basix::polynomials Namespace Reference

Polynomials. More...

Enumerations
enum class	type { legendre = 0 , lagrange = 1 , bernstein = 2 }
	Polynomial types that can be created. More...

Functions
template<std::floating_point T>
std::pair< std::vector< T >, std::array< std::size_t, 2 > >	tabulate (polynomials::type polytype, cell::type celltype, int d, md::mdspan< const T, md::dextents< std::size_t, 2 >> x)
	Tabulate a set of polynomials. More...
int	dim (polynomials::type polytype, cell::type cell, int d)
	Dimension of a polynomial space. More...

Detailed Description

Polynomials.

Enumeration Type Documentation

type

enum basix::polynomials::type

strong

Polynomial types that can be created.

Enumerator
legendre	Legendre polynomials: polynomials that span the full space on a cell.
lagrange	Lagrange polynomials: polynomials that span the Lagrange space on a cell. Note that these will be equal to the Legendre polynomials on all cells except pyramids
bernstein	Bernstein polynomials.

Function Documentation

tabulate()

template<std::floating_point T>

std::pair< std::vector< T >, std::array< std::size_t, 2 > > basix::polynomials::tabulate	(	polynomials::type	polytype,
		cell::type	celltype,
		int	d,
		md::mdspan< const T, md::dextents< std::size_t, 2 >>	x
	)

Tabulate a set of polynomials.

Parameters

[in]	polytype	Polynomial type
[in]	celltype	Cell type
[in]	d	Polynomial degree
[in]	x	Points at which to evaluate the basis. The shape is (number of points, geometric dimension).

Returns

Polynomial sets, for each derivative, tabulated at points. The shape is (basis index, number of points).

dim()

int basix::polynomials::dim	(	polynomials::type	polytype,
		cell::type	cell,
		int	d
	)

Dimension of a polynomial space.

Parameters

[in]	polytype	Polynomial type
[in]	cell	Cell type
[in]	d	Polynomial degree

Returns

The number terms in the basis spanning a space of polynomial degree d.