SmoothCubicSpline Class

SystemObject
  CenterSpace.NMath.CoreOneVariableFunction
    CenterSpace.NMath.CoreTabulatedFunction
      CenterSpace.NMath.CoreSmoothCubicSpline

[SerializableAttribute]
public class SmoothCubicSpline : TabulatedFunction

<SerializableAttribute>
Public Class SmoothCubicSpline
	Inherits TabulatedFunction

[SerializableAttribute]
public ref class SmoothCubicSpline : public TabulatedFunction

[<SerializableAttribute>]
type SmoothCubicSpline = 
    class
        inherit TabulatedFunction
    end

Gives the approximate values y[i] = g(x[i]) + e(i) of a function g and error e, the smoothing spline tries to recover the function g by constructing a function f that minimizes the sum square error and curvature: p*sum(y[i] - f(x[i])^2/dy[i] + (1-p)*int[(f'')^2] where p is a smoothing factor between 1 and 0, dy[i] is the variance in each y[i] (defaults to 1 if not specified), and int stands for integration. The first term in the above expression is the sum squared error of the approximating function f, and the second term is its curvature. The smoothing factor, p, determines how much weight is given to minimizing the sum square error balanced against minimizing the curvature. When p = 1 only the sum square error is minimized and the result is a traditional cubic spline. When p = 0 only the curvature is minimized and the result is a straight line which has 0 curvature.