Feel++
0.92.0
|
Legendre polynomial orthonormal basis. More...
#include <legendre.hpp>
Public Types | |
typedef LegendreTraits< Dim, RealDim, Degree, NormalizationPolicy, T, StoragePolicy > | traits_type |
typedef Discontinuous | continuity_type |
Typedefs | |
typedef Legendre< Dim, RealDim, Degree, NormalizationPolicy, T, StoragePolicy > | self_type |
typedef self_type | basis_type |
typedef traits_type::value_type | value_type |
typedef traits_type::convex_type | convex_type |
typedef traits_type::reference_convex_type | reference_convex_type |
typedef traits_type::diff_pointset_type | diff_pointset_type |
typedef traits_type::storage_policy | storage_policy |
typedef traits_type::matrix_type | matrix_type |
typedef traits_type::vector_matrix_type | vector_matrix_type |
typedef traits_type::matrix_node_type | matrix_node_type |
typedef traits_type::points_type | points_type |
typedef traits_type::node_type | node_type |
Public Member Functions | |
Constructors, destructor | |
Legendre () | |
Legendre (Legendre const &d) | |
~Legendre () | |
Operator overloads | |
self_type const & | operator= (self_type const &d) |
matrix_type | operator() (node_type const &pt) const |
matrix_type | operator() (points_type const &pts) const |
Accessors | |
size_type | size () const |
uint16_type | degree () const |
self_type const & | basis () const |
bool | isNormalized () const |
std::string | familyName () const |
Static Public Attributes | |
static const uint16_type | nDim = Dim |
static const uint16_type | nRealDim = RealDim |
static const uint16_type | nOrder = Degree |
static const uint16_type | nConvexOrder = nOrder+2 |
static const bool | is_normalized = NormalizationPolicy::is_normalized |
static const bool | isTransformationEquivalent = true |
static const bool | isContinuous = false |
static const bool | is_product = true |
Methods | |
matrix_type | coeff () const |
static matrix_type | evaluate (points_type const &__pts) |
template<typename AE > | |
static vector_matrix_type | derivate (ublas::matrix_expression< AE > const &__pts) |
static matrix_type const & | d (uint16_type i) |
derivatives of Dubiner polynomials the derivatives are computed at the nodes of the lattice | |
static matrix_type const & | derivate (uint16_type i) |
derivatives of Dubiner polynomials the derivatives are computed at the nodes of the lattice |
Legendre polynomial orthonormal basis.
This class represents the Legendre polynomials up to degree Degree
on a simplex in dimension Dim
.
The legendre polynomials in 1D, the segment are defined using Jacobi polynomials as follows:
where
is the i-th Jacobi polynomial evaluated at
with weights
.
self_type const& Feel::Legendre< Dim, RealDim, Degree, NormalizationPolicy, T, StoragePolicy >::basis | ( | ) | const [inline] |
matrix_type Feel::Legendre< Dim, RealDim, Degree, NormalizationPolicy, T, StoragePolicy >::coeff | ( | ) | const [inline] |
static matrix_type const& Feel::Legendre< Dim, RealDim, Degree, NormalizationPolicy, T, StoragePolicy >::d | ( | uint16_type | i | ) | [inline, static] |
derivatives of Dubiner polynomials the derivatives are computed at the nodes of the lattice
uint16_type Feel::Legendre< Dim, RealDim, Degree, NormalizationPolicy, T, StoragePolicy >::degree | ( | ) | const [inline] |
static matrix_type const& Feel::Legendre< Dim, RealDim, Degree, NormalizationPolicy, T, StoragePolicy >::derivate | ( | uint16_type | i | ) | [inline, static] |
derivatives of Dubiner polynomials the derivatives are computed at the nodes of the lattice
static matrix_type Feel::Legendre< Dim, RealDim, Degree, NormalizationPolicy, T, StoragePolicy >::evaluate | ( | points_type const & | __pts | ) | [inline, static] |
evaluate the Legendre polynomials at a set of points __pts
Referenced by Feel::Legendre< Dim, Order, Normalized< false >, T >::evaluate().
std::string Feel::Legendre< Dim, RealDim, Degree, NormalizationPolicy, T, StoragePolicy >::familyName | ( | ) | const [inline] |
familyName()
bool Feel::Legendre< Dim, RealDim, Degree, NormalizationPolicy, T, StoragePolicy >::isNormalized | ( | ) | const [inline] |
size_type Feel::Legendre< Dim, RealDim, Degree, NormalizationPolicy, T, StoragePolicy >::size | ( | ) | const [inline] |
Number of polynomials in set