CrossValidatedCubicSpline Class

SystemObject
  Altaxo.Calc.InterpolationCurveBase
    Altaxo.Calc.InterpolationSmoothingCubicSplineBase
      Altaxo.Calc.InterpolationCrossValidatedCubicSpline

public class CrossValidatedCubicSpline : SmoothingCubicSplineBase, 
	IInterpolationFunction, IInterpolationCurve

If the error standard deviation is known, it should be supplied to the routine in 'var'. The degree of smoothing is then determined by minimizing an unbiased estimate of the true mean square error. On the other hand, if the error standard deviation is not known, 'var' should be set to -1.0. The routine then determines the degree of smoothing by minimizing the generalized cross validation. This is asymptotically the same as minimizing the true mean square error (see reference 1). In this case, an estimate of the error standard deviation is returned in 'var' which may be compared with any a priori approximate estimates. In either case, an estimate of the true mean square error is returned in 'wk[4]'. This estimate, however, depends on the error standard deviation estimate, and should only be accepted if the error standard deviation estimate is reckoned to be correct. Bayesian estimates of the standard error of each smoothed data value are returned in the array 'se' (if a non null vector is given for the paramenter 'se' - use (double*)0 if you don't want estimates). These also depend on the error standard deviation estimate and should only be accepted if the error standard deviation estimate is reckoned to be correct. See reference 4. The number of arithmetic operations and the amount of storage required by the routine are both proportional to 'n', so that very large data sets may be analysed. The data points do not have to be equally spaced or uniformly weighted. The residual and the spline coefficients are calculated in the manner described in reference 3, while the trace and various statistics, including the generalized cross validation, are calculated in the manner described in reference 2. When 'var' is known, any value of 'n' greater than 2 is acceptable. It is advisable, however, for 'n' to be greater than about 20 when 'var' is unknown. If the degree of smoothing done by this function when 'var' is unknown is not satisfactory, the user should try specifying the degree of smoothing by setting 'var' to a reasonable value.