bertini::tracking::correct::NewtonCorrector Class Reference

/class NewtonCorrector More...

#include <newton_corrector.hpp>

Public Member Functions
	NewtonCorrector (const System &S)
	Construct a Newton corrector for a system, at the current default precision.
void	Settings (const NewtonConfig &newton_settings)
	Sets the Newton configuration settings.
void	ChangePrecision (unsigned new_precision)
	Change the precision of the predictor variables and reassign the Butcher table variables.
unsigned	precision () const
	Get the corrector's current working precision.
void	ChangeSystem (const System &S)
	Change the system(number of total functions) that the predictor uses.
void	RefreshRandomDirection ()
	(Re)draw the random probe direction used to estimate ||J^{-1}|| (the condition number) from this thread's RNG engine.
std::tuple< Vec< complex_dbl >, Vec< complex_mp > >	ConditionProbe () const
	The condition-number probe direction as drawn (both precisions), so the tracker can share the SAME per-path probe with the predictor – making the predictor's and corrector's ||J^{-1}|| estimates use one consistent direction.
template<typename ComplexT>
SuccessCode	Correct (Vec< ComplexT > &next_space, StepMetadata &meta, System const &S, Vec< ComplexT > const &current_space, ComplexT const &current_time, NumErrorT const &tracking_tolerance, unsigned min_num_newton_iterations, unsigned max_num_newton_iterations, AdaptiveMultiplePrecisionConfig const *AMP_config=nullptr)
	Run Newton's method, optionally with adaptive multiple precision.

Detailed Description

/class NewtonCorrector

A command class which performs a newton correction step.

Purpose

Stores information computed during implementation of the method.

Use

To perform a correction step, you must instantiate an object and call Correct:

NewtonCorrect<Complex,Real> newton(sys)
success_code = newton.Correct( ... )

Constructor & Destructor Documentation

NewtonCorrector()

bertini::tracking::correct::NewtonCorrector::NewtonCorrector ( const System & S )

inline

Construct a Newton corrector for a system, at the current default precision.

Member Function Documentation

ChangePrecision()

void bertini::tracking::correct::NewtonCorrector::ChangePrecision ( unsigned new_precision )

inline

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

Parameters

new_precision

The new precision.

ChangeSystem()

void bertini::tracking::correct::NewtonCorrector::ChangeSystem ( const System & S )

inline

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

Parameters

S	New system

ConditionProbe()

std::tuple< Vec< complex_dbl >, Vec< complex_mp > > bertini::tracking::correct::NewtonCorrector::ConditionProbe ( ) const

inline

The condition-number probe direction as drawn (both precisions), so the tracker can share the SAME per-path probe with the predictor – making the predictor's and corrector's ||J^{-1}|| estimates use one consistent direction.

The multiprecision half is the stored copy, at the precision it was drawn at, not the working copy the corrector holds at its current precision.

See also

RefreshRandomDirection.

Correct()

template<typename ComplexT>

SuccessCode bertini::tracking::correct::NewtonCorrector::Correct ( Vec< ComplexT > & next_space, StepMetadata & meta, System const & S, Vec< ComplexT > const & current_space, ComplexT const & current_time, NumErrorT const & tracking_tolerance, unsigned min_num_newton_iterations, unsigned max_num_newton_iterations, AdaptiveMultiplePrecisionConfig const * AMP_config = nullptr )

inline

Run Newton's method, optionally with adaptive multiple precision.

One method replaces the former fixed/AMP/out-param overloads. When AMP_config is null it is a plain fixed-precision Newton loop (convergence only). When AMP_config is non-null it additionally fills the step metadata (norm_delta_z, norm_J, norm_J_inverse, condition_number_estimate) and enforces AMP criteria B and C, returning HigherPrecisionNecessary on violation.

Parameters

[out]	next_space	The computed next space point.
[out]	meta	Step metadata (corrector fields; only filled in the AMP path).
	S	The system we are tracking on.
	current_space	The base point for newton correcting.
	current_time	The current time value.
	tracking_tolerance	Iterate until the step is shorter than this.
	min_num_newton_iterations	Take at least this many steps (>= 1).
	max_num_newton_iterations	The maximum number of iterations.
	AMP_config	Adaptive-precision settings, or nullptr for fixed precision.

precision()

unsigned bertini::tracking::correct::NewtonCorrector::precision ( ) const

inline

Get the corrector's current working precision.

RefreshRandomDirection()

void bertini::tracking::correct::NewtonCorrector::RefreshRandomDirection ( )

inline

(Re)draw the random probe direction used to estimate ||J^{-1}|| (the condition number) from this thread's RNG engine.

The tracker calls this once at the start of a path track (see Tracker::TrackPath's caller / the per-path reseed point), so the direction is held fixed for the ENTIRE track of that point – every Newton step and the endgame's sample-circle sub-tracks – and, given a per-path RNG reseed, is reproducible regardless of how paths were distributed across workers. It is NOT redrawn per Newton step or per TrackPath, which would both perturb condition estimates and (in the endgame) churn the RNG mid-track.

Settings()

void bertini::tracking::correct::NewtonCorrector::Settings ( const NewtonConfig & newton_settings )

inline

Sets the Newton configuration settings.

Parameters

newton_settings

A Newton struct holding configuration settings.