Smoothing |
Calculates a smoothing cubic spline, whose smoothness is determined by the property Smoothness.
Inheritance HierarchySystemObject
Altaxo.Calc.InterpolationCurveBase
Altaxo.Calc.InterpolationSmoothingCubicSplineBase
Altaxo.Calc.InterpolationSmoothingCubicSpline
Altaxo.Calc.InterpolationCurveBase
Altaxo.Calc.InterpolationSmoothingCubicSplineBase
Altaxo.Calc.InterpolationSmoothingCubicSpline
Namespace: Altaxo.Calc.Interpolation
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
SyntaxC#
public class SmoothingCubicSpline : SmoothingCubicSplineBase, IInterpolationFunction, IInterpolationCurve
The SmoothingCubicSpline type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | SmoothingCubicSpline | Create an instance of SmoothingCubicSpline with a default value for Smoothness of 1. |
Properties| Name | Description | |
|---|---|---|
 | CalculateStandardErrorEstimates |
If true, standard error estimates are calculated and provided in ErrorEstimate.
(Inherited from SmoothingCubicSplineBase) |
| CheckArguments |
If true, the array given as arguments are checked.
(Inherited from SmoothingCubicSplineBase) |
| Coefficient0 |
Returns the spline coefficient of order 0. This are the splined y values at the positions given by x.
(Inherited from SmoothingCubicSplineBase) |
| Coefficient1 |
Returns the spline coefficient of order 1 (linear term).
(Inherited from SmoothingCubicSplineBase) |
| Coefficient2 |
Returns the spline coefficient of order 2 (quadratic term).
(Inherited from SmoothingCubicSplineBase) |
| Coefficient3 |
Returns the spline coefficient of order 2 (cubic term).
(Inherited from SmoothingCubicSplineBase) |
| CombineNeighbouringPoints |
If true, points with x values that are very similar are combined into one point, which helds the average value of x and y
(Inherited from SmoothingCubicSplineBase) |
| ErrorEstimate |
Returns the error estimates of the y points.
(Inherited from SmoothingCubicSplineBase) |
| ErrorStandardDeviation |
If the error standard deviation of the provided points is unknown, set this value to -1. Then a cross validating cubic spline is fitted to the data.
If the error standard deviation is known and is equal for all points, set this value to the error standard deviation of the points.
If the error standard deviation is known and different for each point, set this value to 1, and provide the error standard deviation for each point
by calling Interpolate(IReadOnlyListDouble, IReadOnlyListDouble, Double, IReadOnlyListDouble).
(Inherited from SmoothingCubicSplineBase) |
| EstimatedDegreesOfFreedom |
Estimate of the number of degrees of
freedom of the residual sum of squares
which reduces to the usual value of n-2
when a least squares regression line
was calculated.
(Inherited from SmoothingCubicSplineBase) |
| EstimatedErrorVariance |
Estimate of the error variance.
The value coincides with the output value of var if var is negative on input.
It is calculated with the unscaled values of the df[i] to facilitate
comparisons with a priori variance estimates.
(Inherited from SmoothingCubicSplineBase) |
| EstimatedTrueMeanSquareError |
Estimate of the true mean square error at the data points.
(Inherited from SmoothingCubicSplineBase) |
| GeneralizedCrossValidation |
Generalized cross validation.
(Inherited from SmoothingCubicSplineBase) |
| MeanSquareOfInputStandardDeviation |
Mean square value of the standard deviations in dy[i] (if they were provided).
The values of GeneralizedCrossValidation, MeanSquareResidual and EstimatedTrueMeanSquareError
are calculated with the dy[i] scaled to have a mean square value 1.
The unscaled values of GeneralizedCrossValidation, MeanSquareResidual and EstimatedTrueMeanSquareError
may be calculated by dividing by this value.
(Inherited from SmoothingCubicSplineBase) |
| MeanSquareResidual |
Mean square residual.
(Inherited from SmoothingCubicSplineBase) |
| SmoothingParameter |
Smoothing parameter = rho/(rho+1), that varies between 0 (not smoothed) and 1 (full smoothed).
If the value is 0 (rho=0) an interpolating natural cubic spline has been calculated.
If the value is 1 (rho=infinite) a least squares regression line has been calculated.
(Inherited from SmoothingCubicSplineBase) |
| Smoothness | Get/sets the smoothness parameter. Must be in the interval [0,Infinity], where a value of 0 means no smoothing (evaluation of a cubic spline), while a value of Infinity means evaluation of a regression. |
Methods| Name | Description | |
|---|---|---|
| CubicSplineCoefficients |
Calculate the spline coefficients y2(i) and y3(i) for a natural cubic
spline, given the abscissa x(i), the ordinate y(i), and the 1st
derivative y1(i).
(Inherited from CurveBase) |
| CubicSplineHorner |
Return the interpolation value P(u) for a piecewise cubic curve determined
by the abscissa vector x, the ordinate vector y, the 1st derivative
vector y1, the 2nd derivative vector y2, and the 3rd derivative vector y3,
using the Horner scheme.
(Inherited from CurveBase) |
| CubicSplineHorner1stDerivative | (Inherited from CurveBase) |
| Equals | Determines whether the specified object is equal to the current object. (Inherited from Object) |
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
| GetCurvePoints |
Get curve points to draw an interpolation curve between the abscissa values xlo and xhi.
It calls the virtual methods MpCurveBase::GetXOfU() and GetYOfU() to obtain the
interpolation values. Note, that before method DrawCurve() can be called
the method Interpolate() must have been called. Otherwise, not interpolation
is available.
(Inherited from CurveBase) |
| GetHashCode | Serves as the default hash function. (Inherited from Object) |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| GetXOfU | (Inherited from SmoothingCubicSplineBase) |
| GetY1stDerivativeOfX | (Inherited from SmoothingCubicSplineBase) |
| GetYOfU | (Inherited from SmoothingCubicSplineBase) |
| GetYOfX | (Inherited from SmoothingCubicSplineBase) |
| Interpolate(IReadOnlyListDouble, IReadOnlyListDouble) |
Evaluates either a cross validated cubic spline (if ErrorStandardDeviation is negative,
or a smoothing cubic spline (if ErrorStandardDeviation is greater than or equal to zero).
(Inherited from SmoothingCubicSplineBase) |
| Interpolate(IReadOnlyListDouble, IReadOnlyListDouble, Double) |
Evaluates either a cross validated cubic spline (standardDeviation set to a negative value),
or a smoothing cubic spline (standardDeviation set to a non-negative value).
(Inherited from SmoothingCubicSplineBase) |
| Interpolate(IReadOnlyListDouble, IReadOnlyListDouble, Double, IReadOnlyListDouble) |
Evaluates either a cross validated cubic spline (standardDeviation set to a negative value),
or a smoothing cubic spline (standardDeviation set to a non-negative value).
(Inherited from SmoothingCubicSplineBase) |
| InterpolationKernel | (Overrides SmoothingCubicSplineBaseInterpolationKernel(Double, Double, Double, Int32, Double, Double, Int32, Double, Int32, Double, Double, Double, Double, Double, Int32)) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
| NotExecutedException | (Inherited from SmoothingCubicSplineBase) |
| Parametrize |
Curve length parametrization. Returns the accumulated "distances"
between the points (x(i),y(i)) and (x(i+1),y(i+1)) in t(i+1)
for i = lo ... hi. t(lo) = 0.0 always.
(Inherited from CurveBase) |
| ToString | Returns a string that represents the current object. (Inherited from Object) |
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See Also