/**
* Copyright (C) 2009 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.math.function.special;
import org.apache.commons.lang.Validate;
import com.opengamma.analytics.math.function.DoubleFunction1D;
import com.opengamma.analytics.math.function.RealPolynomialFunction1D;
import com.opengamma.util.tuple.Pair;
/**
*
*/
public class JacobiPolynomialFunction extends OrthogonalPolynomialFunctionGenerator {
@Override
public DoubleFunction1D[] getPolynomials(final int n) {
throw new UnsupportedOperationException("Need values for alpha and beta for Jacobi polynomial function generation");
}
@Override
public Pair<DoubleFunction1D, DoubleFunction1D>[] getPolynomialsAndFirstDerivative(final int n) {
throw new UnsupportedOperationException("Need values for alpha and beta for Jacobi polynomial function generation");
}
public DoubleFunction1D[] getPolynomials(final int n, final double alpha, final double beta) {
Validate.isTrue(n >= 0);
final DoubleFunction1D[] polynomials = new DoubleFunction1D[n + 1];
for (int i = 0; i <= n; i++) {
if (i == 0) {
polynomials[i] = getOne();
} else if (i == 1) {
polynomials[i] = new RealPolynomialFunction1D(new double[] {(alpha - beta) / 2, (alpha + beta + 2) / 2});
} else {
final int j = i - 1;
polynomials[i] = (polynomials[j].multiply(getB(alpha, beta, j)).add(polynomials[j].multiply(getX()).multiply(getC(alpha, beta, j)).add(polynomials[j - 1].multiply(getD(alpha, beta, j)))))
.divide(getA(alpha, beta, j));
}
}
return polynomials;
}
public Pair<DoubleFunction1D, DoubleFunction1D>[] getPolynomialsAndFirstDerivative(final int n, final double alpha, final double beta) {
Validate.isTrue(n >= 0);
@SuppressWarnings("unchecked")
final Pair<DoubleFunction1D, DoubleFunction1D>[] polynomials = new Pair[n + 1];
DoubleFunction1D p, dp, p1, p2;
for (int i = 0; i <= n; i++) {
if (i == 0) {
polynomials[i] = Pair.of(getOne(), getZero());
} else if (i == 1) {
final double a1 = (alpha + beta + 2) / 2;
polynomials[i] = Pair.of((DoubleFunction1D) new RealPolynomialFunction1D(new double[] {(alpha - beta) / 2, a1}), (DoubleFunction1D) new RealPolynomialFunction1D(new double[] {a1}));
} else {
final int j = i - 1;
p1 = polynomials[j].getFirst();
p2 = polynomials[j - 1].getFirst();
final DoubleFunction1D temp1 = p1.multiply(getB(alpha, beta, j));
final DoubleFunction1D temp2 = p1.multiply(getX()).multiply(getC(alpha, beta, j));
final DoubleFunction1D temp3 = p2.multiply(getD(alpha, beta, j));
p = (temp1.add(temp2).add(temp3)).divide(getA(alpha, beta, j));
dp = p.derivative();
polynomials[i] = Pair.of(p, dp);
}
}
return polynomials;
}
private double getA(final double alpha, final double beta, final int n) {
return 2 * (n + 1) * (n + alpha + beta + 1) * (2 * n + alpha + beta);
}
private double getB(final double alpha, final double beta, final int n) {
return (2 * n + alpha + beta + 1) * (alpha * alpha - beta * beta);
}
private double getC(final double alpha, final double beta, final int n) {
final double x = 2 * n + alpha + beta;
return x * (x + 1) * (x + 2);
}
private double getD(final double alpha, final double beta, final int n) {
return -2 * (n + alpha) * (n + beta) * (2 * n + alpha + beta + 2);
}
}