roboptim::GenericTwiceDifferentiableFunction< T > Class Template Reference

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

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

Inheritance diagram for roboptim::GenericTwiceDifferentiableFunction< T >:

List of all members.

Public Types
typedef std::pair< size_type, size_type >	hessianSize_t
	Hessian size type represented as a pair of values.
Public Member Functions
	ROBOPTIM_DIFFERENTIABLE_FUNCTION_FWD_TYPEDEFS_ (GenericDifferentiableFunction< T >)
	ROBOPTIM_ADD_FLAG (ROBOPTIM_IS_TWICE_DIFFERENTIABLE)
	ROBOPTIM_GENERATE_TRAITS_REFS_ (hessian)
	Hessian type.
hessianSize_t	hessianSize () const
	Return the size of a hessian.
bool	isValidHessian (const_hessian_ref hessian) const
	Check if the hessian is valid (check sizes).
hessian_t	hessian (const_argument_ref argument, size_type functionId=0) const
	Compute the hessian at a given point.
void	hessian (hessian_ref hessian, const_argument_ref argument, size_type functionId=0) const
	Compute the hessian at a given point.
virtual std::ostream &	print (std::ostream &) const
	Display the function on the specified output stream.
Protected Member Functions
	GenericTwiceDifferentiableFunction (size_type inputSize, size_type outputSize=1, std::string name=std::string())
	Concrete class constructor should call this constructor.
virtual void	impl_hessian (hessian_ref hessian, const_argument_ref argument, size_type functionId=0) const =0
	Hessian evaluation.
void	setZero (hessian_ref symmetric) const
	Set a symmetric matrix to zero.

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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.

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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.

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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

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

References roboptim::GenericTwiceDifferentiableFunction< T >::impl_hessian(), roboptim::is_malloc_allowed(), roboptim::GenericTwiceDifferentiableFunction< T >::isValidHessian(), roboptim::GenericFunction< T >::logger, 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 [protected, pure 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 [inline, protected]

Set a symmetric matrix to zero.

Note:

there might be an eigen function to do that.

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