nd_cheb.hpp File Reference

n-dimensional Chebyshev polynomial More...

#include "bounding_box.hpp"
#include "util/math_functions.hpp"
#include "util/misc.hpp"
#include <boost/math/special_functions/chebyshev.hpp>
#include <Eigen/Dense>
#include <cstddef>

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Functions
template<size_t Dim, class T = double>
Eigen::Matrix< T, Dim, Eigen::Dynamic >	NiHu::fmm::lintrans (Eigen::Matrix< T, Dim, Eigen::Dynamic > const &x, bounding_box< Dim > const &bbTo, bounding_box< Dim > const &bbFrom)
	linear transform of points from a bounding box to an other More...
template<size_t Dim, class T = double>
Eigen::Matrix< T, Dim, Eigen::Dynamic >	NiHu::fmm::chebnodes (size_t n, bounding_box< Dim > const &bb=bounding_box< Dim >())
	return Chebyshev nodes in a multidimensional bounding box More...
template<class T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	NiHu::fmm::chebanterp0 (size_t N, Eigen::Matrix< T, Eigen::Dynamic, 1 > const &x, Eigen::Matrix< T, Eigen::Dynamic, 1 > const &y)
	1D Chebyshev anterpolation matrix More...
template<class T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	NiHu::fmm::chebanterp0_dy (size_t N, Eigen::Matrix< T, Eigen::Dynamic, 1 > const &x, Eigen::Matrix< T, Eigen::Dynamic, 1 > const &y)
	y-derivative 1D Chebyshev anterpolation matrix More...
template<class T , size_t Dim>
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	NiHu::fmm::chebanterp (size_t N, bounding_box< Dim > const &bb, Eigen::Matrix< T, Dim, Eigen::Dynamic > const &y0)
	ND Chebyshev anterpolation matrix from points to Chebyshev nodes. More...
template<class T , size_t Dim>
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	NiHu::fmm::chebanterp_dny (size_t N, bounding_box< Dim > const &bb, Eigen::Matrix< T, Dim, Eigen::Dynamic > const &y0, Eigen::Matrix< T, Dim, Eigen::Dynamic > const &ny0)
	normal derivative of Chebyshev anterpolation matrix More...

Detailed Description

n-dimensional Chebyshev polynomial

Definition in file nd_cheb.hpp.

Function Documentation

chebanterp()

template<class T , size_t Dim>

Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> NiHu::fmm::chebanterp	(	size_t	N,
		bounding_box< Dim > const &	bb,
		Eigen::Matrix< T, Dim, Eigen::Dynamic > const &	y0
	)

ND Chebyshev anterpolation matrix from points to Chebyshev nodes.

Template Parameters

T	the scalar type
Dim	bounding box dimension

Parameters

[in]	N	Chebyshev order
[in]	bb	the bounding box of Chebyshev nodes
[in]	y0	the source nodes of anterpolation

Definition at line 148 of file nd_cheb.hpp.

chebanterp0()

template<class T >

Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> NiHu::fmm::chebanterp0	(	size_t	N,
		Eigen::Matrix< T, Eigen::Dynamic, 1 > const &	x,
		Eigen::Matrix< T, Eigen::Dynamic, 1 > const &	y
	)

1D Chebyshev anterpolation matrix

Template Parameters

T	the scalar type

Parameters

[in]	N	Chebyshev order
[in]	y	source nodes of anterpolation
[in]	x	receiver nodes of anterpolation

Definition at line 89 of file nd_cheb.hpp.

chebanterp0_dy()

template<class T >

Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> NiHu::fmm::chebanterp0_dy	(	size_t	N,
		Eigen::Matrix< T, Eigen::Dynamic, 1 > const &	x,
		Eigen::Matrix< T, Eigen::Dynamic, 1 > const &	y
	)

y-derivative 1D Chebyshev anterpolation matrix

Template Parameters

T	the scalar type

Parameters

[in]	N	Chebyshev order
[in]	y	source nodes of anterpolation
[in]	x	receiver nodes of anterpolation

Definition at line 117 of file nd_cheb.hpp.

chebanterp_dny()

template<class T , size_t Dim>

Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> NiHu::fmm::chebanterp_dny	(	size_t	N,
		bounding_box< Dim > const &	bb,
		Eigen::Matrix< T, Dim, Eigen::Dynamic > const &	y0,
		Eigen::Matrix< T, Dim, Eigen::Dynamic > const &	ny0
	)

normal derivative of Chebyshev anterpolation matrix

Template Parameters

T	the scalar type
Dim	bounding box dimension

Parameters

[in]	N	Chebyshev order
[in]	bb	the bounding box of Chebyshev nodes
[in]	y0	the source nodes of anterpolation
[in]	ny0	the source normal vectors

Definition at line 172 of file nd_cheb.hpp.

chebnodes()

template<size_t Dim, class T = double>

Eigen::Matrix<T, Dim, Eigen::Dynamic> NiHu::fmm::chebnodes	(	size_t	n,
		bounding_box< Dim > const &	bb = bounding_box<Dim>()
	)

return Chebyshev nodes in a multidimensional bounding box

Template Parameters

Dim	space dimension
T	the scalar type

Parameters

[in]	n	required number of Chebyshev nodes
[in]	bb	the bounding box of Chebyshev nodes

Definition at line 55 of file nd_cheb.hpp.

lintrans()

template<size_t Dim, class T = double>

Eigen::Matrix<T, Dim, Eigen::Dynamic> NiHu::fmm::lintrans	(	Eigen::Matrix< T, Dim, Eigen::Dynamic > const &	x,
		bounding_box< Dim > const &	bbTo,
		bounding_box< Dim > const &	bbFrom
	)

linear transform of points from a bounding box to an other

Template Parameters

Dim	dimension of space
T	the scalar type

Parameters

[in]	x	Dim x N matrix of points to transform
[in]	bbTo	the destination bounding box
[in]	bbFrom	the source bounding box

Definition at line 32 of file nd_cheb.hpp.