Namespaces
namespace	classic
namespace	output
namespace	zero_dim_detail

Classes
struct	AnyAlgorithm
	Type-erased base for all nag algorithms, exposing a single Run() entry point. More...
struct	TolerancesConfig
	Newton and path-tracking tolerances. More...
struct	MidPathConfig
	Configuration for the midpath (path-crossing) check. More...
struct	AutoRetrackConfig
	Configuration for auto-retracking paths flagged as crossed. More...
struct	SharpeningConfig
	Configuration for sharpening computed solutions. More...
struct	RegenerationConfig
	Configuration for the regeneration cascade. More...
struct	PostProcessingConfig
	Configuration for post-processing solutions (reality/finiteness/singularity classification). More...
struct	RecordsConfig
	How a recording algorithm uses the records it finds: not what to compute, but what already-recorded work counts as done. More...
struct	ZeroDimConfig
	Top-level configuration for a zero-dimensional solve (times, precision, threading). More...
struct	MetaConfig
	Top-level meta configuration: which algorithm to run. More...
struct	RandomConfig
	The RNG seed a classic Bertini input file asks for, via randomseed: N;. More...
struct	AlgoTraits
class	PathStarted
	The algorithm is beginning work on one solution path, carrying its index. More...
class	PathComplete
	The algorithm has finished work on one solution path, carrying its index. More...
struct	MidpathChecker
	Detects whether any solution paths crossed during tracking, before the endgame. More...
struct	NewtonRefineResult
	The outcome of a standalone Newton refinement. More...
struct	NumericalIrreducibleDecomposition
	forward declare of the NumericalIrreducibleDecomposition algorithm. More...
struct	AlgoTraits< NumericalIrreducibleDecomposition< TrackerType, EndgameType, SystemType > >
	specify the traits for the algorithm. More...
struct	AnyNID
	Type-erased base for the Numerical Irreducible Decomposition algorithm. More...
struct	Sharpen
struct	HomotopySolver
	The continuation primitive: given a homotopy + a source of start points, track each path through the tracker and endgame, resolve crossings, classify the endpoints, and report. More...
struct	ZeroDimSolver
	The zero-dimensional solve algorithm: given a polynomial system, form a start system and a homotopy, then run the continuation engine. More...
struct	AlgoTraits< HomotopySolver< TrackerType, EndgameType, SystemType > >
	specify the traits for the algorithm. More...
struct	AnyZeroDim
	Type-erased base for a zero-dimensional solve, exposing output and config entry points. More...
struct	AlgorithmMetaData
	metadata structs More...
struct	SolutionMetaData
	Per-solution metadata gathered during and after a path track. More...
struct	EGBoundaryMetaData
	State captured at the endgame boundary, handed off to start the endgame. More...
struct	MidpathCheckReport
	Summary of what the midpath (path-crossing) check found at the endgame boundary, and what the algorithm did about it. More...
struct	SolveReport
	A concise, human-readable summary of a zero-dimensional solve: how every path ended up, and – crucially – whether any path was lost. More...

Typedefs
template<typename T>
using	SolnCont = std::vector<T>
using	SolnIndT = typename SolnCont<complex_dbl>::size_type
	Index type for solutions/paths (over a double-precision solution container).

Enumerations
enum class	RecallPolicy { Nothing , Completed , Everything }
	Which recorded outcomes count as already answered when an identical ask is solved again. More...

Functions
template<typename ComplexT>
unsigned	DefaultInitialAmbientPrecision ()
	The default ambient precision for a ZeroDimConfig, by complex type.
	ADD_BERTINI_EVENT_TYPE (AlgorithmEvent, ConstEvent)
	Generic event for a numerical algebraic geometry algorithm.
	ADD_BERTINI_EVENT_TYPE (AlgorithmStarted, AlgorithmEvent)
	The algorithm has begun (e.g.
	ADD_BERTINI_EVENT_TYPE (AlgorithmComplete, AlgorithmEvent)
	The algorithm has finished.
template<typename ComplexT>
NewtonRefineResult< ComplexT >	NewtonRefine (System const &S, Vec< ComplexT > const &start, NumErrorT tolerance, unsigned max_iterations, ComplexT time=ComplexT(0))
	Newton-refine a point against a square System, without a tracker.
template<typename NumT>
std::ostream &	operator<< (std::ostream &out, const SolutionMetaData< NumT > &meta)
	Stream insertion: write the metadata fields one per line (used by the Python bindings).
template<typename NumT>
std::ostream &	operator<< (std::ostream &out, const EGBoundaryMetaData< NumT > &meta)
	Stream insertion: write the boundary metadata fields one per line (used by the Python bindings).
std::ostream &	operator<< (std::ostream &out, const MidpathCheckReport &r)
	Stream insertion: write the midpath-check report fields one per line.
template<typename ComplexT>
SolveReport	SummarizeSolve (std::vector< SolutionMetaData< ComplexT > > const &metadata, MidpathCheckReport const &midpath)
	Build a SolveReport from the per-endpoint final metadata and the midpath-crossing report.
std::ostream &	operator<< (std::ostream &out, const SolveReport &r)
	Stream insertion: write a human-readable summary of the solve report.
template<typename Target, typename... Ts>
void	InjectParsedTuple (Target &target, std::tuple< Ts... > const &t)
	Inject every element of a tuple of config structs into a Configured-derived target via Set<T>.

Typedef Documentation

◆ SolnCont

template<typename T>

using bertini::algorithm::SolnCont = std::vector<T>

◆ SolnIndT

using bertini::algorithm::SolnIndT = typename SolnCont<complex_dbl>::size_type

Index type for solutions/paths (over a double-precision solution container).

Enumeration Type Documentation

◆ RecallPolicy

enum class bertini::algorithm::RecallPolicy

strong

Which recorded outcomes count as already answered when an identical ask is solved again.

The question recall answers is: a path for this same ask is on record – may its record be used in place of tracking it? A path record is reusable when the run that would reuse it asks no more of that path than the run that produced it. A completed path (success, divergence, a failure under settings that are part of the ask) always qualifies. An abandonment – a path somebody stopped, or a wall-clock limit cut off – was ended for a reason deliberately kept out of the ask, so whether to reuse it is the user's call, and this is where they make it. Transient, like num_threads: it says how to use the records, not what was computed, so it is not part of the configuration's identity.

Enumerator
Nothing	Track every path fresh, even when recorded (observers, benchmarking, re-verification). The fresh run is still recorded.
Completed	The default. Reuse completed paths; re-track abandoned ones – except one cut off by a wall-clock limit no smaller than the current per-path limit, which is reused since the run asks no more of it. An interrupted path is always re-tracked.
Everything	Reuse every recorded outcome as recorded, abandonments included; nothing is re-tracked.

Function Documentation

◆ ADD_BERTINI_EVENT_TYPE() [1/3]

bertini::algorithm::ADD_BERTINI_EVENT_TYPE	(	AlgorithmComplete	,
		AlgorithmEvent	)

The algorithm has finished.

◆ ADD_BERTINI_EVENT_TYPE() [2/3]

bertini::algorithm::ADD_BERTINI_EVENT_TYPE	(	AlgorithmEvent	,
		ConstEvent	)

Generic event for a numerical algebraic geometry algorithm.

◆ ADD_BERTINI_EVENT_TYPE() [3/3]

bertini::algorithm::ADD_BERTINI_EVENT_TYPE	(	AlgorithmStarted	,
		AlgorithmEvent	)

The algorithm has begun (e.g.

the whole zero-dim solve is starting).

◆ DefaultInitialAmbientPrecision()

template<typename ComplexT>

unsigned bertini::algorithm::DefaultInitialAmbientPrecision ( )

inline

The default ambient precision for a ZeroDimConfig, by complex type.

Double-precision solves work at double; multiprecision solves work at the current default precision – which is the precision the MultiplePrecisionTracker is built at, so that in a fixed-multiple solve the start points, the tracker, and the working ("thread") precision are all one and the same value. (Defaulting to DoublePrecision() here left fixed-multiple solves with the tracker at DefaultPrecision() but the ambient/thread precision at double – a mismatch the tracker rejects at start.)

◆ InjectParsedTuple()

template<typename Target, typename... Ts>

void bertini::algorithm::InjectParsedTuple	(	Target &	target,
		std::tuple< Ts... > const &	t )

Inject every element of a tuple of config structs into a Configured-derived target via Set<T>.

Template Parameters

Target	The Configured-derived target type.
Ts	The config struct types in the tuple.

Parameters

target	The target to set the configs on.
t	The tuple of config structs to inject.

◆ NewtonRefine()

template<typename ComplexT>

NewtonRefineResult< ComplexT > bertini::algorithm::NewtonRefine	(	System const &	S,
		Vec< ComplexT > const &	start,
		NumErrorT	tolerance,
		unsigned	max_iterations,
		ComplexT	time = ComplexT(0) )

Newton-refine a point against a square System, without a tracker.

Iterates full Newton steps until the infinity norm of the step falls at or below tolerance, or max_iterations steps have been taken. For a system with a path variable, evaluation is at time time; for an autonomous system time is ignored.

Template Parameters

ComplexT the complex number type to iterate in.

Parameters

S	the system to refine against. Must be square: `NumTotalFunctions()` (user functions plus patches) equal to `NumVariables()`. Deflated systems are the intended customers – square them by randomization if overdetermined.
start	the approximate solution to refine.
tolerance	stop when the infinity norm of a Newton step is at or below this.
max_iterations	refuse to iterate more than this many times.
time	the path-variable value for non-autonomous systems; ignored otherwise.

Returns: a NewtonRefineResult carrying the refined point, the achieved step norm, the iteration count, and the SuccessCode.

Exceptions

std::runtime_error if the system is not square, with a message saying how to square it.

◆ operator<<() [1/4]

template<typename NumT>

std::ostream & bertini::algorithm::operator<<	(	std::ostream &	out,
		const EGBoundaryMetaData< NumT > &	meta )

Stream insertion: write the boundary metadata fields one per line (used by the Python bindings).

◆ operator<<() [2/4]

std::ostream & bertini::algorithm::operator<<	(	std::ostream &	out,
		const MidpathCheckReport &	r )

inline

Stream insertion: write the midpath-check report fields one per line.

◆ operator<<() [3/4]

template<typename NumT>

std::ostream & bertini::algorithm::operator<<	(	std::ostream &	out,
		const SolutionMetaData< NumT > &	meta )

Stream insertion: write the metadata fields one per line (used by the Python bindings).

◆ operator<<() [4/4]

std::ostream & bertini::algorithm::operator<<	(	std::ostream &	out,
		const SolveReport &	r )

inline

Stream insertion: write a human-readable summary of the solve report.

◆ SummarizeSolve()

template<typename ComplexT>

SolveReport bertini::algorithm::SummarizeSolve	(	std::vector< SolutionMetaData< ComplexT > > const &	metadata,
		MidpathCheckReport const &	midpath )

Build a SolveReport from the per-endpoint final metadata and the midpath-crossing report.

Pure aggregation – one pass, no solve state – so it is unit-testable on synthetic metadata.

Namespaces

Classes

Typedefs

Enumerations

Functions

Typedef Documentation

◆ SolnCont

◆ SolnIndT

Enumeration Type Documentation

◆ RecallPolicy

Function Documentation

◆ ADD_BERTINI_EVENT_TYPE() [1/3]

◆ ADD_BERTINI_EVENT_TYPE() [2/3]

◆ ADD_BERTINI_EVENT_TYPE() [3/3]

◆ DefaultInitialAmbientPrecision()

◆ InjectParsedTuple()

◆ NewtonRefine()

◆ operator<<() [1/4]

◆ operator<<() [2/4]

◆ operator<<() [3/4]

◆ operator<<() [4/4]

◆ SummarizeSolve()