roboptim::GenericTwiceDifferentiableFunction< T > Class Template Referenceabstract

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

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

Inheritance diagram for roboptim::GenericTwiceDifferentiableFunction< T >:
roboptim::GenericDifferentiableFunction< T > roboptim::GenericFunction< T > roboptim::GenericQuadraticFunction< T > roboptim::NTimesDerivableFunction< 2 > roboptim::GenericLinearFunction< T > roboptim::NumericQuadraticFunction roboptim::ConstantFunction roboptim::GenericNumericLinearFunction< T > roboptim::IdentityFunction

Public Types

typedef matrix_t hessian_t
 Hessian type. More...
 
typedef std::pair< size_type, size_typehessianSize_t
 Hessian size type represented as a pair of values. More...
 
- Public Types inherited from roboptim::GenericDifferentiableFunction< T >
typedef GenericFunctionTraits< T >::gradient_t gradient_t
 Gradient type. More...
 
typedef GenericFunctionTraits< T >::jacobian_t jacobian_t
 Jacobian type. More...
 
typedef std::pair< size_type, size_typejacobianSize_t
 Jacobian size type (pair of values). More...
 
- Public Types inherited from roboptim::GenericFunction< T >
typedef GenericFunctionTraits< T >::value_type value_type
 Values type. More...
 
typedef GenericFunctionTraits< T >::vector_t vector_t
 Basic vector type. More...
 
typedef GenericFunctionTraits< T >::matrix_t matrix_t
 Basic matrix type. More...
 
typedef GenericFunctionTraits< T >::size_type size_type
 Size type. More...
 
typedef GenericFunctionTraits< T >::result_t result_t
 Type of a function evaluation result. More...
 
typedef GenericFunctionTraits< T >::argument_t argument_t
 Type of a function evaluation argument. More...
 
typedef std::pair< value_type, value_typeinterval_t
 Interval type (lower, upper). More...
 
typedef std::vector< interval_tintervals_t
 Vector of intervals. More...
 
typedef boost::tuple< value_type, value_type, value_typediscreteInterval_t
 Types representing a discrete interval. More...
 

Public Member Functions

 ROBOPTIM_DIFFERENTIABLE_FUNCTION_FWD_TYPEDEFS_ (GenericDifferentiableFunction< T >)
 
hessianSize_t hessianSize () const throw ()
 Return the size of a hessian. More...
 
bool isValidHessian (const hessian_t &hessian) const throw ()
 Check if the hessian is valid (check sizes). More...
 
hessian_t hessian (const argument_t &argument, size_type functionId=0) const throw ()
 Compute the hessian at a given point. More...
 
void hessian (hessian_t &hessian, const argument_t &argument, size_type functionId=0) const throw ()
 Compute the hessian at a given point. More...
 
virtual std::ostream & print (std::ostream &) const throw ()
 Display the function on the specified output stream. More...
 
- Public Member Functions inherited from roboptim::GenericDifferentiableFunction< T >
 ROBOPTIM_FUNCTION_FWD_TYPEDEFS_ (GenericFunction< T >)
 
size_type gradientSize () const throw ()
 Return the gradient size. More...
 
jacobianSize_t jacobianSize () const throw ()
 Return the jacobian size as a pair. More...
 
bool isValidGradient (const gradient_t &gradient) const throw ()
 Check if the gradient is valid (check size). More...
 
bool isValidJacobian (const jacobian_t &jacobian) const throw ()
 Check if the jacobian is valid (check sizes). More...
 
jacobian_t jacobian (const argument_t &argument) const throw ()
 Computes the jacobian. More...
 
void jacobian (jacobian_t &jacobian, const argument_t &argument) const throw ()
 Computes the jacobian. More...
 
gradient_t gradient (const argument_t &argument, size_type functionId=0) const throw ()
 Computes the gradient. More...
 
void gradient (gradient_t &gradient, const argument_t &argument, size_type functionId=0) const throw ()
 Computes the gradient. More...
 
- Public Member Functions inherited from roboptim::GenericFunction< T >
bool isValidResult (const result_t &result) const throw ()
 Check the given result size is valid. More...
 
GenericFunction< T >::size_type inputSize () const throw ()
 Return the input size (i.e. More...
 
GenericFunction< T >::size_type outputSize () const throw ()
 Return the output size (i.e. More...
 
virtual ~GenericFunction () throw ()
 Trivial destructor. More...
 
result_t operator() (const argument_t &argument) const throw ()
 Evaluate the function at a specified point. More...
 
void operator() (result_t &result, const argument_t &argument) const throw ()
 Evaluate the function at a specified point. More...
 
const std::string & getName () const throw ()
 Get function name. More...
 

Protected Member Functions

 GenericTwiceDifferentiableFunction (size_type inputSize, size_type outputSize=1, std::string name=std::string()) throw ()
 Concrete class constructor should call this constructor. More...
 
virtual void impl_hessian (hessian_t &hessian, const argument_t &argument, size_type functionId=0) const =0 throw ()
 Hessian evaluation. More...
 
void setZero (hessian_t &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()) throw ()
 Concrete class constructor should call this constructor. More...
 
virtual void impl_jacobian (jacobian_t &jacobian, const argument_t &arg) const throw ()
 Jacobian evaluation. More...
 
virtual void impl_gradient (gradient_t &gradient, const argument_t &argument, size_type functionId=0) const =0 throw ()
 Gradient evaluation. More...
 
template<>
void impl_jacobian (jacobian_t &jacobian, const argument_t &argument) const throw()
 
- Protected Member Functions inherited from roboptim::GenericFunction< T >
 GenericFunction (size_type inputSize, size_type outputSize=1, std::string name=std::string()) throw ()
 Concrete class constructor should call this constructor. More...
 
virtual void impl_compute (result_t &result, const argument_t &argument) const =0 throw ()
 Function evaluation. More...
 

Additional Inherited Members

- Static Public Member Functions inherited from roboptim::GenericFunction< T >
static value_type epsilon () throw ()
 Get the value of the machine epsilon, useful for floating types comparison. More...
 
static value_type infinity () throw ()
 Get the value that symbolizes positive infinity. More...
 
static interval_t makeInterval (value_type l, value_type u) throw ()
 Construct an interval from a lower and upper bound. More...
 
static interval_t makeInfiniteInterval () throw ()
 Construct an infinite interval. More...
 
static interval_t makeLowerInterval (value_type l) throw ()
 Construct an interval from a lower bound. More...
 
static interval_t makeUpperInterval (value_type u) throw ()
 Construct an interval from an upper bound. More...
 
static double getLowerBound (const interval_t &interval) throw ()
 Get the lower bound of an interval. More...
 
static double getUpperBound (const interval_t &interval) throw ()
 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 double getLowerBound (const discreteInterval_t &interval) throw ()
 Get the lower bound of a discrete interval. More...
 
static double getUpperBound (const discreteInterval_t &interval) throw ()
 Get the upper bound of a discrete interval. More...
 
static double getStep (const discreteInterval_t &interval) throw ()
 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 Protected Attributes inherited from roboptim::GenericFunction< T >
static log4cxx::LoggerPtr logger
 Pointer to function logger (see log4cxx documentation). More...
 

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

Hessian type.

Hessians are symmetric matrices.

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
inputSizeinput size (argument size)
outputSizeoutput size (result size)
namefunction'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
argumentpoint where the hessian will be computed
functionIdevaluated 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
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 >::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 (
)
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::NTimesDerivableFunction< 2 >, roboptim::NumericQuadraticFunction, and roboptim::GenericLinearFunction< T >.

template<typename T>
bool roboptim::GenericTwiceDifferentiableFunction< T >::isValidHessian ( const hessian_t hessian) const
throw (
)
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().

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

Set a symmetric matrix to zero.

Note
there might be an eigen function to do that.

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