A block forming the blend (coupling homotopy) H = sum_i c_i(t) * operand_i of several systems. More...

#include <blend_block.hpp>

Public Types
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.
using	OperandPtr = std::shared_ptr<const SystemT>
	Shorthand for a shared pointer to a (const) operand system.

Public Member Functions
	BlendBlock ()
	Construct an empty blend block at the current default precision.
	BlendBlock (Var path_variable, std::vector< Nd > coefficients, std::vector< OperandPtr > operands)
	BlendBlock (BlendBlock const &other)
	Memory-isolating copy constructor (deep-copies each operand system; ADR-0027).
BlendBlock &	operator= (BlendBlock const &other)
	Memory-isolating copy assignment (deep-copies each operand system; ADR-0027).
	BlendBlock (BlendBlock &&)=default
	Move constructor.
BlendBlock &	operator= (BlendBlock &&)=default
	Move assignment.
size_t	NumFunctions () const
	The number of (natural) functions the blend contributes; the owning System adds any patch.
std::vector< Nd > const &	Coefficients () const
	Accessors for the function-tree expansion (System::ExpandToFunctionTree): the blend is H = sum_i coefficients_[i](t) * operands_[i], so the expansion needs the coefficient nodes, the operand systems (each itself expanded), and the shared path variable.
std::vector< OperandPtr > const &	Operands () const
	Get the operand systems being blended.
Var const &	PathVariable () const
	Get the shared path variable the coefficients are functions of.
void	Describe (std::ostream &out, size_t &row, VariableGroup const &, bool verbose) const
	Human-facing description: terse shows the blend f_a..f_b = c_0(t)A + c_1(t)B, with the coefficient nodes shown symbolically and the operands labelled A, B, ...; verbose lists each operand's functions indented.
std::vector< int >	Degrees () const
	The blend c_0(t)f_0 + c_1(t)f_1 + ... has, per function, the max degree of its operands in the space variables (the t-coefficients are constant in space).
std::vector< int >	Degrees (VariableGroup const &vars) const
	Per-function degrees with respect to a given variable group.
void	Homogenize (VariableGroup const &, std::shared_ptr< node::Variable > const &)
	No-op: a blend's operands are already-prepared and cannot be homogenized.
bool	IsHomogeneous (VariableGroup const &) const
	Query whether the blend is homogeneous (iff all operands are).
bool	IsPolynomial (VariableGroup const &) const
	Query whether the blend is polynomial (iff all operands are).
bool	DependsOnPathVariable () const
	A blend always depends on the path variable (through its coefficients).
bool	HasConstantJacobian () const
	A blend does not have a constant Jacobian.
void	Differentiate () const
	Analytic block: nothing symbolic to differentiate.
void	Reintern (node::ReinternMemo &memo)
	Re-intern this block's nodes after deserialization (ADR-0042): path variable and coefficient nodes (gamma) rebuild through the live intern tables via the shared memo; derivative coefficients are re-derived from the rebuilt ones; operand systems recurse (loaded objects are owned here, so the const is safely cast away).
unsigned	Precision () const
	Get the block's current working precision.
void	Precision (unsigned new_precision) const
	Set the block's working precision (propagated to the operand systems).
template<typename T>
void	EvalInPlace (Eigen::Ref< Vec< T > > result, Vec< T > const &vars, T const &path_value) const
	H(x,t) = sum_i c_i(t) * f_i(x) (natural functions only).
template<typename T>
void	JacobianInPlace (Eigen::Ref< Mat< T > > J, Vec< T > const &vars, T const &path_value) const
	dH/dx = sum_i c_i(t) * (df_i/dx) (natural rows only)
template<typename T>
void	TimeDerivInPlace (Eigen::Ref< Vec< T > > result, Vec< T > const &vars, T const &path_value) const
	dH/dt = sum_i c_i'(t) * f_i(x) (operands are autonomous in t)

Static Public Member Functions
static int	CombineDegrees (int a, int b)
	Combine two per-function degrees, propagating the not-a-polynomial sentinel.

Friends
class	boost::serialization::access

Detailed Description

template<typename SystemT>
class bertini::blocks::BlendBlock< SystemT >

A block forming the blend (coupling homotopy) H = sum_i c_i(t) * operand_i of several systems.

Member Typedef Documentation

◆ Nd

template<typename SystemT>

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

Shorthand for a shared pointer to a generic node.

◆ OperandPtr

template<typename SystemT>

using bertini::blocks::BlendBlock< SystemT >::OperandPtr = std::shared_ptr<const SystemT>

Shorthand for a shared pointer to a (const) operand system.

◆ Var

template<typename SystemT>

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

Shorthand for a shared pointer to a variable node.

Constructor & Destructor Documentation

◆ BlendBlock() [1/4]

template<typename SystemT>

bertini::blocks::BlendBlock< SystemT >::BlendBlock ( )

inline

Construct an empty blend block at the current default precision.

◆ BlendBlock() [2/4]

template<typename SystemT>

bertini::blocks::BlendBlock< SystemT >::BlendBlock	(	Var	path_variable,
		std::vector< Nd >	coefficients,
		std::vector< OperandPtr >	operands )

inline

Parameters

path_variable	The shared path variable t the coefficients are functions of.
coefficients	One coefficient node c_i(t) per operand.
operands	The Systems being blended; all must share NumNaturalFunctions().

◆ BlendBlock() [3/4]

template<typename SystemT>

bertini::blocks::BlendBlock< SystemT >::BlendBlock ( BlendBlock< SystemT > const & other )

inline

Memory-isolating copy constructor (deep-copies each operand system; ADR-0027).

◆ BlendBlock() [4/4]

template<typename SystemT>

bertini::blocks::BlendBlock< SystemT >::BlendBlock ( BlendBlock< SystemT > && )

default

Move constructor.

Member Function Documentation

◆ Coefficients()

template<typename SystemT>

std::vector< Nd > const & bertini::blocks::BlendBlock< SystemT >::Coefficients ( ) const

inline

Accessors for the function-tree expansion (System::ExpandToFunctionTree): the blend is H = sum_i coefficients_[i](t) * operands_[i], so the expansion needs the coefficient nodes, the operand systems (each itself expanded), and the shared path variable.

◆ CombineDegrees()

template<typename SystemT>

int bertini::blocks::BlendBlock< SystemT >::CombineDegrees	(	int	a,
		int	b )

inlinestatic

Combine two per-function degrees, propagating the not-a-polynomial sentinel.

A blend of functions is a polynomial only when every operand is, so a -1 from any operand must survive. A plain maximum starting at zero silently turned it into a claim of degree zero, which is how a transcendental homotopy came to report itself as a constant.

◆ Degrees() [1/2]

template<typename SystemT>

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

inline

The blend c_0(t)f_0 + c_1(t)f_1 + ... has, per function, the max degree of its operands in the space variables (the t-coefficients are constant in space).

A function that is not a polynomial reports -1, and that answer propagates through the blend.

◆ Degrees() [2/2]

template<typename SystemT>

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

inline

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

◆ DependsOnPathVariable()

template<typename SystemT>

bool bertini::blocks::BlendBlock< SystemT >::DependsOnPathVariable ( ) const

inline

A blend always depends on the path variable (through its coefficients).

◆ Describe()

template<typename SystemT>

void bertini::blocks::BlendBlock< SystemT >::Describe	(	std::ostream &	out,
		size_t &	row,
		VariableGroup const &	,
		bool	verbose ) const

inline

Human-facing description: terse shows the blend f_a..f_b = c_0(t)*A + c_1(t)*B, with the coefficient nodes shown symbolically and the operands labelled A, B, ...; verbose lists each operand's functions indented.

◆ Differentiate()

template<typename SystemT>

void bertini::blocks::BlendBlock< SystemT >::Differentiate ( ) const

inline

Analytic block: nothing symbolic to differentiate.

◆ EvalInPlace()

template<typename SystemT>

template<typename T>

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

inline

H(x,t) = sum_i c_i(t) * f_i(x) (natural functions only).

◆ HasConstantJacobian()

template<typename SystemT>

bool bertini::blocks::BlendBlock< SystemT >::HasConstantJacobian ( ) const

inline

A blend does not have a constant Jacobian.

◆ Homogenize()

template<typename SystemT>

void bertini::blocks::BlendBlock< SystemT >::Homogenize	(	VariableGroup const &	,
		std::shared_ptr< node::Variable > const &	)

inline

No-op: a blend's operands are already-prepared and cannot be homogenized.

◆ IsHomogeneous()

template<typename SystemT>

bool bertini::blocks::BlendBlock< SystemT >::IsHomogeneous ( VariableGroup const & ) const

inline

Query whether the blend is homogeneous (iff all operands are).

◆ IsPolynomial()

template<typename SystemT>

bool bertini::blocks::BlendBlock< SystemT >::IsPolynomial ( VariableGroup const & ) const

inline

Query whether the blend is polynomial (iff all operands are).

◆ JacobianInPlace()

template<typename SystemT>

template<typename T>

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

inline

dH/dx = sum_i c_i(t) * (df_i/dx) (natural rows only)

◆ NumFunctions()

template<typename SystemT>

size_t bertini::blocks::BlendBlock< SystemT >::NumFunctions ( ) const

inline

The number of (natural) functions the blend contributes; the owning System adds any patch.

◆ Operands()

template<typename SystemT>

std::vector< OperandPtr > const & bertini::blocks::BlendBlock< SystemT >::Operands ( ) const

inline

Get the operand systems being blended.

◆ operator=() [1/2]

template<typename SystemT>

BlendBlock & bertini::blocks::BlendBlock< SystemT >::operator= ( BlendBlock< SystemT > && )

default

Move assignment.

◆ operator=() [2/2]

template<typename SystemT>

BlendBlock & bertini::blocks::BlendBlock< SystemT >::operator= ( BlendBlock< SystemT > const & other )

inline

Memory-isolating copy assignment (deep-copies each operand system; ADR-0027).

◆ PathVariable()

template<typename SystemT>

Var const & bertini::blocks::BlendBlock< SystemT >::PathVariable ( ) const

inline

Get the shared path variable the coefficients are functions of.

◆ Precision() [1/2]

template<typename SystemT>

unsigned bertini::blocks::BlendBlock< SystemT >::Precision ( ) const

inline

Get the block's current working precision.

◆ Precision() [2/2]

template<typename SystemT>

void bertini::blocks::BlendBlock< SystemT >::Precision ( unsigned new_precision ) const

inline

Set the block's working precision (propagated to the operand systems).

◆ Reintern()

template<typename SystemT>

void bertini::blocks::BlendBlock< SystemT >::Reintern ( node::ReinternMemo & memo )

inline

Re-intern this block's nodes after deserialization (ADR-0042): path variable and coefficient nodes (gamma) rebuild through the live intern tables via the shared memo; derivative coefficients are re-derived from the rebuilt ones; operand systems recurse (loaded objects are owned here, so the const is safely cast away).

Content unchanged.

◆ TimeDerivInPlace()

template<typename SystemT>

template<typename T>

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

inline

dH/dt = sum_i c_i'(t) * f_i(x) (operands are autonomous in t)

◆ boost::serialization::access

template<typename SystemT>

friend class boost::serialization::access

friend

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ Nd

◆ OperandPtr

◆ Var

Constructor & Destructor Documentation

◆ BlendBlock() [1/4]

◆ BlendBlock() [2/4]

◆ BlendBlock() [3/4]

◆ BlendBlock() [4/4]

Member Function Documentation

◆ Coefficients()

◆ CombineDegrees()

◆ Degrees() [1/2]

◆ Degrees() [2/2]

◆ DependsOnPathVariable()

◆ Describe()

◆ Differentiate()

◆ EvalInPlace()

◆ HasConstantJacobian()

◆ Homogenize()

◆ IsHomogeneous()

◆ IsPolynomial()

◆ JacobianInPlace()

◆ NumFunctions()

◆ Operands()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ PathVariable()

◆ Precision() [1/2]

◆ Precision() [2/2]

◆ Reintern()

◆ TimeDerivInPlace()

Friends And Related Symbol Documentation

◆ boost::serialization::access