codac::TubeVector Class Reference

n-dimensional tube \([\mathbf{x}](\cdot)\), defined as an interval of n-dimensional trajectories More...

#include <codac_TubeVector.h>

Inheritance diagram for codac::TubeVector:

Collaboration diagram for codac::TubeVector:

Public Member Functions
Definition
	TubeVector (const Interval &tdomain, int n)
	Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) made of one slice.
	TubeVector (const Interval &tdomain, const IntervalVector &codomain)
	Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) made of one slice.
	TubeVector (const Interval &tdomain, double timestep, int n)
	Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) with some temporal discretization.
	TubeVector (const Interval &tdomain, double timestep, const IntervalVector &codomain)
	Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) with some temporal discretization.
	TubeVector (const Interval &tdomain, double timestep, const TFnc &f)
	Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) from a TFnc object and with some temporal discretization.
	TubeVector (const std::vector< Interval > &v_tdomains, const std::vector< IntervalVector > &v_codomains)
	Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) from a list of \(k\) boxes \(\big([t_1]\times[\mathbf{x}_1],\dots,[t_k]\times[\mathbf{x}_k]\big)\).
	TubeVector (std::initializer_list< Tube > list)
	Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) from a list of Tube objects.
	TubeVector (const TubeVector &x)
	Creates a copy of a n-dimensional tube \([\mathbf{x}](\cdot)\), with the same time discretization.
	TubeVector (const TubeVector &x, const IntervalVector &codomain)
	Creates a copy of a n-dimensional tube \([\mathbf{x}](\cdot)\), with the same time discretization but a specific constant codomain.
	TubeVector (int n, const Tube &x)
	Creates a n-dimensional tube with all the components initialized to \([x](\cdot)\).
	TubeVector (const TrajectoryVector &traj, double timestep)
	Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) enclosing a n-dimensional trajectory \(\mathbf{x}(\cdot)\), possibly with some temporal discretization.
	TubeVector (const TrajectoryVector &lb, const TrajectoryVector &ub, double timestep)
	Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) defined as an interval of two n-dimensional trajectories \([\mathbf{lb}(\cdot),\mathbf{ub}(\cdot)]\).
	TubeVector (const std::string &binary_file_name)
	Restore a n-dimensional tube from serialization.
	TubeVector (const std::string &binary_file_name, TrajectoryVector *&traj)
	Restore a n-dimensional tube from serialization, together with a TrajectoryVector object.
	~TubeVector ()
	TubeVector destructor.
int	size () const
	Returns the dimension of the tube.
void	resize (int n)
	Resizes this TubeVector.
const TubeVector	subvector (int start_index, int end_index) const
	Returns a subvector of this TubeVector.
void	put (int start_index, const TubeVector &subvec)
	Puts a subvector into this TubeVector at a given position.
const TubeVector	primitive () const
	Returns the primitive TubeVector of this tube, with a zero constant of integration.
const TubeVector	primitive (const IntervalVector &c) const
	Returns the primitive TubeVector of this tube.
const TubeVector &	operator= (const TubeVector &x)
	Returns a copy of a TubeVector.
const Interval	tdomain () const
	Returns the temporal definition domain of this tube.
const TrajectoryVector	lb () const
	Returns a possible lower bound \(\mathbf{x}^{-}(\cdot)\) of the tube.
const TrajectoryVector	ub () const
	Returns a possible upper bound \(\mathbf{x}^{+}(\cdot)\) of the tube.
Slices structure
int	nb_slices () const
	Returns the number of slices of this tube.
int	time_to_index (double t) const
	Returns the Slice index related to the temporal key \(t\).
void	sample (double t)
	Samples this tube at \(t\).
void	sample (double t, const IntervalVector &gate)
	Samples this tube at \(t\) with a specific gate value.
void	sample (const Tube &x)
	Samples this tube so that each component will share the same sampling of the scalar \([x](\cdot)\).
void	sample (const TubeVector &x)
	Samples this tube so that its components will share the same sampling of the components of the n-dimensional \([\mathbf{x}](\cdot)\).
Accessing values
const IntervalVector	codomain () const
	Returns the box of feasible values.
double	volume () const
	Returns the volume of this tube.
Tube &	operator[] (int index)
	Returns the ith Tube of this TubeVector.
const Tube &	operator[] (int index) const
	Returns a const reference to the ith Tube of this TubeVector.
const IntervalVector	operator() (int slice_id) const
	Returns the value of the ith slice.
const IntervalVector	operator() (double t) const
	Returns the evaluation of this tube at \(t\).
const IntervalVector	operator() (const Interval &t) const
	Returns the interval evaluation of this tube over \([t]\).
const std::pair< IntervalVector, IntervalVector >	eval (const Interval &t=Interval::ALL_REALS) const
	Returns the interval evaluations of the bounds of the tube \(\underline{\mathbf{x}^-}(\cdot)\) and \(\overline{\mathbf{x}^+}(\cdot)\) over \([t]\).
const IntervalVector	interpol (double t, const TubeVector &v) const
	Returns the optimal evaluation of this tube at \(t\), based on the derivative information \(\dot{\mathbf{x}}(\cdot)\).
const IntervalVector	interpol (const Interval &t, const TubeVector &v) const
	Returns the optimal interval evaluation of this tube over \([t]\), based on the derivative information \(\dot{\mathbf{x}}(\cdot)\).
const Interval	invert (const IntervalVector &y, const Interval &search_tdomain=Interval::ALL_REALS) const
	Returns the interval inversion \([\mathbf{x}]^{-1}([\mathbf{y}])\).
void	invert (const IntervalVector &y, std::vector< Interval > &v_t, const Interval &search_tdomain=Interval::ALL_REALS) const
	Computes the set of continuous values of the inversion \([\mathbf{x}]^{-1}([\mathbf{y}])\).
const Interval	invert (const IntervalVector &y, const TubeVector &v, const Interval &search_tdomain=Interval::ALL_REALS) const
	Returns the optimal interval inversion \([\mathbf{x}]^{-1}([\mathbf{y}])\).
void	invert (const IntervalVector &y, std::vector< Interval > &v_t, const TubeVector &v, const Interval &search_tdomain=Interval::ALL_REALS) const
	Computes the set of continuous values of the optimal inversion \([\mathbf{x}]^{-1}([\mathbf{y}])\).
const TrajectoryVector	diam (bool gates_thicknesses=false) const
	Returns the diameters of the tube as a trajectory.
const TrajectoryVector	diam (const TubeVector &v) const
	Returns the diameters of the tube as a trajectory.
const Vector	max_diam () const
	Returns a vector of the maximum diameters of the tube for each component.
double	max_gate_diam (double &t) const
	Returns the maximum diameter of all gates of the tube vector in all components.
const Slice *	steepest_slice () const
	Returns the slice of the Tube of this TubeVector with the largest difference between the mid values of the input and output gates, in all components.
const Trajectory	diag (bool gates_diag=false) const
	Returns the slices diagonals of the tube as a trajectory.
const Trajectory	diag (int start_index, int end_index, bool gates_diag=false) const
	Returns the slices diagonals of a subvector of this tube as a trajectory.
Tests
bool	operator== (const TubeVector &x) const
	Returns true if this tube is equal to \([\mathbf{x}](\cdot)\).
bool	operator!= (const TubeVector &x) const
	Returns true if this tube is different from \([\mathbf{x}](\cdot)\).
bool	is_subset (const TubeVector &x) const
	Returns true if this tube is a subset of \([\mathbf{x}](\cdot)\).
bool	is_strict_subset (const TubeVector &x) const
	Returns true if this tube is a subset of \([\mathbf{x}](\cdot)\), and not \([\mathbf{x}](\cdot)\) itself.
bool	is_interior_subset (const TubeVector &x) const
	Returns true if this tube is a subset of the interior of \([\mathbf{x}](\cdot)\).
bool	is_strict_interior_subset (const TubeVector &x) const
	Returns true if this tube is a subset of the interior of \([\mathbf{x}](\cdot)\), and not \([\mathbf{x}](\cdot)\) itself.
bool	is_superset (const TubeVector &x) const
	Returns true if this tube is a superset of \([\mathbf{x}](\cdot)\).
bool	is_strict_superset (const TubeVector &x) const
	Returns true if this tube is a superset of \([\mathbf{x}](\cdot)\), and not \([\mathbf{x}](\cdot)\) itself.
bool	is_empty () const
	Returns true if this tube is empty.
const BoolInterval	contains (const TrajectoryVector &x) const
	Returns true if this tube contains the trajectory \(\mathbf{x}(\cdot)\).
bool	overlaps (const TubeVector &x, float ratio=1.) const
	Returns true if this tube overlaps the tube \([\mathbf{x}](\cdot)\).
Setting values
const TubeVector &	set (const IntervalVector &y)
	Sets a constant box value for this tube: \(\forall t, [\mathbf{x}](t)=[\mathbf{y}]\).
const TubeVector &	set (const IntervalVector &y, int slice_id)
	Sets the box value of the ith slice of this tube.
const TubeVector &	set (const IntervalVector &y, double t)
	Sets the box value of this tube at \(t\): \([\mathbf{x}](t)=[\mathbf{y}]\).
const TubeVector &	set (const IntervalVector &y, const Interval &t)
	Sets the box value of this tube over \([t]\): \(\forall t\in[t], [\mathbf{x}](t)=[\mathbf{y}]\).
const TubeVector &	set_empty ()
	Sets this tube to the empty set.
const TubeVector &	inflate (double rad)
	Inflates this tube by adding \([-\mathbf{rad},+\mathbf{rad}]\) to all its codomain components.
const TubeVector &	inflate (const Vector &rad)
	Inflates this tube by adding \([-\mathbf{rad},+\mathbf{rad}]\) to all its codomain components.
const TubeVector &	inflate (const TrajectoryVector &rad)
	Inflates this tube by adding non-constant uncertainties defined in a trajectory.
TubeVector &	truncate_tdomain (const Interval &tdomain)
	Truncates the tdomain of \([\mathbf{x}](\cdot)\).
void	shift_tdomain (double a)
	Shifts the tdomain \([t_0,t_f]\) of \([\mathbf{x}](\cdot)\).
Bisection
const std::pair< TubeVector, TubeVector >	bisect (double t, float ratio=0.49) const
	Bisects this tube.
const std::pair< TubeVector, TubeVector >	bisect (double t, int dim, float ratio=0.49) const
	Bisects this tube along a specific dimension.
Assignments operators
const TubeVector &	operator+= (const Interval &x)
	Operates +=.
const TubeVector &	operator+= (const Trajectory &x)
	Operates +=.
const TubeVector &	operator+= (const Tube &x)
	Operates +=.
const TubeVector &	operator+= (const IntervalVector &x)
	Operates +=.
const TubeVector &	operator+= (const TrajectoryVector &x)
	Operates +=.
const TubeVector &	operator+= (const TubeVector &x)
	Operates +=.
const TubeVector &	operator-= (const Interval &x)
	Operates -=.
const TubeVector &	operator-= (const Trajectory &x)
	Operates -=.
const TubeVector &	operator-= (const Tube &x)
	Operates -=.
const TubeVector &	operator-= (const IntervalVector &x)
	Operates -=.
const TubeVector &	operator-= (const TrajectoryVector &x)
	Operates -=.
const TubeVector &	operator-= (const TubeVector &x)
	Operates -=.
const TubeVector &	operator*= (const Interval &x)
	Operates *=.
const TubeVector &	operator*= (const Trajectory &x)
	Operates *=.
const TubeVector &	operator*= (const Tube &x)
	Operates *=.
const TubeVector &	operator/= (const Interval &x)
	Operates /=.
const TubeVector &	operator/= (const Trajectory &x)
	Operates /=.
const TubeVector &	operator/= (const Tube &x)
	Operates /=.
const TubeVector &	operator|= (const IntervalVector &x)
	Operates |=.
const TubeVector &	operator|= (const TrajectoryVector &x)
	Operates |=.
const TubeVector &	operator|= (const TubeVector &x)
	Operates |=.
const TubeVector &	operator&= (const IntervalVector &x)
	Operates &=.
const TubeVector &	operator&= (const TrajectoryVector &x)
	Operates &=.
const TubeVector &	operator&= (const TubeVector &x)
	Operates &=.
Tree synthesis structure
void	enable_synthesis (SynthesisMode mode=SynthesisMode::BINARY_TREE, double eps=1.e-3) const
	Enables the computation of a synthesis tree.
Integration
const IntervalVector	integral (double t) const
	Computes the box integral \(\int_0^t[\mathbf{x}](\tau)d\tau\).
const IntervalVector	integral (const Interval &t) const
	Computes the box integral \(\int_0^{[t]}[\mathbf{x}](\tau)d\tau\).
const IntervalVector	integral (const Interval &t1, const Interval &t2) const
	Computes the box integral \(\int_{[t_1]}^{[t_2]}[\mathbf{x}](\tau)d\tau\).
const std::pair< IntervalVector, IntervalVector >	partial_integral (const Interval &t) const
	Computes the partial box integral \(\int_{0}^{[t]}[\mathbf{x}](\tau)d\tau\).
const std::pair< IntervalVector, IntervalVector >	partial_integral (const Interval &t1, const Interval &t2) const
	Computes the partial box integral \(\int_{[t_1]}^{[t_2]}[\mathbf{x}](\tau)d\tau\).
Serialization
void	serialize (const std::string &binary_file_name="x.tube", int version_number=SERIALIZATION_VERSION) const
	Serializes this tube.
void	serialize (const std::string &binary_file_name, const TrajectoryVector &traj, int version_number=SERIALIZATION_VERSION) const
	Serializes this tube together with a TrajectoryVector object.
Public Member Functions inherited from codac::DynamicalItem
virtual	~DynamicalItem ()
	DynamicalItem destructor.

Static Public Member Functions
static bool	same_slicing (const TubeVector &x1, const Tube &x2)
	Tests whether a TubeVector object shares the slicing of another Tube object.
static bool	same_slicing (const TubeVector &x1, const TubeVector &x2)
	Tests whether the two TubeVector objects are sharing the same slicing.
static const TubeVector	hull (const std::list< TubeVector > &l_tubes)
	Computes the hull of several tubes.
Static Public Member Functions inherited from codac::DynamicalItem
static bool	valid_tdomain (const Interval &tdomain)
	Verifies that this interval is a feasible tdomain.

Protected Member Functions
	TubeVector ()
	Creates an undefined n-dimensional tube.
const IntervalVector	codomain_box () const
	Returns the box \([\mathbf{x}]([t_0,t_f])\).
void	deserialize (const std::string &binary_file_name, TrajectoryVector *&traj)
	Restores a n-dimensional tube from serialization, together with a TrajectoryVector object.

Protected Attributes
int	m_n = 0
	dimension of this tube
Tube *	m_v_tubes = nullptr
	array of components (scalar tubes)

String
const std::string	class_name () const
	Returns the name of this class.

Detailed Description

n-dimensional tube \([\mathbf{x}](\cdot)\), defined as an interval of n-dimensional trajectories

Note

Use Tube for the one-dimensional case

Constructor & Destructor Documentation

TubeVector() [1/15]

codac::TubeVector::TubeVector ( const Interval & tdomain, int n )

explicit

Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) made of one slice.

Parameters

tdomain	temporal domain \([t_0,t_f]\)
n	dimension of this tube

TubeVector() [2/15]

codac::TubeVector::TubeVector ( const Interval & tdomain, const IntervalVector & codomain )

explicit

Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) made of one slice.

Note

The dimension of the tube is specified by the codomain box

Parameters

tdomain	temporal domain \([t_0,t_f]\)
codomain	IntervalVector value of the slice

TubeVector() [3/15]

codac::TubeVector::TubeVector ( const Interval & tdomain, double timestep, int n )

explicit

Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) with some temporal discretization.

Parameters

tdomain	temporal domain \([t_0,t_f]\)
timestep	sampling value \(\delta\) for the temporal discretization (double)
n	dimension of this tube

TubeVector() [4/15]

codac::TubeVector::TubeVector ( const Interval & tdomain, double timestep, const IntervalVector & codomain )

explicit

Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) with some temporal discretization.

Parameters

tdomain	temporal domain \([t_0,t_f]\)
timestep	sampling value \(\delta\) for the temporal discretization (double)
codomain	IntervalVector value of the slices

TubeVector() [5/15]

codac::TubeVector::TubeVector ( const Interval & tdomain, double timestep, const TFnc & f )

explicit

Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) from a TFnc object and with some temporal discretization.

Note

Due to the slicing implementation of the tube, a wrapping effect will occur to reliably enclose the TFnc object

The dimension of the tube is specified by the output of \([\mathbf{f}]\)

Parameters

tdomain	temporal domain \([t_0,t_f]\)
timestep	sampling value \(\delta\) for the temporal discretization (double)
f	TFnc object that will be enclosed by the tube: \(\forall t\in[t_0,t_f], [\mathbf{f}](t)\subseteq[\mathbf{x}](t)\)

TubeVector() [6/15]

codac::TubeVector::TubeVector ( const std::vector< Interval > & v_tdomains, const std::vector< IntervalVector > & v_codomains )

explicit

Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) from a list of \(k\) boxes \(\big([t_1]\times[\mathbf{x}_1],\dots,[t_k]\times[\mathbf{x}_k]\big)\).

Note

The slicing will be based on the vector of temporal domains.

The \([t_i]\)'s must cover continuously the tdomain of \([\mathbf{x}](\cdot)\).

Parameters

v_tdomains	vector of temporal domains \([t_i]\)
v_codomains	vector of codomains \([\mathbf{x}_i]\) related to the \([t_i]\)'s

TubeVector() [7/15]

codac::TubeVector::TubeVector

(

std::initializer_list< Tube >

list

)

Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) from a list of Tube objects.

Parameters

list	list of \([x_i](\cdot)\) tubes

TubeVector() [8/15]

codac::TubeVector::TubeVector

(

const TubeVector &

x

)

Creates a copy of a n-dimensional tube \([\mathbf{x}](\cdot)\), with the same time discretization.

Parameters

x	TubeVector to be duplicated

TubeVector() [9/15]

codac::TubeVector::TubeVector ( const TubeVector & x, const IntervalVector & codomain )

explicit

Creates a copy of a n-dimensional tube \([\mathbf{x}](\cdot)\), with the same time discretization but a specific constant codomain.

Parameters

x	TubeVector from which the sampling will be duplicated
codomain	IntervalVector value of the slices

TubeVector() [10/15]

codac::TubeVector::TubeVector ( int n, const Tube & x )

explicit

Creates a n-dimensional tube with all the components initialized to \([x](\cdot)\).

Note

The TubeVector object will have the same slicing as the tube \([x](\cdot)\)

Parameters

n	dimension of this tube
x	Tube to be copied for all the components

TubeVector() [11/15]

codac::TubeVector::TubeVector ( const TrajectoryVector & traj, double timestep )

explicit

Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) enclosing a n-dimensional trajectory \(\mathbf{x}(\cdot)\), possibly with some temporal discretization.

Note

Due to the slicing implementation of the tube, a wrapping effect will occur to reliably enclose the TrajectoryVector object

Parameters

traj	TrajectoryVector \(\mathbf{x}(\cdot)\) to enclose
timestep	sampling value \(\delta\) for the temporal discretization

TubeVector() [12/15]

codac::TubeVector::TubeVector ( const TrajectoryVector & lb, const TrajectoryVector & ub, double timestep )

explicit

Creates a n-dimensional tube \([\mathbf{x}](\cdot)\) defined as an interval of two n-dimensional trajectories \([\mathbf{lb}(\cdot),\mathbf{ub}(\cdot)]\).

Note

Due to the slicing implementation of the tube, a wrapping effect will occur to reliably enclose the TrajectoryVector object

Parameters

lb	TrajectoryVector defining the lower bound \(\mathbf{x}^{-}(\cdot)\) of the tube
ub	TrajectoryVector defining the upper bound \(\mathbf{x}^{+}(\cdot)\) of the tube
timestep	sampling value \(\delta\) for the temporal discretization

TubeVector() [13/15]

codac::TubeVector::TubeVector ( const std::string & binary_file_name )

explicit

Restore a n-dimensional tube from serialization.

Note

The TubeVector must have been serialized beforehand by the appropriate method serialize()

Parameters

binary_file_name

path to the binary file

TubeVector() [14/15]

codac::TubeVector::TubeVector ( const std::string & binary_file_name, TrajectoryVector *& traj )

explicit

Restore a n-dimensional tube from serialization, together with a TrajectoryVector object.

Note

The TubeVector and the TrajectoryVector must have been serialized beforehand by the appropriate method serialize()

Parameters

binary_file_name	path to the binary file
traj	a pointer to the TrajectoryVector object to be instantiated

TubeVector() [15/15]

codac::TubeVector::TubeVector ( )

protected

Creates an undefined n-dimensional tube.

Note

Constructor necessary for the deserialize_TubeVector method

Member Function Documentation

size()

int codac::TubeVector::size ( ) const

virtual

Returns the dimension of the tube.

Returns

n

Implements codac::DynamicalItem.

resize()

void codac::TubeVector::resize

(

int

n

)

Resizes this TubeVector.

Note

If the size is increased, the existing components are not modified and the new ones are set to \([t_0,t_f]\mapsto[-\infty,\infty]\)

Parameters

n	the new size to be set

subvector()

const TubeVector codac::TubeVector::subvector	(	int	start_index,
		int	end_index ) const

Returns a subvector of this TubeVector.

Parameters

start_index	first component index of the subvector to be returned
end_index	last component index of the subvector to be returned

Returns

a TubeVector extracted from this TubeVector

put()

void codac::TubeVector::put	(	int	start_index,
		const TubeVector &	subvec )

Puts a subvector into this TubeVector at a given position.

Parameters

start_index	position where the subvector will be put
subvec	the TubeVector to put from start_index

primitive() [1/2]

const TubeVector codac::TubeVector::primitive

(

)

const

Returns the primitive TubeVector of this tube, with a zero constant of integration.

Returns

a new TubeVector object with same slicing, enclosing the feasible primitives of this tube

primitive() [2/2]

const TubeVector codac::TubeVector::primitive

(

const IntervalVector &

c

)

const

Returns the primitive TubeVector of this tube.

Parameters

c	the constant of integration

Returns

a new TubeVector object with same slicing, enclosing the feasible primitives of this tube

operator=()

const TubeVector & codac::TubeVector::operator=

(

const TubeVector &

x

)

Returns a copy of a TubeVector.

Parameters

x	the TubeVector object to be copied

Returns

a new TubeVector object with same slicing and values

tdomain()

const Interval codac::TubeVector::tdomain ( ) const

virtual

Returns the temporal definition domain of this tube.

Returns

an Interval object \([t_0,t_f]\)

Implements codac::DynamicalItem.

lb()

const TrajectoryVector codac::TubeVector::lb

(

)

const

Returns a possible lower bound \(\mathbf{x}^{-}(\cdot)\) of the tube.

Note

The exact lower bound cannot be known. However, the returned trajectory \(\mathbf{x}^{-}(\cdot)\) is guaranteed to be enclosed in the tube \([\mathbf{x}](\cdot)\).

Returns

a candidate for \(\mathbf{x}^{-}(\cdot)\)

ub()

const TrajectoryVector codac::TubeVector::ub

(

)

const

Returns a possible upper bound \(\mathbf{x}^{+}(\cdot)\) of the tube.

Note

The exact upper bound cannot be known. However, the returned trajectory \(\mathbf{x}^{+}(\cdot)\) is guaranteed to be enclosed in the tube \([\mathbf{x}](\cdot)\).

Returns

a candidate for \(\mathbf{x}^{+}(\cdot)\)

nb_slices()

int codac::TubeVector::nb_slices

(

)

const

Returns the number of slices of this tube.

Returns

an integer

time_to_index()

int codac::TubeVector::time_to_index

(

double

t

)

const

Returns the Slice index related to the temporal key \(t\).

Parameters

t	the temporal key (double, must belong to the TubeVector's tdomain)

Returns

an integer

sample() [1/4]

void codac::TubeVector::sample

(

double

t

)

Samples this tube at \(t\).

Note

Without any effect on one component that has two Slice objects already defined at \(t\) (if the gate \([\mathbf{x}](t)\) already exists)

Parameters

t	the temporal key (double, must belong to the TubeVector's tdomain)

sample() [2/4]

void codac::TubeVector::sample	(	double	t,
		const IntervalVector &	gate )

Samples this tube at \(t\) with a specific gate value.

Note

Without any effect on one component that has two Slice objects already defined at \(t\) (if the gate \([\mathbf{x}](t)\) already exists)

Parameters

t	the temporal key (double, must belong to the TubeVector's tdomain)
gate	the IntervalVector value of this tube at \(t\)

sample() [3/4]

void codac::TubeVector::sample

(

const Tube &

x

)

Samples this tube so that each component will share the same sampling of the scalar \([x](\cdot)\).

Note

The previous sampling of this tube is preserved

Parameters

x	the Tube from which the new sampling will come from

sample() [4/4]

void codac::TubeVector::sample

(

const TubeVector &

x

)

Samples this tube so that its components will share the same sampling of the components of the n-dimensional \([\mathbf{x}](\cdot)\).

Note

The previous sampling of this tube is preserved

Parameters

x	the TubeVector from which the new sampling will come from

codomain()

const IntervalVector codac::TubeVector::codomain

(

)

const

Returns the box of feasible values.

Returns

an IntervalVector object \([\mathbf{x}]([t_0,t_f])\)

volume()

double codac::TubeVector::volume

(

)

const

Returns the volume of this tube.

Note

returns POS_INFINITY if the codomain is unbounded

returns 0 if the tube is flat (and so without wrapping effect)

Returns

volume defined as \(w([t_0,t_f])\times w([x_1]([t_0,t_f]))\times\dots\times w([x_n]([t_0,t_f]))\)

operator[]() [1/2]

Tube & codac::TubeVector::operator[]

(

int

index

)

Returns the ith Tube of this TubeVector.

Parameters

index

the index of this ith component

Returns

a reference to the ith component

operator[]() [2/2]

const Tube & codac::TubeVector::operator[]

(

int

index

)

const

Returns a const reference to the ith Tube of this TubeVector.

Parameters

index

the index of this ith component

Returns

a const reference to the ith component

operator()() [1/3]

const IntervalVector codac::TubeVector::operator()

(

int

slice_id

)

const

Returns the value of the ith slice.

Parameters

slice_id

the index of the ith slice

Returns

IntervalVector value of \([\mathbf{x}](i)\)

operator()() [2/3]

const IntervalVector codac::TubeVector::operator()

(

double

t

)

const

Returns the evaluation of this tube at \(t\).

Parameters

t	the temporal key (double, must belong to the TubeVector's tdomain)

Returns

IntervalVector value of \([\mathbf{x}](t)\)

operator()() [3/3]

const IntervalVector codac::TubeVector::operator()

(

const Interval &

t

)

const

Returns the interval evaluation of this tube over \([t]\).

Parameters

t	the subtdomain (Interval, must be a subset of the TubeVector's tdomain)

Returns

IntervalVector envelope \([\mathbf{x}]([t])\)

eval()

const std::pair< IntervalVector, IntervalVector > codac::TubeVector::eval

(

const Interval &

t = Interval::ALL_REALS

)

const

Returns the interval evaluations of the bounds of the tube \(\underline{\mathbf{x}^-}(\cdot)\) and \(\overline{\mathbf{x}^+}(\cdot)\) over \([t]\).

Parameters

t	the subtdomain (Interval, must be a subset of the TubeVector's tdomain)

Returns

the pair \(\big([\underline{\mathbf{x}^-}]([t]),[\overline{\mathbf{x}^+}]([t])\big)\)

interpol() [1/2]

const IntervalVector codac::TubeVector::interpol	(	double	t,
		const TubeVector &	v ) const

Returns the optimal evaluation of this tube at \(t\), based on the derivative information \(\dot{\mathbf{x}}(\cdot)\).

Todo

Change the name of this method?

Parameters

t	the temporal key (double, must belong to the TubeVector's tdomain)
v	the derivative tube such that \(\dot{\mathbf{x}}(\cdot)\in[\mathbf{v}](\cdot)\)

Returns

IntervalVector value of \([\mathbf{x}](t)\)

interpol() [2/2]

const IntervalVector codac::TubeVector::interpol	(	const Interval &	t,
		const TubeVector &	v ) const

Returns the optimal interval evaluation of this tube over \([t]\), based on the derivative information \(\dot{\mathbf{x}}(\cdot)\).

Todo

Change the name of this method?

Parameters

t	the subtdomain (Interval, must be a subset of the TubeVector's tdomain)
v	the derivative tube such that \(\dot{\mathbf{x}}(\cdot)\in[\mathbf{v}](\cdot)\)

Returns

IntervalVector value of \([\mathbf{x}]([t])\)

invert() [1/4]

const Interval codac::TubeVector::invert	(	const IntervalVector &	y,
		const Interval &	search_tdomain = Interval::ALL_REALS ) const

Returns the interval inversion \([\mathbf{x}]^{-1}([\mathbf{y}])\).

Note

If the inversion results in several pre-images, their union is returned

Parameters

y	the box codomain
search_tdomain	the optional temporal domain on which the inversion will be performed

Returns

the hull of \([\mathbf{x}]^{-1}([\mathbf{y}])\)

invert() [2/4]

void codac::TubeVector::invert	(	const IntervalVector &	y,
		std::vector< Interval > &	v_t,
		const Interval &	search_tdomain = Interval::ALL_REALS ) const

Computes the set of continuous values of the inversion \([\mathbf{x}]^{-1}([\mathbf{y}])\).

Parameters

y	the interval codomain
v_t	the vector of the sub-tdomains \([t_k]\) for which \(\forall t\in[t_k] \mid \mathbf{x}(t)\in[\mathbf{y}], \mathbf{x}(\cdot)\in[\mathbf{x}](\cdot)\)
search_tdomain	the optional temporal domain on which the inversion will be performed

invert() [3/4]

const Interval codac::TubeVector::invert	(	const IntervalVector &	y,
		const TubeVector &	v,
		const Interval &	search_tdomain = Interval::ALL_REALS ) const

Returns the optimal interval inversion \([\mathbf{x}]^{-1}([\mathbf{y}])\).

Note

The knowledge of the derivative tube \([\mathbf{v}](\cdot)\) allows a finer inversion

If the inversion results in several pre-images, their union is returned

Parameters

y	the interval codomain
v	the derivative tube vector such that \(\dot{\mathbf{x}}(\cdot)\in[\mathbf{v}](\cdot)\)
search_tdomain	the optional temporal domain on which the inversion will be performed

Returns

the hull of \([\mathbf{x}]^{-1}([\mathbf{y}])\)

invert() [4/4]

void codac::TubeVector::invert	(	const IntervalVector &	y,
		std::vector< Interval > &	v_t,
		const TubeVector &	v,
		const Interval &	search_tdomain = Interval::ALL_REALS ) const

Computes the set of continuous values of the optimal inversion \([\mathbf{x}]^{-1}([\mathbf{y}])\).

Note

The knowledge of the derivative tube \([\mathbf{v}](\cdot)\) allows finer inversions

Parameters

y	the interval codomain
v_t	the vector of the sub-tdomains \([t_k]\) for which \(\exists t\in[t_k] \mid \mathbf{x}(t)\in[\mathbf{y}], \mathbf{x}(\cdot)\in[\mathbf{x}](\cdot), \dot{\mathbf{x}}(\cdot)\in[\mathbf{v}](\cdot)\)
v	the derivative tube such that \(\dot{\mathbf{x}}(\cdot)\in[\mathbf{v}](\cdot)\)
search_tdomain	the optional temporal domain on which the inversion will be performed

diam() [1/2]

const TrajectoryVector codac::TubeVector::diam

(

bool

gates_thicknesses = false

)

const

Returns the diameters of the tube as a trajectory.

Note

Without derivative knowledge, and because the tube is made of boxed slices, the trajectory will be discontinuous and so the returned object will not reliably represent the diameters. It can be mainly used for display purposes.

Parameters

gates_thicknesses

if true, the diameters of the gates will be evaluated too

Returns

the set of diameters associated to temporal inputs

diam() [2/2]

const TrajectoryVector codac::TubeVector::diam

(

const TubeVector &

v

)

const

Returns the diameters of the tube as a trajectory.

Note

Because the tube is made of boxed slices, the trajectory may be discontinuous and so the returned object will not reliably represent the diameters. It can be mainly used for display purposes.

Parameters

v	the derivative tube such that \(\dot{x}(\cdot)\in[v](\cdot)\)

Returns

the set of diameters associated to temporal inputs

max_diam()

const Vector codac::TubeVector::max_diam

(

)

const

Returns a vector of the maximum diameters of the tube for each component.

Returns

the maximal thicknesses of this tube

max_gate_diam()

double codac::TubeVector::max_gate_diam

(

double &

t

)

const

Returns the maximum diameter of all gates of the tube vector in all components.

Parameters

t	instant \(t\) corresponding to this maximal diameter

Returns

the maximal diameter of a component of a gate

steepest_slice()

const Slice * codac::TubeVector::steepest_slice

(

)

const

Returns the slice of the Tube of this TubeVector with the largest difference between the mid values of the input and output gates, in all components.

Returns

a pointer to the steepest slice

diag() [1/2]

const Trajectory codac::TubeVector::diag

(

bool

gates_diag = false

)

const

Returns the slices diagonals of the tube as a trajectory.

Note

Without derivative knowledge, and because the tube is made of boxed slices, the trajectory will be discontinuous and so the returned object will not reliably represent the diagonals. It can be mainly used for display purposes.

Parameters

gates_diag

if true, the diagonals of the gates will be evaluated too

Returns

the set of diagonals associated to temporal inputs

diag() [2/2]

const Trajectory codac::TubeVector::diag	(	int	start_index,
		int	end_index,
		bool	gates_diag = false ) const

Returns the slices diagonals of a subvector of this tube as a trajectory.

Note

Without derivative knowledge, and because the tube is made of boxed slices, the trajectory will be discontinuous and so the returned object will not reliably represent the diagonals. It can be mainly used for display purposes.

Parameters

start_index	first component index of the subvector
end_index	last component index of the subvector
gates_diag	if true, the diagonals of the gates will be evaluated too

Returns

the set of diagonals associated to temporal inputs

operator==()

bool codac::TubeVector::operator==

(

const TubeVector &

x

)

const

Returns true if this tube is equal to \([\mathbf{x}](\cdot)\).

Note

Equality is obtained if the tubes share the same bounds, tdomain and sampling

Parameters

x	the TubeVector object

Returns

true in case of equality

operator!=()

bool codac::TubeVector::operator!=

(

const TubeVector &

x

)

const

Returns true if this tube is different from \([\mathbf{x}](\cdot)\).

Note

The two tubes are different if they do not share the same bounds, tdomain or sampling

Parameters

x	the TubeVector object

Returns

true in case of difference

is_subset()

bool codac::TubeVector::is_subset

(

const TubeVector &

x

)

const

Returns true if this tube is a subset of \([\mathbf{x}](\cdot)\).

Note

The two tubes may not share the same slicing, but must have the same tdomain

Parameters

x	the TubeVector object

Returns

true in case of subset

is_strict_subset()

bool codac::TubeVector::is_strict_subset

(

const TubeVector &

x

)

const

Returns true if this tube is a subset of \([\mathbf{x}](\cdot)\), and not \([\mathbf{x}](\cdot)\) itself.

Note

The two tubes may not share the same slicing, but must have the same tdomain

Parameters

x	the TubeVector object

Returns

true in case of strict subset

is_interior_subset()

bool codac::TubeVector::is_interior_subset

(

const TubeVector &

x

)

const

Returns true if this tube is a subset of the interior of \([\mathbf{x}](\cdot)\).

Note

The two tubes may not share the same slicing, but must have the same tdomain

Parameters

x	the TubeVector object

Returns

true in case of interior subset

is_strict_interior_subset()

bool codac::TubeVector::is_strict_interior_subset

(

const TubeVector &

x

)

const

Returns true if this tube is a subset of the interior of \([\mathbf{x}](\cdot)\), and not \([\mathbf{x}](\cdot)\) itself.

Note

The two tubes may not share the same slicing, but must have the same tdomain

Parameters

x	the TubeVector object

Returns

true in case of strict interior subset

is_superset()

bool codac::TubeVector::is_superset

(

const TubeVector &

x

)

const

Returns true if this tube is a superset of \([\mathbf{x}](\cdot)\).

Note

The two tubes may not share the same slicing, but must have the same tdomain

Parameters

x	the TubeVector object

Returns

true in case of superset

is_strict_superset()

bool codac::TubeVector::is_strict_superset

(

const TubeVector &

x

)

const

Returns true if this tube is a superset of \([\mathbf{x}](\cdot)\), and not \([\mathbf{x}](\cdot)\) itself.

Note

The two tubes may not share the same slicing, but must have the same tdomain

Parameters

x	the TubeVector object

Returns

true in case of strict superset

is_empty()

bool codac::TubeVector::is_empty

(

)

const

Returns true if this tube is empty.

Note

If \([\mathbf{x}](t)=\varnothing\) for some \(t\), then the tube \([\mathbf{x}](\cdot)\) is considered empty

Returns

true in case of emptiness

contains()

const BoolInterval codac::TubeVector::contains

(

const TrajectoryVector &

x

)

const

Returns true if this tube contains the trajectory \(\mathbf{x}(\cdot)\).

Note

Due to the reliable numerical representation of a trajectory, some wrapping effect may appear for its evaluations (either if it is defined by a map of values or an analytic function). Hence, this "contains" test may not be able to conclude, if the thin envelope of \(\mathbf{x}(\cdot)\) overlaps a boundary of the tube.

Parameters

x	the trajectory that might be contained by this tube

Returns

BoolInterval::YES (or BoolInterval::NO) if this tube contains \(\mathbf{x}(\cdot)\) (or does not contain) and BoolInterval::MAYBE in case of ambiguity

overlaps()

bool codac::TubeVector::overlaps	(	const TubeVector &	x,
		float	ratio = 1. ) const

Returns true if this tube overlaps the tube \([\mathbf{x}](\cdot)\).

Parameters

x	the other tube
ratio	an optional overlapping ratio between 0 and 1 (1 by default). For instance, if ratio=0.3 and there is an overlapping of at least 30%, then the function returns true

Returns

true in case of overlapping with respect to the defined ratio

set() [1/4]

const TubeVector & codac::TubeVector::set

(

const IntervalVector &

y

)

Sets a constant box value for this tube: \(\forall t, [\mathbf{x}](t)=[\mathbf{y}]\).

Note

The sampling of this tube is preserved

Parameters

y	IntervalVector value of the slices

Returns

*this

set() [2/4]

const TubeVector & codac::TubeVector::set	(	const IntervalVector &	y,
		int	slice_id )

Sets the box value of the ith slice of this tube.

Parameters

y	IntervalVector value of the ith slice
slice_id	index of the ith Slice

Returns

*this

set() [3/4]

const TubeVector & codac::TubeVector::set	(	const IntervalVector &	y,
		double	t )

Sets the box value of this tube at \(t\): \([\mathbf{x}](t)=[\mathbf{y}]\).

Note

It may create a gate (and so one more slice) if the tube is not already sampled at \(t\). Otherwise, it will update the value of the already existing gate.

Parameters

y	IntervalVector value of the gate
t	the temporal key (double, must belong to the TubeVector's tdomain)

Returns

*this

set() [4/4]

const TubeVector & codac::TubeVector::set	(	const IntervalVector &	y,
		const Interval &	t )

Sets the box value of this tube over \([t]\): \(\forall t\in[t], [\mathbf{x}](t)=[\mathbf{y}]\).

Note

It may create two gates (and so further slices) if the tube is not already sampled at \(t^-\) and \(t^+\). This is done to ensure that \(\forall t\in[t], [\mathbf{x}](t)=[\mathbf{y}]\).

Parameters

y	IntervalVector value to be set
t	the subtdomain (Interval, must be a subset of the TubeVector's tdomain)

Returns

*this

set_empty()

const TubeVector & codac::TubeVector::set_empty

(

)

Sets this tube to the empty set.

Note

By convention, all slices will be set to the empty set

Returns

*this

inflate() [1/3]

const TubeVector & codac::TubeVector::inflate

(

double

rad

)

Inflates this tube by adding \([-\mathbf{rad},+\mathbf{rad}]\) to all its codomain components.

Note

All slices and gates will be inflated

Parameters

rad	half of the inflation

Returns

*this

inflate() [2/3]

const TubeVector & codac::TubeVector::inflate

(

const Vector &

rad

)

Inflates this tube by adding \([-\mathbf{rad},+\mathbf{rad}]\) to all its codomain components.

Note

All slices and gates will be inflated

Parameters

rad	half of the inflation for each component

Returns

*this

inflate() [3/3]

const TubeVector & codac::TubeVector::inflate

(

const TrajectoryVector &

rad

)

Inflates this tube by adding non-constant uncertainties defined in a trajectory.

Note

From the trajectory \(\mathbf{a}(\cdot)\), the function will inflate this tube such that \(\forall t, [\mathbf{x}](t):=[\mathbf{x}](t)+[-\mathbf{a}(t),+\mathbf{a}(t)]\)

All slices and gates will be inflated

Parameters

rad	the TrajectoryVector object defining the non-constant inflation

Returns

*this

truncate_tdomain()

TubeVector & codac::TubeVector::truncate_tdomain

(

const Interval &

tdomain

)

Truncates the tdomain of \([\mathbf{x}](\cdot)\).

Note

The new tdomain must be a subset of the old one

Parameters

tdomain

new temporal domain \([t_0,t_f]\)

Returns

a reference to this tube

shift_tdomain()

void codac::TubeVector::shift_tdomain

(

double

a

)

Shifts the tdomain \([t_0,t_f]\) of \([\mathbf{x}](\cdot)\).

Parameters

a	the offset value so that \([t_0,t_f]:=[t_0+a,t_f+a]\)

bisect() [1/2]

const std::pair< TubeVector, TubeVector > codac::TubeVector::bisect	(	double	t,
		float	ratio = 0.49 ) const

Bisects this tube.

Note

The tube is bisected along the codomain and according to a defined ratio

The bisection is performed on the largest component of the gate \([\mathbf{x}](t)\)

If the tube is not already sampled at \(t\), then a sampling is performed

Parameters

t	the temporal key (double, must belong to the TubeVector's domain)
ratio	the bisection ratio (default value: 0.49)

Returns

a pair of two TubeVector objects resulting from the bisection

bisect() [2/2]

const std::pair< TubeVector, TubeVector > codac::TubeVector::bisect	(	double	t,
		int	dim,
		float	ratio = 0.49 ) const

Bisects this tube along a specific dimension.

Note

The tube is bisected along the codomain and according to a defined ratio

The bisection is performed on the gate \([x_i](t)\)

If the tube is not already sampled at \(t\), then a sampling is performed

Parameters

t	the temporal key (double, must belong to the TubeVector's domain)
dim	the dimension id
ratio	the bisection ratio (default value: 0.49)

Returns

a pair of two TubeVector objects resulting from the bisection

operator+=() [1/6]

const TubeVector & codac::TubeVector::operator+=

(

const Interval &

x

)

Operates +=.

Parameters

x

Interval

Returns

(*this)+=x

operator+=() [2/6]

const TubeVector & codac::TubeVector::operator+=

(

const Trajectory &

x

)

Operates +=.

Parameters

x	Trajectory

Returns

(*this)+=x

operator+=() [3/6]

const TubeVector & codac::TubeVector::operator+=

(

const Tube &

x

)

Operates +=.

Parameters

x

Tube

Returns

(*this)+=x

operator+=() [4/6]

const TubeVector & codac::TubeVector::operator+=

(

const IntervalVector &

x

)

Operates +=.

Parameters

x	IntervalVector

Returns

(*this)+=x

operator+=() [5/6]

const TubeVector & codac::TubeVector::operator+=

(

const TrajectoryVector &

x

)

Operates +=.

Parameters

x	TrajectoryVector

Returns

(*this)+=x

operator+=() [6/6]

const TubeVector & codac::TubeVector::operator+=

(

const TubeVector &

x

)

Operates +=.

Parameters

x	TubeVector

Returns

(*this)+=x

operator-=() [1/6]

const TubeVector & codac::TubeVector::operator-=

(

const Interval &

x

)

Operates -=.

Parameters

x

Interval

Returns

(*this)-=x

operator-=() [2/6]

const TubeVector & codac::TubeVector::operator-=

(

const Trajectory &

x

)

Operates -=.

Parameters

x	Trajectory

Returns

(*this)-=x

operator-=() [3/6]

const TubeVector & codac::TubeVector::operator-=

(

const Tube &

x

)

Operates -=.

Parameters

x

Tube

Returns

(*this)-=x

operator-=() [4/6]

const TubeVector & codac::TubeVector::operator-=

(

const IntervalVector &

x

)

Operates -=.

Parameters

x	IntervalVector

Returns

(*this)-=x

operator-=() [5/6]

const TubeVector & codac::TubeVector::operator-=

(

const TrajectoryVector &

x

)

Operates -=.

Parameters

x	TrajectoryVector

Returns

(*this)-=x

operator-=() [6/6]

const TubeVector & codac::TubeVector::operator-=

(

const TubeVector &

x

)

Operates -=.

Parameters

x	TubeVector

Returns

(*this)-=x

operator*=() [1/3]

const TubeVector & codac::TubeVector::operator*=

(

const Interval &

x

)

Operates *=.

Parameters

x

Interval

Returns

(this)=x

operator*=() [2/3]

const TubeVector & codac::TubeVector::operator*=

(

const Trajectory &

x

)

Operates *=.

Parameters

x	Trajectory

Returns

(this)=x

operator*=() [3/3]

const TubeVector & codac::TubeVector::operator*=

(

const Tube &

x

)

Operates *=.

Parameters

x

Tube

Returns

(this)=x

operator/=() [1/3]

const TubeVector & codac::TubeVector::operator/=

(

const Interval &

x

)

Operates /=.

Parameters

x

Interval

Returns

(*this)/=x

operator/=() [2/3]

const TubeVector & codac::TubeVector::operator/=

(

const Trajectory &

x

)

Operates /=.

Parameters

x	Trajectory

Returns

(*this)/=x

operator/=() [3/3]

const TubeVector & codac::TubeVector::operator/=

(

const Tube &

x

)

Operates /=.

Parameters

x

Tube

Returns

(*this)/=x

operator|=() [1/3]

const TubeVector & codac::TubeVector::operator|=

(

const IntervalVector &

x

)

Operates |=.

Parameters

x	IntervalVector

Returns

(*this)|=x

operator|=() [2/3]

const TubeVector & codac::TubeVector::operator|=

(

const TrajectoryVector &

x

)

Operates |=.

Parameters

x	TrajectoryVector

Returns

(*this)|=x

operator|=() [3/3]

const TubeVector & codac::TubeVector::operator|=

(

const TubeVector &

x

)

Operates |=.

Parameters

x	TubeVector

Returns

(*this)|=x

operator&=() [1/3]

const TubeVector & codac::TubeVector::operator&=

(

const IntervalVector &

x

)

Operates &=.

Parameters

x	IntervalVector

Returns

(*this)&=x

operator&=() [2/3]

const TubeVector & codac::TubeVector::operator&=

(

const TrajectoryVector &

x

)

Operates &=.

Parameters

x	TrajectoryVector

Returns

(*this)&=x

operator&=() [3/3]

const TubeVector & codac::TubeVector::operator&=

(

const TubeVector &

x

)

Operates &=.

Parameters

x	TubeVector

Returns

(*this)&=x

class_name()

const std::string codac::TubeVector::class_name ( ) const

inlinevirtual

Returns the name of this class.

Note

Only used for some generic display method

Returns

the predefined name

Implements codac::DynamicalItem.

{ return "TubeVector"; };

enable_synthesis()

void codac::TubeVector::enable_synthesis	(	SynthesisMode	mode = SynthesisMode::BINARY_TREE,
		double	eps = 1.e-3 ) const

Enables the computation of a synthesis tree.

Note

The synthesis tree speeds up computations such as integrals or evaluations

Parameters

mode	mode of synthesis
eps	precision of the polynomial approximation, if selected

integral() [1/3]

const IntervalVector codac::TubeVector::integral

(

double

t

)

const

Computes the box integral \(\int_0^t[\mathbf{x}](\tau)d\tau\).

Note

From the monotonicity of the integral operator, \(\int_0^t[\mathbf{x}](\tau)d\tau=[\int_0^t\mathbf{x}^-(\tau)d\tau,\int_0^t\mathbf{x}^+(\tau)d\tau]\)

Parameters

t	the temporal key (double, must belong to the TubeVector's domain)

Returns

the set of feasible integral vectors

integral() [2/3]

const IntervalVector codac::TubeVector::integral

(

const Interval &

t

)

const

Computes the box integral \(\int_0^{[t]}[\mathbf{x}](\tau)d\tau\).

Note

From the monotonicity of the integral operator, \(\int_0^{[t]}[\mathbf{x}](\tau)d\tau=[\int_0^{[t]}\mathbf{x}^-(\tau)d\tau,\int_0^{[t]}\mathbf{x}^+(\tau)d\tau]\)

Parameters

t	the subtdomain (Interval, must be a subset of the TubeVector's tdomain)

Returns

the set of feasible integral vectors

integral() [3/3]

const IntervalVector codac::TubeVector::integral	(	const Interval &	t1,
		const Interval &	t2 ) const

Computes the box integral \(\int_{[t_1]}^{[t_2]}[\mathbf{x}](\tau)d\tau\).

Note

From the monotonicity of the integral operator, \(\int_{[t_1]}^{[t_2]}[\mathbf{x}](\tau)d\tau=[\int_{[t_1]}^{[t_2]}\mathbf{x}^-(\tau)d\tau,\int_{[t_1]}^{[t_2]}\mathbf{x}^+(\tau)d\tau]\)

Parameters

t1	lower bound, subset of the TubeVector's tdomain
t2	upper bound, subset of the TubeVector's tdomain

Returns

the set of feasible integral vectors

partial_integral() [1/2]

const std::pair< IntervalVector, IntervalVector > codac::TubeVector::partial_integral

(

const Interval &

t

)

const

Computes the partial box integral \(\int_{0}^{[t]}[\mathbf{x}](\tau)d\tau\).

Note

From the monotonicity of the integral operator, \(\int_{0}^{[t]}[\mathbf{x}](\tau)d\tau=[\int_{0}^{[t]}\mathbf{x}^-(\tau)d\tau,\int_{0}^{[t]}\mathbf{x}^+(\tau)d\tau]\)

Parameters

t	interval upper bound, subset of the TubeVector's tdomain

Returns

the pair \(\big([i^-],[i^+]\big)\), where \([i^-]=\int_{0}^{[t]}\mathbf{x}^-(\tau)d\tau\) and \([i^+]=\int_{0}^{[t]}\mathbf{x}^+(\tau)d\tau\)

partial_integral() [2/2]

const std::pair< IntervalVector, IntervalVector > codac::TubeVector::partial_integral	(	const Interval &	t1,
		const Interval &	t2 ) const

Computes the partial box integral \(\int_{[t_1]}^{[t_2]}[\mathbf{x}](\tau)d\tau\).

Note

From the monotonicity of the integral operator, \(\int_{[t_1]}^{[t_2]}[\mathbf{x}](\tau)d\tau=[\int_{[t_1]}^{[t_2]}\mathbf{x}^-(\tau)d\tau,\int_{[t_1]}^{[t_2]}\mathbf{x}^+(\tau)d\tau]\)

Parameters

t1	interval lower bound, subset of the TubeVector's tdomain
t2	interval upper bound, subset of the TubeVector's tdomain

Returns

the pair \(\big([i^-],[i^+]\big)\), where \([i^-]=\int_{[t_1]}^{[t_2]}\mathbf{x}^-(\tau)d\tau\) and \([i^+]=\int_{[t_1]}^{[t_2]}\mathbf{x}^+(\tau)d\tau\)

serialize() [1/2]

void codac::TubeVector::serialize	(	const std::string &	binary_file_name = "x.tube",
		int	version_number = SERIALIZATION_VERSION ) const

Serializes this tube.

Note

The values and sampling (slices and gates) are serialized

Parameters

binary_file_name	name of the output file (default value: "x.tube")
version_number	serialization version (used for tests purposes, default value: last version)

serialize() [2/2]

void codac::TubeVector::serialize	(	const std::string &	binary_file_name,
		const TrajectoryVector &	traj,
		int	version_number = SERIALIZATION_VERSION ) const

Serializes this tube together with a TrajectoryVector object.

Note

The values and sampling (slices and gates) are serialized

The serialization of a TrajectoryVector defined from a Function object is not supported

The output file will appear in the executable current directory

Parameters

binary_file_name	name of the output file (default value: "x.tube")
traj	the TrajectoryVector object to serialize (for instance, actual but unknown values)
version_number	serialization version (used for tests purposes, default value: last version)

same_slicing() [1/2]

static bool codac::TubeVector::same_slicing ( const TubeVector & x1, const Tube & x2 )

static

Tests whether a TubeVector object shares the slicing of another Tube object.

Note

If true, it means the two tubes are defined with the same amount of slices and identical sampling

Parameters

x1	the TubeVector
x2	the Tube

Returns

true in case of same slicing

same_slicing() [2/2]

static bool codac::TubeVector::same_slicing ( const TubeVector & x1, const TubeVector & x2 )

static

Tests whether the two TubeVector objects are sharing the same slicing.

Note

If true, it means the two tubes are defined with the same amount of slices and identical sampling

Parameters

x1	the first TubeVector
x2	the second TubeVector

Returns

true in case of same slicing

hull()

static const TubeVector codac::TubeVector::hull ( const std::list< TubeVector > & l_tubes )

static

Computes the hull of several tubes.

Parameters

l_tubes

list of tubes

Returns

the tube vector enveloping the other ones

codomain_box()

const IntervalVector codac::TubeVector::codomain_box ( ) const

protectedvirtual

Returns the box \([\mathbf{x}]([t_0,t_f])\).

Note

Used for genericity purposes

Returns

the envelope of codomain values

Implements codac::DynamicalItem.

deserialize()

void codac::TubeVector::deserialize ( const std::string & binary_file_name, TrajectoryVector *& traj )

protected

Restores a n-dimensional tube from serialization, together with a TrajectoryVector object.

Note

The TubeVector and the TrajectoryVector must have been serialized beforehand by the appropriate method serialize()

Parameters

binary_file_name	path to the binary file
traj	a pointer to the TrajectoryVector object to be instantiated

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The documentation for this class was generated from the following file:

• /home/simon/codac/src/core/domains/tube/codac_TubeVector.h