bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType > Struct Template Reference

Owns and builds the target / start system / homotopy for a zero-dim solve. More...

#include <zero_dim_solve.hpp>

Inheritance diagram for bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >:

Public Types
using	StartSystemBaseT = bertini::start_system::StartSystem
	The start-system base type.
using	FactoryT = bertini::start_system::StartSystemFactory<SystemType>
	The start-system factory type.

Public Member Functions
	OwnedHomotopy (SystemType const &target, FactoryT factory, std::string const &path_variable_name)
	Build and own the target, start system, and homotopy from a target system and factory.
SystemType const &	BuiltTarget () const
SystemType const &	UserTarget () const
StartSystemBaseT const &	BuiltStart () const
SystemType const &	BuiltHomotopy () const

Protected Member Functions
void	ConsistencyCheck () const
	Reject targets that cannot have isolated solutions for structural reasons.
void	SquareUp ()
	If the target is over-determined (more equations than the affine dimension), replace it with n generic combinations (System::Randomize) so a start system can track it.
void	RankCheck () const
	Reject a square target whose solution set is still positive-dimensional.

Static Protected Member Functions
static void	PrepareTarget (SystemType &target)
	Homogenize and auto-patch the (already square) target system in place.

Protected Attributes
SystemType	user_target_
	The target exactly as supplied (pristine; the records' target identity).
SystemType	owned_target_
	The owned (cloned, prepared) target system.
std::shared_ptr< StartSystemBaseT >	owned_start_
	The owned start system.
SystemType	owned_homotopy_
	The owned homotopy.
FactoryT	owned_factory_
	The start-system factory used to build the start system.
bool	was_randomized_ = false
	Whether an over-determined target was squared up by randomization.
SystemType	original_natural_target_
	The original (natural, un-homogenized) target, kept to discard extraneous solutions.
Mat< complex_mp >	randomization_matrix_
	The exact coefficient matrix used to square up the system.

Detailed Description

template<typename SystemType>
struct bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >

Owns and builds the target / start system / homotopy for a zero-dim solve.

Constructed as the FIRST base of ZeroDimSolver – before the HomotopySolver engine base, which holds references into these systems – so the homotopy is fully formed before the engine reads it. This holds the system-building half of the algorithm, plus the feasibility / rank checks the algorithm owns. Members carry an owned_ prefix so they do not collide with the engine base's reference members.

Member Typedef Documentation

FactoryT

template<typename SystemType>

using bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::FactoryT = bertini::start_system::StartSystemFactory<SystemType>

The start-system factory type.

StartSystemBaseT

template<typename SystemType>

using bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::StartSystemBaseT = bertini::start_system::StartSystem

The start-system base type.

Constructor & Destructor Documentation

OwnedHomotopy()

template<typename SystemType>

bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::OwnedHomotopy ( SystemType const & target, FactoryT factory, std::string const & path_variable_name )

inline

Build and own the target, start system, and homotopy from a target system and factory.

Member Function Documentation

BuiltHomotopy()

template<typename SystemType>

SystemType const & bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::BuiltHomotopy ( ) const

inline

Returns

The built homotopy.

BuiltStart()

template<typename SystemType>

StartSystemBaseT const & bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::BuiltStart ( ) const

inline

Returns

The built start system.

BuiltTarget()

template<typename SystemType>

SystemType const & bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::BuiltTarget ( ) const

inline

Returns

The built (cloned, prepared) target system.

ConsistencyCheck()

template<typename SystemType>

void bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::ConsistencyCheck ( ) const

inlineprotected

Reject targets that cannot have isolated solutions for structural reasons.

PrepareTarget()

template<typename SystemType>

void bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::PrepareTarget ( SystemType & target )

inlinestaticprotected

Homogenize and auto-patch the (already square) target system in place.

Parameters

target

The target system to prepare.

RankCheck()

template<typename SystemType>

void bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::RankCheck ( ) const

inlineprotected

Reject a square target whose solution set is still positive-dimensional.

ConsistencyCheck only counts equations; a system can be square yet positive-dimensional (e.g. a repeated equation). At a generic point a zero-dimensional system has a full-rank n x n Jacobian, so a rank-deficient Jacobian there means no isolated solutions. Runs only when the (natural, pre-homogenize) system is square; projective/structured inputs whose Jacobian is not n x n are left to ConsistencyCheck.

SquareUp()

template<typename SystemType>

void bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::SquareUp ( )

inlineprotected

If the target is over-determined (more equations than the affine dimension), replace it with n generic combinations (System::Randomize) so a start system can track it.

The randomized system's isolated solutions contain the original's plus extraneous ones; the original system is kept (original_natural_target_) so ZeroDimSolver can filter those out.

UserTarget()

template<typename SystemType>

SystemType const & bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::UserTarget ( ) const

inline

Returns

The target exactly as the USER supplied it: pristine – never squared, homogenized, or patched. The records name THIS system as the ask's target (you asked about your system; the prepared one actually tracked lives, complete, inside the archived homotopy).

Member Data Documentation

original_natural_target_

template<typename SystemType>

SystemType bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::original_natural_target_

protected

The original (natural, un-homogenized) target, kept to discard extraneous solutions.

owned_factory_

template<typename SystemType>

FactoryT bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::owned_factory_

protected

The start-system factory used to build the start system.

owned_homotopy_

template<typename SystemType>

SystemType bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::owned_homotopy_

protected

The owned homotopy.

owned_start_

template<typename SystemType>

std::shared_ptr<StartSystemBaseT> bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::owned_start_

protected

The owned start system.

owned_target_

template<typename SystemType>

SystemType bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::owned_target_

protected

The owned (cloned, prepared) target system.

randomization_matrix_

template<typename SystemType>

Mat<complex_mp> bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::randomization_matrix_

protected

The exact coefficient matrix used to square up the system.

user_target_

template<typename SystemType>

SystemType bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::user_target_

protected

The target exactly as supplied (pristine; the records' target identity).

was_randomized_

template<typename SystemType>

bool bertini::algorithm::zero_dim_detail::OwnedHomotopy< SystemType >::was_randomized_ = false

protected

Whether an over-determined target was squared up by randomization.