#include <polynomial.hpp>

Detailed Description

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>
class Feel::Polynomial< Poly, PolySetType, Container >

polynomial class

The polynomial is expressed in the basis from Poly. The coefficients of the polynomial in this basis are represented by a matrix whose lines are the polymomial components coefficients (1 if

is_scalar == true

, nDim if

is_vectorial ==

* true

and columns are the basis

Evaluating the polynomial at a set of points(or just one point) is then simply a matrix-matrix product.

Author: Christophe Prud'homme

See Also

Public Member Functions
Constructors, destructor
	Polynomial ()

	Polynomial (Poly const &__poly)

	Polynomial (Poly const &__poly, container_type const &__coeff, bool __as_is=false)

	Polynomial (container_type const &__coeff, bool __as_is=false)

template<class AE >
	Polynomial (Poly const &__poly, ublas::matrix_expression< AE > const &__coeff, bool __as_is=false)

	Polynomial (Polynomial const &p)

	~Polynomial ()

Operator overloads
self_type const &	operator= (self_type const &__p)

self_type const &	operator-= (self_type const &__p)

self_type const &	operator() (self_type const &__p) const

component_type	operator[] (int i) const
	extract the i-th component of a vectorial polynomial More...

matrix_type	operator() (node_type const &__x) const

matrix_type	operator() (points_type const &__pts) const

Accessors
bool	isZero () const

matrix_type const &	coeff () const

matrix_type const &	coefficients () const

basis_type const &	basis () const

Mutators
void	setCoefficient (matrix_type const &__c, bool __as_is=false)

Methods
matrix_type	evaluate (node_type const &__x) const

matrix_type	evaluate (points_type const &__pts) const

template<typename AE >
matrix_type	derivate (uint16_type i, ublas::matrix_expression< AE > const &pts) const

template<typename AE >
matrix_type	derivate (uint16_type i, uint16_type j, ublas::matrix_expression< AE > const &pts) const

matrix_type const &	d (uint16_type i) const
	differentiation matrix of Dubiner polynomials the derivatives are computed at the nodes of the lattice More...

self_type	derivative (uint16_type l) const

PolynomialSet< Poly, PolySetType >	toSet (bool asis=false) const

Static Public Attributes
Constants
static const uint16_type	nDim = Poly::nDim

static const uint16_type	nOrder = Poly::nOrder

Typedefs
typedef Polynomial< Poly, PolySetType >	self_type

typedef Poly::value_type	value_type

typedef Poly::basis_type	basis_type

typedef PolySetType< nDim >	polyset_type

typedef Component < polyset_type >::type	component_type

typedef Polynomial< Poly, Scalar >	scalar_component_type

typedef basis_type::points_type	points_type

typedef basis_type::matrix_type	matrix_type

typedef Container	container_type

typedef node< value_type >::type	node_type

static const bool	is_tensor2 = polyset_type::is_tensor2

static const bool	is_vectorial = polyset_type::is_vectorial

static const bool	is_scalar = polyset_type::is_scalar

static const uint16_type	nComponents = polyset_type::nComponents

static const uint16_type	nComponents1 = polyset_type::nComponents1

static const uint16_type	nComponents2 = polyset_type::nComponents2

	BOOST_STATIC_ASSERT ((boost::is_same< typename matrix_type::value_type, value_type >::value))

	BOOST_STATIC_ASSERT ((boost::is_same< typename matrix_type::value_type, typename points_type::value_type >::value))

Constructor & Destructor Documentation

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

Feel::Polynomial< Poly, PolySetType, Container >::Polynomial ( )

inline

default constructor

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

Feel::Polynomial< Poly, PolySetType, Container >::Polynomial ( Poly const & __poly )

inline

constructor giving only the underlying basis

Parameters

__poly polynomial whose we take the basis

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

Feel::Polynomial< Poly, PolySetType, Container >::Polynomial	(	Poly const &	__poly,
		container_type const &	__coeff,
		bool	__as_is = `false`
	)

inline

constructor giving the underlying basis and the coefficient of the polynomial in the basis

Parameters

__poly	polynomial whose we take the basis
__coeff	coefficients of the polynomial in the basis

References Feel::Polynomial< Poly, PolySetType, Container >::setCoefficient().

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

Feel::Polynomial< Poly, PolySetType, Container >::Polynomial	(	container_type const &	__coeff,
		bool	__as_is = `false`
	)

inline

constructor giving the underlying basis and the coefficient of the polynomial in the basis

Parameters

__coeff coefficients of the polynomial in the basis

References Feel::Polynomial< Poly, PolySetType, Container >::setCoefficient().

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

template<class AE >

Feel::Polynomial< Poly, PolySetType, Container >::Polynomial	(	Poly const &	__poly,
		ublas::matrix_expression< AE > const &	__coeff,
		bool	__as_is = `false`
	)

inline

constructor giving the underlying basis and the coefficient of the polynomial in the basis

Parameters

__poly	polynomial whose we take the basis
__coeff	coefficients of the polynomial in the basis

References Feel::Polynomial< Poly, PolySetType, Container >::setCoefficient().

Member Function Documentation

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

basis_type const& Feel::Polynomial< Poly, PolySetType, Container >::basis ( ) const

inline

Returns: the basis in which the polynomial is expressed

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

matrix_type const& Feel::Polynomial< Poly, PolySetType, Container >::coeff ( ) const

inline

Returns: the dof

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

matrix_type const& Feel::Polynomial< Poly, PolySetType, Container >::coefficients ( ) const

inline

Returns: the dof

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

matrix_type const& Feel::Polynomial< Poly, PolySetType, Container >::d ( uint16_type i ) const

inline

differentiation matrix of Dubiner polynomials the derivatives are computed at the nodes of the lattice

i index of the derivative (0 : x, 1 : y, 2 : z )

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

self_type Feel::Polynomial< Poly, PolySetType, Container >::derivative ( uint16_type l ) const

inline

derivative of the polynomial in the l-th direction

Parameters

l	direction of derivation

Returns: the derivative of the polynomial

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

matrix_type Feel::Polynomial< Poly, PolySetType, Container >::evaluate ( node_type const & __x ) const

inline

Evaluate polynomial at point __x

Parameters

__x	the coordinate of the point

Returns: the evaluation of the polynomial at point __x

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

matrix_type Feel::Polynomial< Poly, PolySetType, Container >::evaluate ( points_type const & __pts ) const

inline

Evaluate polynomial at points __pts

Parameters

__pts the matrix of coordinates of the points

Returns: the evaluation of the polynomial at point __x

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

bool Feel::Polynomial< Poly, PolySetType, Container >::isZero ( ) const

inline

Returns: true if the polynomial set is zero, false otherwise

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

matrix_type Feel::Polynomial< Poly, PolySetType, Container >::operator() ( node_type const & __x ) const

inline

Evaluate polynomial at point __x

Parameters

__x	the coordinate of the point

Returns: the evaluation of the polynomial at point __x

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

matrix_type Feel::Polynomial< Poly, PolySetType, Container >::operator() ( points_type const & __pts ) const

inline

Evaluate polynomial at points __pts

Parameters

__pts the matrix of coordinates of the points

Returns: the evaluation of the polynomial at point __x

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

component_type Feel::Polynomial< Poly, PolySetType, Container >::operator[] ( int i ) const

inline

extract the i-th component of a vectorial polynomial

Returns: the i-th component of the polynomial

References Feel::project().

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

void Feel::Polynomial< Poly, PolySetType, Container >::setCoefficient	(	matrix_type const &	__c,
		bool	__as_is = `false`
	)

inline

set the coefficient of the polynomial in the basis.

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>

PolynomialSet<Poly,PolySetType> Feel::Polynomial< Poly, PolySetType, Container >::toSet ( bool asis = false ) const

inline

transform a Polynomial into a PolynomialSet with one polynomial

Returns: a PolynomialSet

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

polynomial.hpp

Detailed Description

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type> class Feel::Polynomial< Poly, PolySetType, Container >

Public Member Functions

Static Public Attributes

Typedefs

Constructor & Destructor Documentation

Member Function Documentation

template<typename Poly, template< uint16_type > class PolySetType = Scalar, typename Container = typename Poly::basis_type::matrix_type>
class Feel::Polynomial< Poly, PolySetType, Container >