Define an abstract mathematical function ( \(C^0\)). More...

#include <roboptim/core/fwd.hh>

Inheritance diagram for roboptim::GenericFunction< T >:

Public Types
typedef T	traits_t
	Traits type. More...

typedef GenericFunctionTraits < T >::value_type	value_type
	Values type. More...

typedef GenericFunctionTraits < T >::size_type	size_type
	Size type. More...

typedef std::string	name_t
	Type of a function argument name. More...

typedef std::vector< name_t >	names_t
	Type of a vector of function argument names. More...

Public Member Functions
	ROBOPTIM_DEFINE_FLAG_TYPE ()

	ROBOPTIM_GENERATE_TRAITS_REFS_ (vector)
	Basic (column) vector type. More...

	ROBOPTIM_GENERATE_TRAITS_REFS_ (rowVector)
	Row vector type. More...

	ROBOPTIM_GENERATE_TRAITS_REFS_ (matrix)
	Basic matrix type. More...

	ROBOPTIM_GENERATE_TRAITS_REFS_ (result)
	Type of a function evaluation result. More...

	ROBOPTIM_GENERATE_TRAITS_REFS_ (argument)
	Type of a function evaluation argument. More...

bool	isValidResult (const_result_ref result) const
	Check the given result size is valid. More...

GenericFunction< T >::size_type	inputSize () const
	Return the input size (i.e. More...

GenericFunction< T >::size_type	outputSize () const
	Return the output size (i.e. More...

virtual	~GenericFunction ()
	Trivial destructor. More...

result_t	operator() (const_argument_ref argument) const
	Evaluate the function at a specified point. More...

void	operator() (result_ref result, const_argument_ref argument) const
	Evaluate the function at a specified point. More...

const std::string &	getName () const
	Get function name. More...

virtual std::ostream &	print (std::ostream &) const
	Display the function on the specified output stream. More...

virtual flag_t	getFlags () const
	Get the type-checking flag. More...

template<typename F >
void	foreach (const discreteInterval_t interval, F functor)

template<typename F >
void	foreach (const interval_t interval, const size_type n, F functor)

Static Public Member Functions
static value_type	epsilon ()
	Get the value of the machine epsilon, useful for floating types comparison. More...

static value_type	infinity ()
	Get the value that symbolizes positive infinity. More...

Static Public Attributes
static const flag_t	flags = ROBOPTIM_IS_FUNCTION
	Flag representing the Roboptim Function type. More...

Protected Member Functions
	GenericFunction (size_type inputSize, size_type outputSize=1, std::string name=std::string())
	Concrete class constructor should call this constructor. More...

virtual void	impl_compute (result_ref result, const_argument_ref argument) const =0
	Function evaluation. More...

Interval
typedef std::pair< value_type, value_type >	interval_t
	Interval type (lower, upper). More...

typedef std::vector< interval_t >	intervals_t
	Vector of intervals. More...

static interval_t	makeInterval (value_type l, value_type u)
	Construct an interval from a lower and upper bound. More...

static interval_t	makeInfiniteInterval ()
	Construct an infinite interval. More...

static interval_t	makeLowerInterval (value_type l)
	Construct an interval from a lower bound. More...

static interval_t	makeUpperInterval (value_type u)
	Construct an interval from an upper bound. More...

static value_type	getLowerBound (const interval_t &interval)
	Get the lower bound of an interval. More...

static value_type	getUpperBound (const interval_t &interval)
	Get the upper bound of an interval. More...

Discrete interval
typedef boost::tuple < value_type, value_type, value_type >	discreteInterval_t
	Types representing a discrete interval. More...

template<class ExpectedType >
ExpectedType *	castInto (bool check=false)
	Cast function to ExpectedType. More...

template<class ExpectedType >
const ExpectedType *	castInto (bool check=false) const
	Cast function to ExpectedType (const). More...

template<class ExpectedType >
bool	asType () const
	Fonction type checking. More...

static discreteInterval_t	makeDiscreteInterval (value_type min, value_type max, value_type step)
	Construct a discrete interval. More...

static discreteInterval_t	makeDiscreteInterval (interval_t interval, value_type step)
	Construct a discrete interval. More...

static value_type	getLowerBound (const discreteInterval_t &interval)
	Get the lower bound of a discrete interval. More...

static value_type	getUpperBound (const discreteInterval_t &interval)
	Get the upper bound of a discrete interval. More...

static value_type	getStep (const discreteInterval_t &interval)
	Get the upper step of a discrete interval. More...

template<typename F >
static void	foreach (const discreteInterval_t interval, F functor)
	Iterate on an interval. More...

template<typename F >
static void	foreach (const interval_t interval, const size_type n, F functor)
	Iterate on an interval. More...

Detailed Description

template<typename T>
class roboptim::GenericFunction< T >

Define an abstract mathematical function ( \(C^0\)).

A function is an object that can be evaluated for a given point.

\[ f : x \rightarrow f(x) \]

\(x \in \mathbb{R}^n\), \(f(x) \in \mathbb{R}^m\) where \(n\) is the input size and \(m\) is the output size.

Functions are pure immutable objects: evaluating a function twice at a given point must give the same result.

This function is parametrized by the matrix type used in this function. Currently, dense (which size may be dynamic or static and sparse Eigen matrices can be used) are supported.

Template Parameters

T	Matrix type

Examples:: result.cc, visualization-gnuplot-function.cc, and visualization-matplotlib-function.cc.

Member Typedef Documentation

template<typename T>

typedef boost::tuple<value_type, value_type, value_type> roboptim::GenericFunction< T >::discreteInterval_t

Types representing a discrete interval.

A discrete interval is a triplet of values:

lower bound,
upper bound,
step.

template<typename T>

typedef std::pair<value_type, value_type> roboptim::GenericFunction< T >::interval_t

Interval type (lower, upper).

Use negative or positive infinity to respectively disable the lower or upper bound.

template<typename T>

typedef std::vector<interval_t> roboptim::GenericFunction< T >::intervals_t

Vector of intervals.

template<typename T>

typedef std::string roboptim::GenericFunction< T >::name_t

Type of a function argument name.

template<typename T>

typedef std::vector<name_t> roboptim::GenericFunction< T >::names_t

Type of a vector of function argument names.

template<typename T>

typedef GenericFunctionTraits<T>::size_type roboptim::GenericFunction< T >::size_type

Size type.

This type is used to represent sizes, indexes, etc.

template<typename T>

typedef T roboptim::GenericFunction< T >::traits_t

Traits type.

Represents the matrix type used to store the underlying data. This can be EigenMatrixDense or EigenMatrixSparse.

template<typename T>

typedef GenericFunctionTraits<T>::value_type roboptim::GenericFunction< T >::value_type

Values type.

Represents the numerical type (i.e. float, double, int...) used for computations.

Constructor & Destructor Documentation

template<typename T >

roboptim::GenericFunction< T >::~GenericFunction ( )

virtual

Trivial destructor.

template<typename T >

roboptim::GenericFunction< T >::GenericFunction	(	size_type	inputSize,
		size_type	outputSize = `1`,
		std::string	name = `std::string ()`
	)

protected

Concrete class constructor should call this constructor.

Parameters

inputSize	function arity
outputSize	result size
name	function's name

Exceptions

std::runtime_error

Member Function Documentation

template<typename T >

template<class ExpectedType >

bool roboptim::GenericFunction< T >::asType ( ) const

Fonction type checking.

Template Parameters

ExpectedType type the function could be compatible with

template<typename T >

template<class ExpectedType >

ExpectedType * roboptim::GenericFunction< T >::castInto ( bool check = false )

Cast function to ExpectedType.

Template Parameters

ExpectedType type we want to cast the function into.

Parameters

check check that the cast is valid, and throws if it is not.

template<typename T >

template<class ExpectedType >

const ExpectedType * roboptim::GenericFunction< T >::castInto ( bool check = false ) const

Cast function to ExpectedType (const).

Template Parameters

ExpectedType type we want to cast the function into.

Parameters

check check that the cast is valid, and throws if it is not.

template<typename T >

GenericFunction< T >::value_type roboptim::GenericFunction< T >::epsilon ( )

static

Get the value of the machine epsilon, useful for floating types comparison.

Returns: machine epsilon value.

template<typename T>

template<typename F >

void roboptim::GenericFunction< T >::foreach	(	const discreteInterval_t	interval,
		F	functor
	)

template<typename T>

template<typename F >

void roboptim::GenericFunction< T >::foreach	(	const interval_t	interval,
		const size_type	n,
		F	functor
	)

template<typename T>

template<typename F >

static void roboptim::GenericFunction< T >::foreach	(	const discreteInterval_t	interval,
		F	functor
	)

static

Iterate on an interval.

Call the functor to each discretization point of the discrete interval.

Parameters

interval	interval on which the method iterates
functor	unary function that will be applied

Template Parameters

F	functor type (has to satisfy the STL unary function concept)

template<typename T>

template<typename F >

static void roboptim::GenericFunction< T >::foreach	(	const interval_t	interval,
		const size_type	n,
		F	functor
	)

static

Iterate on an interval.

Call the functor regularly n times on an interval.

Parameters

interval	interval on which the method iterates
n	number of discretization points
functor	unary function that will be applied

Template Parameters

F	functor type (has to satisfy the STL unary function concept)

template<typename T >

GenericFunction< T >::flag_t roboptim::GenericFunction< T >::getFlags ( ) const

virtual

Get the type-checking flag.

template<typename T >

GenericFunction< T >::value_type roboptim::GenericFunction< T >::getLowerBound ( const interval_t & interval )

static

Get the lower bound of an interval.

Parameters

interval accessed interval

Returns: lower bound of the interval

template<typename T >

GenericFunction< T >::value_type roboptim::GenericFunction< T >::getLowerBound ( const discreteInterval_t & interval )

static

Get the lower bound of a discrete interval.

Parameters

interval accessed discrete interval

Returns: lower bound of the discrete interval

template<typename T >

const std::string & roboptim::GenericFunction< T >::getName ( ) const

Get function name.

Returns: Function name.

Referenced by roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >::generateName(), roboptim::visualization::gnuplot::plot(), roboptim::visualization::matplotlib::plot(), roboptim::visualization::gnuplot::plot_jac(), and roboptim::visualization::gnuplot::plot_xy().

template<typename T >

GenericFunction< T >::value_type roboptim::GenericFunction< T >::getStep ( const discreteInterval_t & interval )

static

Get the upper step of a discrete interval.

Parameters

interval accessed discrete interval

Returns: upper step of the discrete interval

template<typename T >

GenericFunction< T >::value_type roboptim::GenericFunction< T >::getUpperBound ( const interval_t & interval )

static

Get the upper bound of an interval.

Parameters

interval accessed interval

Returns: upper bound of the interval

template<typename T >

GenericFunction< T >::value_type roboptim::GenericFunction< T >::getUpperBound ( const discreteInterval_t & interval )

static

Get the upper bound of a discrete interval.

Parameters

interval accessed discrete interval

Returns: upper bound of the discrete interval

template<typename T>

virtual void roboptim::GenericFunction< T >::impl_compute	(	result_ref	result,
		const_argument_ref	argument
	)		const

protectedpure virtual

Function evaluation.

Evaluate the function, has to be implemented in concrete classes.

Warning: Do not call this function directly, call operator()(result_ref, const_argument_ref) const instead.

Parameters

result	result will be stored in this vector
argument	point at which the function will be evaluated

Implemented in roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >, roboptim::NTimesDerivableFunction< 2 >, roboptim::GenericNumericQuadraticFunction< T >, roboptim::GenericNumericLinearFunction< T >, roboptim::GenericConstantFunction< T >, roboptim::GenericSumOfC1Squares< T >, roboptim::GenericIdentityFunction< T >, roboptim::Polynomial< T >, roboptim::Cos< T >, and roboptim::Sin< T >.

template<typename T >

GenericFunction< T >::value_type roboptim::GenericFunction< T >::infinity ( )

static

Get the value that symbolizes positive infinity.

Returns: representation of positive infinity in the value type

Referenced by roboptim::Problem< T >::constraintsViolationVector(), and roboptim::Result::print().

template<typename T >

GenericFunction< T >::size_type roboptim::GenericFunction< T >::inputSize ( ) const

Return the input size (i.e.

argument's vector size).

Returns: input size

Referenced by roboptim::finiteDifferenceGradientPolicies::Simple< T >::computeGradient(), roboptim::finiteDifferenceGradientPolicies::Policy< T >::computeJacobian(), roboptim::GenericTwiceDifferentiableFunction< T >::hessianSize(), roboptim::Problem< T >::jacobian(), roboptim::visualization::gnuplot::plot(), roboptim::visualization::matplotlib::plot(), and roboptim::visualization::gnuplot::plot_xy().

template<typename T >

bool roboptim::GenericFunction< T >::isValidResult ( const_result_ref result ) const

Check the given result size is valid.

Parameters

result result that will be checked

Returns: true if valid, false if not

template<typename T >

GenericFunction< T >::discreteInterval_t roboptim::GenericFunction< T >::makeDiscreteInterval	(	value_type	min,
		value_type	max,
		value_type	step
	)

static

Construct a discrete interval.

Parameters

min	miminum value of the interval
max	maxinum value of the interval
step	discretization step

template<typename T >

GenericFunction< T >::discreteInterval_t roboptim::GenericFunction< T >::makeDiscreteInterval	(	interval_t	interval,
		value_type	step
	)

static

Construct a discrete interval.

Parameters

interval	continuous interval
step	discretization step

template<typename T >

GenericFunction< T >::interval_t roboptim::GenericFunction< T >::makeInfiniteInterval ( )

static

Construct an infinite interval.

Returns: interval representing \([-\infty, +\infty]\)

Examples:: problem-cc.cc.

template<typename T >

GenericFunction< T >::interval_t roboptim::GenericFunction< T >::makeInterval	(	value_type	l,
		value_type	u
	)

static

Construct an interval from a lower and upper bound.

Parameters

l	lower bound
u	upper bound

Returns: interval representing \([l, u]\)

template<typename T >

GenericFunction< T >::interval_t roboptim::GenericFunction< T >::makeLowerInterval ( value_type l )

static

Construct an interval from a lower bound.

Parameters

l	lower bound

Returns: interval representing \([l, +\infty]\)

template<typename T >

GenericFunction< T >::interval_t roboptim::GenericFunction< T >::makeUpperInterval ( value_type u )

static

Construct an interval from an upper bound.

Parameters

u	upper bound

Returns: interval representing \([-\infty, u]\)

template<typename T >

GenericFunction< T >::result_t roboptim::GenericFunction< T >::operator() ( const_argument_ref argument ) const

Evaluate the function at a specified point.

The program will abort if the argument does not have the expected size.

Parameters

argument point at which the function will be evaluated

Returns: computed result

template<typename T >

void roboptim::GenericFunction< T >::operator()	(	result_ref	result,
		const_argument_ref	argument
	)		const

Evaluate the function at a specified point.

The program will abort if the argument does not have the expected size.

Parameters

result	result will be stored in this vector
argument	point at which the function will be evaluated

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

References roboptim::is_malloc_allowed(), and roboptim::set_is_malloc_allowed().

template<typename T >

GenericFunction< T >::size_type roboptim::GenericFunction< T >::outputSize ( ) const

Return the output size (i.e.

result's vector size).

Returns: output size

Referenced by roboptim::visualization::gnuplot::plot(), roboptim::visualization::matplotlib::plot(), and roboptim::visualization::gnuplot::plot_xy().

template<typename T >

std::ostream & roboptim::GenericFunction< T >::print ( std::ostream & o ) const

virtual

Display the function on the specified output stream.

Parameters

o	output stream used for display

Returns: output stream

References roboptim::indent().

template<typename T>

roboptim::GenericFunction< T >::ROBOPTIM_DEFINE_FLAG_TYPE ( )

template<typename T>

roboptim::GenericFunction< T >::ROBOPTIM_GENERATE_TRAITS_REFS_ ( vector )

Basic (column) vector type.

This basic vector type is used each time a vector of values is required.

Attention: It is good practice in RobOptim to rely on this type when a vector of values is needed instead of relying on a particular implementation.

template<typename T>

roboptim::GenericFunction< T >::ROBOPTIM_GENERATE_TRAITS_REFS_ ( rowVector )

Row vector type.

This basic vector type is used each time a row vector of values is required (e.g. gradients).

template<typename T>

roboptim::GenericFunction< T >::ROBOPTIM_GENERATE_TRAITS_REFS_ ( matrix )

Basic matrix type.

This basic matrix type is used each time a two dimensional matrix of values is needed.

Attention: It is good practice in RobOptim to rely on this type when a matrix of values is needed instead of relying on a particular implementation.

template<typename T>

roboptim::GenericFunction< T >::ROBOPTIM_GENERATE_TRAITS_REFS_ ( result )

Type of a function evaluation result.

template<typename T>

roboptim::GenericFunction< T >::ROBOPTIM_GENERATE_TRAITS_REFS_ ( argument )

Type of a function evaluation argument.

Member Data Documentation

template<typename T>

const flag_t roboptim::GenericFunction< T >::flags = ROBOPTIM_IS_FUNCTION

static

Flag representing the Roboptim Function type.

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Interval

Discrete interval

Detailed Description

template<typename T> class roboptim::GenericFunction< T >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename T>
class roboptim::GenericFunction< T >