roboptim::Function Class Reference
[Mathematical abstract functions]

Define an abstract mathematical function ($C^0$). More...

#include <roboptim/core/function.hh>

Inheritance diagram for roboptim::Function:
roboptim::DerivableFunction roboptim::FiniteDifferenceGradient< FdgPolicy > roboptim::TwiceDerivableFunction roboptim::NTimesDerivableFunction< 2 > roboptim::QuadraticFunction roboptim::LinearFunction roboptim::NumericQuadraticFunction roboptim::ConstantFunction roboptim::IdentityFunction roboptim::NumericLinearFunction

List of all members.

Public Types

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.

Public Member Functions

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

Static Public Member Functions

static const value_type infinity () throw ()
 Get the value that symbolizes positive infinity.

Protected Member Functions

 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.

Interval



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.
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.

Discrete interval



typedef boost::tuple
< value_type, value_type,
value_type > 		discreteInterval_t
 Types representing a discrete interval. A discrete interval is a triplet of values:

  • lower bound,
  • upper bound,
  • step.

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 mathematical function ($C^0$).

A function is an object that can be evaluated for a given point.

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

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

Functions are pure immutable objects: evaluating a function twice at a given point must give the same result.

Examples:

visualization-gnuplot-function.cc.

Member Typedef Documentation

typedef vector_t roboptim::Function::argument_t

Type of a function evaluation argument.

typedef boost::tuple<value_type, value_type, value_type> roboptim::Function::discreteInterval_t

Types representing a discrete interval. A discrete interval is a triplet of values:

  • lower bound,
  • upper bound,
  • step.

typedef std::pair<value_type, value_type> roboptim::Function::interval_t

Interval type (lower, upper). Use negative or positive infinity to respectively disable the lower or upper bound.

typedef std::vector<interval_t> roboptim::Function::intervals_t

Vector of intervals.

typedef ublas::matrix<value_type> roboptim::Function::matrix_t

Basic matrix type.

This basic matrix type is used each time a two dimensional matrix of values is needed.

Attention:
It is good practice in RobOptim to rely on this type when a matrix of values is needed instead of relying on a particular implementation.
typedef vector_t roboptim::Function::result_t

Type of a function evaluation result.

typedef std::size_t roboptim::Function::size_type

Size type.

This type is used to represent sizes, indexes, etc.

typedef double roboptim::Function::value_type

Values type.

Represents the numerical type (i.e. float, double, int...) used for computations.

typedef ublas::vector<value_type> roboptim::Function::vector_t

Basic vector type.

This basic vector type is used each time a vector of values is required.

Attention:
It is good practice in RobOptim to rely on this type when a vector of values is needed instead of relying on a particular implementation.

Constructor & Destructor Documentation

roboptim::Function::~Function (  )  throw () [virtual]

Trivial destructor.

roboptim::Function::Function ( size_type  inputSize,
size_type  outputSize = 1,
std::string  name = std::string () 
) throw () [protected]

Concrete class constructor should call this constructor.

Parameters:
inputSize function arity
outputSize result size
name function's name
Examples:
visualization-gnuplot-function.cc.

Member Function Documentation

template<typename F >
static void roboptim::Function::foreach ( const interval_t  interval,
const size_type  n,
F  functor 
) [inline, static]

Iterate on an interval.

Call the functor regularly n times on an interval.

Parameters:
interval interval on which the method iterates
n number of discretization points
functor unary function that will be applied
Template Parameters:
F functor type (has to satisfy the STL unary function concept)
template<typename F >
static void roboptim::Function::foreach ( const discreteInterval_t  interval,
F  functor 
) [inline, static]

Iterate on an interval.

Call the functor to each discretization point of the discrete interval.

Parameters:
interval interval on which the method iterates
functor unary function that will be applied
Template Parameters:
F functor type (has to satisfy the STL unary function concept)
static double roboptim::Function::getLowerBound ( const discreteInterval_t &  interval  )  throw () [inline, static]

Get the lower bound of a discrete interval.

Parameters:
interval accessed discrete interval
Returns:
lower bound of the discrete interval
static double roboptim::Function::getLowerBound ( const interval_t &  interval  )  throw () [inline, static]

Get the lower bound of an interval.

Parameters:
interval accessed interval
Returns:
lower bound of the interval
const std::string& roboptim::Function::getName (  )  const throw () [inline]

Get function name.

Returns:
Function's name.

Referenced by roboptim::visualization::gnuplot::plot(), and roboptim::visualization::gnuplot::plot_xy().

static double roboptim::Function::getStep ( const discreteInterval_t &  interval  )  throw () [inline, static]

Get the upper step of a discrete interval.

Parameters:
interval accessed discrete interval
Returns:
upper step of the discrete interval
static double roboptim::Function::getUpperBound ( const discreteInterval_t &  interval  )  throw () [inline, static]

Get the upper bound of a discrete interval.

Parameters:
interval accessed discrete interval
Returns:
upper bound of the discrete interval
static double roboptim::Function::getUpperBound ( const interval_t &  interval  )  throw () [inline, static]

Get the upper bound of an interval.

Parameters:
interval accessed interval
Returns:
upper bound of the interval
virtual void roboptim::Function::impl_compute ( result_t &  result,
const argument_t &  argument 
) const throw () [protected, pure virtual]

Function evaluation.

Evaluate the function, has to be implemented in concrete classes.

Warning:
Do not call this function directly, call operator()(result_t&, const argument_t&) const throw () instead.
Parameters:
result result will be stored in this vector
argument point at which the function will be evaluated

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

Examples:
finite-difference-gradient.cc, and visualization-gnuplot-function.cc.
static const value_type roboptim::Function::infinity (  )  throw () [inline, static]

Get the value that symbolizes positive infinity.

Returns:
representation of positive infinity in the value type

Referenced by makeInfiniteInterval(), makeLowerInterval(), makeUpperInterval(), and roboptim::Problem< F, CLIST >::print().

size_type roboptim::Function::inputSize (  )  const throw () [inline]

Return the input size (i.e. argument's vector size).

Returns:
input size

Referenced by roboptim::finiteDifferenceGradientPolicies::Simple::computeGradient(), roboptim::visualization::gnuplot::plot(), and roboptim::visualization::gnuplot::plot_xy().

bool roboptim::Function::isValidResult ( const result_t &  result  )  const throw () [inline]

Check the given result size is valid.

Parameters:
result result that will be checked
Returns:
true if valid, false if not
static discreteInterval_t roboptim::Function::makeDiscreteInterval ( interval_t  interval,
value_type  step 
) [inline, static]

Construct a discrete interval.

Parameters:
interval continuous interval
step discretization step
static discreteInterval_t roboptim::Function::makeDiscreteInterval ( value_type  min,
value_type  max,
value_type  step 
) [inline, static]

Construct a discrete interval.

Parameters:
min miminum value of the interval
max maxinum value of the interval
step discretization step
static interval_t roboptim::Function::makeInfiniteInterval (  )  throw () [inline, static]

Construct an infinite interval.

Returns:
interval representing $[-\infty, +\infty]$

References infinity().

Referenced by roboptim::Problem< F, CLIST >::Problem().

static interval_t roboptim::Function::makeInterval ( value_type  l,
value_type  u 
) throw () [inline, static]

Construct an interval from a lower and upper bound.

Parameters:
l lower bound
u upper bound
Returns:
interval representing $[l, u]$
static interval_t roboptim::Function::makeLowerInterval ( value_type  l  )  throw () [inline, static]

Construct an interval from a lower bound.

Parameters:
l lower bound
Returns:
interval representing $[l, +\infty]$

References infinity().

static interval_t roboptim::Function::makeUpperInterval ( value_type  u  )  throw () [inline, static]

Construct an interval from an upper bound.

Parameters:
u upper bound
Returns:
interval representing $[-\infty, u]$

References infinity().

void roboptim::Function::operator() ( result_t &  result,
const argument_t &  argument 
) const throw () [inline]

Evaluate the function at a specified point.

The program will abort if the argument does not have the expected size.

Parameters:
result result will be stored in this vector
argument point at which the function will be evaluated

References RoboptimCoreDout.

result_t roboptim::Function::operator() ( const argument_t &  argument  )  const throw () [inline]

Evaluate the function at a specified point.

The program will abort if the argument does not have the expected size.

Parameters:
argument point at which the function will be evaluated
Returns:
computed result
size_type roboptim::Function::outputSize (  )  const throw () [inline]

Return the output size (i.e. result's vector size).

Returns:
input size

Referenced by roboptim::finiteDifferenceGradientPolicies::FivePointsRule::computeGradient(), roboptim::finiteDifferenceGradientPolicies::Simple::computeGradient(), roboptim::visualization::gnuplot::plot(), and roboptim::visualization::gnuplot::plot_xy().

std::ostream & roboptim::Function::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 in roboptim::ConstantFunction, roboptim::DerivableFunction, roboptim::IdentityFunction, roboptim::LinearFunction, roboptim::NTimesDerivableFunction< 2 >, roboptim::NumericLinearFunction, roboptim::NumericQuadraticFunction, roboptim::QuadraticFunction, and roboptim::TwiceDerivableFunction.

Referenced by roboptim::operator<<().