Compute automatically a gradient with finite differences. More...

#include <roboptim/core/fwd.hh>

Inheritance diagram for roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >:

Public Member Functions
	ROBOPTIM_DIFFERENTIABLE_FUNCTION_FWD_TYPEDEFS_ (GenericDifferentiableFunction< T >)

	GenericFiniteDifferenceGradient (const boost::shared_ptr< const GenericFunction< T > > &f, value_type e=finiteDifferenceEpsilon)
	Instantiate a finite differences gradient. More...

	GenericFiniteDifferenceGradient (const GenericFunction< T > &f, value_type e=finiteDifferenceEpsilon)
	Instantiate a finite differences gradient. More...

	~GenericFiniteDifferenceGradient ()

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

Public Member Functions inherited from roboptim::GenericDifferentiableFunction< T >
	ROBOPTIM_FUNCTION_FWD_TYPEDEFS_ (GenericFunction< T >)

	ROBOPTIM_ADD_FLAG (ROBOPTIM_IS_DIFFERENTIABLE)

	ROBOPTIM_GENERATE_TRAITS_REFS_ (gradient)
	Gradient type. More...

	ROBOPTIM_GENERATE_TRAITS_REFS_ (jacobian)
	Jacobian type. More...

size_type	gradientSize () const
	Return the gradient size. More...

jacobianSize_t	jacobianSize () const
	Return the jacobian size as a pair. More...

bool	isValidGradient (const_gradient_ref gradient) const
	Check if the gradient is valid (check size). More...

bool	isValidJacobian (const_jacobian_ref jacobian) const
	Check if the jacobian is valid (check sizes). More...

jacobian_t	jacobian (const_argument_ref argument) const
	Computes the jacobian. More...

void	jacobian (jacobian_ref jacobian, const_argument_ref argument) const
	Computes the jacobian. More...

gradient_t	gradient (const_argument_ref argument, size_type functionId=0) const
	Computes the gradient. More...

void	gradient (gradient_ref gradient, const_argument_ref argument, size_type functionId=0) const
	Computes the gradient. More...

Public Member Functions inherited from roboptim::GenericFunction< T >
	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 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)

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...

Protected Member Functions
virtual void	impl_compute (result_ref, const_argument_ref) const
	Function evaluation. More...

virtual void	impl_gradient (gradient_ref, const_argument_ref argument, size_type=0) const
	Gradient evaluation. More...

virtual void	impl_jacobian (jacobian_ref jacobian, const_argument_ref argument) const
	Jacobian evaluation. More...

std::string	generateName (const GenericFunction< T > &adaptee) const

Protected Member Functions inherited from roboptim::GenericDifferentiableFunction< T >
	GenericDifferentiableFunction (size_type inputSize, size_type outputSize=1, std::string name=std::string())
	Concrete class constructor should call this constructor. More...

template<>
void	impl_jacobian (jacobian_ref jacobian, const_argument_ref argument) const

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

Protected Attributes
const boost::shared_ptr< const GenericFunction< T > >	adaptee_
	Shared pointer to the wrapped function. More...

const value_type	epsilon_

argument_t	xEps_

Additional Inherited Members
Public Types inherited from roboptim::GenericDifferentiableFunction< T >
typedef std::pair< size_type, size_type >	jacobianSize_t
	Jacobian size type (pair of values). More...

Static Public Member Functions inherited from roboptim::GenericFunction< T >
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 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...

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...

Static Public Attributes inherited from roboptim::GenericFunction< T >
static const flag_t	flags = ROBOPTIM_IS_FUNCTION
	Flag representing the Roboptim Function type. More...

Detailed Description

template<typename T, typename FdgPolicy>
class roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >

Compute automatically a gradient with finite differences.

Finite difference gradient is a method to approximate a function's gradient. It is particularly useful in RobOptim to avoid the need to compute the analytical gradient manually.

This class takes a Function as its input and wraps it into a derivable function.

The one dimensional formula with the Simple policy is:

\[f'(x)\approx {f(x+\epsilon)-f(x)\over \epsilon}\]

where \(\epsilon\) is a constant given when calling the class constructor.

For sparse functions, the default behavior is to treat all values as nonzeros. That way, the function can be used in an optimization problem (sparse solvers expect the full sparse pattern during the initialization). The downside to this approach is the lower performance, as the Jacobian matrix will be a dense matrix treated as a sparse one.

Constructor & Destructor Documentation

template<typename T, typename FdgPolicy>

roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >::GenericFiniteDifferenceGradient	(	const boost::shared_ptr< const GenericFunction< T > > &	f,
		value_type	e = `finiteDifferenceEpsilon`
	)

Instantiate a finite differences gradient.

Instantiate a derivable function that will wrap a non derivable function and compute automatically its gradient using finite differences.

Parameters

f	shared pointer to the function that will be wrapped.
e	epsilon used in finite difference computation

template<typename T, typename FdgPolicy>

roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >::GenericFiniteDifferenceGradient	(	const GenericFunction< T > &	f,
		value_type	e = `finiteDifferenceEpsilon`
	)

Instantiate a finite differences gradient.

WARNING: prefer the shared_ptr alternative if possible.

Instantiate a derivable function that will wrap a non derivable function and compute automatically its gradient using finite differences.

Parameters

f	function that will e wrapped
e	epsilon used in finite difference computation

template<typename T , typename FdgPolicy >

roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >::~GenericFiniteDifferenceGradient ( )

Member Function Documentation

template<typename T , typename FdgPolicy >

std::string roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >::generateName ( const GenericFunction< T > & adaptee ) const

protected

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

template<typename T , typename FdgPolicy >

void roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >::impl_compute	(	result_ref	result,
		const_argument_ref	argument
	)		const

protectedvirtual

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

Implements roboptim::GenericFunction< T >.

template<typename T , typename FdgPolicy >

void roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >::impl_gradient	(	gradient_ref	gradient,
		const_argument_ref	argument,
		size_type	functionId = `0`
	)		const

protectedvirtual

Gradient evaluation.

Compute the gradient, has to be implemented in concrete classes. The gradient is computed for a specific sub-function whose id is passed through the functionId argument.

Warning: Do not call this function directly, call gradient instead.

Parameters

gradient	gradient will be stored in this vector
argument	point where the gradient will be computed
functionId	evaluated function id in the split representation

Implements roboptim::GenericDifferentiableFunction< T >.

template<typename T , typename FdgPolicy >

void roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >::impl_jacobian	(	jacobian_ref	jacobian,
		const_argument_ref	arg
	)		const

protectedvirtual

Jacobian evaluation.

Computes the jacobian, can be overridden by concrete classes. The default behavior is to compute the jacobian from the gradient.

Warning: Do not call this function directly, call jacobian instead.

Parameters

jacobian	jacobian will be store in this argument
arg	point where the jacobian will be computed

Reimplemented from roboptim::GenericDifferentiableFunction< T >.

template<typename T , typename FdgPolicy >

std::ostream & roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >::print ( std::ostream & o ) const

virtual

Display the function on the specified output stream.

Parameters

o	output stream used for display

Returns: output stream

Reimplemented from roboptim::GenericDifferentiableFunction< T >.

References roboptim::decindent(), roboptim::iendl(), and roboptim::incindent().

template<typename T, typename FdgPolicy>

roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >::ROBOPTIM_DIFFERENTIABLE_FUNCTION_FWD_TYPEDEFS_ ( GenericDifferentiableFunction< T > )

Member Data Documentation

template<typename T, typename FdgPolicy>

const boost::shared_ptr<const GenericFunction<T> > roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >::adaptee_

protected

Shared pointer to the wrapped function.

template<typename T, typename FdgPolicy>

const value_type roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >::epsilon_

protected

template<typename T, typename FdgPolicy>

argument_t roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >::xEps_

mutableprotected

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

template<typename T, typename FdgPolicy> class roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename T, typename FdgPolicy>
class roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >