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 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.

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.

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 $\mathbb{R}^n \rightarrow \mathbb{R}^m$ 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

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, finite-difference-gradient.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 () [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::ConstantFunction, roboptim::FiniteDifferenceGradient< FdgPolicy >, roboptim::IdentityFunction, roboptim::NTimesDerivableFunction< 2 >, roboptim::NumericLinearFunction, and roboptim::NumericQuadraticFunction.

void roboptim::DerivableFunction::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:
jacobianjacobian will be store in this argument
argpoint where the jacobian will be computed

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

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
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.

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