GMpoly_cell.hpp File Reference

#include <cassert>
#include <cmath>
#include <algorithm>
#include <array>
#include <iostream>
#include <vector>
#include <unordered_map>
#include <mesh.hpp>
#include <quadraturerule.hpp>
#include <basis.hpp>
#include <typeinfo>

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Classes
struct	HArDCore3D::VecHash
	Hash function for VectorZd type. More...

Namespaces
namespace	HArDCore3D

Typedefs
typedef std::unordered_map< VectorZd, double, VecHash >	HArDCore3D::MonomialCellIntegralsType
	Type for list of integrals of monomials.

Functions
std::vector< MonomialCellIntegralsType >	HArDCore3D::IntegrateCellMonomials_onEdges (const Cell &T, const size_t maxdeg)
	Compute all the integrals, on the edges of a cell, of this cell's monomials up to a max degree.
std::vector< MonomialCellIntegralsType >	HArDCore3D::IntegrateCellMonomials_onFaces (const Cell &T, const size_t maxdeg, std::vector< MonomialCellIntegralsType > &integrals_edges)
	Compute all the integrals, on the faces of a cell, of this cell's monomials up to a max degree.
MonomialCellIntegralsType	HArDCore3D::IntegrateCellMonomials (const Cell &T, const int maxdeg)
	Compute all the integrals of a cell's monomials on the cell.
MonomialCellIntegralsType	HArDCore3D::CheckIntegralsDegree (const Cell &T, const size_t degree, const MonomialCellIntegralsType &mono_int_map={})
	Checks if the degree of an existing list of monomial integrals is sufficient, other re-compute and return a proper list.
template<typename BasisType >
Eigen::MatrixXd	HArDCore3D::transformGM (const Family< BasisType > &family_basis, const char RC, const Eigen::MatrixXd &anc_GM)
	Transforms a Gram Matrix from an ancestor to a family basis.
template<typename BasisType >
Eigen::MatrixXd	HArDCore3D::transformGM (const RestrictedBasis< BasisType > &restr_basis, const char RC, const Eigen::MatrixXd &anc_GM)
	Transforms a Gram Matrix from an ancestor to a restricted basis.
template<typename BasisType >
Eigen::MatrixXd	HArDCore3D::transformGM (const ShiftedBasis< BasisType > &shifted_basis, const char RC, const Eigen::MatrixXd &anc_GM)
	Transforms a Gram Matrix from an ancestor to a shifted basis.
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const MonomialScalarBasisCell &basis1, const MonomialScalarBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of local scalar monomial bases.
template<typename BasisType >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const BasisType &basis, MonomialCellIntegralsType mono_int_map={})
	This overload to simplify the call to GramMatrix in case the two bases are the same.
template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of any pair of tensorized scalar bases.
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const RolyComplBasisCell &basis1, const RolyComplBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of RolyCompl bases.
template<typename BasisType1 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const RolyComplBasisCell &rolycompl_basis, const TensorizedVectorFamily< BasisType1, N > &tens_family, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a RolyCompl basis and a tensorized scalar basis.
template<typename BasisType1 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &tens_family, const RolyComplBasisCell &rolycompl_basis, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a tensorized scalar basis and a RolyCompl basis.
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const GolyComplBasisCell &basis1, const GolyComplBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of GolyCompl bases.
template<typename BasisType1 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const GolyComplBasisCell &golycompl_basis, const TensorizedVectorFamily< BasisType1, N > &tens_family, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a GolyCompl basis and a tensorized scalar basis.
template<typename BasisType1 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &tens_family, const GolyComplBasisCell &golycompl_basis, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a tensorized scalar basis and a GolyCompl basis.
Eigen::MatrixXd	HArDCore3D::GMRolyComplScalar (const Cell &T, const RolyComplBasisCell &rolycompl_basis, const MonomialScalarBasisCell &mono_basis, const size_t m, MonomialCellIntegralsType mono_int_map={})
	Computes the Gram Matrix of the mth component of a RolyCompl Basis and a monomial basis.
template<typename BasisType >
Eigen::MatrixXd	HArDCore3D::GMRolyComplScalar (const Cell &T, const RolyComplBasisCell &basis1, const BasisType &basis2, const size_t m, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of the mth component of a RolyCompl Basis and any basis.
Eigen::MatrixXd	HArDCore3D::GMGolyComplScalar (const Cell &T, const GolyComplBasisCell &golycompl_basis, const MonomialScalarBasisCell &mono_basis, const size_t s, MonomialCellIntegralsType mono_int_map, const size_t m=3, const size_t k1=3, const size_t k2=3)
	Computes the Gram Matrix of the sth section of a GolyCompl Basis and a monomial basis.
template<typename BasisType >
Eigen::MatrixXd	HArDCore3D::GMGolyComplScalar (const Cell &T, const GolyComplBasisCell &basis1, const BasisType &basis2, const size_t s, MonomialCellIntegralsType mono_int_map, const size_t m=3, const size_t k1=3, const size_t k2=3)
	Generic template to compute the Gram Matrix of the sth section of a GolyCompl Basis and any basis with an extra power of the mth variable.
Eigen::MatrixXd	HArDCore3D::GMGolyCompl (const Cell &T, const GolyComplBasisCell &basis1, const GolyComplBasisCell &basis2, const size_t s1, const size_t s2, MonomialCellIntegralsType mono_int_map, const size_t m1=3, const size_t m2=3, const size_t k1=3, const size_t k2=3)
	Computes the Gram Matrix of the (optionally k1th derivative of the) s1th section of GolyCompl (optionally multiplied by the m1th variable) and the (optionally k2th derivative of the) s2th section of GolyCompl (optionally multiplied by the m2th variable)
template<typename BasisType >
constexpr bool	HArDCore3D::useAncestor ()
	Determines if the ancestor of a basis will be used to compute a Gram matrix for this basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const BasisType1 &basis1, const BasisType2 &basis2, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of any pair of bases.
Eigen::MatrixXd	HArDCore3D::GMScalarDerivative (const Cell &T, const MonomialScalarBasisCell &basis1, const MonomialScalarBasisCell &basis2, const size_t m, MonomialCellIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of local scalar monomial bases, taking a partial derivative of the first (w.r.t. homogeneous coordinates, without scaling)
Eigen::MatrixXd	HArDCore3D::GMScalarDerivative (const Cell &T, const MonomialScalarBasisCell &basis1, const MonomialScalarBasisCell &basis2, const size_t m, const size_t l, MonomialCellIntegralsType mono_int_map={})
	Computes the Gram Matrix of a pair of local scalar monomial bases, taking partial derivatives of each of them (w.r.t. homogeneous coordinates, without scaling)
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GMScalarDerivative (const Cell &T, const BasisType1 &basis1, const BasisType2 &basis2, const size_t m, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of any pair of scalar bases, taking a partial derivative of the first (w.r.t. homogeneous coordinates, without scaling)
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GMScalarDerivative (const Cell &T, const BasisType1 &basis1, const BasisType2 &basis2, const size_t m, const size_t l, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of any pair of scalar bases, taking partial derivatives of each of them (w.r.t. homogeneous coordinates, without scaling)
template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const GradientBasis< BasisType1 > &grad_basis, const TensorizedVectorFamily< BasisType2, N > &tens_family, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a gradient basis and a tensorized scalar basis.
template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &tens_family, const GradientBasis< BasisType2 > &grad_basis, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a tensorized scalar basis and a gradient basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const GradientBasis< BasisType1 > &grad_basis1, const GradientBasis< BasisType2 > &grad_basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a gradient basis and another gradient basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const CurlBasis< BasisType1 > &basis1, const CurlBasis< BasisType2 > &basis2, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of Curl of any pair of bases.
template<typename BasisType1 , typename BasisType2 >
boost::disable_if< boost::is_same< BasisType2, MonomialCellIntegralsType >, Eigen::MatrixXd >::type	HArDCore3D::GramMatrix (const Cell &T, const CurlBasis< BasisType1 > &basis1, const BasisType2 &basis2, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of a Curl basis and any other basis.
template<typename BasisType1 , typename Basis2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const BasisType1 &basis1, const CurlBasis< Basis2 > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of any basis and a Curl basis.
template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixCurlCurl (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the curl of a tensorized basis and the curl of another tensorized basis.
Eigen::MatrixXd	HArDCore3D::GramMatrixCurlCurl (const Cell &T, const GolyComplBasisCell &basis1, const GolyComplBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Compute the Gram Matrix of the curl of a GolyCompl basis and the curl of another GolyCompl basis.
template<typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixCurlCurl (const Cell &T, const GolyComplBasisCell &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the curl of a GolyCompl basis and the curl of a tensorized basis.
template<typename BasisType1 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixCurlCurl (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &basis1, const GolyComplBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the curl of a tensorized basis and the curl of a GolyCompl basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrixCurlCurl (const Cell &T, const BasisType1 &basis1, const BasisType2 &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the curl of any basis and the curl of any other basis.
template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixCurl (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a Curl<Tensorized> basis and a tensorized scalar basis.
template<typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixCurl (const Cell &T, const GolyComplBasisCell &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a Curl<GolyCompl> basis and a tensorized scalar basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrixCurl (const Cell &T, const BasisType1 &basis1, const BasisType2 &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the curl of any basis and any other basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrixCurl (const Cell &T, const BasisType1 &basis1, const CurlBasis< BasisType2 > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the curl of any two bases when one CurlBasis is at a lower level than the other.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const DivergenceBasis< BasisType1 > &basis1, const DivergenceBasis< BasisType2 > &basis2, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of Divergence of any pair of bases.
Eigen::MatrixXd	HArDCore3D::GMRolyComplScalarDiv (const Cell &T, const MonomialScalarBasisCell &mono_basis, const RolyComplBasisCell &rolycompl_basis, const size_t k, MonomialCellIntegralsType mono_int_map)
	Gram Matrix of the divergence of a RolyCompl Basis and the kth derivative of a monomial basis.
template<typename BasisType >
Eigen::MatrixXd	HArDCore3D::GMRolyComplScalarDiv (const Cell &T, const BasisType &basis1, const RolyComplBasisCell &basis2, const size_t k, MonomialCellIntegralsType mono_int_map)
	Gram Matrix of the divergence of a RolyCompl basis and the k-th derivative of any scalar basis.
template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixDivDiv (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the divergence of a tensorized basis and the divergence of another tensorized basis.
Eigen::MatrixXd	HArDCore3D::GramMatrixDivDiv (const Cell &T, const RolyComplBasisCell &basis1, const RolyComplBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Compute the Gram Matrix of the divergence of a RolyCompl basis and the divergence of another RolyCompl basis.
template<typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixDivDiv (const Cell &T, const RolyComplBasisCell &basis1, const TensorizedVectorFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the divergence of a RolyCompl basis and the divergence of a tensorized basis.
template<typename BasisType1 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixDivDiv (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &basis1, const RolyComplBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the divergence of a tensorized basis and the divergence of a RolyCompl basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrixDivDiv (const Cell &T, const BasisType1 &basis1, const BasisType2 &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the divergence of any basis and the divergence of any other basis.
template<typename BasisType1 , typename BasisType2 >
boost::disable_if< boost::is_same< BasisType2, MonomialCellIntegralsType >, Eigen::MatrixXd >::type	HArDCore3D::GramMatrix (const Cell &T, const DivergenceBasis< BasisType1 > &basis1, const BasisType2 &basis2, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of a Divergence basis and any other basis.
template<typename BasisType1 , typename Basis2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const BasisType1 &basis1, const DivergenceBasis< Basis2 > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of any basis and a Divergence basis.
template<typename BasisType1 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrixDiv (const Cell &T, const TensorizedVectorFamily< BasisType1, N > &basis1, const MonomialScalarBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of a Divergence<Tensorized> basis and a monomial scalar basis.
Eigen::MatrixXd	HArDCore3D::GramMatrixDiv (const Cell &T, const RolyComplBasisCell &basis1, const MonomialScalarBasisCell &basis2, MonomialCellIntegralsType mono_int_map={})
	Computes the Gram Matrix of a Divergence<RolyCompl> basis and a monomial scalar basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrixDiv (const Cell &T, const BasisType1 &basis1, const BasisType2 &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the divergence of any basis and any other basis.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrixDiv (const Cell &T, const BasisType1 &basis1, const DivergenceBasis< BasisType2 > &basis2, MonomialCellIntegralsType mono_int_map={})
	Template to compute the Gram Matrix of the divergence of any two bases when one DivergenceBasis is at a lower level than the other.
template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const MatrixFamily< BasisType1, N > &basis1, const MatrixFamily< BasisType2, N > &basis2, MonomialCellIntegralsType mono_int_map={})
	Gram Matrix of any pair of MatrixFamily bases.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const DivergenceBasis< MatrixFamily< BasisType1, dimspace > > &basis1, const TensorizedVectorFamily< BasisType2, dimspace > &basis2, MonomialCellIntegralsType mono_int_map={})
	Gram Matrix of the divergence of a MatrixFamily and a tensorized family (only valid if, in MatrixFamily and TensorizedVectorFamily, we have N=dimspace).
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const TensorizedVectorFamily< BasisType1, dimspace > &basis1, const DivergenceBasis< MatrixFamily< BasisType2, dimspace > > &basis2, MonomialCellIntegralsType mono_int_map={})
	Generic template to compute the Gram Matrix of a vector valued basis and the divergence of a MatrixFamily.
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const GradientBasis< TensorizedVectorFamily< BasisType1, dimspace > > &basis1, const MatrixFamily< BasisType2, dimspace > &basis2, MonomialCellIntegralsType mono_int_map={})
	Gram Matrix of the gradient basis of a tensorized family and a matrix family (only valid if N=dimspace in Tensorized and MatrixFamily).
template<typename BasisType1 , typename BasisType2 >
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const MatrixFamily< BasisType1, dimspace > &basis1, const GradientBasis< TensorizedVectorFamily< BasisType2, dimspace > > &basis2, MonomialCellIntegralsType mono_int_map={})
	Gram Matrix of a Matrix family and the gradient of a tensorized family.
template<typename BasisType1 , typename BasisType2 , size_t N>
Eigen::MatrixXd	HArDCore3D::GramMatrix (const Cell &T, const GradientBasis< TensorizedVectorFamily< BasisType1, N > > &basis1, const GradientBasis< TensorizedVectorFamily< BasisType2, N > > &basis2, MonomialCellIntegralsType mono_int_map={})
	Gram Matrix of two gradient bases of tensorized families.