Class Function represents a function $R^n\to R$ . More...

#include <capd/map/Function.h>

Public Types
typedef VectorType::ScalarType	ScalarType

typedef BasicFunction< ScalarType >	BaseFunction

typedef BaseFunction::size_type	size_type

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

typedef capd::autodiff::Node	NodeType

Public Member Functions
	Function ()
	creates an univariate constant function f(x)=0 More...

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

	Function (const char *s)
	parses expression from given string. Allocates memory for ODE solver of order 'order' More...

	Function (const Function &f)
	copying constructor More...

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

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

Function &	operator= (const char *)
	substitution from string. Parse expression and compute new DAG. More...

Function &	operator= (const Function &f)
	assignment from an object More...

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

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

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

void	setParameters (const VectorType &values)
	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...

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...

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 VectorType>
class capd::map::Function< VectorType >

Class Function represents a function $R^n\to R$ .

It provides methods for computation of value, gradient and normalized derivatives (Taylor coefficients) of this function at a given point.

The function is internally represented as an optimized array that encodes Direct Acyclic Graph associated to the expression defining function. The expression defining function can be specified as a human readable string or a routine.

The template parameter is a Vector that satisfies capd::vectalg::Vector interface. This includes:

vectors of variable length. They give flexibility but they are slower due to memory allocations and deallocations. Recommended for short programs.
vectors of fixed length - they are allocated on stack instead of storage (dynamic allocation) and thus tey are fast. Recommended for programs running long time.
arbitrary precision vectors - with static and dynamic allocation

Member Typedef Documentation

◆ BaseFunction

template<typename VectorType >

typedef BasicFunction<ScalarType> capd::map::Function< VectorType >::BaseFunction

◆ DAG

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

inherited

◆ NodeType

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

inherited

◆ ScalarType

template<typename VectorType >

typedef VectorType::ScalarType capd::map::Function< VectorType >::ScalarType

◆ size_type

template<typename VectorType >

typedef BaseFunction::size_type capd::map::Function< VectorType >::size_type

Constructor & Destructor Documentation

◆ Function() [1/5]

template<typename VectorType >

capd::map::Function< VectorType >::Function ( void )

creates an univariate constant function f(x)=0

◆ Function() [2/5]

template<typename VectorType >

capd::map::Function< VectorType >::Function ( const std::string & s )

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

◆ Function() [3/5]

template<typename VectorType >

capd::map::Function< VectorType >::Function ( const char * s )

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

◆ Function() [4/5]

template<typename VectorType >

capd::map::Function< VectorType >::Function ( const Function< VectorType > & f )

copying constructor

◆ Function() [5/5]

template<typename VectorType >

template<typename Functional >

capd::map::Function< VectorType >::Function	(	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

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()

template<typename VectorType >

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

protected

◆ clean()

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

protectedinherited

resets all allocated data

◆ 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

◆ 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()

template<typename VectorType >

VectorType capd::map::Function< VectorType >::gradient ( VectorType u ) const

returns gradient of the function computed at vector u

◆ imageDimension()

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

inlineinherited

returns number of functions (dimension of counterdomain)

◆ operator()() [1/2]

template<typename VectorType >

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

evaluates function (for univariate case)

◆ operator()() [2/2]

template<typename VectorType >

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

evaluates function at a given vector

◆ operator=() [1/3]

template<typename VectorType >

Function< VectorType > & capd::map::Function< VectorType >::operator= ( const char * s )

substitution from string. Parse expression and compute new DAG.

◆ operator=() [2/3]

template<typename VectorType >

Function< VectorType > & capd::map::Function< VectorType >::operator= ( const Function< VectorType > & f )

assignment from an object

◆ operator=() [3/3]

template<typename VectorType >

Function< VectorType > & capd::map::Function< VectorType >::operator= ( const std::string & s )

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 VectorType::ScalarType &	value
	)

inherited

sets new value of a parameter of index d.

◆ setParameters() [1/2]

template<typename VectorType >

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

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 VectorType::ScalarType *	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 files:

capd/map/Function.h
capd/map/Function.hpp

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<typename VectorType> class capd::map::Function< VectorType >

Member Typedef Documentation

◆ BaseFunction

◆ DAG

◆ NodeType

◆ ScalarType

◆ size_type

Constructor & Destructor Documentation

◆ Function() [1/5]

◆ Function() [2/5]

◆ Function() [3/5]

◆ Function() [4/5]

◆ Function() [5/5]

Member Function Documentation

◆ addMultiindexToMask()

◆ applyC1Mask()

◆ check()

◆ clean()

◆ copyObject()

◆ createDefault()

◆ createEvalPath()

◆ createFromText()

◆ deleteNodes()

◆ differentiateTime()

◆ dimension()

◆ eval() [1/2]

◆ eval() [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()

◆ imageDimension()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator=() [1/3]

◆ operator=() [2/3]

◆ operator=() [3/3]

◆ 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 VectorType>
class capd::map::Function< VectorType >