Dune::Functions::MonomialSet< RangeFieldType, dimension, maxDegree > Struct Template Reference

Function, which evaluates all monomials up to degree maxDegree in a given coordinate. More...

#include <dune/functions/analyticfunctions/monomialset.hh>

Classes
struct	Derivative
	Set of all first order derivatives of monomials up to degree maxDegree as vector of vector valued functions. More...

Public Member Functions
template<class DomainFieldType >
constexpr Dune::FieldVector< RangeFieldType, size >	operator() (const Dune::FieldVector< DomainFieldType, dim > &x) const
	Return array of monomial evaluations. More...

Static Public Member Functions
static constexpr std::array< std::array< std::size_t, dim >, size >	exponents ()
	Return array of monomial exponents with shape size x dim More...

Friends
constexpr friend auto	derivative (const MonomialSet &m)
	Construct the Derivative object from a MonomialSet.

Detailed Description

template<class RangeFieldType, int dimension, int maxDegree>
struct Dune::Functions::MonomialSet< RangeFieldType, dimension, maxDegree >

Function, which evaluates all monomials up to degree maxDegree in a given coordinate.

Template Parameters

RangeFieldType	scalar type.
dim	Domain dimension.
maxDegree	Maximal monomial degree.

The Range of this (differentiable) function is a vector of monomial evaluations [1,x,y,z,xx,xy,yy,xz,yz,zz,...] in the coordinate vector [x,y,z]. The maximal degree of the provided monomial evaluations is given by the parameter maxDegree. The number of coordinate components is given by the dimension. From maxDegree and dimension the total number of monomials can be computed as binomial(maxDegree+dimension, dimension) and is provided as static constant ::size in the class.

The function models the Concept::DifferentiableFunction<Range(Domain)> concept.

The MonomialSet function is specialized for dim = 1, dim = 2, and dim = 3 only.

Member Function Documentation

exponents()

template<class RangeFieldType , int dimension, int maxDegree>

static constexpr std::array< std::array< std::size_t, dim >, size > Dune::Functions::MonomialSet< RangeFieldType, dimension, maxDegree >::exponents ( )

staticconstexpr

Return array of monomial exponents with shape size x dim

The k-the entry of the returned array is the exponent multi-index of the monomial corresponding the the k-th component of the function. Note that the ordering is tensor based, e.g., for the set of 3d monomials 1,x,y,z,xx,xy,yy,xz,yz,zz, ... we get the exponents: [ [0,0,0], [1,0,0], [0,1,0], [0,0,1], [2,0,0], [1,1,0], [0,2,0], [1,0,1], [0,1,1], [0,0,2], ...]

operator()()

template<class RangeFieldType , int dimension, int maxDegree>

template<class DomainFieldType >

constexpr Dune::FieldVector< RangeFieldType, size > Dune::Functions::MonomialSet< RangeFieldType, dimension, maxDegree >::operator() ( const Dune::FieldVector< DomainFieldType, dim > &  x ) const

constexpr

Return array of monomial evaluations.

The k-the entry of the returned array is the value of the monomial corresponding the the k-th entry of the return value of exponents().

Template Parameters

DomainFieldType

The scalar type of the domain.

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The documentation for this struct was generated from the following file:

• dune/functions/analyticfunctions/monomialset.hh