#include <DelaunayInterpolation.h>

Public Member Functions
void	calc_node_gradient (const double f, const int method, double grad, const int n_it=20) const
	Subroutine to calculate the gradient at each node.

void	clear ()
	Clear the data.

std::tuple< AMP::Array< TYPE >, AMP::Array< int > >	copy_tessellation () const
	Function to copy the tessellation.

void	create_tessellation (const AMP::Array< TYPE > &x)
	Function to construct the tessellation.

void	create_tessellation (const Array< TYPE > &x, const Array< int > &tri)
	Function to construct the tessellation using a given tessellation.

void	create_tessellation (size_t N, const TYPE x, const TYPE y, const TYPE *z)
	Function to construct the tessellation.

	DelaunayInterpolation ()
	Empty constructor.

	DelaunayInterpolation (const DelaunayInterpolation &)=delete

template<class TYPE2 >
Array< size_t >	find_nearest (const Array< TYPE2 > &xi) const
	Subroutine to find the nearest neighbor to a point.

template<class TYPE2 >
Array< int >	find_tri (const Array< TYPE2 > &xi, bool extrap=false) const
	Subroutine to find the triangle that contains the point.

size_t	get_N_tri () const
	Function to return the number of triangles in the tessellation.

AMP::Array< int >	get_tri () const
	Function to return the triangles in the tessellation.

AMP::Array< int >	get_tri_nab () const
	Function to return the triangles neignbors.

template<class TYPE2 >
std::tuple< AMP::Array< double >, AMP::Array< double > >	interp_cubic (const AMP::Array< double > &f, const AMP::Array< double > &g, const AMP::Array< TYPE2 > &xi, const AMP::Array< int > &index, int extrap=0) const
	Subroutine to perform cubic interpoaltion.

template<class TYPE2 >
std::tuple< AMP::Array< double >, AMP::Array< double > >	interp_linear (const AMP::Array< double > &f, const AMP::Array< TYPE2 > &xi, const AMP::Array< int > &index, bool extrap=false) const
	Subroutine to perform linear interpoaltion.

template<class TYPE2 >
Array< double >	interp_nearest (const Array< double > &f, const Array< TYPE2 > &xi, const Array< size_t > &nearest) const
	Subroutine to perform nearest-neighbor interpoaltion.

DelaunayInterpolation &	operator= (const DelaunayInterpolation &)=delete

	~DelaunayInterpolation ()
	Empty destructor.

Static Public Member Functions
static void	compute_Barycentric (const int ndim, const double x, const double xi, double *L)
	Subroutine to compute the Barycentric coordinates.

Private Member Functions
void	create_kdtree () const
	Subroutine to get the list of triangle that are connected to each triangle.

void	create_node_neighbors () const
	Subroutine to get the list of nodes that are connected to each node.

void	create_node_tri () const
	Subroutine to get the starting triangle for each node.

void	create_tri_neighbors () const
	Subroutine to get the list of triangle that are connected to each triangle.

void	interp_cubic_single (const double f[], const double g[], const double xi[], const int index, double &fi, double *gi, int extrap) const

Private Attributes
unsigned *	d_N_node

size_t	d_N_node_sum

unsigned **	d_node_list

int *	d_node_tri

kdtree *	d_tree

Array< int >	d_tri

Array< int >	d_tri_nab

Array< TYPE >	d_x

Detailed Description

template<class TYPE>
class AMP::DelaunayInterpolation< TYPE >

This class provides Delaunay based N-dimensional simplex interpolation.

Definition at line 19 of file DelaunayInterpolation.h.

Constructor & Destructor Documentation

◆ DelaunayInterpolation() [1/2]

template<class TYPE >

AMP::DelaunayInterpolation< TYPE >::DelaunayInterpolation ( )

Empty constructor.

◆ DelaunayInterpolation() [2/2]

template<class TYPE >

AMP::DelaunayInterpolation< TYPE >::DelaunayInterpolation ( const DelaunayInterpolation< TYPE > & )

delete

◆ ~DelaunayInterpolation()

template<class TYPE >

AMP::DelaunayInterpolation< TYPE >::~DelaunayInterpolation ( )

Empty destructor.

Member Function Documentation

◆ calc_node_gradient()

template<class TYPE >

void AMP::DelaunayInterpolation< TYPE >::calc_node_gradient	(	const double *	f,
		const int	method,
		double *	grad,
		const int	n_it = `20`
	)		const

Subroutine to calculate the gradient at each node.

This function gets a list of the nodes that connect to each node

Parameters

f	Function values at the vertices( ndim )
method	Gradient method to use 1 - Use a simple least squares method using only the local nodes. This method is relatively fast, but only first order in the gradient, causing the truncation error of the interpolate to be O(x^3). Note that it will still give a better cubic interpolation than MATLAB's cubic in griddata. 2 - Least squares method that solves a sparse system. This method is second order in the gradient yielding an interpolant that has truncation error O(x^4), but requires soving a sparse 2nx2n system. This can be reasonably fast for most systems, but is memory limited for large systems (it can grow as O(n^2ndim^2)). Currently this method is NOT implemented in the C++ version. 3 - Least squares method that uses the matrix computed by method 2 and block Gauss-Seidel iteration to improve the gradient calculated by method 1. Usually only a finite number of iterations are needed to significantly reduce the error. Technically, this method has a trunction error that is still O(x^3), but for most purposes, this term is reduced so it is less than the O(x^4) term. For most systems, this method is not significantly faster than method 2, but it does not have the same memory limitations and is O(nndim^2) in memory. Typically 10-20 iterations are all that is necessary. 4 - This is the same as method 3, but does not store any internal data. This saves us from creating a large temporary structure ~10ndim^2N at a cost of ~2x in performance.
grad	(Output) Calculated gradient at the nodes( ndim x N )
n_it	Optional argument specifying the number of Gauss-Seidel iterations. Only used if method = 3 or 4.

◆ clear()

template<class TYPE >

void AMP::DelaunayInterpolation< TYPE >::clear ( )

Clear the data.

◆ compute_Barycentric()

template<class TYPE >

static void AMP::DelaunayInterpolation< TYPE >::compute_Barycentric	(	const int	ndim,
		const double *	x,
		const double *	xi,
		double *	L
	)

static

Subroutine to compute the Barycentric coordinates.

This function computes the Barycentric coordinates and the matrix T to convert from Barycentric coordinates to cartesian (x=T*L).

Parameters

ndim	Number of dimensions
x	Coordinates of the triangle vertices( ndim x ndim+1 )
xi	Coordinates of the desired point( ndim x 1 )
L	(output) The Barycentric coordinates of the point( ndim+1 x 1 )

◆ copy_tessellation()

template<class TYPE >

std::tuple< AMP::Array< TYPE >, AMP::Array< int > > AMP::DelaunayInterpolation< TYPE >::copy_tessellation ( ) const

Function to copy the tessellation.

This function copies the internal tessellation to a user-provided array.

◆ create_kdtree()

template<class TYPE >

void AMP::DelaunayInterpolation< TYPE >::create_kdtree ( ) const

private

Subroutine to get the list of triangle that are connected to each triangle.

◆ create_node_neighbors()

template<class TYPE >

void AMP::DelaunayInterpolation< TYPE >::create_node_neighbors ( ) const

private

Subroutine to get the list of nodes that are connected to each node.

◆ create_node_tri()

template<class TYPE >

void AMP::DelaunayInterpolation< TYPE >::create_node_tri ( ) const

private

Subroutine to get the starting triangle for each node.

◆ create_tessellation() [1/3]

template<class TYPE >

void AMP::DelaunayInterpolation< TYPE >::create_tessellation ( const AMP::Array< TYPE > & x )

Function to construct the tessellation.

This function creates the tessellation using the given points.

Parameters

x	The coordinates of the vertices( ndim x N )

◆ create_tessellation() [2/3]

template<class TYPE >

void AMP::DelaunayInterpolation< TYPE >::create_tessellation	(	const Array< TYPE > &	x,
		const Array< int > &	tri
	)

Function to construct the tessellation using a given tessellation.

This function sets the internal tessellation to match a provided tessellation. It does not check if the provided tessellation is valid. It allows the user to provide their own tesselation if desired. If sucessful, this routine returns 0.

Parameters

x	The coordinates of the vertices( ndim x N ) or to update the coordinate pointers before each call. See update_coordinates for more information.
tri	The tesselation( ndim+1 x N_tri )

◆ create_tessellation() [3/3]

template<class TYPE >

void AMP::DelaunayInterpolation< TYPE >::create_tessellation	(	size_t	N,
		const TYPE *	x,
		const TYPE *	y,
		const TYPE *	z
	)

Function to construct the tessellation.

This function creates the tessellation using the given points.

Parameters

N	The number of vertices
x	The coordinates of the x vertices
y	The coordinates of the y vertices (may be NULL for 1D)
z	The coordinates of the z vertices (may be NULL for 1D/2D)

◆ create_tri_neighbors()

template<class TYPE >

void AMP::DelaunayInterpolation< TYPE >::create_tri_neighbors ( ) const

private

Subroutine to get the list of triangle that are connected to each triangle.

◆ find_nearest()

template<class TYPE >

template<class TYPE2 >

Array< size_t > AMP::DelaunayInterpolation< TYPE >::find_nearest ( const Array< TYPE2 > & xi ) const

Subroutine to find the nearest neighbor to a point.

This function finds the nearest neighbor to each point. It is able to do perform the search in O(N^(1/ndim)) on average. Note: this function requires the calculate of the node lists if they are not stored (see set_storage_level)

Parameters

xi	Coordinates of the query points ( ndim x Ni )

Returns: Return the index of the nearest neighbor (N)

◆ find_tri()

template<class TYPE >

template<class TYPE2 >

Array< int > AMP::DelaunayInterpolation< TYPE >::find_tri	(	const Array< TYPE2 > &	xi,
		bool	extrap = `false`
	)		const

Subroutine to find the triangle that contains the point.

This function finds the triangle that contains the given points. This uses a simple search method, which may not be the most efficient. It is O(N*Ni). Note: this function requires the calculate of the node lists and triangle neighbor lists if they have not been calculated

Parameters

xi	Coordinates of the query points ( ndim x Ni )
extrap	If the point is outside the convex hull, return the nearest triangle instead of -1

Returns: Ouput index of triangle containing the point ( -1: Point is outside convex hull, -2: Search failed )

◆ get_N_tri()

template<class TYPE >

size_t AMP::DelaunayInterpolation< TYPE >::get_N_tri ( ) const

Function to return the number of triangles in the tessellation.

This function returns the number of triangles in the tessellation.

◆ get_tri()

template<class TYPE >

AMP::Array< int > AMP::DelaunayInterpolation< TYPE >::get_tri ( ) const

Function to return the triangles in the tessellation.

◆ get_tri_nab()

template<class TYPE >

AMP::Array< int > AMP::DelaunayInterpolation< TYPE >::get_tri_nab ( ) const

Function to return the triangles neignbors.

◆ interp_cubic()

template<class TYPE >

template<class TYPE2 >

std::tuple< AMP::Array< double >, AMP::Array< double > > AMP::DelaunayInterpolation< TYPE >::interp_cubic	(	const AMP::Array< double > &	f,
		const AMP::Array< double > &	g,
		const AMP::Array< TYPE2 > &	xi,
		const AMP::Array< int > &	index,
		int	extrap = `0`
	)		const

Subroutine to perform cubic interpoaltion.

This function performs cubic interpoaltion. Note: If the point is not contained within a triangle NaN will be returned.

Parameters

f	Function values at the triangle vertices( 1 x N )
g	Gradient of f(x) at the triangle vertices( ndim x N ) (see calc_node_gradient if unknown)
xi	Coordinates of the query points( ndim x Ni )
index	The index of the triangle containing the point (see find_tri)
extrap	Do we want to extrapolate from the current triangle 0: Do not extrapolate (NaNs will be used for points outside the domain) 1: Extrapolate using linear interpolation (using the nearest point and it's gradient) 2: Extrapolate using quadratic interpolation (using linear extrapolation for the gradient)

Returns: Return the interpolated function values and gradient at xi <fi,gi> fi - The interpolated function values ( Ni ) gi - The interpolated gradient ( ndim x Ni )

◆ interp_cubic_single()

template<class TYPE >

void AMP::DelaunayInterpolation< TYPE >::interp_cubic_single	(	const double	f[],
		const double	g[],
		const double	xi[],
		const int	index,
		double &	fi,
		double *	gi,
		int	extrap
	)		const

private

◆ interp_linear()

template<class TYPE >

template<class TYPE2 >

std::tuple< AMP::Array< double >, AMP::Array< double > > AMP::DelaunayInterpolation< TYPE >::interp_linear	(	const AMP::Array< double > &	f,
		const AMP::Array< TYPE2 > &	xi,
		const AMP::Array< int > &	index,
		bool	extrap = `false`
	)		const

Subroutine to perform linear interpoaltion.

This function performs linear interpoaltion. If a valid triangle index is not given, NaN will be returned. If extrap is false and the point is not within the triangle, NaN will be returned.

Parameters

f	Function values at the triangle vertices( 1 x N )
xi	Coordinates of the query points( ndim x Ni )
index	The index of the triangle containing the point (see find_tri)
extrap	Do we want to extrapolate from the current triangle Note: extrapolating can incure large error if sliver triangles on the boundary are present

Returns: Return the interpolated function values and gradient at xi <fi,gi> fi - The interpolated function values ( Ni ) gi - The interpolated gradient ( ndim x Ni )

◆ interp_nearest()

template<class TYPE >

template<class TYPE2 >

Array< double > AMP::DelaunayInterpolation< TYPE >::interp_nearest	(	const Array< double > &	f,
		const Array< TYPE2 > &	xi,
		const Array< size_t > &	nearest
	)		const

Subroutine to perform nearest-neighbor interpoaltion.

This function performs nearest-neighbor interpoaltion.

Parameters

f	Function values at the triangle vertices( 1 x N )
xi	Coordinates of the query points( ndim x Ni )
nearest	The nearest-neighbor points (see find_nearest)( 1 x Ni)

Returns: Return the interpolated function values at xi( 1 x Ni)

◆ operator=()

template<class TYPE >

DelaunayInterpolation & AMP::DelaunayInterpolation< TYPE >::operator= ( const DelaunayInterpolation< TYPE > & )

delete

Member Data Documentation

◆ d_N_node

template<class TYPE >

unsigned* AMP::DelaunayInterpolation< TYPE >::d_N_node

mutableprivate

Definition at line 262 of file DelaunayInterpolation.h.

◆ d_N_node_sum

template<class TYPE >

size_t AMP::DelaunayInterpolation< TYPE >::d_N_node_sum

mutableprivate

Definition at line 261 of file DelaunayInterpolation.h.

◆ d_node_list

template<class TYPE >

unsigned** AMP::DelaunayInterpolation< TYPE >::d_node_list

mutableprivate

Definition at line 263 of file DelaunayInterpolation.h.

◆ d_node_tri

template<class TYPE >

int* AMP::DelaunayInterpolation< TYPE >::d_node_tri

mutableprivate

Definition at line 265 of file DelaunayInterpolation.h.

◆ d_tree

template<class TYPE >

kdtree* AMP::DelaunayInterpolation< TYPE >::d_tree

mutableprivate

Definition at line 266 of file DelaunayInterpolation.h.

◆ d_tri

template<class TYPE >

Array<int> AMP::DelaunayInterpolation< TYPE >::d_tri

private

Definition at line 259 of file DelaunayInterpolation.h.

◆ d_tri_nab

template<class TYPE >

Array<int> AMP::DelaunayInterpolation< TYPE >::d_tri_nab

mutableprivate

Definition at line 260 of file DelaunayInterpolation.h.

◆ d_x

template<class TYPE >

Array<TYPE> AMP::DelaunayInterpolation< TYPE >::d_x

private

Definition at line 258 of file DelaunayInterpolation.h.

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

src/utils/DelaunayInterpolation.h

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ DelaunayInterpolation() [1/2]

◆ DelaunayInterpolation() [2/2]

◆ ~DelaunayInterpolation()

Member Function Documentation

◆ calc_node_gradient()

◆ clear()

◆ compute_Barycentric()

◆ copy_tessellation()

◆ create_kdtree()

◆ create_node_neighbors()

◆ create_node_tri()

◆ create_tessellation() [1/3]

◆ create_tessellation() [2/3]

◆ create_tessellation() [3/3]

◆ create_tri_neighbors()

◆ find_nearest()

◆ find_tri()

◆ get_N_tri()

◆ get_tri()

◆ get_tri_nab()

◆ interp_cubic()

◆ interp_cubic_single()

◆ interp_linear()

◆ interp_nearest()

◆ operator=()

Member Data Documentation

◆ d_N_node

◆ d_N_node_sum

◆ d_node_list

◆ d_node_tri

◆ d_tree

◆ d_tri

◆ d_tri_nab

◆ d_x