Public Member Functions | |
PolynomialsP (const unsigned int p) | |
unsigned int | degree () const |
void | directional_degrees (unsigned int n, unsigned int(°rees)[dim]) const |
Private Member Functions | |
void | create_polynomial_ordering (std::vector< unsigned int > &index_map) const |
Private Attributes | |
const unsigned int | p |
This class implements the polynomial space of degree p
based on the monomials . I.e. in
d
dimensions it constructs all polynomials of the form , where
. The base polynomials are given a specific ordering, e.g. in 2 dimensions:
. The ordering of the monomials in
matches the ordering of the monomials in
for
.
PolynomialsP< dim >::PolynomialsP | ( | const unsigned int | p | ) |
Constructor. Creates all basis functions of .
unsigned int PolynomialsP< dim >::degree | ( | ) | const [inline] |
Returns the degree p
of the polynomial space P_p
.
Note, that this number is PolynomialSpace::degree()-1
, compare definition in PolynomialSpace.
References PolynomialsP< dim >::p.
void PolynomialsP< dim >::directional_degrees | ( | unsigned int | n, | |
unsigned int(&) | degrees[dim] | |||
) | const [inline] |
For the n
th polynomial this function gives the degrees i,j,k in the x,y,z directions.
void PolynomialsP< dim >::create_polynomial_ordering | ( | std::vector< unsigned int > & | index_map | ) | const [private] |
Fills the index_map
.
const unsigned int PolynomialsP< dim >::p [private] |
Degree p
of the polynomial space , i.e. the number
p
which was given to the constructor.
Referenced by PolynomialsP< dim >::degree().