nltool::PolynomialSystem Class Reference

Inheritance diagram for nltool::PolynomialSystem:

List of all members.

Public Member Functions
	PolynomialSystem (int dim, int deg, int nbMon, const bool stable, int s)
	PolynomialSystem (int dim, std::vector< Polynom > polys)
	PolynomialSystem (int dim, string polysys)
	PolynomialSystem ()
virtual	~PolynomialSystem ()
Vector	eval (const Vector &x)
DynamicalSystem &	derivate (const unsigned dx)
Number	maximize (const unsigned indice, const Template &constraintsA, const Vector &constraintsB, Vector &pt)
Number	minimize (const unsigned indice, const Template &constraintsA, const Vector &constraintsB, Vector &pt)
void	linearInterpollation (Vector point, Matrix &A, Vector &b)
Number	eval (const Vector &x, const int indice)
Vector	evalDiscretised (const Vector &x, Number dt)
Number	curvature (const Vector &x, const int indice, const Vector &d1, const Vector &d2)
PolynomialSystem	getDiscretizedSystem (Number dt)
PolynomialSystem	replaceVariable (std::vector< Polynom > expression)
PolynomialSystem	derivate (const int dx)
multiIndice	getMaxDegree ()
Public Attributes
std::vector< Polynom >	polynomials
multiIndice	maxDegrees

---

Constructor & Destructor Documentation

nltool::PolynomialSystem::PolynomialSystem	(	int	dim,
		int	deg,
		int	nbMon,
		const bool	stable,
		int	s
	)

Constructor for a randomly generated polynomial system

Parameters:

dim	the system dimension
deg	the maximal degree for the monomials
nbMon	the maximal number of monomials by polynomials
stable	try to create a stable system
s	random generator seed

nltool::PolynomialSystem::PolynomialSystem	(	int	dim,
		std::vector< Polynom >	polys
	)

Base constructor

Parameters:

dim	the system dimension
polys	a vector of polynomials

nltool::PolynomialSystem::PolynomialSystem	(	int	dim,
		string	polysys
	)

Base constructor

Parameters:

dim	the system dimension
polysys	a string representing the polynomial system

nltool::PolynomialSystem::PolynomialSystem

(

)

Non consistent constructor

nltool::PolynomialSystem::~PolynomialSystem

(

)

[virtual]

Destructor

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Member Function Documentation

Number nltool::PolynomialSystem::curvature	(	const Vector &	x,
		const int	indice,
		const Vector &	d1,
		const Vector &	d2
	)

Computes the directional curvature of the system

Parameters:

x	a state-space point
indice	a variable indice
d1	first direction
d2	second direction

Returns:

the directional curvature evakuated at x

DynamicalSystem & nltool::PolynomialSystem::derivate

(

const unsigned

dx

)

[virtual]

Derivation function

Parameters:

dx	partial derivative indice

Returns:

a system corresponding to the partial derivative of this polynomial system

Reimplemented from nltool::DynamicalSystem.

PolynomialSystem nltool::PolynomialSystem::derivate

(

const int

dx

)

Derivation function

Parameters:

dx	derivative variable

Returns:

polynomial system derivated

Vector nltool::PolynomialSystem::eval

(

const Vector &

x

)

[virtual]

Evalutation function

Parameters:

x	a point in the state space

Returns:

a vector with the value of each polynomials

Reimplemented from nltool::DynamicalSystem.

Number nltool::PolynomialSystem::eval	(	const Vector &	x,
		const int	indice
	)

Evaluation function

Parameters:

x	a state-space point
indice

Returns:

evaluation results for each variable dynamics

Vector nltool::PolynomialSystem::evalDiscretised	(	const Vector &	x,
		Number	dt
	)

Evaluation function of the euler discretization of the system

Parameters:

x	a state-space point
dt	time step for the discretization

Returns:

evaluation results for each variable dynamics

PolynomialSystem nltool::PolynomialSystem::getDiscretizedSystem

(

Number

dt

)

returns an Euler discretization of the polynomial system

Parameters:

dt

time step

Returns:

a polynomial system corresponding to the Euler discretization of this system

void nltool::PolynomialSystem::linearInterpollation	(	Vector	point,
		Matrix &	A,
		Vector &	b
	)

Compute a linear interpollation of the system

Parameters:

point	a list of n+1 points
A	The affine part of the linear interpollation
b	The constant part of the linear interpollation

Number nltool::PolynomialSystem::maximize	(	const unsigned	indice,
		const Template &	constraintsA,
		const Vector &	constraintsB,
		Vector &	pt
	)

Maximize one of the polynomials It uses the Bernstein coefficient to return a quick approximation of the optimization.

Parameters:

indice	polynomial indice
constraintsA	represents the matrix A in the constraints Ax<=b
constraintsB	represents the vector b in the constraints Ax<=b
pt	solution

Returns:

the optimization result

Number nltool::PolynomialSystem::minimize	(	const unsigned	indice,
		const Template &	constraintsA,
		const Vector &	constraintsB,
		Vector &	pt
	)

Minimize one of the polynomials It uses the Bernstein coefficient to return a quick approximation of the optimization.

Parameters:

indice	polynomial indice
constraintsA	represents the matrix A in the constraints Ax<=b
constraintsB	represents the vector b in the constraints Ax<=b
pt	solution

Returns:

the optimization result

PolynomialSystem nltool::PolynomialSystem::replaceVariable

(

std::vector< Polynom >

expression

)

Replace all the variables by a list of n polynomials

Parameters:

expression

the list of polynomials

Returns:

a new polynomial system with all variables replaced by the polynomials expression

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

• src/include/PolynomialSystem.h
• src/PolynomialSystem.cpp