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
, nDim
if
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
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| Polynomial () |
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| Polynomial (Poly const &__poly) |
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| Polynomial (Poly const &__poly, container_type const &__coeff, bool __as_is=false) |
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| Polynomial (container_type const &__coeff, bool __as_is=false) |
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template<class AE > |
| Polynomial (Poly const &__poly, ublas::matrix_expression< AE > const &__coeff, bool __as_is=false) |
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| Polynomial (Polynomial const &p) |
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| ~Polynomial () |
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self_type const & | operator= (self_type const &__p) |
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self_type const & | operator-= (self_type const &__p) |
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self_type const & | operator() (self_type const &__p) const |
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component_type | operator[] (int i) const |
| extract the i-th component of a vectorial polynomial More...
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matrix_type | operator() (node_type const &__x) const |
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matrix_type | operator() (points_type const &__pts) const |
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bool | isZero () const |
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matrix_type const & | coeff () const |
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matrix_type const & | coefficients () const |
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basis_type const & | basis () const |
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void | setCoefficient (matrix_type const &__c, bool __as_is=false) |
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matrix_type | evaluate (node_type const &__x) const |
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matrix_type | evaluate (points_type 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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matrix_type const & | d (uint16_type i) const |
| differentiation matrix of Dubiner polynomials the derivatives are computed at the nodes of the lattice More...
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self_type | derivative (uint16_type l) const |
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PolynomialSet< Poly, PolySetType > | toSet (bool asis=false) const |
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typedef Polynomial< Poly,
PolySetType > | self_type |
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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< nDim > | polyset_type |
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typedef Component
< polyset_type >::type | component_type |
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typedef Polynomial< Poly, Scalar > | scalar_component_type |
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typedef basis_type::points_type | points_type |
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typedef basis_type::matrix_type | matrix_type |
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typedef Container | container_type |
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typedef node< value_type >::type | node_type |
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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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| 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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