template<typename T>
class drake::systems::RungeKutta5Integrator< T >
A fifth-order, seven-stage, first-same-as-last (FSAL) Runge Kutta integrator with a fourth order error estimate.
For a discussion of this Runge-Kutta method, see [Dormand, 1980] and [Hairer, 1993]. The embedded error estimate was derived as described in [Hairer, 1993], where all the coefficients are tabulated.
The Butcher tableau for this integrator follows:
0 |
1/5 | 1/5
3/10 | 3/40 9/40
4/5 | 44/45 -56/15 32/9
8/9 | 19372/6561 −25360/2187 64448/6561 −212/729
1 | 9017/3168 −355/33 46732/5247 49/176 −5103/18656
1 | 35/384 0 500/1113 125/192 −2187/6784 11/84
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35/384 0 500/1113 125/192 −2187/6784 11/84 0
5179/57600 0 7571/16695 393/640 −92097/339200 187/2100 1/40
where the second to last row is the 5th-order (propagated) solution and the last row gives a 4th-order accurate solution used for error control.
- [Dormand, 1980] J. Dormand and P. Prince. "A family of embedded
Runge-Kutta formulae", Journal of Computational and Applied Mathematics, 1980, 6(1): 19–26.
- [Hairer, 1993] E. Hairer, S. Nørsett, and G. Wanner. Solving ODEs I. 2nd rev. ed. Springer, 1993. pp. 178-9.
- Template Parameters
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| ~RungeKutta5Integrator () override=default |
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| RungeKutta5Integrator (const System< T > &system, Context< T > *context=nullptr) |
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bool | supports_error_estimation () const override |
| The integrator supports error estimation. More...
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int | get_error_estimate_order () const override |
| The order of the asymptotic term in the error estimate. More...
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| RungeKutta5Integrator (const RungeKutta5Integrator &)=delete |
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RungeKutta5Integrator & | operator= (const RungeKutta5Integrator &)=delete |
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| RungeKutta5Integrator (RungeKutta5Integrator &&)=delete |
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RungeKutta5Integrator & | operator= (RungeKutta5Integrator &&)=delete |
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| 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...
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virtual | ~IntegratorBase ()=default |
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void | Reset () |
| Resets the integrator to initial values, i.e., default construction values. More...
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void | Initialize () |
| An integrator must be initialized before being used. More...
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StepResult | IntegrateNoFurtherThanTime (const T &publish_time, const T &update_time, const T &boundary_time) |
| (Internal use only) 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...
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void | IntegrateWithMultipleStepsToTime (const T &t_final) |
| Stepping function for integrators operating outside of Simulator that advances the continuous state exactly to t_final . More...
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bool | IntegrateWithSingleFixedStepToTime (const T &t_target) |
| Stepping function for integrators operating outside of Simulator that advances the continuous state using a single step to t_target . More...
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const Context< T > & | get_context () const |
| Returns a const reference to the internally-maintained Context holding the most recent state in the trajectory. More...
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Context< T > * | get_mutable_context () |
| Returns a mutable pointer to the internally-maintained Context holding the most recent state in the trajectory. More...
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void | reset_context (Context< T > *context) |
| Replace the pointer to the internally-maintained Context with a different one. More...
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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...
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bool | is_initialized () const |
| Indicates whether the integrator has been initialized. More...
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const T & | get_previous_integration_step_size () const |
| Gets the size of the last (previous) integration step. More...
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| IntegratorBase (const IntegratorBase &)=delete |
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IntegratorBase & | operator= (const IntegratorBase &)=delete |
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| IntegratorBase (IntegratorBase &&)=delete |
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IntegratorBase & | operator= (IntegratorBase &&)=delete |
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void | set_target_accuracy (double accuracy) |
| Request that the integrator attempt to achieve a particular accuracy for the continuous portions of the simulation. More...
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double | get_target_accuracy () const |
| Gets the target accuracy. More...
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double | get_accuracy_in_use () const |
| Gets the accuracy in use by the integrator. More...
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const ContinuousState< T > * | get_error_estimate () const |
| Gets the error estimate (used only for integrators that support error estimation). More...
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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...
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void | set_fixed_step_mode (bool flag) |
| Sets an integrator with error control to fixed step mode. More...
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bool | get_fixed_step_mode () const |
| Gets whether an integrator is running in fixed step mode. More...
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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...
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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...
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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...
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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...
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void | request_initial_step_size_target (const T &step_size) |
| Request that the first attempted integration step have a particular size. More...
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const T & | get_initial_step_size_target () const |
| Gets the target size of the first integration step. More...
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void | set_maximum_step_size (const T &max_step_size) |
| Sets the maximum step size that may be taken by this integrator. More...
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const T & | get_maximum_step_size () const |
| Gets the maximum step size that may be taken by this integrator. More...
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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 IntegrateNoFurtherThanTime(). More...
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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...
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const T & | get_requested_minimum_step_size () const |
| Gets the requested minimum step size h_min for this integrator. More...
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void | set_throw_on_minimum_step_size_violation (bool throws) |
| Sets whether the integrator should throw a std::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...
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bool | get_throw_on_minimum_step_size_violation () const |
| Reports the current setting of the throw_on_minimum_step_size_violation flag. More...
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T | 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...
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void | ResetStatistics () |
| Forget accumulated statistics. More...
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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...
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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...
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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...
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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...
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const T & | get_actual_initial_step_size_taken () const |
| The actual size of the successful first step. More...
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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...
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const T & | get_largest_step_size_taken () const |
| The size of the largest step taken since the last Initialize() or ResetStatistics() call. More...
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int64_t | get_num_steps_taken () const |
| The number of integration steps taken since the last Initialize() or ResetStatistics() call. More...
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void | add_derivative_evaluations (double evals) |
| Manually increments the statistic for the number of ODE evaluations. More...
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void | StartDenseIntegration () |
| Starts dense integration, allocating a new dense output for this integrator to use. More...
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const trajectories::PiecewisePolynomial< T > * | get_dense_output () const |
| Returns a const pointer to the integrator's current PiecewisePolynomial instance, holding a representation of the continuous state trajectory since the last StartDenseIntegration() call. More...
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std::unique_ptr< trajectories::PiecewisePolynomial< T > > | StopDenseIntegration () |
| Stops dense integration, yielding ownership of the current dense output to the caller. More...
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enum | StepResult {
kReachedPublishTime = 1,
kReachedZeroCrossing = 2,
kReachedUpdateTime = 3,
kTimeHasAdvanced = 4,
kReachedBoundaryTime = 5,
kReachedStepLimit = 6
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| Status returned by IntegrateNoFurtherThanTime(). More...
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virtual void | DoResetStatistics () |
| Resets any statistics particular to a specific integrator. More...
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const ContinuousState< T > & | EvalTimeDerivatives (const Context< T > &context) |
| Evaluates the derivative function and updates call statistics. More...
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template<typename U > |
const ContinuousState< U > & | EvalTimeDerivatives (const System< U > &system, const Context< U > &context) |
| Evaluates the derivative function (and updates call statistics). More...
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void | set_accuracy_in_use (double accuracy) |
| Sets the working ("in use") accuracy for this integrator. More...
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bool | StepOnceErrorControlledAtMost (const T &h_max) |
| Default code for advancing the continuous state of the system by a single step of h_max (or smaller, depending on error control). More...
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T | CalcStateChangeNorm (const ContinuousState< T > &dx_state) const |
| Computes the infinity norm of a change in continuous state. More...
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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...
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virtual void | DoReset () |
| Derived classes can override this method to perform routines when Reset() is called. More...
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trajectories::PiecewisePolynomial< T > * | get_mutable_dense_output () |
| Returns a mutable pointer to the internally-maintained PiecewisePolynomial instance, holding a representation of the continuous state trajectory since the last time StartDenseIntegration() was called. More...
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bool | DoDenseStep (const T &h) |
| Calls DoStep(h) while recording the resulting step in the dense output. More...
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ContinuousState< T > * | get_mutable_error_estimate () |
| Gets an error estimate of the state variables recorded by the last call to StepOnceFixedSize(). More...
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void | set_actual_initial_step_size_taken (const T &h) |
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void | set_smallest_adapted_step_size_taken (const T &h) |
| Sets the size of the smallest-step-taken statistic as the result of a controlled integration step adjustment. More...
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void | set_largest_step_size_taken (const T &h) |
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void | set_ideal_next_step_size (const T &h) |
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