RbfSurface.Gradient Method

public override void Gradient(
	ReadOnlySpan<double> point,
	Span<double> result
)

Public Overrides Sub Gradient ( 
	point As ReadOnlySpan(Of Double),
	result As Span(Of Double)
)

public:
virtual void Gradient(
	ReadOnlySpan<double> point, 
	Span<double> result
) override

abstract Gradient : 
        point : ReadOnlySpan<float> * 
        result : Span<float> -> unit 
override Gradient : 
        point : ReadOnlySpan<float> * 
        result : Span<float> -> unit 

Parameters

point  ReadOnlySpan<Double>

A read-only span representing the coordinates of the point.

result  Span<Double>

A span to receive the gradient vector.

The gradient of an RBF interpolant is computed as:

∇f(x) = Σᵢ wᵢ φ'(rᵢ) (x - pᵢ) / rᵢ

where rᵢ = ||x - pᵢ|| is the distance to the i-th center, φ'(r) is the derivative of the radial basis function kernel, and wᵢ are the interpolation weights.

For conditionally positive definite (CPD) kernels with polynomial augmentation, the gradient also includes contributions from the polynomial tail.

Reference