/**
* @param pp
* @param xKeys
* @return Second derivatives of piecewise polynomial functions at xKeys When _dim in
* PiecewisePolynomialResult is greater than 1, i.e., the struct contains multiple piecewise
* polynomials, a row vector of return value corresponds to each piecewise polynomial
*/
public DoubleMatrix2D differentiateTwice(
final PiecewisePolynomialResult pp, final double[] xKeys) {
ArgumentChecker.notNull(pp, "pp");
ArgumentChecker.isFalse(pp.getOrder() < 3, "polynomial degree < 2");
final double[][] coefs = pp.getCoefMatrix().getData();
final double[] knots = pp.getKnots().getData();
final int nKnots = pp.getNumberOfIntervals() + 1;
final int nCoefs = pp.getOrder();
final int dim = pp.getDimensions();
double[][] res = new double[dim * (nKnots - 1)][nCoefs - 2];
for (int i = 0; i < dim * (nKnots - 1); ++i) {
Arrays.fill(res[i], 0.);
}
for (int i = 0; i < dim * (nKnots - 1); ++i) {
for (int j = 0; j < nCoefs - 2; ++j) {
res[i][j] = coefs[i][j] * (nCoefs - j - 1) * (nCoefs - j - 2);
}
}
PiecewisePolynomialResult ppDiff =
new PiecewisePolynomialResult(
new DoubleMatrix1D(knots), DoubleMatrix2D.noCopy(res), nCoefs - 1, pp.getDimensions());
return evaluate(ppDiff, xKeys);
}
/**
* @param pp PiecewisePolynomialResult
* @param initialKey
* @param xKeys
* @return Integral of piecewise polynomial between initialKey and xKeys
*/
public DoubleMatrix1D integrate(
final PiecewisePolynomialResult pp, final double initialKey, final double[] xKeys) {
ArgumentChecker.notNull(pp, "pp");
ArgumentChecker.notNull(xKeys, "xKeys");
ArgumentChecker.isFalse(Double.isNaN(initialKey), "initialKey containing NaN");
ArgumentChecker.isFalse(Double.isInfinite(initialKey), "initialKey containing Infinity");
ArgumentChecker.isTrue(pp.getDimensions() == 1, "Dimension should be 1");
final double[] knots = pp.getKnots().getData();
final int nCoefs = pp.getOrder();
final int nKnots = pp.getNumberOfIntervals() + 1;
final double[][] coefMatrix = pp.getCoefMatrix().getData();
double[][] res = new double[nKnots - 1][nCoefs + 1];
for (int i = 0; i < nKnots - 1; ++i) {
Arrays.fill(res[i], 0.);
}
for (int i = 0; i < nKnots - 1; ++i) {
for (int j = 0; j < nCoefs; ++j) {
res[i][j] = coefMatrix[i][j] / (nCoefs - j);
}
}
double[] constTerms = new double[nKnots - 1];
Arrays.fill(constTerms, 0.);
int indicator = 0;
if (initialKey <= knots[1]) {
indicator = 0;
} else {
for (int i = 1; i < nKnots - 1; ++i) {
if (knots[i] < initialKey) {
indicator = i;
}
}
}
double sum = getValue(res[indicator], initialKey, knots[indicator]);
for (int i = indicator; i < nKnots - 2; ++i) {
constTerms[i + 1] = constTerms[i] + getValue(res[i], knots[i + 1], knots[i]) - sum;
sum = 0.;
}
constTerms[indicator] = -getValue(res[indicator], initialKey, knots[indicator]);
for (int i = indicator - 1; i > -1; --i) {
constTerms[i] = constTerms[i + 1] - getValue(res[i], knots[i + 1], knots[i]);
}
for (int i = 0; i < nKnots - 1; ++i) {
res[i][nCoefs] = constTerms[i];
}
final PiecewisePolynomialResult ppInt =
new PiecewisePolynomialResult(
new DoubleMatrix1D(knots), DoubleMatrix2D.noCopy(res), nCoefs + 1, 1);
return new DoubleMatrix1D(evaluate(ppInt, xKeys).getData()[0]);
}