roboptim::GenericTwiceDifferentiableFunction< T > Class Template Referenceabstract

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 Member Functions

 ROBOPTIM_DIFFERENTIABLE_FUNCTION_FWD_TYPEDEFS_ (GenericDifferentiableFunction< T >)
 
 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...
 

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...
 

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

◆ hessianSize_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

◆ GenericTwiceDifferentiableFunction()

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
inputSizeinput size (argument size)
outputSizeoutput size (result size)
namefunction's name
Exceptions
std::runtime_error

Member Function Documentation

◆ hessian() [1/2]

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
argumentpoint where the hessian will be computed
functionIdevaluated function id in the split representation
Returns
computed hessian

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

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

◆ hessian() [2/2]

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
hessianhessian will be stored here
argumentpoint where the hessian will be computed
functionIdevaluated function id in the split representation

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

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

◆ hessianSize()

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

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

◆ impl_hessian()

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
hessianhessian will be stored here
argumentpoint where the hessian will be computed
functionIdevaluated function id in the split representation

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

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

◆ isValidHessian()

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

Check if the hessian is valid (check sizes).

Parameters
hessianhessian 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().

◆ print()

template<typename T >
std::ostream & roboptim::GenericTwiceDifferentiableFunction< T >::print ( std::ostream &  o) const
virtual

Display the function on the specified output stream.

Parameters
ooutput stream used for display
Returns
output stream

Reimplemented in roboptim::NTimesDerivableFunction< 2 >, roboptim::Polynomial< T >, roboptim::Cos< T >, and roboptim::Sin< T >.

References roboptim::indent().

◆ ROBOPTIM_DIFFERENTIABLE_FUNCTION_FWD_TYPEDEFS_()

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

◆ ROBOPTIM_GENERATE_TRAITS_REFS_()

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

Hessian type.

Hessians are symmetric matrices.

◆ setZero()

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().