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SmoothingCubicSplineBasespfit1 Method

Fits a cubic smoothing spline to data with relative weighting dy for a given value of the smoothing parameter rho using an algorithm based on that of C.H.Reinsch (1967), Numer. Math. 10, 177-183. The trace of the influence matrix is calculated using an algorithm developed by M.F.hutchinson and F.R.de Hoog (Numer. Math., in press), enabling the generalized cross validation and related statistics to be calculated in order n operations. The arrays a, c, r and t are assumed to have been initialized by the subroutine spint. Overflow and underflow problems are avoided by using p=rho/(1 + rho) and q=1/(1 + rho) instead of rho and by scaling the differences x[i+1] - x[i] by avh. the values in df are assumed to have been scaled so that the sum of their squared values is n. The value in var, when it is non-negative, is assumed to have been scaled to compensate for the scaling of the values in df. The value returned in fun is an estimate of the true mean square when var is non-negative, and is the generalized cross validation when var is negative.

Namespace: Altaxo.Calc.Interpolation
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
protected static void spfit1(
	double[] x,
	double avh,
	double[] dy,
	int n,
	double rho,
	out double p,
	out double q,
	out double fun,
	double var,
	double[] stat,
	double[] a,
	double[][] C,
	int ic,
	double[][] R,
	double[][] T,
	double[] u,
	double[] v
)

Parameters

x  Double
Abscissae values of the data points.
avh  Double
Scaling parameter for the x-intervals.
dy  Double

[Missing <param name="dy"/> documentation for "M:Altaxo.Calc.Interpolation.SmoothingCubicSplineBase.spfit1(System.Double[],System.Double,System.Double[],System.Int32,System.Double,System.Double@,System.Double@,System.Double@,System.Double,System.Double[],System.Double[],System.Double[][],System.Int32,System.Double[][],System.Double[][],System.Double[],System.Double[])"]

n  Int32
Number of data points.
rho  Double
Smooting parameter (0.. Infinity).
p  Double
Is equal to rho/(1 + rho).
q  Double
Is equal to 1/(1 + rho).
fun  Double
Estimate of the true mean square when var is non-negative, and is the generalized cross validation when var is negative.
var  Double
Variance of the ordinate values of the data points (if known), or a negative value (if unkown).
stat  Double
Array holding some statistical values on return.
a  Double
Spline coefficients of order 0, i.e. the ordinate values of the spline (at the same abscissae values as the original data points).
C  Double
Spline coefficients of order 1, 2 and 3.
ic  Int32
Number of coefficents of order 1,2 and 3. Is one less the number of data points.
R  Double
Work array.
T  Double
Work array.
u  Double
Work array.
v  Double
Work array.
See Also