Interpolation.RationalInterpolationExtrapolation Method

Evaluates the value and the corresponding error estimate at a given point of the rational interpolation (or extrapolation) function where the function on the denominator and numerator are functions of the same single variable.

public double[] RationalInterpolationExtrapolation(
   double[] tabulationPointsInX,
   double[] functionValuesAtTabulationPoints,
   double pointOfEvaluation
);

Parameters

tabulationPointsInX: An array of points where the function is tabulated.
functionValuesAtTabulationPoints: An array of doubles of the values of the function evaluated at the interpolation points, i.e. functionValuesAtTabulationPoints[i] = f(tabulationPointsInX[i]), where f is the function under consideration.
pointOfEvaluation: The value for which the diagonal rational function is evaluated.

Return Value

An array of length 2, where the first element of the array corresponds to the value of the rational function at the given point and the second elements corresponds to the error estimate.

Remarks

Details

Given an array of tabulation points tabulationPointsInX and the corresponding function values functionValuesAtTabulationPoints, at the point of evaluation, pointOfEvaluation. This method returns an array containing two elements (i.e. of length 2) corresponding to the rational (i.e. quotient of two polynomials) interpolating functions value at the interpolation point pointOfEvaluation, and the corresponding error estimate. That is, the value returned is that of the diagonal rational function, evaluated at the point pointOfEvaluation, which passes through n+1 (=xCoordinates.length) points {(xCoordinates[i], yCoordinates[i]): i = 0,...,n-1}.

Restrictions on the Parameters

The parameters tabulationPointsInX and functionValuesAtTabulationPoints array should each contain at least one element. If these arrays have different lengths the shorter one will be chosen as reference. That is, the longer array will be truncated to the length of the shorter array before the methods is applied.

Form of the Returned Result

The returned results from this methods will be an array of length 2, where the first element of the array corresponds to the value of the rational function at the given point and the second elements corresponds to the error estimate.

Exceptions

Exception Type	Condition
InterpolationException	Thrown when the input values do not meet the requirements mentioned above.