The polynomial evaluation block: function trees + derivatives + SLP. More...

#include <polynomial_block.hpp>

Public Types
using	NE = std::shared_ptr<node::NamedExpression>
	Shorthand for a shared pointer to a named expression.
using	Nd = std::shared_ptr<node::Node>
	Shorthand for a shared pointer to a generic node.
using	Var = std::shared_ptr<node::Variable>
	Shorthand for a shared pointer to a variable node.

Public Member Functions
	PolynomialBlock ()
	Construct an empty polynomial block at the current default precision.
void	AddFunction (Nd const &f)
	Add a function (one row of the block).
void	AddConstant (NE const &f)
	Add a named constant subfunction.
void	SetVariableOrdering (VariableGroup const &vars) const
	The variable ordering + path variable the function trees are evaluated against; the owning System keeps these in sync (they change as variable groups are added / the system is homogenized).
void	SetPathVariable (Var const &t) const
	Set the path variable the function trees are evaluated against.
void	ClearPathVariable () const
	Clear the path variable.
std::vector< Nd > &	Functions ()
	Get mutable access to the block's functions.
std::vector< Nd > const &	Functions () const
	Get const access to the block's functions.
std::vector< NE > const &	ConstantSubfunctions () const
	Get the block's constant subfunctions.
size_t	NumConstants () const
	Get the number of constant subfunctions.
bool	IsDifferentiated () const
	Query whether the block's derivatives have been computed.
void	Invalidate () const
	Mark the block's derivatives as stale (to be recomputed on next use).
std::vector< int >	Degrees () const
	Per-function degrees (total, and with respect to a variable group).
std::vector< int >	Degrees (VariableGroup const &vars) const
	Per-function degrees with respect to a given variable group.
void	Homogenize (VariableGroup const &group, Var const &hom_var)
	Homogenize each function w.r.t.
bool	IsHomogeneous (VariableGroup const &vars) const
	Query whether every function is homogeneous with respect to a variable group.
bool	IsPolynomial (VariableGroup const &vars) const
	Query whether every function is polynomial in a variable group.
size_t	NumFunctions () const
	Get the number of functions in the block.
bool	DependsOnPathVariable () const
	Query whether the block depends on the path variable.
void	Describe (std::ostream &out, size_t &row, VariableGroup const &, bool) const
	Human-facing description: one line per function, f_k = <expression>.
unsigned	Precision () const
	Get the block's current working precision.
void	Precision (unsigned new_precision) const
	Set the block's working precision (delegated to the compiled SLP).
template<typename T>
void	EvalInPlace (Eigen::Ref< Vec< T > > result, Vec< T > const &vars, T const &path_value) const
	Evaluate the block's functions in place at the given variable and path-variable values.
template<typename T>
void	JacobianInPlace (Eigen::Ref< Mat< T > > J, Vec< T > const &vars, T const &path_value) const
	Evaluate the block's Jacobian in place at the given variable and path-variable values.
template<typename T>
void	TimeDerivInPlace (Eigen::Ref< Vec< T > > result, Vec< T > const &vars, T const &path_value) const
	Evaluate the block's time derivative in place (zero if there is no path variable).
VariableGroup const &	VariableOrdering () const
	Get the variable ordering the functions are evaluated against.
bool	HavePathVariable () const
	Query whether the block has a path variable.
Var	GetPathVariable () const
	Get the block's path variable (may be null).
size_t	NumNaturalFunctions () const
	Get the number of natural (pre-randomization) functions.
std::vector< Nd > const &	GetNaturalFunctions () const
	Get the block's natural function trees.
std::vector< Nd > const &	GetSpaceDerivatives () const
	Get the per-variable space-derivative trees (computing them if needed).
std::vector< Nd > const &	GetTimeDerivatives () const
	Get the time-derivative trees (computing them if needed).
void	Differentiate () const
	Build the symbolic derivatives (and, for SLP eval, compile the SLP from this block).
void	SimplifyFunctions () const
	Simplify the function trees (and invalidate the derivatives, which must be rebuilt).
void	SimplifyDerivatives () const
	Simplify the derivative trees.
void	Reintern (node::ReinternMemo &memo)
	Re-intern this block's nodes after deserialization (ADR-0042): functions, constant subfunctions, variable ordering, and path variable are rebuilt through the live intern tables via the shared memo; the derivative/SLP caches (which reference the old nodes) are dropped and recompute on demand.

Friends
class	boost::serialization::access

Detailed Description

The polynomial evaluation block: function trees + derivatives + SLP.

Member Typedef Documentation

◆ Nd

using bertini::blocks::PolynomialBlock::Nd = std::shared_ptr<node::Node>

Shorthand for a shared pointer to a generic node.

◆ NE

using bertini::blocks::PolynomialBlock::NE = std::shared_ptr<node::NamedExpression>

Shorthand for a shared pointer to a named expression.

◆ Var

using bertini::blocks::PolynomialBlock::Var = std::shared_ptr<node::Variable>

Shorthand for a shared pointer to a variable node.

Constructor & Destructor Documentation

◆ PolynomialBlock()

bertini::blocks::PolynomialBlock::PolynomialBlock ( )

inline

Construct an empty polynomial block at the current default precision.

Member Function Documentation

◆ AddConstant()

void bertini::blocks::PolynomialBlock::AddConstant ( NE const & f )

inline

Add a named constant subfunction.

◆ AddFunction()

void bertini::blocks::PolynomialBlock::AddFunction ( Nd const & f )

inline

Add a function (one row of the block).

◆ ClearPathVariable()

void bertini::blocks::PolynomialBlock::ClearPathVariable ( ) const

inline

Clear the path variable.

◆ ConstantSubfunctions()

std::vector< NE > const & bertini::blocks::PolynomialBlock::ConstantSubfunctions ( ) const

inline

Get the block's constant subfunctions.

◆ Degrees() [1/2]

std::vector< int > bertini::blocks::PolynomialBlock::Degrees ( ) const

inline

Per-function degrees (total, and with respect to a variable group).

◆ Degrees() [2/2]

std::vector< int > bertini::blocks::PolynomialBlock::Degrees ( VariableGroup const & vars ) const

inline

Per-function degrees with respect to a given variable group.

◆ DependsOnPathVariable()

bool bertini::blocks::PolynomialBlock::DependsOnPathVariable ( ) const

inline

Query whether the block depends on the path variable.

◆ Describe()

void bertini::blocks::PolynomialBlock::Describe	(	std::ostream &	out,
		size_t &	row,
		VariableGroup const &	,
		bool	) const

inline

Human-facing description: one line per function, f_k = <expression>.

Polynomials are the content, so terse and verbose are the same (the expression is shown either way).

◆ Differentiate()

void bertini::blocks::PolynomialBlock::Differentiate ( ) const

inline

Build the symbolic derivatives (and, for SLP eval, compile the SLP from this block).

Derivatives are NOT simplified here; explicit simplification is System::Simplify (SimplifyDerivatives), an opt-in the user invokes.

◆ EvalInPlace()

template<typename T>

void bertini::blocks::PolynomialBlock::EvalInPlace	(	Eigen::Ref< Vec< T > >	result,
		Vec< T > const &	vars,
		T const &	path_value ) const

inline

Evaluate the block's functions in place at the given variable and path-variable values.

◆ Functions() [1/2]

std::vector< Nd > & bertini::blocks::PolynomialBlock::Functions ( )

inline

Get mutable access to the block's functions.

◆ Functions() [2/2]

std::vector< Nd > const & bertini::blocks::PolynomialBlock::Functions ( ) const

inline

Get const access to the block's functions.

◆ GetNaturalFunctions()

std::vector< Nd > const & bertini::blocks::PolynomialBlock::GetNaturalFunctions ( ) const

inline

Get the block's natural function trees.

◆ GetPathVariable()

Var bertini::blocks::PolynomialBlock::GetPathVariable ( ) const

inline

Get the block's path variable (may be null).

◆ GetSpaceDerivatives()

std::vector< Nd > const & bertini::blocks::PolynomialBlock::GetSpaceDerivatives ( ) const

inline

Get the per-variable space-derivative trees (computing them if needed).

◆ GetTimeDerivatives()

std::vector< Nd > const & bertini::blocks::PolynomialBlock::GetTimeDerivatives ( ) const

inline

Get the time-derivative trees (computing them if needed).

◆ HavePathVariable()

bool bertini::blocks::PolynomialBlock::HavePathVariable ( ) const

inline

Query whether the block has a path variable.

◆ Homogenize()

void bertini::blocks::PolynomialBlock::Homogenize	(	VariableGroup const &	group,
		Var const &	hom_var )

inline

Homogenize each function w.r.t.

the group + its homogenizing var, functionally: each function is rebound to a freshly homogenized copy, so any external holder of the original function node never observes it change (shared variables are preserved).

◆ Invalidate()

void bertini::blocks::PolynomialBlock::Invalidate ( ) const

inline

Mark the block's derivatives as stale (to be recomputed on next use).

◆ IsDifferentiated()

bool bertini::blocks::PolynomialBlock::IsDifferentiated ( ) const

inline

Query whether the block's derivatives have been computed.

◆ IsHomogeneous()

bool bertini::blocks::PolynomialBlock::IsHomogeneous ( VariableGroup const & vars ) const

inline

Query whether every function is homogeneous with respect to a variable group.

◆ IsPolynomial()

bool bertini::blocks::PolynomialBlock::IsPolynomial ( VariableGroup const & vars ) const

inline

Query whether every function is polynomial in a variable group.

◆ JacobianInPlace()

template<typename T>

void bertini::blocks::PolynomialBlock::JacobianInPlace	(	Eigen::Ref< Mat< T > >	J,
		Vec< T > const &	vars,
		T const &	path_value ) const

inline

Evaluate the block's Jacobian in place at the given variable and path-variable values.

◆ NumConstants()

size_t bertini::blocks::PolynomialBlock::NumConstants ( ) const

inline

Get the number of constant subfunctions.

◆ NumFunctions()

size_t bertini::blocks::PolynomialBlock::NumFunctions ( ) const

inline

Get the number of functions in the block.

◆ NumNaturalFunctions()

size_t bertini::blocks::PolynomialBlock::NumNaturalFunctions ( ) const

inline

Get the number of natural (pre-randomization) functions.

◆ Precision() [1/2]

unsigned bertini::blocks::PolynomialBlock::Precision ( ) const

inline

Get the block's current working precision.

◆ Precision() [2/2]

void bertini::blocks::PolynomialBlock::Precision ( unsigned new_precision ) const

inline

Set the block's working precision (delegated to the compiled SLP).

◆ Reintern()

void bertini::blocks::PolynomialBlock::Reintern ( node::ReinternMemo & memo )

inline

Re-intern this block's nodes after deserialization (ADR-0042): functions, constant subfunctions, variable ordering, and path variable are rebuilt through the live intern tables via the shared memo; the derivative/SLP caches (which reference the old nodes) are dropped and recompute on demand.

Content is unchanged.

◆ SetPathVariable()

void bertini::blocks::PolynomialBlock::SetPathVariable ( Var const & t ) const

inline

Set the path variable the function trees are evaluated against.

◆ SetVariableOrdering()

void bertini::blocks::PolynomialBlock::SetVariableOrdering ( VariableGroup const & vars ) const

inline

The variable ordering + path variable the function trees are evaluated against; the owning System keeps these in sync (they change as variable groups are added / the system is homogenized).

◆ SimplifyDerivatives()

void bertini::blocks::PolynomialBlock::SimplifyDerivatives ( ) const

inline

Simplify the derivative trees.

Simplification is functional and purely structural (Node::Simplified, ADR-0011), so it needs no point and no node evaluation. Requires the derivatives to already exist.

◆ SimplifyFunctions()

void bertini::blocks::PolynomialBlock::SimplifyFunctions ( ) const

inline

Simplify the function trees (and invalidate the derivatives, which must be rebuilt).

◆ TimeDerivInPlace()

template<typename T>

void bertini::blocks::PolynomialBlock::TimeDerivInPlace	(	Eigen::Ref< Vec< T > >	result,
		Vec< T > const &	vars,
		T const &	path_value ) const

inline

Evaluate the block's time derivative in place (zero if there is no path variable).

◆ VariableOrdering()

VariableGroup const & bertini::blocks::PolynomialBlock::VariableOrdering ( ) const

inline

Get the variable ordering the functions are evaluated against.

◆ boost::serialization::access

friend class boost::serialization::access

friend

Public Types

Public Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ Nd

◆ NE

◆ Var

Constructor & Destructor Documentation

◆ PolynomialBlock()

Member Function Documentation

◆ AddConstant()

◆ AddFunction()

◆ ClearPathVariable()

◆ ConstantSubfunctions()

◆ Degrees() [1/2]

◆ Degrees() [2/2]

◆ DependsOnPathVariable()

◆ Describe()

◆ Differentiate()

◆ EvalInPlace()

◆ Functions() [1/2]

◆ Functions() [2/2]

◆ GetNaturalFunctions()

◆ GetPathVariable()

◆ GetSpaceDerivatives()

◆ GetTimeDerivatives()

◆ HavePathVariable()

◆ Homogenize()

◆ Invalidate()

◆ IsDifferentiated()

◆ IsHomogeneous()

◆ IsPolynomial()

◆ JacobianInPlace()

◆ NumConstants()

◆ NumFunctions()

◆ NumNaturalFunctions()

◆ Precision() [1/2]

◆ Precision() [2/2]

◆ Reintern()

◆ SetPathVariable()

◆ SetVariableOrdering()

◆ SimplifyDerivatives()

◆ SimplifyFunctions()

◆ TimeDerivInPlace()

◆ VariableOrdering()

Friends And Related Symbol Documentation

◆ boost::serialization::access