Public Types | Public Member Functions | Protected Member Functions
roboptim::GenericDifferentiableFunction< T > Class Template Reference
Mathematical abstract functions

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

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

Inheritance diagram for roboptim::GenericDifferentiableFunction< T >:
roboptim::GenericFunction< T > roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy > roboptim::GenericSumOfC1Squares< T > roboptim::GenericTwiceDifferentiableFunction< T > roboptim::Cos< T > roboptim::GenericQuadraticFunction< T > roboptim::NTimesDerivableFunction< 2 > roboptim::Polynomial< T > roboptim::Sin< T > roboptim::GenericLinearFunction< T > roboptim::GenericNumericQuadraticFunction< T > roboptim::GenericConstantFunction< T > roboptim::GenericIdentityFunction< T > roboptim::GenericNumericLinearFunction< T >

List of all members.

Public Types

typedef std::pair< size_type,
size_type > 		jacobianSize_t
 Jacobian size type (pair of values).

Public Member Functions

 ROBOPTIM_FUNCTION_FWD_TYPEDEFS_ (GenericFunction< T >)
 ROBOPTIM_GENERATE_TRAITS_REFS_ (gradient)
 Gradient type.
 ROBOPTIM_GENERATE_TRAITS_REFS_ (jacobian)
 Jacobian type.
size_type gradientSize () const
 Return the gradient size.
jacobianSize_t jacobianSize () const
 Return the jacobian size as a pair.
bool isValidGradient (const_gradient_ref gradient) const
 Check if the gradient is valid (check size).
bool isValidJacobian (const_jacobian_ref jacobian) const
 Check if the jacobian is valid (check sizes).
jacobian_t jacobian (const_argument_ref argument) const
 Computes the jacobian.
void jacobian (jacobian_ref jacobian, const_argument_ref argument) const
 Computes the jacobian.
gradient_t gradient (const_argument_ref argument, size_type functionId=0) const
 Computes the gradient.
void gradient (gradient_ref gradient, const_argument_ref argument, size_type functionId=0) const
 Computes the gradient.
virtual std::ostream & print (std::ostream &o) const
 Display the function on the specified output stream.

Protected Member Functions

 GenericDifferentiableFunction (size_type inputSize, size_type outputSize=1, std::string name=std::string())
 Concrete class constructor should call this constructor.
virtual void impl_jacobian (jacobian_ref jacobian, const_argument_ref arg) const
 Jacobian evaluation.
virtual void impl_gradient (gradient_ref gradient, const_argument_ref argument, size_type functionId=0) const =0
 Gradient evaluation.
template<>
void impl_jacobian (jacobian_ref jacobian, const_argument_ref argument) const

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

Jacobian size type (pair of values).

Constructor & Destructor Documentation

template<typename T >
roboptim::GenericDifferentiableFunction< T >::GenericDifferentiableFunction ( size_type  inputSize,
size_type  outputSize = 1,
std::string  name = std::string () 
) [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>
gradient_t roboptim::GenericDifferentiableFunction< T >::gradient ( const_argument_ref  argument,
size_type  functionId = 0 
) const [inline]

Computes the gradient.

Parameters:
argumentpoint at which the gradient will be computed
functionIdfunction id in split representation
Returns:
gradient vector
Examples:
finite-difference-gradient.cc.

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

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

template<typename T>
void roboptim::GenericDifferentiableFunction< T >::gradient ( gradient_ref  gradient,
const_argument_ref  argument,
size_type  functionId = 0 
) const [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

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

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

template<typename T>
size_type roboptim::GenericDifferentiableFunction< T >::gradientSize ( ) const [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_ref  gradient,
const_argument_ref  argument,
size_type  functionId = 0 
) const [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:
gradientgradient will be store in this argument
argumentpoint where the gradient will be computed
functionIdevaluated function id in the split representation

Implemented in roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >, roboptim::NTimesDerivableFunction< 2 >, roboptim::GenericNumericQuadraticFunction< T >, roboptim::GenericNumericQuadraticFunction< T >, roboptim::GenericIdentityFunction< T >, roboptim::GenericNumericLinearFunction< T >, roboptim::GenericConstantFunction< T >, roboptim::GenericNumericLinearFunction< T >, roboptim::GenericIdentityFunction< T >, roboptim::Cos< T >, roboptim::Sin< T >, roboptim::GenericSumOfC1Squares< T >, roboptim::Cos< T >, roboptim::Sin< T >, and roboptim::Polynomial< T >.

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

template<>
void roboptim::GenericDifferentiableFunction< EigenMatrixSparse >::impl_jacobian ( jacobian_ref  jacobian,
const_argument_ref  argument 
) const [inline, protected]

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

Reimplemented in roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >, roboptim::GenericNumericQuadraticFunction< T >, roboptim::Cos< T >, roboptim::Sin< T >, roboptim::GenericConstantFunction< T >, roboptim::GenericNumericLinearFunction< T >, roboptim::GenericNumericQuadraticFunction< T >, roboptim::GenericIdentityFunction< T >, roboptim::Cos< T >, roboptim::Polynomial< T >, and roboptim::Sin< T >.

template<typename T >
void roboptim::GenericDifferentiableFunction< T >::impl_jacobian ( jacobian_ref  jacobian,
const_argument_ref  arg 
) const [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:
jacobianjacobian will be store in this argument
argpoint where the jacobian will be computed

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

Reimplemented in roboptim::GenericFiniteDifferenceGradient< T, FdgPolicy >, roboptim::GenericNumericQuadraticFunction< T >, roboptim::Cos< T >, roboptim::Sin< T >, roboptim::GenericConstantFunction< T >, roboptim::GenericNumericLinearFunction< T >, roboptim::GenericNumericQuadraticFunction< T >, roboptim::GenericIdentityFunction< T >, roboptim::Cos< T >, roboptim::Polynomial< T >, and roboptim::Sin< T >.

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

template<typename T>
bool roboptim::GenericDifferentiableFunction< T >::isValidGradient ( const_gradient_ref  gradient) const [inline]

Check if the gradient is valid (check size).

Parameters:
gradientchecked gradient
Returns:
true if valid, false if not

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

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

template<typename T>
bool roboptim::GenericDifferentiableFunction< T >::isValidJacobian ( const_jacobian_ref  jacobian) const [inline]

Check if the jacobian is valid (check sizes).

Parameters:
jacobianchecked jacobian
Returns:
true if valid, false if not

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

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

template<typename T>
jacobian_t roboptim::GenericDifferentiableFunction< T >::jacobian ( const_argument_ref  argument) const [inline]

Computes the jacobian.

Parameters:
argumentpoint at which the jacobian will be computed
Returns:
jacobian matrix

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

Referenced by roboptim::checkJacobian(), roboptim::checkJacobianAndThrow(), and roboptim::visualization::gnuplot::plot_jac().

template<typename T>
void roboptim::GenericDifferentiableFunction< T >::jacobian ( jacobian_ref  jacobian,
const_argument_ref  argument 
) const [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

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

ROBOPTIM_DO_NOT_CHECK_ALLOCATION

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

template<typename T>
jacobianSize_t roboptim::GenericDifferentiableFunction< T >::jacobianSize ( ) const [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::GenericDifferentiableFunction< T >::isValidJacobian(), and roboptim::GenericDifferentiableFunction< T >::jacobian().

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

Display the function on the specified output stream.

Parameters:
ooutput stream used for display
Returns:
output stream

Reimplemented from roboptim::GenericFunction< T >.

Reimplemented in roboptim::GenericTwiceDifferentiableFunction< T >, roboptim::NTimesDerivableFunction< 2 >, roboptim::GenericNumericQuadraticFunction< T >, roboptim::GenericConstantFunction< T >, roboptim::GenericNumericLinearFunction< T >, roboptim::GenericIdentityFunction< T >, roboptim::Polynomial< T >, roboptim::GenericLinearFunction< T >, roboptim::GenericQuadraticFunction< T >, roboptim::Cos< T >, and roboptim::Sin< T >.

References roboptim::indent().

template<typename T>
roboptim::GenericDifferentiableFunction< T >::ROBOPTIM_FUNCTION_FWD_TYPEDEFS_ ( GenericFunction< T >  )
template<typename T>
roboptim::GenericDifferentiableFunction< T >::ROBOPTIM_GENERATE_TRAITS_REFS_ ( gradient  )

Gradient type.

template<typename T>
roboptim::GenericDifferentiableFunction< T >::ROBOPTIM_GENERATE_TRAITS_REFS_ ( jacobian  )

Jacobian type.

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