roboptim::DerivableFunction Class Reference

Define an abstract derivable function ( $C^1$). More...

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

+ Inheritance diagram for roboptim::DerivableFunction:

List of all members.

Public Types

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

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.
virtual std::ostream & print (std::ostream &o) const throw ()
 Display the function on the specified output stream.
- 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

 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.

Additional Inherited Members

- Static Public Member Functions inherited from roboptim::Function
static const value_type infinity () throw ()
 Get the value that symbolizes positive infinity.
static interval_t makeInterval (value_type l, value_type u) throw ()
 Construct an interval from a lower and upper bound.
static interval_t makeInfiniteInterval () throw ()
 Construct an infinite interval.
static interval_t makeLowerInterval (value_type l) throw ()
 Construct an interval from a lower bound.
static interval_t makeUpperInterval (value_type u) throw ()
 Construct an interval from an upper bound.
static double getLowerBound (const interval_t &interval) throw ()
 Get the lower bound of an interval.
static double getUpperBound (const interval_t &interval) throw ()
 Get the upper bound of an interval.
static discreteInterval_t makeDiscreteInterval (value_type min, value_type max, value_type step)
 Construct a discrete interval.
static discreteInterval_t makeDiscreteInterval (interval_t interval, value_type step)
 Construct a discrete interval.
static double getLowerBound (const discreteInterval_t &interval) throw ()
 Get the lower bound of a discrete interval.
static double getUpperBound (const discreteInterval_t &interval) throw ()
 Get the upper bound of a discrete interval.
static double getStep (const discreteInterval_t &interval) throw ()
 Get the upper step of a discrete interval.
template<typename F >
static void foreach (const discreteInterval_t interval, F functor)
 Iterate on an interval.
template<typename F >
static void foreach (const interval_t interval, const size_type n, F functor)
 Iterate on an interval.

Detailed Description

Define an abstract derivable function ( $C^1$).

 A derivable function which provides a way to compute its
 gradient/jacobian.

\[ f : x \rightarrow f(x) \]

$x \in \mathbb{R}^n$, $f(x) \in \mathbb{R}^m$ where $n$ is the input size and $m$ is the output size.

 Gradient computation is done through the #impl_gradient method
 that has to implemented by the concrete class inheriting this
 class.

 Jacobian computation is automatically done by concatenating
 gradients together, however this naive implementation can be
 overridden by the concrete class.

 The gradient of a \form#8
 function where \form#9 and \form#10 is a matrix.
 As this representation is costly, RobOptim considers
 these functions as \form#7 \form#11
 functions. Through that mechanism, gradients are always vectors
 and jacobian are always matrices.
 When the gradient or the jacobian has to be computed, one has to
 precise which of the \form#7 functions should be considered.

 If \form#12, then the function id must always be 0 and can be safely
 ignored in the gradient/jacobian computation.
 The class provides a default value for the function id so that
 these functions do not have to explicitly set the function id.  
Examples:
finite-difference-gradient.cc.

Member Typedef Documentation

Jacobian size type (pair of values).


Constructor & Destructor Documentation

roboptim::DerivableFunction::DerivableFunction ( 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

gradient_t roboptim::DerivableFunction::gradient ( const argument_t argument,
size_type  functionId = 0 
) const throw ()
inline

Computes the gradient.

Parameters:
argumentpoint at which the gradient will be computed
functionIdfunction id in split representation
Returns:
gradient vector
Examples:
constant-function.cc, identity-function.cc, and numeric-quadratic-function.cc.

Referenced by roboptim::checkGradient(), roboptim::checkGradientAndThrow(), and roboptim::IdentityFunction::impl_gradient().

void roboptim::DerivableFunction::gradient ( gradient_t gradient,
const argument_t argument,
size_type  functionId = 0 
) const throw ()
inline

Computes the gradient.

Program will abort if the gradient size is wrong before or after the gradient computation.

Parameters:
gradientgradient will be stored in this argument
argumentpoint at which the gradient will be computed
functionIdfunction id in split representation
Returns:
gradient vector

References RoboptimCoreDout.

size_type roboptim::DerivableFunction::gradientSize ( ) const throw ()
inline

Return the gradient size.

Gradient size is equals to the input size.

virtual void roboptim::DerivableFunction::impl_gradient ( gradient_t gradient,
const argument_t argument,
size_type  functionId = 0 
) const throw ()
protectedpure virtual

Gradient evaluation.

Compute the gradient, has to be implemented in concrete classes. The gradient is computed for a specific sub-function which id is passed through the functionId argument.

Warning:
Do not call this function directly, call gradient instead.
Parameters:
gradientgradient will be store in this argument
argumentpoint where the gradient will be computed
functionIdevaluated function id in the split representation

Implemented in roboptim::NTimesDerivableFunction< 2 >, roboptim::FiniteDifferenceGradient< FdgPolicy >, roboptim::NumericQuadraticFunction, roboptim::NumericLinearFunction, roboptim::ConstantFunction, and roboptim::IdentityFunction.

void roboptim::DerivableFunction::impl_jacobian ( jacobian_t jacobian,
const argument_t arg 
) const throw ()
protectedvirtual

Jacobian evaluation.

Computes the jacobian, can be overridden by concrete classes. The default behavior is to compute the jacobian from the gradient.

Warning:
Do not call this function directly, call jacobian instead.
Parameters:
jacobianjacobian will be store in this argument
argpoint where the jacobian will be computed

Reimplemented in roboptim::NumericLinearFunction, roboptim::ConstantFunction, and roboptim::IdentityFunction.

bool roboptim::DerivableFunction::isValidGradient ( const gradient_t gradient) const throw ()
inline

Check if the gradient is valid (check size).

Parameters:
gradientchecked gradient
Returns:
true if valid, false if not
bool roboptim::DerivableFunction::isValidJacobian ( const jacobian_t jacobian) const throw ()
inline

Check if the jacobian is valid (check sizes).

Parameters:
jacobianchecked jacobian
Returns:
true if valid, false if not
jacobian_t roboptim::DerivableFunction::jacobian ( const argument_t argument) const throw ()
inline

Computes the jacobian.

Parameters:
argumentpoint at which the jacobian will be computed
Returns:
jacobian matrix
Examples:
constant-function.cc, numeric-linear-function.cc, and numeric-quadratic-function.cc.
void roboptim::DerivableFunction::jacobian ( jacobian_t jacobian,
const argument_t argument 
) const throw ()
inline

Computes the jacobian.

Program will abort if the jacobian size is wrong before or after the jacobian computation.

Parameters:
jacobianjacobian will be stored in this argument
argumentpoint at which the jacobian will be computed

References RoboptimCoreDout.

jacobianSize_t roboptim::DerivableFunction::jacobianSize ( ) const throw ()
inline

Return the jacobian size as a pair.

Gradient size is equals to (output size, input size).

Referenced by roboptim::IdentityFunction::impl_jacobian().

std::ostream & roboptim::DerivableFunction::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::Function.

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