// -------------------------------------------------------------------------
@Override
protected double doInterpolate(double xValue) {
// x-value is less than the x-value of the last node (lowerIndex < intervalCount)
int lowerIndex = lowerBoundIndex(xValue, xValues);
int higherIndex = lowerIndex + 1;
// at start of curve
if (lowerIndex == 0) {
RealPolynomialFunction1D quadratic = quadratics[0];
double x = xValue - xValues[1];
return quadratic.applyAsDouble(x);
}
// at end of curve
if (higherIndex == intervalCount) {
RealPolynomialFunction1D quadratic = quadratics[intervalCount - 2];
double x = xValue - xValues[intervalCount - 1];
return quadratic.applyAsDouble(x);
}
// normal case
RealPolynomialFunction1D quadratic1 = quadratics[lowerIndex - 1];
RealPolynomialFunction1D quadratic2 = quadratics[higherIndex - 1];
double w =
WEIGHT_FUNCTION.getWeight(
(xValues[higherIndex] - xValue) / (xValues[higherIndex] - xValues[lowerIndex]));
return w * quadratic1.applyAsDouble(xValue - xValues[lowerIndex])
+ (1 - w) * quadratic2.applyAsDouble(xValue - xValues[higherIndex]);
}
@Override
protected double doFirstDerivative(double xValue) {
int lowerIndex = lowerBoundIndex(xValue, xValues);
int higherIndex = lowerIndex + 1;
// at start of curve, or only one interval
if (lowerIndex == 0 || intervalCount == 1) {
RealPolynomialFunction1D quadraticFirstDerivative = quadraticsFirstDerivative[0];
double x = xValue - xValues[1];
return quadraticFirstDerivative.applyAsDouble(x);
}
// at end of curve
if (higherIndex >= intervalCount) {
RealPolynomialFunction1D quadraticFirstDerivative =
quadraticsFirstDerivative[intervalCount - 2];
double x = xValue - xValues[intervalCount - 1];
return quadraticFirstDerivative.applyAsDouble(x);
}
RealPolynomialFunction1D quadratic1 = quadratics[lowerIndex - 1];
RealPolynomialFunction1D quadratic2 = quadratics[higherIndex - 1];
RealPolynomialFunction1D quadratic1FirstDerivative =
quadraticsFirstDerivative[lowerIndex - 1];
RealPolynomialFunction1D quadratic2FirstDerivative =
quadraticsFirstDerivative[higherIndex - 1];
double w =
WEIGHT_FUNCTION.getWeight(
(xValues[higherIndex] - xValue) / (xValues[higherIndex] - xValues[lowerIndex]));
return w * quadratic1FirstDerivative.applyAsDouble(xValue - xValues[lowerIndex])
+ (1 - w) * quadratic2FirstDerivative.applyAsDouble(xValue - xValues[higherIndex])
+ (quadratic2.applyAsDouble(xValue - xValues[higherIndex])
- quadratic1.applyAsDouble(xValue - xValues[lowerIndex]))
/ (xValues[higherIndex] - xValues[lowerIndex]);
}