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

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

Inheritance diagram for roboptim::GenericTwiceDifferentiableFunction< T >:

Collaboration diagram for roboptim::GenericTwiceDifferentiableFunction< T >:

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

Detailed Description

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

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

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 #DifferentialeFunction documentation for more information.

Member Typedef Documentation

template<typename T >

typedef matrix_t roboptim::GenericTwiceDifferentiableFunction< T >::hessian_t

Hessian type.

Hessians are symmetric matrices.

Reimplemented in roboptim::GenericLinearFunction< T >.

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 ()`
	)		throw () `[protected]`

Concrete class constructor should call this constructor.

Parameters:

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

Member Function Documentation

template<typename T >

hessian_t roboptim::GenericTwiceDifferentiableFunction< T >::hessian	(	const argument_t &	argument,
		size_type	functionId = `0`
	)		const throw () `[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

Examples:: numeric-quadratic-function.cc.

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

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

template<typename T >

void roboptim::GenericTwiceDifferentiableFunction< T >::hessian	(	hessian_t &	hessian,
		const argument_t &	argument,
		size_type	functionId = `0`
	)		const throw () `[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::GenericTwiceDifferentiableFunction< T >::isValidHessian(), and roboptim::GenericFunction< T >::logger.

template<typename T >

hessianSize_t roboptim::GenericTwiceDifferentiableFunction< T >::hessianSize ( ) const throw () [inline]

Return the size of a hessian.

Hessian size is equales 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_t &	hessian,
		const argument_t &	argument,
		size_type	functionId = `0`
	)		const throw () `[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::NumericQuadraticFunction, and roboptim::GenericLinearFunction< T >.

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

template<typename T >

bool roboptim::GenericTwiceDifferentiableFunction< T >::isValidHessian ( const hessian_t & hessian ) const throw () [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 >::hessian(), and roboptim::GenericTwiceDifferentiableFunction< T >::hessianSize().

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

template<typename T >

std::ostream & roboptim::GenericTwiceDifferentiableFunction< T >::print ( std::ostream & o ) const throw () [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::GenericLinearFunction< T >, roboptim::NumericQuadraticFunction, roboptim::GenericNumericLinearFunction< T >, roboptim::GenericQuadraticFunction< T >, roboptim::IdentityFunction, and roboptim::ConstantFunction.

References roboptim::indent().

template<typename T >

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

template<typename T >

void roboptim::GenericTwiceDifferentiableFunction< T >::setZero ( hessian_t & symmetric ) const [inline, protected]

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

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 >