TimeMap class provides class that serves as Poincare section of the form x_i = c. More...

#include <capd/poincare/NonlinearSection.h>

Public Types
typedef MatrixT	MatrixType

typedef MatrixType::RowVectorType	VectorType

typedef MatrixType::ScalarType	ScalarType

typedef VectorType::size_type	size_type
	integral type used to index containers (vectors, matrices, etc) More...

typedef capd::dynset::AbstractSet< VectorType >	Set
	type of abstract base class for all sets More...

typedef AbstractSection< MatrixT >::JetType	JetType

typedef capd::map::Function< VectorType >	BaseFunction
	parses expression from given string. Allocates memory for ODE solver of order 'order' More...

typedef capd::diffAlgebra::Hessian< ScalarType, VectorType::csDim, VectorType::csDim >	HessianType

typedef SectionDerivativesEnclosure< MatrixType >	SectionDerivativesEnclosureType

typedef capd::autodiff::DagIndexer< ScalarType >	DAG

typedef capd::autodiff::Node	NodeType

Public Member Functions
	NonlinearSection (const std::string &s)
	parses expression from given string. Allocates memory for ODE solver of order 'order' More...

	NonlinearSection (const char *s)

template<typename Functional >
	NonlinearSection (Functional f, int dimIn, int noParam, size_type degree=1)
	parses expression from given routine. More...

NonlinearSection &	operator= (const std::string &s)
	substitution from string. Parse expression and compute new DAG. More...

NonlinearSection &	operator= (const char *s)

ScalarType	operator() (const VectorType &v) const
	evaluates function at a given vector More...

VectorType	gradient (const VectorType &v) const
	returns gradient of the function computed at vector u More...

ScalarType	evalAt (const capd::dynset::AbstractSet< VectorType > &s) const

void	computeDT (const JetType &, const JetType &, JetType &, size_type) const

virtual ScalarType	gradientByVector (const VectorType &x, const VectorType &u) const

virtual bool	isSpecialSection () const
	This is very important function. More...

virtual ScalarType	evalAt (const Set &set) const =0
	This function computes value of section function on a given set. More...

virtual void	computeDT (const MatrixType &derivativeOfFlow, const VectorType &gradientOnPx, const ScalarType &denominator, VectorType &result) const
	computes gradient of return time More...

virtual MatrixType	computeDP (const VectorType &Px, const MatrixType &derivativeOfFlow, const VectorType &fieldOnPx, VectorType &dT) const
	Simultaneous computation of gradient of return time and derivative of Poincare Map dP. More...

virtual void	computeDP (const VectorType &Px, const MatrixType &derivativeOfFlow, const HessianType &hessianOfFlow, const VectorType &fieldOnPx, const VectorType &d2Phidt2, const MatrixType &derOfVectorFieldOnPx, MatrixType &DP, HessianType &D2P, VectorType &dT, MatrixType &d2T) const
	Simultaneous computation of first and second Taylor coefficients of return time and Poincare map. More...

ScalarType	operator() (const ScalarType &v) const
	evaluates function (for univariate case) More...

ScalarType	operator() (const MatrixT::RowVectorType &v) const
	evaluates function at a given vector More...

MatrixT::RowVectorType	gradient (MatrixT::RowVectorType u) const
	returns gradient of the function computed at vector u More...

void	setParameters (const MatrixT::RowVectorType &values)
	simultaneously sets values of many parameters. It is assumed that given vector contains values of subsequent parameters. More...

void	setParameters (const VectorType::ScalarType *values, size_type d)
	simultaneously sets values of many parameters. It is assumed that given vector contains values of subsequent parameters. More...

size_type	dimension () const
	returns number of main variables (does not count time and parameters) More...

size_type	imageDimension () const
	returns number of functions (dimension of counterdomain) More...

void	setOrder (size_type)
	allocates necessary memory for ODE solver of order 'order' More...

size_type	getOrder () const
	returns current order of expansion with respect to the time variable More...

void	setParameter (size_type d, const VectorType::ScalarType &value)
	sets new value of a parameter of index d. More...

void	setParameter (const std::string &name, const ScalarType &value)
	sets new value of a parameter. If parameter not found there is no effect. More...

ScalarType	getParameter (size_type d) const

ScalarType	getParameter (const std::string &name) const

void	setCurrentTime (const ScalarType &a_time) const
	sets actual value of variable that represents time in an ODE. More...

const ScalarType &	getCurrentTime () const
	returns actual value of variable that represents time in an ODE More...

void	differentiateTime () const
	sets first derivative of time with respect to time equal to 1 More...

void	setMask (Iterator b, Iterator e)
	The iterator range [b,e) should contain a range of Multiinideces the user requires to compute. More...

void	addMultiindexToMask (const capd::vectalg::Multiindex &mi)
	Adds new multiindex (along with dependencies) to the existing mask. More...

void	resetMask ()
	Resets the mask of derivatives. More...

const bool *	getMask () const

bool	getMask (size_type i) const

bool	getMask (size_type i, size_type j) const

Protected Member Functions
void	check (const std::string &s)

void	reset (Function f, int dimIn, int dimOut, int noParam)
	parses expression from given routine. More...

void	createDefault ()
	used to create a default object without expression. Creates a univariate constant function f(x)=0 More...

void	createFromText (std::string s)
	parses expression from given string. Allocates memory for ODE solver of order 'order' More...

void	copyObject (const BasicFunction &f)
	an auxiliary function used in copying constructor and assignment operator More...

void	clean ()
	resets all allocated data More...

void	realloc (size_type degree)
	reallocates memory for computation of derivatives up to order 'degree' More...

void	createEvalPath ()
	creates an evaluation path for the expression. Nodes that do not need evaluation (constants, vars) are removed from DAG of expression. Moreover, evaluation is optimized. More...

void	setArgument (const V &v) const

void	applyC1Mask () const

void	evalHomogenousPolynomial () const

void	evalHomogenousPolynomial (size_type degree, size_type coeffNo=0) const

void	eval (size_type coeffNo) const

void	eval (size_type degree, size_type coeffNo) const

void	deleteNodes ()

Protected Attributes
std::vector< capd::autodiff::AbstractNode< ScalarType > * >	m_nodes

std::vector< capd::autodiff::Node >	m_fullGraph
	graph representing the expression More...

std::vector< capd::autodiff::MyNode >	m_evalPath
	reduced graph - only nodes with nontrivial evaluations are left More...

std::vector< int >	m_pos
	indices of roots of expressions for each component More...

std::vector< std::string >	m_var
	variables, time and parameters More...

DAG	m_dag
	data structure that stores all the coefficients. Provides suitable indexing and evaluation of expression. More...

size_type	m_indexOfFirstParam
	if equal to m_var.size() then no parameters specified More...

Detailed Description

template<typename MatrixT>
class capd::poincare::NonlinearSection< MatrixT >

TimeMap class provides class that serves as Poincare section of the form x_i = c.

The section is defined by:

integer - index of variable
constant c that defines affine hyperplane x_i=c

Member Typedef Documentation

◆ BaseFunction

template<typename MatrixT >

typedef capd::map::Function<VectorType> capd::poincare::NonlinearSection< MatrixT >::BaseFunction

parses expression from given string. Allocates memory for ODE solver of order 'order'

◆ DAG

typedef capd::autodiff::DagIndexer<ScalarType> capd::map::BasicFunction< VectorType::ScalarType >::DAG

inherited

◆ HessianType

template<class MatrixT >

typedef capd::diffAlgebra::Hessian<ScalarType,VectorType::csDim,VectorType::csDim> capd::poincare::AbstractSection< MatrixT >::HessianType

inherited

◆ JetType

template<typename MatrixT >

typedef AbstractSection<MatrixT>::JetType capd::poincare::NonlinearSection< MatrixT >::JetType

◆ MatrixType

template<typename MatrixT >

typedef MatrixT capd::poincare::NonlinearSection< MatrixT >::MatrixType

◆ NodeType

typedef capd::autodiff::Node capd::map::BasicFunction< VectorType::ScalarType >::NodeType

inherited

◆ ScalarType

template<typename MatrixT >

typedef MatrixType::ScalarType capd::poincare::NonlinearSection< MatrixT >::ScalarType

◆ SectionDerivativesEnclosureType

template<class MatrixT >

typedef SectionDerivativesEnclosure<MatrixType> capd::poincare::AbstractSection< MatrixT >::SectionDerivativesEnclosureType

inherited

◆ Set

template<typename MatrixT >

typedef capd::dynset::AbstractSet<VectorType> capd::poincare::NonlinearSection< MatrixT >::Set

type of abstract base class for all sets

◆ size_type

template<typename MatrixT >

typedef VectorType::size_type capd::poincare::NonlinearSection< MatrixT >::size_type

integral type used to index containers (vectors, matrices, etc)

◆ VectorType

template<typename MatrixT >

typedef MatrixType::RowVectorType capd::poincare::NonlinearSection< MatrixT >::VectorType

Constructor & Destructor Documentation

◆ NonlinearSection() [1/3]

template<typename MatrixT >

capd::poincare::NonlinearSection< MatrixT >::NonlinearSection ( const std::string & s )

inline

parses expression from given string. Allocates memory for ODE solver of order 'order'

◆ NonlinearSection() [2/3]

template<typename MatrixT >

capd::poincare::NonlinearSection< MatrixT >::NonlinearSection ( const char * s )

inline

◆ NonlinearSection() [3/3]

template<typename MatrixT >

template<typename Functional >

capd::poincare::NonlinearSection< MatrixT >::NonlinearSection	(	Functional	f,
		int	dimIn,
		int	noParam,
		size_type	degree = `1`
	)

inline

parses expression from given routine.

Allocates memory for jet propagation of degree 'degree'

Parameters

f	- routine that defines function, its signature is: void (NodeType time, NodeType in[], int dimIn, NodeType out[], int dimOut, NodeType param[], int noParam)
dimIn	- number of input variables (dimension of domain)
dimOut	- number of output variables (dimension of codomain)
noParam	- number of parameters substitution from string. Parse expression and compute new DAG.

Member Function Documentation

◆ addMultiindexToMask()

void capd::map::BasicFunction< VectorType::ScalarType >::addMultiindexToMask ( const capd::vectalg::Multiindex & mi )

inlineinherited

Adds new multiindex (along with dependencies) to the existing mask.

Parameters

mi	multiindex to be added to the mask

Warning: causes undefined behavior if the mask has not been set before call to this method.

◆ applyC1Mask()

void capd::map::BasicFunction< VectorType::ScalarType >::applyC1Mask

protectedinherited

◆ check()

void capd::map::Function< MatrixT::RowVectorType >::check ( const std::string & s )

protectedinherited

◆ clean()

void capd::map::BasicFunction< VectorType::ScalarType >::clean

protectedinherited

resets all allocated data

◆ computeDT()

template<typename MatrixT >

void capd::poincare::NonlinearSection< MatrixT >::computeDT	(	const JetType &	,
		const JetType &	,
		JetType &	,
		size_type
	)		const

inline

◆ copyObject()

void capd::map::BasicFunction< VectorType::ScalarType >::copyObject ( const BasicFunction< VectorType::ScalarType > & f )

protectedinherited

an auxiliary function used in copying constructor and assignment operator

◆ createDefault()

void capd::map::BasicFunction< VectorType::ScalarType >::createDefault

protectedinherited

used to create a default object without expression. Creates a univariate constant function f(x)=0

◆ createEvalPath()

void capd::map::BasicFunction< VectorType::ScalarType >::createEvalPath

protectedinherited

creates an evaluation path for the expression. Nodes that do not need evaluation (constants, vars) are removed from DAG of expression. Moreover, evaluation is optimized.

◆ createFromText()

void capd::map::BasicFunction< VectorType::ScalarType >::createFromText ( std::string s )

protectedinherited

parses expression from given string. Allocates memory for ODE solver of order 'order'

◆ deleteNodes()

void capd::map::BasicFunction< VectorType::ScalarType >::deleteNodes

protectedinherited

◆ differentiateTime()

void capd::map::BasicFunction< VectorType::ScalarType >::differentiateTime

inherited

sets first derivative of time with respect to time equal to 1

◆ dimension()

size_type capd::map::BasicFunction< VectorType::ScalarType >::dimension ( ) const

inlineinherited

returns number of main variables (does not count time and parameters)

◆ eval() [1/2]

void capd::map::BasicFunction< VectorType::ScalarType >::eval ( size_type coeffNo ) const

inlineprotectedinherited

◆ eval() [2/2]

void capd::map::BasicFunction< VectorType::ScalarType >::eval	(	size_type	degree,
		size_type	coeffNo
	)		const

inlineprotectedinherited

◆ evalAt() [1/2]

template<typename MatrixT >

ScalarType capd::poincare::NonlinearSection< MatrixT >::evalAt ( const capd::dynset::AbstractSet< VectorType > & s ) const

inline

◆ evalAt() [2/2]

template<class MatrixT >

virtual ScalarType capd::poincare::AbstractSection< MatrixT >::evalAt ( const Set & set ) const

pure virtualinherited

This function computes value of section function on a given set.

◆ evalHomogenousPolynomial() [1/2]

void capd::map::BasicFunction< VectorType::ScalarType >::evalHomogenousPolynomial ( ) const

inlineprotectedinherited

◆ evalHomogenousPolynomial() [2/2]

void capd::map::BasicFunction< VectorType::ScalarType >::evalHomogenousPolynomial	(	size_type	degree,
		size_type	coeffNo = `0`
	)		const

inlineprotectedinherited

◆ getCurrentTime()

const VectorType::ScalarType & capd::map::BasicFunction< VectorType::ScalarType >::getCurrentTime

inherited

returns actual value of variable that represents time in an ODE

◆ getMask() [1/3]

const bool* capd::map::BasicFunction< VectorType::ScalarType >::getMask ( ) const

inlineinherited

◆ getMask() [2/3]

bool capd::map::BasicFunction< VectorType::ScalarType >::getMask ( size_type i ) const

inlineinherited

◆ getMask() [3/3]

bool capd::map::BasicFunction< VectorType::ScalarType >::getMask	(	size_type	i,
		size_type	j
	)		const

inlineinherited

◆ getOrder()

size_type capd::map::BasicFunction< VectorType::ScalarType >::getOrder ( ) const

inlineinherited

returns current order of expansion with respect to the time variable

◆ getParameter() [1/2]

BasicFunction< VectorType::ScalarType >::ScalarType capd::map::BasicFunction< VectorType::ScalarType >::getParameter ( const std::string & name ) const

inherited

◆ getParameter() [2/2]

BasicFunction< VectorType::ScalarType >::ScalarType capd::map::BasicFunction< VectorType::ScalarType >::getParameter ( size_type d ) const

inherited

◆ gradient() [1/2]

template<typename MatrixT >

VectorType capd::poincare::NonlinearSection< MatrixT >::gradient ( const VectorType & u ) const

inlinevirtual

returns gradient of the function computed at vector u

Implements capd::poincare::AbstractSection< MatrixT >.

◆ gradient() [2/2]

MatrixT::RowVectorType capd::map::Function< MatrixT::RowVectorType >::gradient ( MatrixT::RowVectorType u ) const

inherited

returns gradient of the function computed at vector u

◆ gradientByVector()

template<class MatrixT >

virtual ScalarType capd::poincare::AbstractSection< MatrixT >::gradientByVector	(	const VectorType &	x,
		const VectorType &	u
	)		const

inlinevirtualinherited

Reimplemented in capd::poincare::CoordinateSection< MatrixT >, and capd::poincare::CoordinateSection< MatrixType >.

◆ imageDimension()

size_type capd::map::BasicFunction< VectorType::ScalarType >::imageDimension ( ) const

inlineinherited

returns number of functions (dimension of counterdomain)

◆ isSpecialSection()

template<class MatrixT >

virtual bool capd::poincare::AbstractSection< MatrixT >::isSpecialSection ( ) const

inlinevirtualinherited

This is very important function.

If it returns true, class PoincareMap delegates computation of value of section(set) to the section. Otherwise it is assumed that the set has more information to compute value of section(set) in most optimal way. This is quite natural as the set knows its own representation. This function returns true for instance if the PoincareSection is given by x_i=c, where x_i is i-th coordinate and c is constant.

Reimplemented in capd::poincare::CoordinateSection< MatrixT >, and capd::poincare::CoordinateSection< MatrixType >.

◆ operator()() [1/3]

Function< MatrixT::RowVectorType >::ScalarType capd::map::Function< MatrixT::RowVectorType >::operator() ( const MatrixT::RowVectorType & v ) const

inherited

evaluates function at a given vector

◆ operator()() [2/3]

Function< MatrixT::RowVectorType >::ScalarType capd::map::Function< MatrixT::RowVectorType >::operator() ( const ScalarType & v ) const

inherited

evaluates function (for univariate case)

◆ operator()() [3/3]

template<typename MatrixT >

ScalarType capd::poincare::NonlinearSection< MatrixT >::operator() ( const VectorType & v ) const

inlinevirtual

evaluates function at a given vector

Implements capd::poincare::AbstractSection< MatrixT >.

◆ operator=() [1/2]

template<typename MatrixT >

NonlinearSection& capd::poincare::NonlinearSection< MatrixT >::operator= ( const char * s )

inline

◆ operator=() [2/2]

template<typename MatrixT >

NonlinearSection& capd::poincare::NonlinearSection< MatrixT >::operator= ( const std::string & s )

inline

substitution from string. Parse expression and compute new DAG.

◆ realloc()

void capd::map::BasicFunction< VectorType::ScalarType >::realloc ( size_type degree )

protectedinherited

reallocates memory for computation of derivatives up to order 'degree'

◆ reset()

void capd::map::BasicFunction< VectorType::ScalarType >::reset	(	Function	f,
		int	dimIn,
		int	dimOut,
		int	noParam
	)

protectedinherited

parses expression from given routine.

Assignment of new function parsed from a routine.

Allocates memory for jet propagation of degree 'degree'

Parameters

f	- routine that defines function, its signature is: void (NodeType time, NodeType in[], int dimIn, NodeType out[], int dimOut, NodeType param[], int noParam)
dimIn	- number of input variables (dimension of domain)
dimOut	- number of output variables (dimension of codomain)
noParam	- number of parameters

◆ resetMask()

void capd::map::BasicFunction< VectorType::ScalarType >::resetMask ( )

inlineinherited

Resets the mask of derivatives.

In consequence, full jet of derivatives will be computed after call to any method that computes derivative, hessian or jet.

◆ setArgument()

void capd::map::BasicFunction< VectorType::ScalarType >::setArgument ( const V & v ) const

protectedinherited

◆ setCurrentTime()

void capd::map::BasicFunction< VectorType::ScalarType >::setCurrentTime ( const ScalarType & a_time ) const

inherited

sets actual value of variable that represents time in an ODE.

◆ setMask()

void capd::map::BasicFunction< VectorType::ScalarType >::setMask	(	Iterator	b,
		Iterator	e
	)

inlineinherited

The iterator range [b,e) should contain a range of Multiinideces the user requires to compute.

The method automatically adds all the depending partial derivatives to this collection and defines a mask for computation of partial derivtives.

Parameters

[b,e) iterator range which contains collection of multiindices

Warning: The method causes undefined behavior if a multiindex in the collection exceeds limits of the map (like dimension, maximal allowed degree).

◆ setOrder()

void capd::map::BasicFunction< VectorType::ScalarType >::setOrder ( size_type order )

inherited

allocates necessary memory for ODE solver of order 'order'

◆ setParameter() [1/2]

void capd::map::BasicFunction< VectorType::ScalarType >::setParameter	(	const std::string &	name,
		const ScalarType &	value
	)

inherited

sets new value of a parameter. If parameter not found there is no effect.

◆ setParameter() [2/2]

void capd::map::BasicFunction< VectorType::ScalarType >::setParameter	(	size_type	d,
		const Scalar &	value
	)

inherited

sets new value of a parameter of index d.

◆ setParameters() [1/2]

void capd::map::Function< MatrixT::RowVectorType >::setParameters ( const MatrixT::RowVectorType & values )

inherited

simultaneously sets values of many parameters. It is assumed that given vector contains values of subsequent parameters.

◆ setParameters() [2/2]

void capd::map::BasicFunction< VectorType::ScalarType >::setParameters	(	const Scalar *	values,
		size_type	d
	)

inherited

simultaneously sets values of many parameters. It is assumed that given vector contains values of subsequent parameters.

Member Data Documentation

◆ m_dag

DAG capd::map::BasicFunction< VectorType::ScalarType >::m_dag

mutableprotectedinherited

data structure that stores all the coefficients. Provides suitable indexing and evaluation of expression.

◆ m_evalPath

std::vector<capd::autodiff::MyNode> capd::map::BasicFunction< VectorType::ScalarType >::m_evalPath

protectedinherited

reduced graph - only nodes with nontrivial evaluations are left

◆ m_fullGraph

std::vector<capd::autodiff::Node> capd::map::BasicFunction< VectorType::ScalarType >::m_fullGraph

protectedinherited

graph representing the expression

◆ m_indexOfFirstParam

size_type capd::map::BasicFunction< VectorType::ScalarType >::m_indexOfFirstParam

protectedinherited

if equal to m_var.size() then no parameters specified

◆ m_nodes

std::vector<capd::autodiff::AbstractNode<ScalarType>*> capd::map::BasicFunction< VectorType::ScalarType >::m_nodes

protectedinherited

◆ m_pos

std::vector<int> capd::map::BasicFunction< VectorType::ScalarType >::m_pos

protectedinherited

indices of roots of expressions for each component

◆ m_var

std::vector<std::string> capd::map::BasicFunction< VectorType::ScalarType >::m_var

protectedinherited

variables, time and parameters

The documentation for this class was generated from the following file:

capd/poincare/NonlinearSection.h

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<typename MatrixT> class capd::poincare::NonlinearSection< MatrixT >

Member Typedef Documentation

◆ BaseFunction

◆ DAG

◆ HessianType

◆ JetType

◆ MatrixType

◆ NodeType

◆ ScalarType

◆ SectionDerivativesEnclosureType

◆ Set

◆ size_type

◆ VectorType

Constructor & Destructor Documentation

◆ NonlinearSection() [1/3]

◆ NonlinearSection() [2/3]

◆ NonlinearSection() [3/3]

Member Function Documentation

◆ addMultiindexToMask()

◆ applyC1Mask()

◆ check()

◆ clean()

◆ computeDT()

◆ copyObject()

◆ createDefault()

◆ createEvalPath()

◆ createFromText()

◆ deleteNodes()

◆ differentiateTime()

◆ dimension()

◆ eval() [1/2]

◆ eval() [2/2]

◆ evalAt() [1/2]

◆ evalAt() [2/2]

◆ evalHomogenousPolynomial() [1/2]

◆ evalHomogenousPolynomial() [2/2]

◆ getCurrentTime()

◆ getMask() [1/3]

◆ getMask() [2/3]

◆ getMask() [3/3]

◆ getOrder()

◆ getParameter() [1/2]

◆ getParameter() [2/2]

◆ gradient() [1/2]

◆ gradient() [2/2]

◆ gradientByVector()

◆ imageDimension()

◆ isSpecialSection()

◆ operator()() [1/3]

◆ operator()() [2/3]

◆ operator()() [3/3]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ realloc()

◆ reset()

◆ resetMask()

◆ setArgument()

◆ setCurrentTime()

◆ setMask()

◆ setOrder()

◆ setParameter() [1/2]

◆ setParameter() [2/2]

◆ setParameters() [1/2]

◆ setParameters() [2/2]

Member Data Documentation

◆ m_dag

◆ m_evalPath

◆ m_fullGraph

◆ m_indexOfFirstParam

◆ m_nodes

◆ m_pos

◆ m_var

template<typename MatrixT>
class capd::poincare::NonlinearSection< MatrixT >