A block of system functions, each a product of linear forms. More...

#include <products_of_linears_block.hpp>

Public Member Functions
	ProductsOfLinearsBlock ()
	ProductsOfLinearsBlock (size_t num_vars, std::vector< Mat< complex_mp > > factors)
size_t	NumFunctions () const
	Number of functions (rows the block contributes to the system).
std::vector< int >	Degrees () const
	Each function is a product of its linear factors, so its degree is the factor count.
std::vector< int >	Degrees (VariableGroup const &) const
	Per-function degrees with respect to a given variable group (same as the total degrees).
bool	IsHomogenized () const
	Whether Homogenize has folded the constant column onto a homogenizing variable.
void	Homogenize (VariableGroup const &, std::shared_ptr< node::Variable > const &)
	Homogenize with respect to an affine variable group: fold each factor's constant column onto the homogenizing variable.
bool	IsHomogeneous (VariableGroup const &) const
	Homogeneous once Homogenize has run, or when every factor's constant column is zero (the form the m-homogeneous start system builds directly).
bool	IsPolynomial (VariableGroup const &) const
	Always true: a product of linear forms is a polynomial.
size_t	NumVariables () const
	Number of variables the block expects in the input vector.
std::vector< Mat< complex_mp > > const &	Factors () const
	The master (highest-precision) coefficient matrices, one per function; matrix i is (number of factors of f_i) x (num_vars+1), the last column being the constant/augmenting term.
void	Describe (std::ostream &out, size_t &row, VariableGroup const &vars, bool verbose) const
	Human-facing description: terse shows prod of k linear forms; verbose shows the actual product of affine factors (x - 1) * (x + 1).
bool	DependsOnPathVariable () const
	Products of linears do not depend on the path variable.
bool	HasConstantJacobian () const
	The Jacobian is not constant (it depends on x), unlike a slice.
void	Differentiate () const
	Analytic block: nothing symbolic to differentiate.
unsigned	Precision () const
	Get the block's current working precision.
void	Precision (unsigned new_precision) const
	Set the working precision; recasts the mpfr working coefficients from the master.
template<typename T>
void	EvalInPlace (Eigen::Ref< Vec< T > > result, Vec< T > const &vars, T const &) const
	Evaluate the block's function values into a caller-provided segment.
template<typename T>
void	JacobianInPlace (Eigen::Ref< Mat< T > > J, Vec< T > const &vars, T const &) const
	Evaluate the block's Jacobian (d f_i / d x_j) into a caller-provided block.
template<typename T>
void	TimeDerivInPlace (Eigen::Ref< Vec< T > > result, Vec< T > const &, T const &) const
	Time-derivative into a caller-provided segment.

Friends
class	boost::serialization::access

Detailed Description

A block of system functions, each a product of linear forms.

Value-in / value-out: evaluation takes the variable vector and writes into a caller- provided segment, so the block is self-contained and unit-testable without a System.

Constructor & Destructor Documentation

◆ ProductsOfLinearsBlock() [1/2]

bertini::blocks::ProductsOfLinearsBlock::ProductsOfLinearsBlock ( )

inline

◆ ProductsOfLinearsBlock() [2/2]

bertini::blocks::ProductsOfLinearsBlock::ProductsOfLinearsBlock	(	size_t	num_vars,
		std::vector< Mat< complex_mp > >	factors )

inline

Parameters

num_vars	The number of variables (n). Each coefficient row has n+1 entries (the trailing entry multiplies the augmenting 1 – the constant / homogenizing term).
factors	One augmented coefficient matrix per function; matrix i has shape (number-of-factors_i) x (num_vars + 1).

Member Function Documentation

◆ Degrees() [1/2]

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

inline

Each function is a product of its linear factors, so its degree is the factor count.

◆ Degrees() [2/2]

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

inline

Per-function degrees with respect to a given variable group (same as the total degrees).

◆ DependsOnPathVariable()

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

inline

Products of linears do not depend on the path variable.

◆ Describe()

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

inline

Human-facing description: terse shows prod of k linear forms; verbose shows the actual product of affine factors (x - 1) * (x + 1).

◆ Differentiate()

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

inline

Analytic block: nothing symbolic to differentiate.

◆ EvalInPlace()

template<typename T>

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

inline

Evaluate the block's function values into a caller-provided segment.

The path variable is ignored (products of linears are autonomous).

Parameters

result	Length-NumFunctions() segment to write into.
vars	Length-NumVariables() current variable values.

◆ Factors()

std::vector< Mat< complex_mp > > const & bertini::blocks::ProductsOfLinearsBlock::Factors ( ) const

inline

The master (highest-precision) coefficient matrices, one per function; matrix i is (number of factors of f_i) x (num_vars+1), the last column being the constant/augmenting term.

Exposed so the function-tree expansion (System::ExpandToFunctionTree) can rebuild f_i = prod_r L_r.

◆ HasConstantJacobian()

bool bertini::blocks::ProductsOfLinearsBlock::HasConstantJacobian ( ) const

inline

The Jacobian is not constant (it depends on x), unlike a slice.

◆ Homogenize()

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

inline

Homogenize with respect to an affine variable group: fold each factor's constant column onto the homogenizing variable.

The System prepends the homogenizing variable to the ordering, so its column is the old constant column moved to the front – exactly what LinearFormsBlock does. The m-homogeneous start system builds its block already homogeneous (zero constant column, homogenizing variables among the columns) and is never asked; an affine block built by add_products_of_linears – a regeneration deformation, say – used to meet a no-op here and then be reported homogeneous, so a homogenized System kept an affine block with the wrong variable count and could neither be expanded to nodes nor tracked projectively (b2#376). A second affine group is not yet supported and throws.

◆ IsHomogeneous()

bool bertini::blocks::ProductsOfLinearsBlock::IsHomogeneous ( VariableGroup const & ) const

inline

Homogeneous once Homogenize has run, or when every factor's constant column is zero (the form the m-homogeneous start system builds directly).

◆ IsHomogenized()

bool bertini::blocks::ProductsOfLinearsBlock::IsHomogenized ( ) const

inline

Whether Homogenize has folded the constant column onto a homogenizing variable.

Then every column is a variable column and the block evaluates M*[vars] with no augmenting

Derived from the shape (a constructed block always has num_vars+1 columns), so it adds no state and the canonical encoding is unchanged.

◆ IsPolynomial()

bool bertini::blocks::ProductsOfLinearsBlock::IsPolynomial ( VariableGroup const & ) const

inline

Always true: a product of linear forms is a polynomial.

◆ JacobianInPlace()

template<typename T>

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

inline

Evaluate the block's Jacobian (d f_i / d x_j) into a caller-provided block.

The path variable is ignored (products of linears are autonomous).

Parameters

J	A NumFunctions() x NumVariables() block to write into.
vars	Length-NumVariables() current variable values.

◆ NumFunctions()

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

inline

Number of functions (rows the block contributes to the system).

◆ NumVariables()

size_t bertini::blocks::ProductsOfLinearsBlock::NumVariables ( ) const

inline

Number of variables the block expects in the input vector.

◆ Precision() [1/2]

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

inline

Get the block's current working precision.

◆ Precision() [2/2]

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

inline

Set the working precision; recasts the mpfr working coefficients from the master.

◆ TimeDerivInPlace()

template<typename T>

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

inline

Time-derivative into a caller-provided segment.

Products of linears are autonomous (no path-variable dependence), so this is identically zero.

◆ boost::serialization::access

friend class boost::serialization::access

friend

Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ ProductsOfLinearsBlock() [1/2]

◆ ProductsOfLinearsBlock() [2/2]

Member Function Documentation

◆ Degrees() [1/2]

◆ Degrees() [2/2]

◆ DependsOnPathVariable()

◆ Describe()

◆ Differentiate()

◆ EvalInPlace()

◆ Factors()

◆ HasConstantJacobian()

◆ Homogenize()

◆ IsHomogeneous()

◆ IsHomogenized()

◆ IsPolynomial()

◆ JacobianInPlace()

◆ NumFunctions()

◆ NumVariables()

◆ Precision() [1/2]

◆ Precision() [2/2]

◆ TimeDerivInPlace()

Friends And Related Symbol Documentation

◆ boost::serialization::access