roboptim::TwiceDerivableFunction Class Reference

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

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

+ Inheritance diagram for roboptim::TwiceDerivableFunction:

List of all members.

Public Types

typedef
ublas::symmetric_matrix
< value_type, ublas::lower > 
hessian_t
 Hessian type.
typedef std::pair< size_type,
size_type
hessianSize_t
 Hessian size type represented as a pair of values.
- Public Types inherited from roboptim::DerivableFunction
typedef vector_t gradient_t
 Gradient type.
typedef matrix_t jacobian_t
 Jacobian type.
typedef std::pair< value_type,
value_type
jacobianSize_t
 Jacobian size type (pair of values).
- Public Types inherited from roboptim::Function
typedef double value_type
 Values type.
typedef std::size_t size_type
 Size type.
typedef ublas::vector< value_typevector_t
 Basic vector type.
typedef ublas::matrix< value_typematrix_t
 Basic matrix type.
typedef vector_t result_t
 Type of a function evaluation result.
typedef vector_t argument_t
 Type of a function evaluation argument.
typedef std::pair< value_type,
value_type
interval_t
 Interval type (lower, upper). Use negative or positive infinity to respectively disable the lower or upper bound.
typedef std::vector< interval_tintervals_t
 Vector of intervals.
typedef boost::tuple
< value_type, value_type,
value_type
discreteInterval_t
 Types representing a discrete interval. A discrete interval is a triplet of values:

Public Member Functions

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.
- Public Member Functions inherited from roboptim::DerivableFunction
size_type gradientSize () const throw ()
 Return the gradient size.
jacobianSize_t jacobianSize () const throw ()
 Return the jacobian size as a pair.
bool isValidGradient (const gradient_t &gradient) const throw ()
 Check if the gradient is valid (check size).
bool isValidJacobian (const jacobian_t &jacobian) const throw ()
 Check if the jacobian is valid (check sizes).
jacobian_t jacobian (const argument_t &argument) const throw ()
 Computes the jacobian.
void jacobian (jacobian_t &jacobian, const argument_t &argument) const throw ()
 Computes the jacobian.
gradient_t gradient (const argument_t &argument, size_type functionId=0) const throw ()
 Computes the gradient.
void gradient (gradient_t &gradient, const argument_t &argument, size_type functionId=0) const throw ()
 Computes the gradient.
- Public Member Functions inherited from roboptim::Function
bool isValidResult (const result_t &result) const throw ()
 Check the given result size is valid.
size_type inputSize () const throw ()
 Return the input size (i.e. argument's vector size).
size_type outputSize () const throw ()
 Return the output size (i.e. result's vector size).
virtual ~Function () throw ()
 Trivial destructor.
result_t operator() (const argument_t &argument) const throw ()
 Evaluate the function at a specified point.
void operator() (result_t &result, const argument_t &argument) const throw ()
 Evaluate the function at a specified point.
const std::string & getName () const throw ()
 Get function name.

Protected Member Functions

 TwiceDerivableFunction (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.
- Protected Member Functions inherited from roboptim::DerivableFunction
 DerivableFunction (size_type inputSize, size_type outputSize=1, std::string name=std::string()) throw ()
 Concrete class constructor should call this constructor.
virtual void impl_jacobian (jacobian_t &jacobian, const argument_t &arg) const throw ()
 Jacobian evaluation.
virtual void impl_gradient (gradient_t &gradient, const argument_t &argument, size_type functionId=0) const =0 throw ()
 Gradient evaluation.
- Protected Member Functions inherited from roboptim::Function
 Function (size_type inputSize, size_type outputSize=1, std::string name=std::string()) throw ()
 Concrete class constructor should call this constructor.
virtual void impl_compute (result_t &result, const argument_t &argument) const =0 throw ()
 Function evaluation.

Detailed Description

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 \form#8
 function where \form#9 and \form#10 is a tensor.
 To avoid this costly representation, the function is split
 into \form#7 \form#11 functions.
 See #DerivableFunction documentation for more information.  

Member Typedef Documentation

typedef ublas::symmetric_matrix<value_type, ublas::lower> roboptim::TwiceDerivableFunction::hessian_t

Hessian type.

Hessians are symmetric matrices.

Hessian size type represented as a pair of values.


Constructor & Destructor Documentation

roboptim::TwiceDerivableFunction::TwiceDerivableFunction ( 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

hessian_t roboptim::TwiceDerivableFunction::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.
void roboptim::TwiceDerivableFunction::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

References RoboptimCoreDout.

hessianSize_t roboptim::TwiceDerivableFunction::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
virtual void roboptim::TwiceDerivableFunction::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::LinearFunction.

bool roboptim::TwiceDerivableFunction::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
std::ostream & roboptim::TwiceDerivableFunction::print ( std::ostream &  o) const throw ()
virtual

Display the function on the specified output stream.

Parameters:
ooutput stream used for display
Returns:
output stream

Reimplemented from roboptim::DerivableFunction.

Reimplemented in roboptim::NTimesDerivableFunction< 2 >, roboptim::NumericQuadraticFunction, roboptim::QuadraticFunction, roboptim::LinearFunction, roboptim::NumericLinearFunction, roboptim::ConstantFunction, and roboptim::IdentityFunction.