Calculates the second derivatives of the cubic spline interpolation polynomial at the given functions tabulation points when the first derivative at the boundary (equivalently the end points) is given.
functionValuesAtTabulationPoints[i] = f(tabulationPointsInX[i]).functionValuesAtTabulationPoints[i] = f(tabulationPointsInX[i]).tabulationPointsInX[0].tabulatedPointInX[n-1].The values of the second derivatives can be used within CubicSplinePointwisePreEvaluation in order to evaluate the interpolation function at a given point.
Details
Given arrays tabulationPointsInX[0..n-1] and
tabulationPointsInY[0..n-1] containing a tabulated function,
i.e. tabulationPointsInY[i] = f(tabulationPointsInY[i]), with
tabulationPointsInX[0] < tabulationPointsInX[1] < ... < tabulationPointsInX[n-1],
and given values derivativeInterpolationAt0 and derivativeInterpolationAtn_1
for the first derivative of the interpolating function at the points tabulationPointsInX[0]
and tabulationPointsInX[n-1], respectively. This method returns an array
of length n, that contains the second derivatives of the interpolation
function at the tabulation points tabulationPointsInX[i]. If
derivativeInterpolationAt0 and/or derivativeInterpolationAtn_1
are equal to 1030 or larger, then the method sets
the second derivative at the boundary to be zero.
Remarks of this methods application
| Exception Type | Condition |
|---|---|
| InterpolationException | Thrown when the input values do not meet the requirements mentioned above. |
Inter Class | Interpolation Namespace