Classes
class	AMPEndgame
	Specifies some necessaries for AMP style endgame implementations, which differ from the fixed precision ones. More...
struct	EGPrecSelector< tracking::AMPTracker >
	Selects the AMP endgame precision policy for the adaptive-precision tracker. More...
class	EndgameBase
	Base endgame class for all endgames offered in Bertini2. More...
class	CauchyEndgame
	Class used to finish tracking paths during Homotopy Continuation. More...
class	PowerSeriesEndgame
	class used to finish tracking paths during Homotopy Continuation More...
class	FixedPrecEndgame
	Fixed-precision endgame precision policy (refines and ensures precision at a single working precision). More...
struct	EGPrecSelector
	Base empty class. More...
struct	EndgameSelector
	Facilitates lookup of required endgame type based on tracker type. More...
struct	SecurityConfig
	Security (divergence-bailout) configuration for an endgame. More...
struct	EndgameConfig
	Configuration common to all endgames (sampling and final-approximation tolerances). More...
struct	PowerSeriesConfig
	Power-series-endgame configuration. More...
struct	CauchyConfig
	Cauchy-endgame configuration. More...
struct	TrackBackConfig
	Track-back endgame configuration. More...
struct	AlgoTraits
struct	AlgoTraits< PowerSeriesEndgame< PrecT > >
	specialization for PowerSeries, which uses CRTP More...
struct	AlgoTraits< CauchyEndgame< PrecT > >
	specialization for Cauchy, which uses CRTP More...
class	ComputedSamplePoint
	A new sample point on the path was computed, adding one point to the sequence of the endgame's approach to the target time. More...
class	CircleAdvanced
	Advanced around the circle around target time. More...
class	PrecisionChanged
	Event emitted when the endgame's working precision changes. More...
struct	EGPrecSelector< tracking::DoublePrecisionTracker >
	Selects the fixed-precision endgame policy for the double-precision tracker. More...
struct	EGPrecSelector< tracking::MultiplePrecisionTracker >
	Selects the fixed-precision endgame policy for the multiple-precision tracker. More...
struct	EGPrecSelector< tracking::FixedPrecisionTracker< D > >
	Selects the fixed-precision endgame policy for a fixed-precision tracker. More...
struct	GoryDetailLogger
	Logs the endgame run, with gory detail. More...
struct	EventRecorder
	Counts endgame events and captures their payloads, for tests and diagnostics. More...
struct	SampleSequenceCollector
	Collects an endgame's approach to the root as a time-indexed sequence, for callers that need to watch a quantity BEHAVE as the point improves rather than judge it at a single point. More...
class	EndgamePrecPolicyBase
	A common base type for various precision types, fixed and adaptive. More...

Functions
	ADD_BERTINI_EVENT_TYPE (EndgameEvent, ConstEvent)
	Generic event for Endgames.
	ADD_BERTINI_EVENT_TYPE (EndgameFailure, ConstEvent)
	Generic failure event for Endgames.
	ADD_BERTINI_EVENT_TYPE (EndgameSuccess, ConstEvent)
	Generic success event for Endgames.
	ADD_BERTINI_EVENT_TYPE (MinTrackTimeReached, EndgameFailure)
	MinTrackTime reached during endgame.
	ADD_BERTINI_EVENT_TYPE (RefiningFailed, EndgameFailure)
	Refining a sample failed for some reason.
	ADD_BERTINI_EVENT_TYPE (CycleNumTooHigh, EndgameFailure)
	Cycle number computed was too high.
	ADD_BERTINI_EVENT_TYPE (SecurityMaxNormReached, EndgameFailure)
	Security max norm reached.
	ADD_BERTINI_EVENT_TYPE (Initializing, EndgameEvent)
	Started running the endgame.
	ADD_BERTINI_EVENT_TYPE (SamplesRecomputedAtHigherPrecision, EndgameEvent)
	The adaptive endgame needed a higher precision before it had its first approximation, and recomputes its sample window at the new precision.
	ADD_BERTINI_EVENT_TYPE (TimeAdvanced, EndgameEvent)
	Time advancing.
	ADD_BERTINI_EVENT_TYPE (ClosedLoop, EndgameEvent)
	Walked a complete loop around the target time.
	ADD_BERTINI_EVENT_TYPE (ApproximatedRoot, EndgameEvent)
	Approximated a root at target time.
	ADD_BERTINI_EVENT_TYPE (Converged, EndgameSuccess)
	Converged – endgame is done!
	ADD_BERTINI_EVENT_TYPE (SampleRefined, EndgameEvent)
	Refined a sample.
	ADD_BERTINI_EVENT_TYPE (InEGOperatingZone, EndgameEvent)
	Made it into the EG operating zone, or so we believe.
template<typename ComplexT>
Vec< ComplexT >	HermiteInterpolateAndSolve (ComplexT const &target_time, const unsigned int num_sample_points, const TimeCont< ComplexT > &times, const SampCont< ComplexT > &samples, const SampCont< ComplexT > &derivatives, ContStart shift_from=ContStart::Back)
	Estimates the root to interpolating polynomial.

Function Documentation

◆ ADD_BERTINI_EVENT_TYPE() [1/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	ApproximatedRoot	,
		EndgameEvent	)

Approximated a root at target time.

◆ ADD_BERTINI_EVENT_TYPE() [2/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	ClosedLoop	,
		EndgameEvent	)

Walked a complete loop around the target time.

◆ ADD_BERTINI_EVENT_TYPE() [3/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	Converged	,
		EndgameSuccess	)

Converged – endgame is done!

◆ ADD_BERTINI_EVENT_TYPE() [4/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	CycleNumTooHigh	,
		EndgameFailure	)

Cycle number computed was too high.

◆ ADD_BERTINI_EVENT_TYPE() [5/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	EndgameEvent	,
		ConstEvent	)

Generic event for Endgames.

◆ ADD_BERTINI_EVENT_TYPE() [6/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	EndgameFailure	,
		ConstEvent	)

Generic failure event for Endgames.

◆ ADD_BERTINI_EVENT_TYPE() [7/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	EndgameSuccess	,
		ConstEvent	)

Generic success event for Endgames.

◆ ADD_BERTINI_EVENT_TYPE() [8/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	InEGOperatingZone	,
		EndgameEvent	)

Made it into the EG operating zone, or so we believe.

◆ ADD_BERTINI_EVENT_TYPE() [9/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	Initializing	,
		EndgameEvent	)

Started running the endgame.

◆ ADD_BERTINI_EVENT_TYPE() [10/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	MinTrackTimeReached	,
		EndgameFailure	)

MinTrackTime reached during endgame.

◆ ADD_BERTINI_EVENT_TYPE() [11/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	RefiningFailed	,
		EndgameFailure	)

Refining a sample failed for some reason.

◆ ADD_BERTINI_EVENT_TYPE() [12/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	SampleRefined	,
		EndgameEvent	)

Refined a sample.

◆ ADD_BERTINI_EVENT_TYPE() [13/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	SamplesRecomputedAtHigherPrecision	,
		EndgameEvent	)

The adaptive endgame needed a higher precision before it had its first approximation, and recomputes its sample window at the new precision.

The samples it announced at the lower precision are superseded – the endgame discards them and tracks the window again from the boundary point – so an observer keeping the sequence of samples should drop them too. (A precision increase LATER in the run, once approximations exist, keeps the samples and widens them in place; that one announces only PrecisionChanged.) Emitted right after the matching PrecisionChanged.

◆ ADD_BERTINI_EVENT_TYPE() [14/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	SecurityMaxNormReached	,
		EndgameFailure	)

Security max norm reached.

◆ ADD_BERTINI_EVENT_TYPE() [15/15]

bertini::endgame::ADD_BERTINI_EVENT_TYPE	(	TimeAdvanced	,
		EndgameEvent	)

Time advancing.

◆ HermiteInterpolateAndSolve()

template<typename ComplexT>

Vec< ComplexT > bertini::endgame::HermiteInterpolateAndSolve	(	ComplexT const &	target_time,
		const unsigned int	num_sample_points,
		const TimeCont< ComplexT > &	times,
		const SampCont< ComplexT > &	samples,
		const SampCont< ComplexT > &	derivatives,
		ContStart	shift_from = ContStart::Back )

Estimates the root to interpolating polynomial.

Input: target_time is the time value that we wish to interpolate at. samples are space values that correspond to the time values in times. derivatives are the dx_dt or dx_ds values at the (time,sample) values.

Output: Since we have a target_time the function returns the corrsponding space value at that time.

Details: We compare our approximations to the tracked value to come up with the cycle number. Also, we use the Hermite interpolation to interpolate at the origin. Once two interpolants are withing FinalTol we say we have converged.

Parameters

target_time	The time value that we wish to interpolate at.
num_sample_points	The number of (time, sample) points used in the interpolation.
times	The time values of the samples used for interpolation.
samples	The space values corresponding to the time values in `times`.
derivatives	The dx/dt (or dx/ds) values at the (time, sample) points.
shift_from	Which end of the sample containers to interpolate from.

Template Parameters

ComplexT The complex number type.

Classes

Functions