Ndpolator structures

Core data types defined and used by ndpolator. More...

Data Structures
struct	ndp_axis
	Single axis structure containing vertices for one dimension. More...
struct	ndp_axes
	Multi-axis collection with basic and associated axes. More...
struct	ndp_query_pts
	Query points structure with indices, flags and coordinates. More...
struct	ndp_table
	self-contained ndpolation table with axes, grid values and spatial indices. More...
struct	ndp_hypercube
	N-dimensional hypercube containing vertex values for interpolation. More...
struct	ndp_query
	Main query structure containing query points, hypercubes and results. More...

Detailed Description

Core data types defined and used by ndpolator.

These structures define the grid, axes, and query data that ndpolator works with.

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Data Structure Documentation

ndp_axis

struct ndp_axis

Single axis structure containing vertices for one dimension.

An axis, in ndpolator language, is an array of length len and vertices val. Axes span ndpolator dimensions: for N-dimensional interpolation and/or extrapolation, there need to be N axes. Note that axes themselves do not have any function values associated to them; they only span the N-dimensional grid.

Data Fields
int	len	Axis length (number of vertices)
double *	val	Axis vertices array
int	owns_data	Flag indicating if ndp_axis owns the val array

ndp_axes

struct ndp_axes

Multi-axis collection with basic and associated axes.

This structure stores all axes that span the ndpolator grid. Each axis must be of the ndp_axis type. Function values are associated to each combination (cartesian product) of axis indices.

There are two types of axes that ndpolator recognizes: basic and associated. Basic axes span the sparse grid: function values can either be defined, or null. Associated axes, on the other hand, are guaranteed to have function values defined for all combinations of basic indices that have function values defined. For example, if (i, j, k) are basic indices that have a defined function value, then (i, j, k, l, m) are guaranteed to be defined as well, where l and m index associated axes.

Data Fields
int	len
int	nbasic
ndp_axis **	axis

Field Documentation

len

int len

Number of axes

nbasic

int nbasic

Number of basic axes (must precede any associated axes in the axis array)

axis

ndp_axis** axis

Array of ndp_axis pointers

ndp_query_pts

struct ndp_query_pts

Query points structure with indices, flags and coordinates.

Query points (points of interest) are given by n coordinates that correspond to n ndp_axis instances stored in ndp_axes. Their number is given by the nelems field and their dimension by the naxes field. The indices array provides superior corners of the hypercube that contains a query point; the flags array tags each query point component with one of the ndp_vertex_flag flags: NDP_ON_GRID, NDP_ON_VERTEX, or NDP_OUT_OF_BOUNDS. The actual query points (as passed to ndpolator, in axis units) are stored in the requested array, and the unit-hypercube normalized coordinates are stored in the normed array.

Data Fields
int	nelems	Number of query points
int	naxes	Query point dimension (number of axes)
int *	indices	Array of superior hypercube indices
int *	flags	Array of flags, one per query point component
double *	requested	Array of absolute query points (in axis units)
double *	normed	Array of unit-hypercube normalized query points

ndp_table

struct ndp_table

self-contained ndpolation table with axes, grid values and spatial indices.

Ndpolator uses ndp_table to store all relevant parameters for interpolation and/or extrapolation. It stores the axes that span the interpolation hyperspace (in a ndp_axes structure), the function values across the interpolation hyperspace (grid and kdtree), function value length (vdim), and several private fields that further optimize interpolation.

Data Fields
int	vdim
ndp_axes *	axes
double *	grid
int	owns_data
struct kdtree *	vtree
struct kdtree *	hctree

Field Documentation

vdim

int vdim

Vertex dimension (i.e., function value length): 1 for scalars, >1 for arrays

axes

ndp_axes* axes

ndp_axes instance that defines all axes

grid

double* grid

Array holding all function values in C-native order

owns_data

int owns_data

Flag indicating if ndp_table owns the grid array

vtree

struct kdtree* vtree

Vertex k-d tree spatial index for nearest neighbor search

hctree

struct kdtree* hctree

Hypercube k-d tree spatial index for nearest neighbor search

ndp_hypercube

struct ndp_hypercube

N-dimensional hypercube containing vertex values for interpolation.

Hypercubes are subgrids that enclose (or are adjacent to, in the case of extrapolation) the passed query points, one per query point. They are qualified by their dimension (an N-dimensional hypercube has 2^N vertices) and their function value length. Note that hypercube dimension can be less than the dimension of the grid itself: if a query point coincides with any of the axes, that will reduce the dimensionality of the hypercube. If all query point components coincide with the axes (i.e, the vertex itself is requested), then the hypercube dimension equals 0, so there is no interpolation at all – only that vertex's function value is returned.

Data Fields
int	dim	Dimension of the hypercube
int	vdim	Function value length
int	fdhc	Flag indicating whether the hypercube is fully defined
double *	v	Hypercube vertex function values in C order (last dimension stride-1)

ndp_query

struct ndp_query

Main query structure containing query points, hypercubes and results.

Query is ndpolator's main work structure. It stores the query points (called elements in the structure), the corresponding axis indices, flags, and hypercubes. Once interpolation/extrapolation is done (by calling ndpolate), interpolated values are also stored in it.

Data Fields
int	nelems	Number of query points
int	extrapolation_method	ndp_extrapolation_method used for this query
int	search_algorithm	ndp_search_algorithm used for this query
ndp_hypercube **	hypercubes	Array of hypercubes, one per query point
double *	interps	Array of interpolation/extrapolation results
double *	dists	Array of distances to nearest fully defined hypercube