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

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

Inheritance diagram for roboptim::GenericDifferentiableFunction< T >:

Collaboration diagram for roboptim::GenericDifferentiableFunction< T >:

Public Types
typedef GenericFunctionTraits < T >::gradient_t	gradient_t
	Gradient type.
typedef GenericFunctionTraits < T >::jacobian_t	jacobian_t
	Jacobian type.
typedef std::pair< size_type, size_type >	jacobianSize_t
	Jacobian size type (pair of values).
Public Member Functions
	ROBOPTIM_FUNCTION_FWD_TYPEDEFS_ (GenericFunction< T >)
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.
Protected Member Functions
	GenericDifferentiableFunction (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.
template<>
void	impl_jacobian (jacobian_t &jacobian, const argument_t &argument) const throw()

Detailed Description

template<typename T>
class roboptim::GenericDifferentiableFunction< T >

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 $\mathbb{R}^n \rightarrow \mathbb{R}^m$ function where $n > 1$ and $m > 1$ is a matrix. As this representation is costly, RobOptim considers these functions as $m$ $\mathbb{R}^n \rightarrow \mathbb{R}$ 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 $m$ functions should be considered.

If $m = 1$ , 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

template<typename T>

typedef GenericFunctionTraits<T>::gradient_t roboptim::GenericDifferentiableFunction< T >::gradient_t

Gradient type.

Reimplemented in roboptim::SumOfC1Squares.

template<typename T>

typedef GenericFunctionTraits<T>::jacobian_t roboptim::GenericDifferentiableFunction< T >::jacobian_t

Jacobian type.

Reimplemented in roboptim::SumOfC1Squares.

template<typename T>

typedef std::pair<size_type, size_type> roboptim::GenericDifferentiableFunction< T >::jacobianSize_t

Jacobian size type (pair of values).

Reimplemented in roboptim::SumOfC1Squares.

Constructor & Destructor Documentation

template<typename T >

roboptim::GenericDifferentiableFunction< T >::GenericDifferentiableFunction	(	size_type	inputSize,
		size_type	outputSize = `1`,
		std::string	name = `std::string ()`
	)		throw () `[protected]`

Concrete class constructor should call this constructor.

Parameters:

inputSize	input size (argument size)
outputSize	output size (result size)
name	function's name

Member Function Documentation

template<typename T>

gradient_t roboptim::GenericDifferentiableFunction< T >::gradient	(	const argument_t &	argument,
		size_type	functionId = `0`
	)		const throw () `[inline]`

Computes the gradient.

Parameters:

argument	point at which the gradient will be computed
functionId	function id in split representation

Returns:: gradient vector

Examples:: constant-function.cc, finite-difference-gradient.cc, identity-function.cc, and numeric-quadratic-function.cc.

References roboptim::GenericDifferentiableFunction< T >::gradientSize().

Referenced by roboptim::checkGradient(), roboptim::checkGradientAndThrow(), and roboptim::GenericDifferentiableFunction< T >::isValidGradient().

template<typename T>

void roboptim::GenericDifferentiableFunction< T >::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:

gradient	gradient will be stored in this argument
argument	point at which the gradient will be computed
functionId	function id in split representation

Returns:: gradient vector

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

References roboptim::GenericDifferentiableFunction< T >::impl_gradient(), roboptim::GenericFunction< T >::inputSize(), roboptim::GenericDifferentiableFunction< T >::isValidGradient(), and roboptim::GenericFunction< T >::logger.

template<typename T>

size_type roboptim::GenericDifferentiableFunction< T >::gradientSize ( ) const throw () [inline]

Return the gradient size.

Gradient size is equals to the input size.

References roboptim::GenericFunction< T >::inputSize().

Referenced by roboptim::GenericDifferentiableFunction< T >::gradient(), and roboptim::GenericDifferentiableFunction< T >::isValidGradient().

template<typename T>

virtual void roboptim::GenericDifferentiableFunction< T >::impl_gradient	(	gradient_t &	gradient,
		const argument_t &	argument,
		size_type	functionId = `0`
	)		const throw () `[protected, pure 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:

gradient	gradient will be store in this argument
argument	point where the gradient will be computed
functionId	evaluated function id in the split representation

Implemented in roboptim::NTimesDerivableFunction< 2 >, roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >, roboptim::GenericNumericLinearFunction< T >, roboptim::SumOfC1Squares, roboptim::NumericQuadraticFunction, roboptim::IdentityFunction, and roboptim::ConstantFunction.

Referenced by roboptim::GenericDifferentiableFunction< T >::gradient().

template<>

void roboptim::GenericDifferentiableFunction< EigenMatrixSparse >::impl_jacobian	(	jacobian_t &	jacobian,
		const argument_t &	argument
	)		const throw() `[inline, protected]`

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

Reimplemented in roboptim::GenericNumericLinearFunction< T >, roboptim::IdentityFunction, and roboptim::ConstantFunction.

template<typename T >

void roboptim::GenericDifferentiableFunction< T >::impl_jacobian	(	jacobian_t &	jacobian,
		const argument_t &	arg
	)		const throw () `[protected, virtual]`

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:

jacobian	jacobian will be store in this argument
arg	point where the jacobian will be computed

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

Reimplemented in roboptim::GenericNumericLinearFunction< T >, roboptim::IdentityFunction, and roboptim::ConstantFunction.

Referenced by roboptim::GenericDifferentiableFunction< T >::jacobian().

template<typename T>

bool roboptim::GenericDifferentiableFunction< T >::isValidGradient ( const gradient_t & gradient ) const throw () [inline]

Check if the gradient is valid (check size).

Parameters:

gradient checked gradient

Returns:: true if valid, false if not

References roboptim::GenericDifferentiableFunction< T >::gradient(), and roboptim::GenericDifferentiableFunction< T >::gradientSize().

Referenced by roboptim::GenericDifferentiableFunction< T >::gradient().

template<typename T>

bool roboptim::GenericDifferentiableFunction< T >::isValidJacobian ( const jacobian_t & jacobian ) const throw () [inline]

Check if the jacobian is valid (check sizes).

Parameters:

jacobian checked jacobian

Returns:: true if valid, false if not

References roboptim::GenericDifferentiableFunction< T >::jacobian(), and roboptim::GenericDifferentiableFunction< T >::jacobianSize().

Referenced by roboptim::GenericDifferentiableFunction< T >::jacobian().

template<typename T>

jacobian_t roboptim::GenericDifferentiableFunction< T >::jacobian ( const argument_t & argument ) const throw () [inline]

Computes the jacobian.

Parameters:

argument point at which the jacobian will be computed

Returns:: jacobian matrix

Examples:: constant-function.cc, numeric-linear-function.cc, and numeric-quadratic-function.cc.

References roboptim::GenericDifferentiableFunction< T >::jacobianSize().

Referenced by roboptim::GenericDifferentiableFunction< T >::isValidJacobian(), roboptim::GenericDifferentiableFunction< T >::jacobian(), and roboptim::visualization::gnuplot::plot_jac().

template<typename T>

void roboptim::GenericDifferentiableFunction< T >::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:

jacobian	jacobian will be stored in this argument
argument	point at which the jacobian will be computed

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

References roboptim::GenericDifferentiableFunction< T >::impl_jacobian(), roboptim::GenericFunction< T >::inputSize(), roboptim::GenericDifferentiableFunction< T >::isValidJacobian(), roboptim::GenericDifferentiableFunction< T >::jacobian(), and roboptim::GenericFunction< T >::logger.

template<typename T>

jacobianSize_t roboptim::GenericDifferentiableFunction< T >::jacobianSize ( ) const throw () [inline]

Return the jacobian size as a pair.

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

References roboptim::GenericFunction< T >::inputSize(), and roboptim::GenericFunction< T >::outputSize().

Referenced by roboptim::IdentityFunction::impl_jacobian(), roboptim::GenericDifferentiableFunction< T >::isValidJacobian(), and roboptim::GenericDifferentiableFunction< T >::jacobian().

template<typename T >

std::ostream & roboptim::GenericDifferentiableFunction< T >::print ( std::ostream & o ) const throw () [virtual]

Display the function on the specified output stream.

Parameters:

o	output stream used for display

Returns:: output stream

Reimplemented from roboptim::GenericFunction< T >.

Reimplemented in roboptim::GenericTwiceDifferentiableFunction< T >, roboptim::NTimesDerivableFunction< 2 >, roboptim::GenericLinearFunction< T >, roboptim::NumericQuadraticFunction, roboptim::GenericNumericLinearFunction< T >, roboptim::GenericQuadraticFunction< T >, roboptim::IdentityFunction, and roboptim::ConstantFunction.

References roboptim::indent().

template<typename T>

roboptim::GenericDifferentiableFunction< T >::ROBOPTIM_FUNCTION_FWD_TYPEDEFS_ ( GenericFunction< T > )

Public Types

Public Member Functions

Protected Member Functions

Detailed Description

template<typename T> class roboptim::GenericDifferentiableFunction< T >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

template<typename T>
class roboptim::GenericDifferentiableFunction< T >