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...

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

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

◆ 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

◆ 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

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

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

◆ 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

◆ 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

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()

◆ createFromText()

◆ deleteNodes()

◆ differentiateTime()

◆ eval() [1/2]

◆ eval() [2/2]

◆ evalHomogenousPolynomial() [1/2]

◆ evalHomogenousPolynomial() [2/2]

◆ getCurrentTime()

◆ getMask() [1/3]

◆ getMask() [2/3]

◆ getMask() [3/3]

◆ getParameter() [1/2]

◆ getParameter() [2/2]

◆ gradient()

◆ 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 >