Defines Lagrange polynomials in the 1D reference element (the interval \(4[-1.1]\)) More...

#include <ptems/spaces/lagrangepolynomials.hpp>

Inheritance diagram for ptems::LagrangePolynomials< 1 >:

Collaboration diagram for ptems::LagrangePolynomials< 1 >:

Static Public Member Functions
template<typename T >
static T *	Polynomials (const ReferenceElement< 1 > &, const Vector< 1 > &pt, T *result, std::size_t polydeg)
	Computes the value of the Lagrange polynomials at a specified point which each Lagrange polynomial is 1 at one (different) point in the \(p+1\) equidistributed points on the reference interval \(4[-1.1]\) and zero at the rest, where \(p\) is the polynomial degree. More...

template<typename T >
static FuncAndGradData< 1, T > *	Gradient (const ReferenceElement< 1 > &, const Vector< 1 > &pt, FuncAndGradData< 1, T > *result, std::size_t polydeg)
	Computes the value of the Lagrange polynomials, and their first order derivatives, at a specified point which each Lagrange polynomial is 1 at one (different) point in the \(p+1\) equidistributed points on the reference interval \(4[-1.1]\) and zero at the rest, where \(p\) is the polynomial degree. More...

template<typename T >
static FuncGradAndHessianData< 1, T > *	Hessian (const ReferenceElement< 1 > &, const Vector< 1 > &pt, FuncGradAndHessianData< 1, T > *result, std::size_t polydeg)
	Computes the value of the Lagrange polynomials, and their first and second order derivatives, at a specified point which each Lagrange polynomial is 1 at one (different) point in the \(p+1\) equidistributed points on the reference interval \(4[-1.1]\) and zero at the rest, where \(p\) is the polynomial degree. More...

static constexpr std::size_t	NumberDoFs ([[maybe_unused]] const ReferenceElement< 1 > &refElement, std::size_t polydeg)
	Gets the number of degrees of freedom required for a polynomial of the specified degree on the specified reference element. More...

Detailed Description

Defines Lagrange polynomials in the 1D reference element (the interval \(4[-1.1]\))

Member Function Documentation

◆ Gradient()

template<typename T >

static FuncAndGradData<1,T>* ptems::LagrangePolynomials< 1 >::Gradient	(	const ReferenceElement< 1 > &	,
		const Vector< 1 > &	pt,
		FuncAndGradData< 1, T > *	result,
		std::size_t	polydeg
	)

inlinestatic

Computes the value of the Lagrange polynomials, and their first order derivatives, at a specified point which each Lagrange polynomial is 1 at one (different) point in the \(p+1\) equidistributed points on the reference interval \(4[-1.1]\) and zero at the rest, where \(p\) is the polynomial degree.

Template Parameters

T	The type of the result

Parameters

pt	The point to compute the values of the lagrange polynomial at
result	Array of at least `polydeg+1` entries to store the result into
polydeg	The polynomial degree of the Lagrange basis functions

Returns: Pointer to the entry AFTER the last basis filled (=result+polydeg+1)

◆ Hessian()

template<typename T >

static FuncGradAndHessianData<1,T>* ptems::LagrangePolynomials< 1 >::Hessian	(	const ReferenceElement< 1 > &	,
		const Vector< 1 > &	pt,
		FuncGradAndHessianData< 1, T > *	result,
		std::size_t	polydeg
	)

inlinestatic

Computes the value of the Lagrange polynomials, and their first and second order derivatives, at a specified point which each Lagrange polynomial is 1 at one (different) point in the \(p+1\) equidistributed points on the reference interval \(4[-1.1]\) and zero at the rest, where \(p\) is the polynomial degree.

Template Parameters

T	The type of the result

Parameters

pt	The point to compute the values of the lagrange polynomial at
result	Array of at least `polydeg+1` entries to store the result into
polydeg	The polynomial degree of the Lagrange basis functions

Returns: Pointer to the entry AFTER the last basis filled (=result+polydeg+1)

◆ NumberDoFs()

static constexpr std::size_t ptems::Polynomials< 1 >::NumberDoFs	(	[[maybe_unused] ] const ReferenceElement< 1 > &	refElement,
		std::size_t	polydeg
	)

inlinestaticconstexprinherited

Gets the number of degrees of freedom required for a polynomial of the specified degree on the specified reference element.

Parameters

refElement	The reference interval (parameter is ignored)
polydeg	The degree of the polynomial

Returns: The number of degrees of freedom

◆ Polynomials()

template<typename T >

static T* ptems::LagrangePolynomials< 1 >::Polynomials	(	const ReferenceElement< 1 > &	,
		const Vector< 1 > &	pt,
		T *	result,
		std::size_t	polydeg
	)

inlinestatic

Computes the value of the Lagrange polynomials at a specified point which each Lagrange polynomial is 1 at one (different) point in the \(p+1\) equidistributed points on the reference interval \(4[-1.1]\) and zero at the rest, where \(p\) is the polynomial degree.

Template Parameters

T	The type of the result

Parameters

pt	The point to compute the values of the lagrange polynomial at
result	Array of at least `polydeg+1` entries to store the result into
polydeg	The polynomial degree of the Lagrange basis functions

Returns: Pointer to the entry AFTER the last basis filled (=result+polydeg+1)

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

ptems/spaces/lagrangepolynomials.hpp

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ Gradient()

◆ Hessian()

◆ NumberDoFs()

◆ Polynomials()