Define an abstract function which is twice-derivable ( \(C^2\)). More...

#include <roboptim/core/twice-differentiable-function.hh>

Inheritance diagram for roboptim::GenericTwiceDifferentiableFunction< T >:

Public Types
typedef std::pair< size_type, size_type >	hessianSize_t
	Hessian size type represented as a pair of values. More...

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

Public Types inherited from roboptim::GenericFunction< T >
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...

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...

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

Public Member Functions
	ROBOPTIM_DIFFERENTIABLE_FUNCTION_FWD_TYPEDEFS_ (GenericDifferentiableFunction< T >)

	ROBOPTIM_ADD_FLAG (ROBOPTIM_IS_TWICE_DIFFERENTIABLE)

	ROBOPTIM_GENERATE_TRAITS_REFS_ (hessian)
	Hessian type. More...

hessianSize_t	hessianSize () const
	Return the size of a hessian. More...

bool	isValidHessian (const_hessian_ref hessian) const
	Check if the hessian is valid (check sizes). More...

hessian_t	hessian (const_argument_ref argument, size_type functionId=0) const
	Compute the hessian at a given point. More...

void	hessian (hessian_ref hessian, const_argument_ref argument, size_type functionId=0) const
	Compute the hessian at a given point. More...

virtual std::ostream &	print (std::ostream &) 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
	GenericTwiceDifferentiableFunction (size_type inputSize, size_type outputSize=1, std::string name=std::string())
	Concrete class constructor should call this constructor. More...

virtual void	impl_hessian (hessian_ref hessian, const_argument_ref argument, size_type functionId=0) const =0
	Hessian evaluation. More...

void	setZero (hessian_ref symmetric) const
	Set a symmetric matrix to zero. More...

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...

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

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

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

Additional Inherited Members
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>
class roboptim::GenericTwiceDifferentiableFunction< T >

Define an abstract function which is twice-derivable ( \(C^2\)).

A twice-derivable function is a derivable function which provides a way to compute its hessian.

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

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

Hessian computation is done through the impl_hessian method that has to implemented by the concrete class inheriting this class.

The hessian of a \(\mathbb{R}^n \rightarrow \mathbb{R}^m\) function where \(n > 1\) and \(m > 1\) is a tensor. To avoid this costly representation, the function is split into \(m\) \(\mathbb{R}^n \rightarrow \mathbb{R}\) functions. See DifferentiableFunction documentation for more information.

Member Typedef Documentation

template<typename T >

typedef std::pair<size_type, size_type> roboptim::GenericTwiceDifferentiableFunction< T >::hessianSize_t

Hessian size type represented as a pair of values.

Constructor & Destructor Documentation

template<typename T >

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

protected

Concrete class constructor should call this constructor.

Parameters

inputSize	input size (argument size)
outputSize	output size (result size)
name	function's name

Exceptions

std::runtime_error

Member Function Documentation

template<typename T >

hessian_t roboptim::GenericTwiceDifferentiableFunction< T >::hessian	(	const_argument_ref	argument,
		size_type	functionId = `0`
	)		const

inline

Compute the hessian at a given point.

Program will abort if the argument size is wrong.

Parameters

argument	point where the hessian will be computed
functionId	evaluated function id in the split representation

Returns: computed hessian

References roboptim::GenericTwiceDifferentiableFunction< T >::hessianSize(), and roboptim::GenericTwiceDifferentiableFunction< T >::setZero().

template<typename T >

void roboptim::GenericTwiceDifferentiableFunction< T >::hessian	(	hessian_ref	hessian,
		const_argument_ref	argument,
		size_type	functionId = `0`
	)		const

inline

Compute the hessian at a given point.

Program will abort if the argument size is wrong.

Parameters

hessian	hessian will be stored here
argument	point where the hessian will be computed
functionId	evaluated function id in the split representation

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

References roboptim::GenericTwiceDifferentiableFunction< T >::impl_hessian(), roboptim::is_malloc_allowed(), roboptim::GenericTwiceDifferentiableFunction< T >::isValidHessian(), and roboptim::set_is_malloc_allowed().

template<typename T >

hessianSize_t roboptim::GenericTwiceDifferentiableFunction< T >::hessianSize ( ) const

inline

Return the size of a hessian.

Hessian size is equal to (input size, input size).

Returns: hessian's size as a pair

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

Referenced by roboptim::GenericTwiceDifferentiableFunction< T >::hessian(), and roboptim::GenericTwiceDifferentiableFunction< T >::isValidHessian().

template<typename T >

virtual void roboptim::GenericTwiceDifferentiableFunction< T >::impl_hessian	(	hessian_ref	hessian,
		const_argument_ref	argument,
		size_type	functionId = `0`
	)		const

protectedpure virtual

Hessian evaluation.

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

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

Parameters

hessian	hessian will be stored here
argument	point where the hessian will be computed
functionId	evaluated function id in the split representation

Implemented in roboptim::NTimesDerivableFunction< 2 >, roboptim::GenericNumericQuadraticFunction< T >, roboptim::Cos< T >, roboptim::Sin< T >, roboptim::Polynomial< T >, roboptim::Cos< T >, roboptim::Sin< T >, and roboptim::GenericLinearFunction< T >.

Referenced by roboptim::GenericTwiceDifferentiableFunction< T >::hessian().

template<typename T >

bool roboptim::GenericTwiceDifferentiableFunction< T >::isValidHessian ( const_hessian_ref hessian ) const

inline

Check if the hessian is valid (check sizes).

Parameters

hessian hessian that will be checked

Returns: true if valid, false if not

References roboptim::GenericTwiceDifferentiableFunction< T >::hessianSize().

Referenced by roboptim::GenericTwiceDifferentiableFunction< T >::hessian().

template<typename T >

std::ostream & roboptim::GenericTwiceDifferentiableFunction< 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

Reimplemented from roboptim::GenericDifferentiableFunction< T >.

Reimplemented in roboptim::NTimesDerivableFunction< 2 >, roboptim::GenericNumericQuadraticFunction< T >, roboptim::GenericConstantFunction< T >, roboptim::GenericNumericLinearFunction< T >, roboptim::Polynomial< T >, roboptim::GenericIdentityFunction< T >, roboptim::GenericLinearFunction< T >, roboptim::GenericQuadraticFunction< T >, roboptim::Cos< T >, and roboptim::Sin< T >.

References roboptim::indent().

template<typename T >

roboptim::GenericTwiceDifferentiableFunction< T >::ROBOPTIM_ADD_FLAG ( ROBOPTIM_IS_TWICE_DIFFERENTIABLE )

template<typename T >

roboptim::GenericTwiceDifferentiableFunction< T >::ROBOPTIM_DIFFERENTIABLE_FUNCTION_FWD_TYPEDEFS_ ( GenericDifferentiableFunction< T > )

template<typename T >

roboptim::GenericTwiceDifferentiableFunction< T >::ROBOPTIM_GENERATE_TRAITS_REFS_ ( hessian )

Hessian type.

Hessians are symmetric matrices.

template<typename T >

void roboptim::GenericTwiceDifferentiableFunction< T >::setZero ( hessian_ref symmetric ) const

inlineprotected

Set a symmetric matrix to zero.

Note: there might be an eigen function to do that.

Referenced by roboptim::GenericTwiceDifferentiableFunction< T >::hessian().

Public Types

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

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

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

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