@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]);
}
// -------------------------------------------------------------------------
@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 DoubleArray doParameterSensitivity(double xValue) {
int lowerIndex = lowerBoundIndex(xValue, xValues);
int higherIndex = lowerIndex + 1;
int n = xValues.length;
double[] result = new double[n];
// at start of curve
if (lowerIndex == 0) {
double[] temp = quadraticSensitivities(xValues, xValue, 1);
result[0] = temp[0];
result[1] = temp[1];
result[2] = temp[2];
return DoubleArray.ofUnsafe(result);
}
// at end of curve
if (higherIndex == intervalCount) {
double[] temp = quadraticSensitivities(xValues, xValue, n - 2);
result[n - 3] = temp[0];
result[n - 2] = temp[1];
result[n - 1] = temp[2];
return DoubleArray.ofUnsafe(result);
}
// at last node
if (lowerIndex == intervalCount) {
result[n - 1] = 1;
return DoubleArray.ofUnsafe(result);
}
double[] temp1 = quadraticSensitivities(xValues, xValue, lowerIndex);
double[] temp2 = quadraticSensitivities(xValues, xValue, higherIndex);
double w =
WEIGHT_FUNCTION.getWeight(
(xValues[higherIndex] - xValue) / (xValues[higherIndex] - xValues[lowerIndex]));
result[lowerIndex - 1] = w * temp1[0];
result[lowerIndex] = w * temp1[1] + (1 - w) * temp2[0];
result[higherIndex] = w * temp1[2] + (1 - w) * temp2[1];
result[higherIndex + 1] = (1 - w) * temp2[2];
return DoubleArray.ofUnsafe(result);
}