Source Edit

Radial basis function interpolation

This module implements RBF interpolation of scattered data in arbitrary dimensions.

Example:

import src/numericalnim/rbf
import arraymancer

let points = [[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]].toTensor
let values = [[0.0], [1.0], [2.0], [3.0]].toTensor

let interp = newRbf(points, values)

let evalPoints = [[0.5, 0.5], [0.314, 0.281]].toTensor
let val = interp.eval(evalPoints)

Imports

utils

Types

RbfBaseType[T] = object points*: Tensor[float] values*: Tensor[T] coeffs*: Tensor[float] epsilon*: float f*: RbfFunc: Source Edit
RbfFunc = proc (r: Tensor[float]; epsilon: float): Tensor[float]: Source Edit
RbfGrid[T] = object indices*: seq[seq[int]] values*: Tensor[T] points*: Tensor[float] gridSize*, gridDim*: int gridDelta*: float: Source Edit
RbfType[T] = object limits*: tuple[upper: Tensor[float], lower: Tensor[float]] grid*: RbfGrid[RbfBaseType[T]] nValues*: int: Source Edit

Procs

proc compactRbfFunc(r: Tensor[float]; epsilon: float): Tensor[float] {. ...raises: [], tags: [], forbids: [].}: Source Edit
proc constructMeshedPatches[T](grid: RbfGrid[T]): Tensor[float]: Source Edit
proc eval[T](rbf: RbfBaseType[T]; x: Tensor[float]): Tensor[T]: Source Edit
proc eval[T](rbf: RbfType[T]; x: Tensor[float]): Tensor[T]: Source Edit
proc evalAlt[T](rbf: RbfType[T]; x: Tensor[float]): Tensor[T]: Source Edit
proc findAllBetween[T](grid: RbfGrid[T]; x: Tensor[float]; rho1, rho2: float): seq[ int]: Source Edit
proc findAllWithin[T](grid: RbfGrid[T]; x: Tensor[float]; rho: float): seq[int]: Source Edit
proc findIndex[T](grid: RbfGrid[T]; point: Tensor[float]): int: Source Edit
proc newRbf[T](points: Tensor[float]; values: Tensor[T]; gridSize: int = 0; rbfFunc: RbfFunc = compactRbfFunc; epsilon: float = 1): RbfType[T]: Construct a Radial basis function interpolator using Partition of Unity.

Inputs:

points: The positions of the data points. Shape: (nPoints, nDims)

values: The values at the points. Can be multivalued. Shape: (nPoints, nValues)

gridSize: The number of cells along each dimension. Setting it to the default 0 will automatically choose a value based on the number of points.

rbfFunc: The RBF function that accepts shape parameter. Default is a C^2 compactly supported function.

epsilon: shape parameter. Default 1.

Returns:

Interpolant that can be evaluated using interp.eval(points).

Source Edit
proc newRbfBase[T](points: Tensor[float]; values: Tensor[T]; rbfFunc: RbfFunc = compactRbfFunc; epsilon: float = 1): RbfBaseType[ T]: Source Edit
proc newRbfGrid[T](points: Tensor[float]; values: Tensor[T]; gridSize: int = 0): RbfGrid[ T]: Source Edit
proc scalePoint(x: Tensor[float]; limits: tuple[upper: Tensor[float], lower: Tensor[float]]): Tensor[ float] {....raises: [ValueError], tags: [], forbids: [].}: Source Edit

Iterators

iterator neighbours[T](grid: RbfGrid[T]; k: int; searchLevels: int = 1): int: Source Edit
iterator neighboursExcludingCenter[T](grid: RbfGrid[T]; k: int): int: Source Edit

Templates

template compactRbfFuncScalar(r: float; epsilon: float): float: Source Edit