Define an abstract function which is derivable twice ( ).
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#include <roboptim/core/twice-derivable-function.hh>
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. | |
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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). | |
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typedef double | value_type |
Values type. | |
typedef std::size_t | size_type |
Size type. | |
typedef ublas::vector< value_type > | vector_t |
Basic vector type. | |
typedef ublas::matrix< value_type > | matrix_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_t > | intervals_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. | |
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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. | |
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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. | |
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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. | |
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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. |
Define an abstract function which is derivable twice ( ).
A twice derivable function is a derivable function which provides a way to compute its hessian.
,
where
is the input size and
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.
typedef ublas::symmetric_matrix<value_type, ublas::lower> roboptim::TwiceDerivableFunction::hessian_t |
Hessian type.
Hessians are symmetric matrices.
typedef std::pair<size_type, size_type> roboptim::TwiceDerivableFunction::hessianSize_t |
Hessian size type represented as a pair of values.
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protected |
Concrete class constructor should call this constructor.
inputSize | input size (argument size) |
outputSize | output size (result size) |
name | function's name |
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inline |
Compute the hessian at a given point.
Program will abort if the argument size is wrong.
argument | point where the hessian will be computed |
functionId | evaluated function id in the split representation |
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inline |
Compute the hessian at a given point.
Program will abort if the argument size is wrong.
hessian | hessian will be stored here |
argument | point where the hessian will be computed |
functionId | evaluated function id in the split representation |
References RoboptimCoreDout.
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inline |
Return the size of a hessian.
Hessian size is equales to (input size, input size).
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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.
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::LinearFunction.
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inline |
Check if the hessian is valid (check sizes).
hessian | hessian that will be checked |
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virtual |
Display the function on the specified output stream.
o | output stream used for display |
Reimplemented from roboptim::DerivableFunction.
Reimplemented in roboptim::NTimesDerivableFunction< 2 >, roboptim::NumericQuadraticFunction, roboptim::QuadraticFunction, roboptim::LinearFunction, roboptim::NumericLinearFunction, roboptim::ConstantFunction, and roboptim::IdentityFunction.