template<typename Poly, template< uint16_type > class PolySetType>
class Feel::PolynomialSet< Poly, PolySetType >
a Set of polynomials
This class represents a set of polynomials
defined in a certain basis given by the template argument. The coefficients of the polynomials in the basis are represented by a matrix whose line represents the polynomials and columns the basis index
where
is the mapping between the polynomial and its coefficients. We have that the polynomial set is represented as follows:
- Author
- Christophe Prud'homme
- See Also
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template<size_type context_v, size_type context_g, typename BasisType , typename GeoType , typename ElementType > |
boost::shared_ptr< Context
< context_v, BasisType,
GeoType, ElementType > > | context (boost::shared_ptr< BasisType > b, boost::shared_ptr< GeoType > gm, precompute_ptrtype &pc) |
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template<int contextv, int contextg, typename BasisType , typename GeoType , typename ElementType > |
boost::shared_ptr< Context
< contextv, BasisType, GeoType,
ElementType > > | ctx (boost::shared_ptr< BasisType > const &b, boost::shared_ptr< typename GeoType::template Context< contextg, ElementType > > const &gm, precompute_ptrtype pc, ElementType &e) |
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template<int contextv, typename BasisType , typename GeoType , typename ElementType > |
boost::shared_ptr< Context
< contextv, BasisType, GeoType,
ElementType > > | ctx (boost::shared_ptr< BasisType > const &b, boost::shared_ptr< typename GeoType::template Context< contextv, ElementType > > const &gm, precompute_ptrtype pc, ElementType &e) |
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precompute_ptrtype | preCompute (self_ptrtype p, points_type const &P) |
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std::vector< std::map
< typename
convex_type::permutation_type,
precompute_ptrtype > > | preComputeOnFaces (self_ptrtype p, points_type const &P) |
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| PolynomialSet () |
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| PolynomialSet (Poly const &p) |
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| PolynomialSet (Poly const &p, matrix_type const &c, bool __as_is=false) |
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| PolynomialSet (matrix_type const &c, bool __as_is=false) |
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| PolynomialSet (PolynomialSet const &p) |
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virtual | ~PolynomialSet () |
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self_type & | operator= (self_type const &pset) |
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component_type | operator[] (uint16_type i) const |
| extract the i-th component of a vectorial polynomial set More...
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void | setCoefficient (matrix_type const &__c, bool __as_is=false) |
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PolynomialSet< Poly, PolySetType > | polynomials (std::vector< uint16_type > const &list_p) const |
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PolynomialSet< Poly, PolySetType > | polynomialsUpToDimension (int dim_p) const |
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PolynomialSet< Poly, PolySetType > | polynomialsRange (uint16_type dim_bot, uint16_type dim_top) const |
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Polynomial< Poly, PolySetType > | polynomial (uint16_type i) const |
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template<typename AE > |
ublas::vector< value_type > | evaluate (uint16_type i, ublas::vector_expression< AE > const &__pt) const |
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template<typename AE > |
ublas::matrix< value_type > | evaluate (ublas::vector_expression< AE > const &__pt) const |
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template<typename AE > |
matrix_type | evaluate (ublas::matrix_expression< AE > const &__pts) const |
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matrix_type const & | d (uint16_type i) const |
| derivatives of Dubiner polynomials the derivatives are computed at the nodes of the lattice More...
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matrix_type | d (uint16_type i, uint16_type j) const |
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self_type | derivate (uint16_type l) const |
| Derivate with respect to the l-th direction. More...
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template<typename AE > |
ublas::vector< matrix_type > | derivate (ublas::matrix_expression< AE > const &pts) const |
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template<typename AE > |
matrix_type | derivate (uint16_type i, ublas::matrix_expression< AE > const &pts) const |
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template<typename AE > |
matrix_type | derivate (uint16_type i, uint16_type j, ublas::matrix_expression< AE > const &pts) const |
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gradient_polynomialset_type | gradient () const |
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gradient_polynomialset_type | gradient (mpl::int_< 0 >) const |
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gradient_polynomialset_type | gradient (mpl::int_< 1 >) const |
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uint16_type | nbDof () const |
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void | insert (PolynomialSet< Poly, PolySetType > const &p, bool erase=false) |
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typedef PolynomialSet< Poly,
PolySetType > | self_type |
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typedef boost::shared_ptr
< self_type > | self_ptrtype |
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typedef Poly::value_type | value_type |
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typedef Poly::basis_type | basis_type |
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typedef PolySetType< nRealDim > | polyset_type |
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typedef PolynomialSet< Poly,
Scalar > | component_type |
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typedef Polynomial< Poly,
PolySetType > | polynomial_type |
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typedef polynomial_type | polynomial_view_type |
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typedef Poly::convex_type | convex_type |
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typedef basis_type::matrix_type | matrix_type |
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typedef basis_type::points_type | points_type |
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typedef PolynomialSet< Poly,
Vectorial > | gradient_polynomialset_type |
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static const bool | is_product = Poly::is_product |
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static const bool | is_tensor2 = polyset_type::is_tensor2 |
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static const bool | is_vectorial = polyset_type::is_vectorial |
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static const bool | is_scalar = polyset_type::is_scalar |
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static const uint16_type | nComponents = polyset_type::nComponents |
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static const uint16_type | nComponents1 = polyset_type::nComponents1 |
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static const uint16_type | nComponents2 = polyset_type::nComponents2 |
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static const uint16_type | rank = polyset_type::rank |
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| BOOST_STATIC_ASSERT ((boost::is_same< typename matrix_type::value_type, value_type >::value)) |
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| BOOST_STATIC_ASSERT ((boost::is_same< typename matrix_type::value_type, typename points_type::value_type >::value)) |
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