RBFSmoothing |
Provides a two-dimensional radial basis function (RBF) smoother for scattered (x,y,z) data.
Inheritance HierarchyNamespace: Altaxo.Calc.Interpolation
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3572.0 (4.8.3572.0)
SyntaxC#
public class RBFSmoothingInterpolation2D
The RBFSmoothingInterpolation2D type exposes the following members.
Properties| Name | Description | |
|---|---|---|
 | Count | Gets the number of support points used by this model. |
| Epsilon | Gets the kernel shape parameter (used by some kernels). |
| Kernel | Gets the kernel used by this model. |
| Lambda | Gets the smoothing parameter used during fitting. |
| Tail | Gets the polynomial tail type used by this model. |
Methods| Name | Description | |
|---|---|---|
 | AsFunction | Returns a delegate that evaluates this smoother. |
| Equals | Determines whether the specified object is equal to the current object. (Inherited from Object) |
| Evaluate | Evaluates the fitted smoother at the provided point. |
| EvaluateGradient | Evaluates the gradient of the fitted smoother at the provided point. |
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
 | Fit(IReadOnlyListDouble, IReadOnlyListDouble, IReadOnlyListDouble, RBFSmoothingInterpolation2DKernelKind, Double, Double, RBFSmoothingInterpolation2DPolynomialTail, Boolean) | Fits an RBF smoother to scattered (x,y,z) data. |
| Fit(ReadOnlySpanDouble, ReadOnlySpanDouble, ReadOnlySpanDouble, RBFSmoothingInterpolation2DKernelKind, Double, Double, RBFSmoothingInterpolation2DPolynomialTail, Boolean) | Fits an RBF smoother to scattered (x,y,z) data. |
| GetHashCode | Serves as the default hash function. (Inherited from Object) |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
| ToString | Returns a string that represents the current object. (Inherited from Object) |
Remarks
This implementation fits a model of the form
f(x,y) = p(x,y) + Σ wᵢ φ(‖(x,y)-(xᵢ,yᵢ)‖) using a Tikhonov/"ridge" smoothing term controlled by Lambda.
If the input data contains multiple points with identical (x,y) coordinates, the default behavior is to
collapse such duplicate sites by averaging their z-values before fitting.
Literature:
- M. D. Buhmann, Radial Basis Functions: Theory and Implementations, Cambridge University Press, 2003.
- H. Wendland, Scattered Data Approximation, Cambridge University Press, 2005.
- G. Wahba, Spline Models for Observational Data, SIAM, 1990 (thin-plate smoothing splines).
See Also