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Drake
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Drake
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An abstract class providing methods shared by implicit integrators.
| T | The scalar type, which must be one of the default nonsymbolic scalars. |
#include <drake/systems/analysis/implicit_integrator.h>
Classes | |
| class | IterationMatrix |
| A class for storing the factorization of an iteration matrix and using it to solve linear systems of equations. More... | |
Public Types | |
| enum | JacobianComputationScheme { kForwardDifference, kCentralDifference, kAutomatic } |
 Public Types inherited from IntegratorBase< T > | |
| enum | StepResult { kReachedPublishTime = 1, kReachedZeroCrossing = 2, kReachedUpdateTime = 3, kTimeHasAdvanced = 4, kReachedBoundaryTime = 5, kReachedStepLimit = 6 } |
| Status returned by IntegrateNoFurtherThanTime(). More... | |
Public Member Functions | |
| virtual | ~ImplicitIntegrator () |
| ImplicitIntegrator (const System< T > &system, Context< T > *context=nullptr) | |
| int | max_newton_raphson_iterations () const |
| The maximum number of Newton-Raphson iterations to take before the Newton-Raphson process decides that convergence will not be attained. More... | |
Methods for getting and setting the Jacobian scheme. | |
Methods for getting and setting the scheme used to determine the Jacobian matrix necessary for solving the requisite nonlinear system if equations. Selecting the wrong Jacobian determination scheme will slow (possibly critically) the implicit integration process. Automatic differentiation is recommended if the System supports it for reasons of both higher accuracy and increased speed. Forward differencing (i.e., numerical differentiation) exhibits error in the approximation close to √ε, where ε is machine epsilon, from n forward dynamics calls (where n is the number of state variables). Central differencing yields the most accurate numerically differentiated Jacobian matrix, but expends double the computational effort for approximately three digits greater accuracy: the total error in the central-difference approximation is close to ε^(2/3), from 2n forward dynamics calls. See [Nocedal 2004, pp. 167-169].
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| void | set_reuse (bool reuse) |
Sets whether the integrator attempts to reuse Jacobian matrices and iteration matrix factorizations (default is true). More... | |
| bool | get_reuse () const |
| Gets whether the integrator attempts to reuse Jacobian matrices and iteration matrix factorizations. More... | |
| void | set_use_full_newton (bool flag) |
| Sets whether the method operates in "full Newton" mode, in which case Jacobian and iteration matrices are freshly computed on every Newton-Raphson iteration. More... | |
| bool | get_use_full_newton () const |
| Gets whether this method is operating in "full Newton" mode. More... | |
| void | set_jacobian_computation_scheme (JacobianComputationScheme scheme) |
| Sets the Jacobian computation scheme. More... | |
| JacobianComputationScheme | get_jacobian_computation_scheme () const |
Cumulative statistics functions. | |
The functions return statistics specific to the implicit integration process. | |
| int64_t | get_num_derivative_evaluations_for_jacobian () const |
| Gets the number of ODE function evaluations (calls to EvalTimeDerivatives()) used only for computing the Jacobian matrices since the last call to ResetStatistics(). More... | |
| int64_t | get_num_jacobian_evaluations () const |
| Gets the number of Jacobian computations (i.e., the number of times that the Jacobian matrix was reformed) since the last call to ResetStatistics(). More... | |
| int64_t | get_num_newton_raphson_iterations () const |
| Gets the number of iterations used in the Newton-Raphson nonlinear systems of equation solving process since the last call to ResetStatistics(). More... | |
| int64_t | get_num_iteration_matrix_factorizations () const |
| Gets the number of factorizations of the iteration matrix since the last call to ResetStatistics(). More... | |
| int64_t | get_num_error_estimator_derivative_evaluations () const |
| Gets the number of ODE function evaluations (calls to EvalTimeDerivatives()) used only for the error estimation process since the last call to ResetStatistics(). More... | |
Error-estimation statistics functions. | |
The functions return statistics specific to the error estimation process. Gets the number of ODE function evaluations (calls to CalcTimeDerivatives()) used only for computing the Jacobian matrices needed by the error estimation process since the last call to ResetStatistics(). | |
| int64_t | get_num_error_estimator_derivative_evaluations_for_jacobian () const |
| int64_t | get_num_error_estimator_newton_raphson_iterations () const |
| Gets the number of iterations used in the Newton-Raphson nonlinear systems of equation solving process for the error estimation process since the last call to ResetStatistics(). More... | |
| int64_t | get_num_error_estimator_jacobian_evaluations () const |
| Gets the number of Jacobian matrix computations used only during the error estimation process since the last call to ResetStatistics(). More... | |
| int64_t | get_num_error_estimator_iteration_matrix_factorizations () const |
| Gets the number of factorizations of the iteration matrix used only during the error estimation process since the last call to ResetStatistics(). More... | |
| 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 () |
| 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... | |
| 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... | |
| void | IntegrateWithMultipleStepsToTime (const T &t_final) |
Stepping function for integrators operating outside of Simulator that advances the continuous state exactly to t_final. More... | |
| 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... | |
| 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... | |
| void | reset_context (std::unique_ptr< Context< T >> context) |
| Same as above but allows the integrator to take ownership of the context. 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... | |
| IntegratorBase (const IntegratorBase &)=delete | |
| IntegratorBase & | operator= (const IntegratorBase &)=delete |
| IntegratorBase (IntegratorBase &&)=delete | |
| IntegratorBase & | operator= (IntegratorBase &&)=delete |
| 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... | |
| virtual bool | supports_error_estimation () const =0 |
| Derived classes must override this function to indicate whether the integrator supports error estimation. More... | |
| virtual int | get_error_estimate_order () const =0 |
| Derived classes must override this function to return the order of the asymptotic term in the integrator's error estimate. More... | |
| const ContinuousState< T > * | get_error_estimate () const |
| Gets the error estimate (used only for integrators that support error estimation). 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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::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... | |
| 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... | |
| 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... | |
| void | add_derivative_evaluations (double evals) |
| Manually increments the statistic for the number of ODE evaluations. More... | |
| void | StartDenseIntegration () |
| Starts dense integration, allocating a new dense output for this integrator to use. More... | |
| 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... | |
| std::unique_ptr< trajectories::PiecewisePolynomial< T > > | StopDenseIntegration () |
| Stops dense integration, yielding ownership of the current dense output to the caller. More... | |
| std::unique_ptr< IntegratorBase< T > > | Clone () const |
| Returns a copy of this integrator with reset statistics, reinitialized internal integrator states, and a cloned system context. More... | |
Protected Types | |
| enum | ConvergenceStatus { kDiverged, kConverged, kNotConverged } |
Protected Member Functions | |
| virtual int | do_max_newton_raphson_iterations () const |
| Derived classes can override this method to change the number of Newton-Raphson iterations (10 by default) to take before the Newton-Raphson process decides that convergence will not be attained. More... | |
| bool | MaybeFreshenMatrices (const T &t, const VectorX< T > &xt, const T &h, int trial, const std::function< void(const MatrixX< T > &J, const T &h, typename ImplicitIntegrator< T >::IterationMatrix *)> &compute_and_factor_iteration_matrix, typename ImplicitIntegrator< T >::IterationMatrix *iteration_matrix) |
| Computes necessary matrices (Jacobian and iteration matrix) for Newton-Raphson (NR) iterations, as necessary. More... | |
| void | FreshenMatricesIfFullNewton (const T &t, const VectorX< T > &xt, const T &h, const std::function< void(const MatrixX< T > &J, const T &h, typename ImplicitIntegrator< T >::IterationMatrix *)> &compute_and_factor_iteration_matrix, typename ImplicitIntegrator< T >::IterationMatrix *iteration_matrix) |
| Computes necessary matrices (Jacobian and iteration matrix) for full Newton-Raphson (NR) iterations, if full Newton-Raphson method is activated (if it's not activated, this method is a no-op). More... | |
| bool | IsUpdateZero (const VectorX< T > &xc, const VectorX< T > &dxc, double eps=-1.0) const |
| Checks whether a proposed update is effectively zero, indicating that the Newton-Raphson process converged. More... | |
| ConvergenceStatus | CheckNewtonConvergence (int iteration, const VectorX< T > &xtplus, const VectorX< T > &dx, const T &dx_norm, const T &last_dx_norm) const |
| Checks a Newton-Raphson iteration process for convergence. More... | |
| virtual void | DoResetImplicitIntegratorStatistics () |
| Resets any statistics particular to a specific implicit integrator. More... | |
| virtual void | DoImplicitIntegratorReset () |
| Derived classes can override this method to perform routines when Reset() is called. More... | |
| virtual void | DoResetCachedJacobianRelatedMatrices () |
| Resets any cached Jacobian or iteration matrices owned by child classes. More... | |
| bool | IsBadJacobian (const MatrixX< T > &J) const |
| Checks to see whether a Jacobian matrix is "bad" (has any NaN or Inf values) and needs to be recomputed. More... | |
| virtual std::unique_ptr< ImplicitIntegrator< T > > | DoImplicitIntegratorClone () const =0 |
| Derived classes must implement this method to return a copy of themselves as an IntegratorBase instance. More... | |
| virtual int64_t | do_get_num_newton_raphson_iterations () const =0 |
| virtual int64_t | do_get_num_error_estimator_derivative_evaluations () const =0 |
| virtual int64_t | do_get_num_error_estimator_derivative_evaluations_for_jacobian () const =0 |
| virtual int64_t | do_get_num_error_estimator_newton_raphson_iterations () const =0 |
| virtual int64_t | do_get_num_error_estimator_jacobian_evaluations () const =0 |
| virtual int64_t | do_get_num_error_estimator_iteration_matrix_factorizations () const =0 |
| MatrixX< T > & | get_mutable_jacobian () |
| void | DoResetStatistics () override |
| Resets any statistics particular to a specific integrator. More... | |
| void | DoReset () final |
| Derived classes can override this method to perform routines when Reset() is called. More... | |
| const MatrixX< T > & | CalcJacobian (const T &t, const VectorX< T > &x) |
| void | ComputeForwardDiffJacobian (const System< T > &system, const T &t, const VectorX< T > &xt, Context< T > *context, MatrixX< T > *J) |
| void | ComputeCentralDiffJacobian (const System< T > &system, const T &t, const VectorX< T > &xt, Context< T > *context, MatrixX< T > *J) |
| void | ComputeAutoDiffJacobian (const System< T > &system, const T &t, const VectorX< T > &xt, const Context< T > &context, MatrixX< T > *J) |
| virtual bool | DoImplicitIntegratorStep (const T &h)=0 |
Derived classes must implement this method to (1) integrate the continuous portion of this system forward by a single step of size h and (2) set the error estimate (via get_mutable_error_estimate()). More... | |
| void | increment_num_iter_factorizations () |
| void | increment_jacobian_computation_derivative_evaluations (int count) |
| void | increment_jacobian_evaluations () |
| void | set_jacobian_is_fresh (bool flag) |
| template<> | |
| void | ComputeAutoDiffJacobian (const System< AutoDiffXd > &, const AutoDiffXd &, const VectorX< AutoDiffXd > &, const Context< AutoDiffXd > &, MatrixX< AutoDiffXd > *) |
| Protected Member Functions inherited from IntegratorBase< T > | |
| const ContinuousState< T > & | EvalTimeDerivatives (const Context< T > &context) |
| Evaluates the derivative function and updates call statistics. More... | |
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| const ContinuousState< U > & | EvalTimeDerivatives (const System< U > &system, const Context< U > &context) |
| 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... | |
| 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... | |
| T | 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 | DoInitialize () |
| Derived classes can override this method to perform special initialization. More... | |
| 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... | |
| bool | DoDenseStep (const T &h) |
| Calls DoStep(h) while recording the resulting step in the dense output. 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 &h) |
| 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... | |
| void | set_largest_step_size_taken (const T &h) |
| void | set_ideal_next_step_size (const T &h) |
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Checks a Newton-Raphson iteration process for convergence.
The logic is based on the description on p. 121 from [Hairer, 1996] E. Hairer and G. Wanner. Solving Ordinary Differential Equations II (Stiff and Differential-Algebraic Problems). Springer, 1996. This function is called after the dx is computed in an iteration, to determine if the Newton process converged, diverged, or needs further iterations.
| iteration | the iteration index, starting at 0 for the first iteration. |
| xtplus | the state x at the current iteration. |
| dx | the state change dx the difference between xtplus at the current and the previous iteration. |
| dx_norm | the weighted norm of dx |
| last_dx_norm | the weighted norm of dx from the previous iteration. This parameter is ignored during the first iteration. |
kConverged for convergence, kDiverged for divergence, otherwise kNotConverged if Newton-Raphson should simply continue.
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Derived classes can override this method to change the number of Newton-Raphson iterations (10 by default) to take before the Newton-Raphson process decides that convergence will not be attained.
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Derived classes must implement this method to return a copy of themselves as an IntegratorBase instance.
The returned object must correctly duplicate all member variables specific to the derived class, while the parent class members are assumed to be handled by the parent class.
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Derived classes can override this method to perform routines when Reset() is called.
This default method does nothing.
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Derived classes must implement this method to (1) integrate the continuous portion of this system forward by a single step of size h and (2) set the error estimate (via get_mutable_error_estimate()).
This method is called during the integration process (via StepOnceErrorControlledAtMost(), IntegrateNoFurtherThanTime(), and IntegrateWithSingleFixedStepToTime()).
| h | The integration step to take. |
true if successful, false if the integrator was unable to take a single step of size h (due to, e.g., an integrator convergence failure). t, the time and state will be advanced to t+h if the method returns true; otherwise, the time and state should be reset to those at t. true for some, albeit possibly very small, positive value of h. The derived integrator's stepping algorithm can make this guarantee, for example, by switching to an algorithm not subject to convergence failures (e.g., explicit Euler) for very small step sizes.
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Derived classes can override this method to perform routines when Reset() is called.
This default method does nothing.
Reimplemented from IntegratorBase< T >.
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Resets any cached Jacobian or iteration matrices owned by child classes.
This is called when the user changes the Jacobian computation scheme; the child class should use this to reset its cached matrices.
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Resets any statistics particular to a specific implicit integrator.
The default implementation of this function does nothing. If your integrator collects its own statistics, you should re-implement this method and reset them there.
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Resets any statistics particular to a specific integrator.
The default implementation of this function does nothing. If your integrator collects its own statistics, you should re-implement this method and reset them there.
Reimplemented from IntegratorBase< T >.
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Computes necessary matrices (Jacobian and iteration matrix) for full Newton-Raphson (NR) iterations, if full Newton-Raphson method is activated (if it's not activated, this method is a no-op).
| t | the time at which to compute the Jacobian. | |
| xt | the continuous state at which the Jacobian is computed. | |
| h | the integration step size (for computing iteration matrices). | |
| compute_and_factor_iteration_matrix | a function pointer for computing and factoring the iteration matrix. | |
| [out] | iteration_matrix | the updated and factored iteration matrix on return. |
| JacobianComputationScheme get_jacobian_computation_scheme | ( | ) | const |
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| int64_t get_num_derivative_evaluations_for_jacobian | ( | ) | const |
Gets the number of ODE function evaluations (calls to EvalTimeDerivatives()) used only for computing the Jacobian matrices since the last call to ResetStatistics().
This count includes those derivative calculations necessary for computing Jacobian matrices during error estimation processes.
| int64_t get_num_error_estimator_derivative_evaluations | ( | ) | const |
Gets the number of ODE function evaluations (calls to EvalTimeDerivatives()) used only for the error estimation process since the last call to ResetStatistics().
This count includes those needed to compute Jacobian matrices.
| int64_t get_num_error_estimator_derivative_evaluations_for_jacobian | ( | ) | const |
| int64_t get_num_error_estimator_iteration_matrix_factorizations | ( | ) | const |
Gets the number of factorizations of the iteration matrix used only during the error estimation process since the last call to ResetStatistics().
| int64_t get_num_error_estimator_jacobian_evaluations | ( | ) | const |
Gets the number of Jacobian matrix computations used only during the error estimation process since the last call to ResetStatistics().
| int64_t get_num_error_estimator_newton_raphson_iterations | ( | ) | const |
Gets the number of iterations used in the Newton-Raphson nonlinear systems of equation solving process for the error estimation process since the last call to ResetStatistics().
| int64_t get_num_iteration_matrix_factorizations | ( | ) | const |
Gets the number of factorizations of the iteration matrix since the last call to ResetStatistics().
This count includes those refactorizations necessary during error estimation processes.
| int64_t get_num_jacobian_evaluations | ( | ) | const |
Gets the number of Jacobian computations (i.e., the number of times that the Jacobian matrix was reformed) since the last call to ResetStatistics().
This count includes those evaluations necessary during error estimation processes.
| int64_t get_num_newton_raphson_iterations | ( | ) | const |
Gets the number of iterations used in the Newton-Raphson nonlinear systems of equation solving process since the last call to ResetStatistics().
This count includes those Newton-Raphson iterations used during error estimation processes.
| bool get_reuse | ( | ) | const |
Gets whether the integrator attempts to reuse Jacobian matrices and iteration matrix factorizations.
false when full-Newton mode is on. | bool get_use_full_newton | ( | ) | const |
Gets whether this method is operating in "full Newton" mode.
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Checks to see whether a Jacobian matrix is "bad" (has any NaN or Inf values) and needs to be recomputed.
A divergent Newton-Raphson iteration can cause the state to overflow, which is how the Jacobian can become "bad". This is an O(n²) operation, where n is the state dimension.
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Checks whether a proposed update is effectively zero, indicating that the Newton-Raphson process converged.
| xc | the continuous state. |
| dxc | the update to the continuous state. |
| eps | the tolerance that will be used to determine whether the change in any dimension of the state is nonzero. eps will be treated as an absolute tolerance when the magnitude of a particular dimension of the state is no greater than unity and as a relative tolerance otherwise. For non-positive eps (default), an appropriate tolerance will be computed. |
true if the update is effectively zero. | int max_newton_raphson_iterations | ( | ) | const |
The maximum number of Newton-Raphson iterations to take before the Newton-Raphson process decides that convergence will not be attained.
This number affects the speed with which a solution is found. If the number is too small, Jacobian/iteration matrix reformations and refactorizations will be performed unnecessarily. If the number is too large, the Newton-Raphson process will waste time evaluating derivatives when convergence is infeasible. [Hairer, 1996] states, "It is our experience that the code becomes more efficient when we allow a relatively high number of iterations (e.g., [7 or 10])", p. 121. Note that the focus of that quote is a 5th order integrator that uses a quasi-Newton approach.
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Computes necessary matrices (Jacobian and iteration matrix) for Newton-Raphson (NR) iterations, as necessary.
This method has been designed for use in DoImplicitIntegratorStep() processes that follow this model:
trial parameter below. In this model, DoImplicitIntegratorStep() returns failure if the NR iterations reach a fourth trial.Note that the sophisticated logic above only applies when the Jacobian reuse is activated (default, see get_reuse()).
| t | the time at which to compute the Jacobian. | |
| xt | the continuous state at which the Jacobian is computed. | |
| h | the integration step size (for computing iteration matrices). | |
| trial | which trial (1-4) the Newton-Raphson process is in when calling this method. | |
| compute_and_factor_iteration_matrix | a function pointer for computing and factoring the iteration matrix. | |
| [out] | iteration_matrix | the updated and factored iteration matrix on return. |
false if the calling stepping method should indicate failure; true otherwise. trial <= 4. | void set_jacobian_computation_scheme | ( | JacobianComputationScheme | scheme | ) |
Sets the Jacobian computation scheme.
This function can be safely called at any time (i.e., the integrator need not be re-initialized afterward).
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| void set_reuse | ( | bool | reuse | ) |
Sets whether the integrator attempts to reuse Jacobian matrices and iteration matrix factorizations (default is true).
Forming Jacobian matrices and factorizing iteration matrices are generally the two most expensive operations performed by this integrator. For small systems (those with on the order of ten state variables), the additional accuracy that using fresh Jacobians and factorizations buys- which can permit increased step sizes but should have no effect on solution accuracy- can outweigh the small factorization cost.
== true. | void set_use_full_newton | ( | bool | flag | ) |
Sets whether the method operates in "full Newton" mode, in which case Jacobian and iteration matrices are freshly computed on every Newton-Raphson iteration.
When set to true, this mode overrides the reuse mode.