment. More...

void set_largest_step_size_taken (const T &dt)

void set_ideal_next_step_size (const T &dt)

## Detailed Description

### template<class T> class drake::systems::RungeKutta3Integrator< T >

A third-order Runge Kutta integrator with a third order error estimate.

Template Parameters
 T A double or autodiff type.

This class uses Drake's -inl.h pattern. When seeing linker errors from this class, please refer to http://drake.mit.edu/cxx_inl.html.

Instantiated templates for the following kinds of T's are provided:

• double
• AutoDiffXd

For a discussion of this Runge-Kutta method, see [Butcher, 1987]. The embedded error estimate was derived using the method mentioned in [Hairer, 1993].

The Butcher tableaux for this integrator follows:

       |
0      |
1/2    | 1/2
1      | -1          2
---------------------------------------------------------------------------
1/6         2/3       1/6
0           1         0


where the second to last row is the 3rd-order propagated solution and the last row is the 2nd-order midpoint used for the error estimate.

The following documentation is pulled from Simbody's implementation of this integrator: "This is a 3-stage, first-same-as-last (FSAL) 3rd order method which gives us an embedded 2nd order method as well, so we can extract a 3rd-order error estimate for the 2nd-order result, which error estimate can then be used for step size control, since it will behave as h^3. We then propagate the 3rd order result (whose error is unknown), which Hairer calls 'local extrapolation'. We call the initial state (t0,y0) and want (t0+h,y1). We are given the initial derivative f0=f(t0,y0), which most likely is left over from an evaluation at the end of the last step."

• [Butcher, 1987] J. C. Butcher. The Numerical Analysis of Ordinary Differential Equations. John Wiley & Sons, 1987. p. 325.
• [Hairer, 1993] E. Hairer, S. Noersett, and G. Wanner. Solving ODEs I. 2nd rev. ed. Springer, 1993. p. 166.

## Constructor & Destructor Documentation

 RungeKutta3Integrator ( const RungeKutta3Integrator< T > & )
delete
 RungeKutta3Integrator ( RungeKutta3Integrator< T > && )
delete
 ~RungeKutta3Integrator ( )
overridedefault
 RungeKutta3Integrator ( const System< T > & system, Context< T > * context = nullptr )
inlineexplicit

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## Member Function Documentation

 int get_error_estimate_order ( ) const
inlineoverridevirtual

This integrator provides third order error estimates.

Implements IntegratorBase< T >.

 RungeKutta3Integrator& operator= ( RungeKutta3Integrator< T > && )
delete
 RungeKutta3Integrator& operator= ( const RungeKutta3Integrator< T > & )
delete
 bool supports_error_estimation ( ) const
inlineoverridevirtual

The integrator supports error estimation.

Implements IntegratorBase< T >.

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