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

#include <roboptim/core/function.hh>

Inheritance diagram for roboptim::GenericFunction< T >:

Public Types
typedef GenericFunctionTraits < T >::value_type	value_type
	Values type.
typedef GenericFunctionTraits < T >::vector_t	vector_t
	Basic vector type.
typedef GenericFunctionTraits < T >::matrix_t	matrix_t
	Basic matrix type.
typedef GenericFunctionTraits < T >::size_type	size_type
	Size type.
typedef GenericFunctionTraits < T >::result_t	result_t
	Type of a function evaluation result.
typedef GenericFunctionTraits < T >::argument_t	argument_t
	Type of a function evaluation argument.
Public Member Functions
bool	isValidResult (const result_t &result) const throw ()
	Check the given result size is valid.
GenericFunction< T >::size_type	inputSize () const throw ()
	Return the input size (i.e.
GenericFunction< T >::size_type	outputSize () const throw ()
	Return the output size (i.e.
virtual	~GenericFunction () throw ()
	Trivial destructor.
result_t	operator() (const argument_t &argument) const throw ()
	Evaluate the function at a specified point.
void	operator() (result_t &result, const argument_t &argument) const throw ()
	Evaluate the function at a specified point.
const std::string &	getName () const throw ()
	Get function name.
virtual std::ostream &	print (std::ostream &) const throw ()
	Display the function on the specified output stream.
Static Public Member Functions
static value_type	epsilon () throw ()
	Get the value of the machine epsilon, useful for floating types comparison.
static value_type	infinity () throw ()
	Get the value that symbolizes positive infinity.
Protected Member Functions
	GenericFunction (size_type inputSize, size_type outputSize=1, std::string name=std::string()) throw ()
	Concrete class constructor should call this constructor.
virtual void	impl_compute (result_t &result, const argument_t &argument) const =0 throw ()
	Function evaluation.
Static Protected Attributes
static log4cxx::LoggerPtr	logger
	Pointer to function logger (see log4cxx documentation).
Interval
typedef std::pair< value_type, value_type >	interval_t
	Interval type (lower, upper).
typedef std::vector< interval_t >	intervals_t
	Vector of intervals.
static interval_t	makeInterval (value_type l, value_type u) throw ()
	Construct an interval from a lower and upper bound.
static interval_t	makeInfiniteInterval () throw ()
	Construct an infinite interval.
static interval_t	makeLowerInterval (value_type l) throw ()
	Construct an interval from a lower bound.
static interval_t	makeUpperInterval (value_type u) throw ()
	Construct an interval from an upper bound.
static double	getLowerBound (const interval_t &interval) throw ()
	Get the lower bound of an interval.
static double	getUpperBound (const interval_t &interval) throw ()
	Get the upper bound of an interval.
Discrete interval
typedef boost::tuple < value_type, value_type, value_type >	discreteInterval_t
	Types representing a discrete interval.
static discreteInterval_t	makeDiscreteInterval (value_type min, value_type max, value_type step)
	Construct a discrete interval.
static discreteInterval_t	makeDiscreteInterval (interval_t interval, value_type step)
	Construct a discrete interval.
static double	getLowerBound (const discreteInterval_t &interval) throw ()
	Get the lower bound of a discrete interval.
static double	getUpperBound (const discreteInterval_t &interval) throw ()
	Get the upper bound of a discrete interval.
static double	getStep (const discreteInterval_t &interval) throw ()
	Get the upper step of a discrete interval.
template<typename F >
static void	foreach (const discreteInterval_t interval, F functor)
	Iterate on an interval.
template<typename F >
static void	foreach (const interval_t interval, const size_type n, F functor)
	Iterate on an interval.

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:: visualization-gnuplot-function.cc.

Member Typedef Documentation

template<typename T>

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

Type of a function evaluation argument.

Reimplemented in roboptim::SumOfC1Squares, and roboptim::GenericLinearFunction< T >.

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 GenericFunctionTraits<T>::matrix_t roboptim::GenericFunction< T >::matrix_t

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.

Examples:: numeric-quadratic-function.cc.

template<typename T>

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

Type of a function evaluation result.

Reimplemented in roboptim::GenericLinearFunction< T >.

template<typename T>

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

Size type.

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

Reimplemented in roboptim::GenericLinearFunction< T >, and roboptim::GenericQuadraticFunction< T >.

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.

template<typename T>

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

Basic 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.

Reimplemented in roboptim::GenericLinearFunction< T >.

Examples:: numeric-quadratic-function.cc.

Member Function Documentation

template<typename T>

static value_type roboptim::GenericFunction< T >::epsilon ( ) throw () [inline, static]

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

Returns:: machine epsilon value.

Referenced by roboptim::detail::ltvector::operator()().

template<typename T>

template<typename F >

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

References roboptim::GenericFunction< T >::getLowerBound(), roboptim::GenericFunction< T >::getStep(), and roboptim::GenericFunction< T >::getUpperBound().

template<typename T>

template<typename F >

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

References roboptim::GenericFunction< T >::getLowerBound(), and roboptim::GenericFunction< T >::getUpperBound().

template<typename T>

static double roboptim::GenericFunction< T >::getLowerBound ( const interval_t & interval ) throw () [inline, static]

Get the lower bound of an interval.

Parameters:

interval accessed interval

Returns:: lower bound of the interval

Referenced by roboptim::GenericFunction< T >::foreach(), and roboptim::GenericFunction< T >::makeDiscreteInterval().

template<typename T>

static double roboptim::GenericFunction< T >::getLowerBound ( const discreteInterval_t & interval ) throw () [inline, 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 throw () [inline]

Get function name.

Returns:: Function name.

Referenced by roboptim::visualization::gnuplot::plot(), roboptim::visualization::gnuplot::plot_jac(), roboptim::visualization::gnuplot::plot_xy(), and roboptim::GenericFunction< T >::print().

template<typename T>

static double roboptim::GenericFunction< T >::getStep ( const discreteInterval_t & interval ) throw () [inline, static]

Get the upper step of a discrete interval.

Parameters:

interval accessed discrete interval

Returns:: upper step of the discrete interval

Referenced by roboptim::GenericFunction< T >::foreach().

template<typename T>

static double roboptim::GenericFunction< T >::getUpperBound ( const interval_t & interval ) throw () [inline, static]

Get the upper bound of an interval.

Parameters:

interval accessed interval

Returns:: upper bound of the interval

Referenced by roboptim::GenericFunction< T >::foreach(), and roboptim::GenericFunction< T >::makeDiscreteInterval().

template<typename T>

static double roboptim::GenericFunction< T >::getUpperBound ( const discreteInterval_t & interval ) throw () [inline, 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_t &	result,
		const argument_t &	argument
	)		const throw () `[protected, pure virtual]`

Function evaluation.

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

Warning:: Do not call this function directly, call operator()(result_t&, const argument_t&) const throw () instead.

Parameters:

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

Implemented in roboptim::NTimesDerivableFunction< 2 >, roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >, roboptim::GenericNumericLinearFunction< T >, roboptim::SumOfC1Squares, roboptim::NumericQuadraticFunction, roboptim::IdentityFunction, and roboptim::ConstantFunction.

Referenced by roboptim::GenericFunction< T >::operator()().

template<typename T>

static value_type roboptim::GenericFunction< T >::infinity ( ) throw () [inline, static]

Get the value that symbolizes positive infinity.

Returns:: representation of positive infinity in the value type

Referenced by roboptim::GenericFunction< T >::makeInfiniteInterval(), roboptim::GenericFunction< T >::makeLowerInterval(), roboptim::GenericFunction< T >::makeUpperInterval(), roboptim::Problem< F, boost::mpl::vector<> >::print(), and roboptim::Problem< F, CLIST >::print().

template<typename T>

GenericFunction<T>::size_type roboptim::GenericFunction< T >::inputSize ( ) const throw () [inline]

Return the input size (i.e.

argument's vector size).

Returns:: input size

Referenced by roboptim::finiteDifferenceGradientPolicies::Simple< T >::computeGradient(), roboptim::GenericDifferentiableFunction< T >::gradient(), roboptim::GenericDifferentiableFunction< T >::gradientSize(), roboptim::GenericTwiceDifferentiableFunction< T >::hessianSize(), roboptim::GenericDifferentiableFunction< T >::jacobian(), roboptim::GenericDifferentiableFunction< T >::jacobianSize(), roboptim::GenericFunction< T >::operator()(), roboptim::visualization::gnuplot::plot(), and roboptim::visualization::gnuplot::plot_xy().

template<typename T>

bool roboptim::GenericFunction< T >::isValidResult ( const result_t & result ) const throw () [inline]

Check the given result size is valid.

Parameters:

result result that will be checked

Returns:: true if valid, false if not

References roboptim::GenericFunction< T >::outputSize().

Referenced by roboptim::GenericFunction< T >::operator()().

template<typename T>

static discreteInterval_t roboptim::GenericFunction< T >::makeDiscreteInterval	(	value_type	min,
		value_type	max,
		value_type	step
	)		`[inline, static]`

Construct a discrete interval.

Parameters:

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

template<typename T>

static discreteInterval_t roboptim::GenericFunction< T >::makeDiscreteInterval	(	interval_t	interval,
		value_type	step
	)		`[inline, static]`

Construct a discrete interval.

Parameters:

interval	continuous interval
step	discretization step

References roboptim::GenericFunction< T >::getLowerBound(), and roboptim::GenericFunction< T >::getUpperBound().

template<typename T>

static interval_t roboptim::GenericFunction< T >::makeInfiniteInterval ( ) throw () [inline, static]

Construct an infinite interval.

Returns:: interval representing $[-\infty, +\infty]$

References roboptim::GenericFunction< T >::infinity().

Referenced by roboptim::Problem< F, boost::mpl::vector<> >::Problem(), and roboptim::Problem< F, CLIST >::Problem().

template<typename T>

static interval_t roboptim::GenericFunction< T >::makeInterval	(	value_type	l,
		value_type	u
	)		throw () `[inline, static]`

Construct an interval from a lower and upper bound.

Parameters:

l	lower bound
u	upper bound

Returns:: interval representing

Referenced by roboptim::GenericFunction< T >::makeLowerInterval(), and roboptim::GenericFunction< T >::makeUpperInterval().

template<typename T>

static interval_t roboptim::GenericFunction< T >::makeLowerInterval ( value_type l ) throw () [inline, static]

Construct an interval from a lower bound.

Parameters:

l	lower bound

Returns:: interval representing $[l, +\infty]$

References roboptim::GenericFunction< T >::infinity(), and roboptim::GenericFunction< T >::makeInterval().

template<typename T>

static interval_t roboptim::GenericFunction< T >::makeUpperInterval ( value_type u ) throw () [inline, static]

Construct an interval from an upper bound.

Parameters:

u	upper bound

Returns:: interval representing $[-\infty, u]$

References roboptim::GenericFunction< T >::infinity(), and roboptim::GenericFunction< T >::makeInterval().

template<typename T>

result_t roboptim::GenericFunction< T >::operator() ( const argument_t & argument ) const throw () [inline]

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

References roboptim::GenericFunction< T >::outputSize().

template<typename T>

void roboptim::GenericFunction< T >::operator()	(	result_t &	result,
		const argument_t &	argument
	)		const throw () `[inline]`

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::GenericFunction< T >::impl_compute(), roboptim::GenericFunction< T >::inputSize(), roboptim::GenericFunction< T >::isValidResult(), and roboptim::GenericFunction< T >::logger.

template<typename T>

GenericFunction<T>::size_type roboptim::GenericFunction< T >::outputSize ( ) const throw () [inline]

Return the output size (i.e.

result's vector size).

Returns:: input size

Referenced by roboptim::finiteDifferenceGradientPolicies::Simple< T >::computeGradient(), roboptim::finiteDifferenceGradientPolicies::FivePointsRule< T >::computeGradient(), roboptim::GenericFunction< T >::isValidResult(), roboptim::GenericDifferentiableFunction< T >::jacobianSize(), roboptim::GenericFunction< T >::operator()(), roboptim::visualization::gnuplot::plot(), and roboptim::visualization::gnuplot::plot_xy().

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Static Protected Attributes

Interval

Discrete interval

Detailed Description

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

Member Typedef Documentation

Member Function Documentation

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