Interpolation.ScatteredRbfInterpolator Method

Definition

Namespace: Numerics.NET
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 10.1.0

Overload List

ScatteredRbfInterpolator(Double[,], Double[], RbfOptions) Creates a radial basis function (RBF) interpolator for scattered N-dimensional data.
ScatteredRbfInterpolator(IReadOnlyList<Vector<Double>>, Vector<Double>, RbfOptions) Creates a radial basis function (RBF) interpolator for scattered N-dimensional data.
ScatteredRbfInterpolator(Matrix<Double>, Vector<Double>, RbfOptions) Creates a radial basis function (RBF) interpolator for scattered N-dimensional data.
ScatteredRbfInterpolator(Double[], Double[], Double[], RbfOptions) Creates a radial basis function (RBF) interpolator for scattered 2D data using array inputs.
ScatteredRbfInterpolator(Vector<Double>, Vector<Double>, Vector<Double>, RbfOptions) Creates a radial basis function (RBF) interpolator for scattered 2D data.
ScatteredRbfInterpolator(Double[], Double[], Double[], Double[], RbfOptions) Creates a radial basis function (RBF) interpolator for scattered 3D data using array inputs.
ScatteredRbfInterpolator(Vector<Double>, Vector<Double>, Vector<Double>, Vector<Double>, RbfOptions) Creates a radial basis function (RBF) interpolator for scattered 3D data.

ScatteredRbfInterpolator(Double[,], Double[], RbfOptions)

Creates a radial basis function (RBF) interpolator for scattered N-dimensional data.
C# 
public static RbfSurface ScatteredRbfInterpolator(
	double[,] points,
	double[] values,
	RbfOptions? rbfOptions = null
)

Parameters

points  Double[2]
A 2D array where each row represents a sample point. Shape: (nPoints, dimension).
values  Double[]
An array of function values at each sample point. Length: nPoints.
rbfOptions  RbfOptions  (Optional)
Options for RBF interpolation. If null, default options are used.

Return Value

RbfSurface
A RbfSurface that interpolates the scattered data using RBF.

Remarks

This method creates a smooth surface that exactly passes through all data points (when regularization is zero). RBF interpolation works in any number of dimensions N ≥ 1.

Construction cost is O(N³) where N is the number of points, and evaluation cost is O(N) per query point.

ScatteredRbfInterpolator(IReadOnlyList<Vector<Double>>, Vector<Double>, RbfOptions)

Creates a radial basis function (RBF) interpolator for scattered N-dimensional data.
C# 
public static RbfSurface ScatteredRbfInterpolator(
	IReadOnlyList<Vector<double>> points,
	Vector<double> values,
	RbfOptions? rbfOptions = null
)

Parameters

points  IReadOnlyList<Vector<Double>>
A collection of vectors, where each vector represents a sample point.
values  Vector<Double>
A vector of function values at each sample point.
rbfOptions  RbfOptions  (Optional)
Options for RBF interpolation. If null, default options are used.

Return Value

RbfSurface
A RbfSurface that interpolates the scattered data using RBF.

Remarks

This method creates a smooth surface that exactly passes through all data points (when regularization is zero). All points in points must have the same dimension.

Construction cost is O(N³) where N is the number of points, and evaluation cost is O(N) per query point.

ScatteredRbfInterpolator(Matrix<Double>, Vector<Double>, RbfOptions)

Creates a radial basis function (RBF) interpolator for scattered N-dimensional data.
C# 
public static RbfSurface ScatteredRbfInterpolator(
	Matrix<double> points,
	Vector<double> values,
	RbfOptions? rbfOptions = null
)

Parameters

points  Matrix<Double>
A matrix where each row represents a sample point. Shape: (nPoints, dimension).
values  Vector<Double>
A vector of function values at each sample point. Length: nPoints.
rbfOptions  RbfOptions  (Optional)
Options for RBF interpolation. If null, default options are used.

Return Value

RbfSurface
A RbfSurface that interpolates the scattered data using RBF.

Remarks

This method creates a smooth surface that exactly passes through all data points (when regularization is zero). RBF interpolation works in any number of dimensions N ≥ 1.

The form of the interpolant depends on the kernel type:

  • Strictly positive definite (PD) kernels (Gaussian, Multiquadric, InverseMultiquadric, InverseQuadratic): Standard RBF interpolation without polynomial augmentation.
  • Conditionally positive definite (CPD) kernels (ThinPlate, Linear, Cubic, Quintic): RBF interpolation with automatic polynomial augmentation. An affine polynomial tail is added to ensure well-posedness and to guarantee exact reproduction of linear functions.

Construction cost is O(N³) where N is the number of points, and evaluation cost is O(N) per query point.

ScatteredRbfInterpolator(Double[], Double[], Double[], RbfOptions)

Creates a radial basis function (RBF) interpolator for scattered 2D data using array inputs.
C# 
public static RbfSurface ScatteredRbfInterpolator(
	double[] x,
	double[] y,
	double[] values,
	RbfOptions? rbfOptions = null
)

Parameters

x  Double[]
The x-coordinates of the scattered points.
y  Double[]
The y-coordinates of the scattered points.
values  Double[]
The function values at each scattered point.
rbfOptions  RbfOptions  (Optional)
Options for RBF interpolation. If null, default options are used.

Return Value

RbfSurface
A RbfSurface that performs 2D scattered RBF interpolation.

ScatteredRbfInterpolator(Vector<Double>, Vector<Double>, Vector<Double>, RbfOptions)

Creates a radial basis function (RBF) interpolator for scattered 2D data.
C# 
public static RbfSurface ScatteredRbfInterpolator(
	Vector<double> x,
	Vector<double> y,
	Vector<double> values,
	RbfOptions? rbfOptions = null
)

Parameters

x  Vector<Double>
The x-coordinates of the scattered points.
y  Vector<Double>
The y-coordinates of the scattered points.
values  Vector<Double>
The function values at each scattered point.
rbfOptions  RbfOptions  (Optional)
Options for RBF interpolation. If null, default options are used.

Return Value

RbfSurface
A RbfSurface that performs 2D scattered RBF interpolation.

Remarks

This method creates a smooth surface that exactly passes through all data points (when regularization is zero). RBF interpolation is suitable for 2D scattered data.

ScatteredRbfInterpolator(Double[], Double[], Double[], Double[], RbfOptions)

Creates a radial basis function (RBF) interpolator for scattered 3D data using array inputs.
C# 
public static RbfSurface ScatteredRbfInterpolator(
	double[] x,
	double[] y,
	double[] z,
	double[] values,
	RbfOptions? rbfOptions = null
)

Parameters

x  Double[]
The x-coordinates of the scattered points.
y  Double[]
The y-coordinates of the scattered points.
z  Double[]
The z-coordinates of the scattered points.
values  Double[]
The function values at each scattered point.
rbfOptions  RbfOptions  (Optional)
Options for RBF interpolation. If null, default options are used.

Return Value

RbfSurface
A RbfSurface that performs 3D scattered RBF interpolation.

ScatteredRbfInterpolator(Vector<Double>, Vector<Double>, Vector<Double>, Vector<Double>, RbfOptions)

Creates a radial basis function (RBF) interpolator for scattered 3D data.
C# 
public static RbfSurface ScatteredRbfInterpolator(
	Vector<double> x,
	Vector<double> y,
	Vector<double> z,
	Vector<double> values,
	RbfOptions? rbfOptions = null
)

Parameters

x  Vector<Double>
The x-coordinates of the scattered points.
y  Vector<Double>
The y-coordinates of the scattered points.
z  Vector<Double>
The z-coordinates of the scattered points.
values  Vector<Double>
The function values at each scattered point.
rbfOptions  RbfOptions  (Optional)
Options for RBF interpolation. If null, default options are used.

Return Value

RbfSurface
A RbfSurface that performs 3D scattered RBF interpolation.

Remarks

This method creates a smooth surface that exactly passes through all data points (when regularization is zero). RBF interpolation is suitable for 3D scattered data.

See Also