A class which stores all the explicit single-step multi-stage ODE predictor methods. More...

#include <explicit_predictors.hpp>

Public Member Functions
	ExplicitRKPredictor (const System &S)
	Construct a predictor to work on a system.
	ExplicitRKPredictor (Predictor method, const System &S)
	Constructor for a particular predictor method.
void	PredictorMethod (Predictor method)
	/brief Sets the local variables to correspond to a particular predictor method
void	ChangeSystem (const System &S)
	Change the system (number of total functions) that the predictor uses.
void	ResizeK ()
	Resize the internal Runge-Kutta stage matrix K to match the current system and stage count.
void	SetConditionProbe (std::tuple< Vec< complex_dbl >, Vec< complex_mp > > const &probe)
	Adopt an externally-owned condition-number probe direction (both precisions).
unsigned	precision () const
	get the current precision of the predictor
void	ChangePrecision (unsigned new_precision)
	/brief Change the precision of the predictor variables and reassign the Butcher table variables.
void	PrecisionSanityCheck () const
	Assert (in debug builds) that the predictor's state is all at the expected precision.
template<typename ComplexT>
SuccessCode	Predict (Vec< ComplexT > &next_space, StepMetadata &meta, System const &S, const Vec< ComplexT > &current_space, ComplexT current_time, ComplexT const &delta_t, unsigned &num_steps_since_last_condition_number_computation, unsigned frequency_of_CN_estimation, NumErrorT const &tracking_tolerance, AdaptiveMultiplePrecisionConfig const *AMP_config=nullptr)
	Perform a generic predictor step.
Predictor	PredictorMethod ()
	Get the currently used prediction method.
unsigned	Order ()
	Get the order of the currently used prediction method.
bool	HasErrorEstimate ()
	Get whether the current prediction method provides an error estimate.

Protected Member Functions
template<typename ComplexT>
SuccessCode	FullStep (Vec< ComplexT > &next_space, System const &S, Vec< ComplexT > const &current_space, ComplexT const &current_time, ComplexT const &delta_t)
	Performs a full prediction step from current_time to current_time + delta_t.
template<typename ComplexT>
void	SetNormsCond (NumErrorT &norm_J, NumErrorT &norm_J_inverse, NumErrorT &condition_number_estimate, unsigned &num_steps_since_last_condition_number_computation, unsigned frequency_of_CN_estimation)
	Compute and (when due) refresh the Jacobian norms and condition-number estimate.
template<typename ComplexT>
SuccessCode	SetErrorEstimate (NumErrorT &error_estimate, ComplexT const &delta_t)
	Computes the error estimate of this prediction step.
template<typename ComplexT>
SuccessCode	SetSizeProportion (NumErrorT &size_proportion, ComplexT const &delta_t)
	Compute the size proportion variable for AMP computation.
template<typename ComplexT>
SuccessCode	EvalRHS (System const &S, const Vec< ComplexT > &space, const ComplexT &time, Mat< ComplexT > &K, unsigned stage)
	Evaluates the RHS of the Davidenko differential equation at a particular time and space.

Detailed Description

A class which stores all the explicit single-step multi-stage ODE predictor methods.

Purpose

Stores all the information needed to implement the predictor method

Butcher Table
Number of Stages
Order of the method.

Also stores information computed during implementation of the method.

Use

Each predictor method is stored as a static Butcher table. To perform a predict step, you must instantiate an object with a particular predictor method and call Predict:

ExplicitRKPredictors<Complex,Real> euler(Predictor::Euler, sys)

success_code = euler.Predict( ... )

bertini::tracking::Predictor::Euler

@ Euler

Definition config.hpp:57

Constructor & Destructor Documentation

◆ ExplicitRKPredictor() [1/2]

bertini::tracking::predict::ExplicitRKPredictor::ExplicitRKPredictor ( const System & S )

inline

Construct a predictor to work on a system.

Parameters

S	the system the predictor will be predicting on.

◆ ExplicitRKPredictor() [2/2]

bertini::tracking::predict::ExplicitRKPredictor::ExplicitRKPredictor	(	Predictor	method,
		const System &	S )

inline

Constructor for a particular predictor method.

Parameters

method	The predictor method to be implemented.
S	the system to be predicting on.

Member Function Documentation

◆ ChangePrecision()

void bertini::tracking::predict::ExplicitRKPredictor::ChangePrecision ( unsigned new_precision )

inline

/brief Change the precision of the predictor variables and reassign the Butcher table variables.

Parameters

new_precision The new precision.

◆ ChangeSystem()

void bertini::tracking::predict::ExplicitRKPredictor::ChangeSystem ( const System & S )

inline

Change the system (number of total functions) that the predictor uses.

Parameters

S	New system to switch to.

◆ EvalRHS()

template<typename ComplexT>

SuccessCode bertini::tracking::predict::ExplicitRKPredictor::EvalRHS	(	System const &	S,
		const Vec< ComplexT > &	space,
		const ComplexT &	time,
		Mat< ComplexT > &	K,
		unsigned	stage )

inlineprotected

Evaluates the RHS of the Davidenko differential equation at a particular time and space.

Parameters

S	The homotopy system
space	The space variable used to evaluate RHS
time	The time variable used to evaluate RHS
K	Matrix of stage variables
stage	Which stage variable(column of K) should be filled by this computation

Returns: Success code of this computation

◆ FullStep()

template<typename ComplexT>

SuccessCode bertini::tracking::predict::ExplicitRKPredictor::FullStep	(	Vec< ComplexT > &	next_space,
		System const &	S,
		Vec< ComplexT > const &	current_space,
		ComplexT const &	current_time,
		ComplexT const &	delta_t )

inlineprotected

Performs a full prediction step from current_time to current_time + delta_t.

Parameters

next_space	The computed prediction space
S	The homotopy system
current_space	The current space values
current_time	The current time values
delta_t	The time step

Returns: SuccessCode determining result of the computation

◆ HasErrorEstimate()

bool bertini::tracking::predict::ExplicitRKPredictor::HasErrorEstimate ( )

inline

Get whether the current prediction method provides an error estimate.

Returns: Yes or no.

◆ Order()

unsigned bertini::tracking::predict::ExplicitRKPredictor::Order ( )

inline

Get the order of the currently used prediction method.

This is the lowest order of the predictor. The order of the error estimate is this plus one.

Returns: The aforementioned order.

◆ precision()

unsigned bertini::tracking::predict::ExplicitRKPredictor::precision ( ) const

inline

get the current precision of the predictor

◆ PrecisionSanityCheck()

void bertini::tracking::predict::ExplicitRKPredictor::PrecisionSanityCheck ( ) const

inline

Assert (in debug builds) that the predictor's state is all at the expected precision.

◆ Predict()

template<typename ComplexT>

SuccessCode bertini::tracking::predict::ExplicitRKPredictor::Predict	(	Vec< ComplexT > &	next_space,
		StepMetadata &	meta,
		System const &	S,
		const Vec< ComplexT > &	current_space,
		ComplexT	current_time,
		ComplexT const &	delta_t,
		unsigned &	num_steps_since_last_condition_number_computation,
		unsigned	frequency_of_CN_estimation,
		NumErrorT const &	tracking_tolerance,
		AdaptiveMultiplePrecisionConfig const *	AMP_config = nullptr )

inline

Perform a generic predictor step.

Parameters

next_space	The computed prediction.
meta	Step metadata, populated during the step with the Jacobian norms and condition number estimate.
S	The system being solved.
current_space	The current space variable vector.
current_time	The current time.
delta_t	The size of the time step.
num_steps_since_last_condition_number_computation	Updated in this function.
frequency_of_CN_estimation	How many steps to take between condition number estimates.
tracking_tolerance	How tightly to track the path.
AMP_config	Optional adaptive-multiple-precision configuration; when null, fixed-precision behaviour is used.

Returns: SuccessCode indicating how the prediction went.

◆ PredictorMethod() [1/2]

Predictor bertini::tracking::predict::ExplicitRKPredictor::PredictorMethod ( )

inline

Get the currently used prediction method.

Returns: The current method.

◆ PredictorMethod() [2/2]

void bertini::tracking::predict::ExplicitRKPredictor::PredictorMethod ( Predictor method )

inline

/brief Sets the local variables to correspond to a particular predictor method

Parameters

method Enum class that determines the predictor method

◆ ResizeK()

void bertini::tracking::predict::ExplicitRKPredictor::ResizeK ( )

inline

Resize the internal Runge-Kutta stage matrix K to match the current system and stage count.

◆ SetConditionProbe()

void bertini::tracking::predict::ExplicitRKPredictor::SetConditionProbe ( std::tuple< Vec< complex_dbl >, Vec< complex_mp > > const & probe )

inline

Adopt an externally-owned condition-number probe direction (both precisions).

The tracker calls this once per path so the predictor estimates ||J^{-1}|| against the SAME random direction as the corrector (ADR-0024: one tracker-owned, per-path probe). Standalone use (e.g. unit tests with no tracker) keeps the per-system probe drawn in ChangeSystem.

◆ SetErrorEstimate()

template<typename ComplexT>

SuccessCode bertini::tracking::predict::ExplicitRKPredictor::SetErrorEstimate	(	NumErrorT &	error_estimate,
		ComplexT const &	delta_t )

inlineprotected

Computes the error estimate of this prediction step.

Parameters

error_estimate	Computed error estimate
delta_t	The time step

Returns: Success code or the computation

◆ SetNormsCond()

template<typename ComplexT>

void bertini::tracking::predict::ExplicitRKPredictor::SetNormsCond	(	NumErrorT &	norm_J,
		NumErrorT &	norm_J_inverse,
		NumErrorT &	condition_number_estimate,
		unsigned &	num_steps_since_last_condition_number_computation,
		unsigned	frequency_of_CN_estimation )

inlineprotected

Compute and (when due) refresh the Jacobian norms and condition-number estimate.

Template Parameters

ComplexT The complex number type to compute at.

Parameters

[out]	norm_J	Set to \|\|J\|\|.
[out]	norm_J_inverse	Set to the estimate of \|\|J^{-1}\|\|.
[out]	condition_number_estimate	Set to the product of the two norms.
[in,out]	num_steps_since_last_condition_number_computation	Steps elapsed since the last estimate; advanced/reset here, so it MUST be the caller's counter by reference (passing by value silently turns any frequency > 1 into "never refresh").
	frequency_of_CN_estimation	Recompute the estimate once this many steps have passed.

◆ SetSizeProportion()

template<typename ComplexT>

SuccessCode bertini::tracking::predict::ExplicitRKPredictor::SetSizeProportion	(	NumErrorT &	size_proportion,
		ComplexT const &	delta_t )

inlineprotected

Compute the size proportion variable for AMP computation.

Parameters

size_proportion	Computed size proportion
delta_t	The time step

Returns: Success code of the computation

Public Member Functions

Protected Member Functions

Detailed Description

Purpose

Use

Constructor & Destructor Documentation

◆ ExplicitRKPredictor() [1/2]

◆ ExplicitRKPredictor() [2/2]

Member Function Documentation

◆ ChangePrecision()

◆ ChangeSystem()

◆ EvalRHS()

◆ FullStep()

◆ HasErrorEstimate()

◆ Order()

◆ precision()

◆ PrecisionSanityCheck()

◆ Predict()

◆ PredictorMethod() [1/2]

◆ PredictorMethod() [2/2]

◆ ResizeK()

◆ SetConditionProbe()

◆ SetErrorEstimate()

◆ SetNormsCond()

◆ SetSizeProportion()