HArDCore2D::HessianBasis< BasisType > Class Template Reference

Basis for the space of Hessians of polynomials. More...

#include <basis.hpp>

Public Types
typedef MatrixRd	FunctionValue
typedef void	GradientValue
typedef void	CurlValue
typedef void	DivergenceValue
typedef void	RotorValue
typedef void	HessianValue
typedef BasisType::GeometricSupport	GeometricSupport
typedef BasisType	AncestorType

Public Member Functions
	HessianBasis (const BasisType &basis)
	Constructor. More...
size_t	dimension () const
	Compute the dimension of the basis. More...
FunctionValue	function (size_t i, const VectorRd &x) const
	Evaluate the i-th basis function at point x. More...
constexpr const BasisType &	ancestor () const
	Return the ancestor (basis that the gradient was taken of) More...

Static Public Attributes
constexpr static const TensorRankE	tensorRank = Matrix
constexpr static const bool	hasAncestor = true
static const bool	hasFunction = true
static const bool	hasGradient = false
static const bool	hasCurl = false
static const bool	hasDivergence = false
static const bool	hasRotor = false
static const bool	hasHessian = false

Detailed Description

template<typename BasisType>
class HArDCore2D::HessianBasis< BasisType >

Basis for the space of Hessians of polynomials.

To construct a basis of H^k, this assumes that the scalar basis it is constructed from is an ancestor basis of P^{k+2}/P^1, space of polynomials of degree k+2 without trivial polynomials with zero Hessian. This can also be used to create a family of Hessians (not necessarily linearly independent, if the ancestor basis is not a basis of P^{k+2}/P^1)

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

• src/Common/basis.hpp