/**
* 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 OrthonormalHermitePolynomialFunction extends OrthogonalPolynomialFunctionGenerator {
private static final double C1 = 1. / Math.pow(Math.PI, 0.25);
private static final double C2 = Math.sqrt(2) * C1;
private static final RealPolynomialFunction1D F0 = new RealPolynomialFunction1D(new double[] {C1});
private static final RealPolynomialFunction1D DF1 = new RealPolynomialFunction1D(new double[] {C2});
@Override
public DoubleFunction1D[] getPolynomials(final int n) {
Validate.isTrue(n >= 0);
final DoubleFunction1D[] polynomials = new DoubleFunction1D[n + 1];
for (int i = 0; i <= n; i++) {
if (i == 0) {
polynomials[i] = F0;
} else if (i == 1) {
polynomials[i] = polynomials[0].multiply(Math.sqrt(2)).multiply(getX());
} else {
polynomials[i] = polynomials[i - 1].multiply(getX()).multiply(Math.sqrt(2. / i)).subtract(polynomials[i - 2].multiply(Math.sqrt((i - 1.) / i)));
}
}
return polynomials;
}
@Override
public Pair<DoubleFunction1D, DoubleFunction1D>[] getPolynomialsAndFirstDerivative(final int n) {
Validate.isTrue(n >= 0);
@SuppressWarnings("unchecked")
final Pair<DoubleFunction1D, DoubleFunction1D>[] polynomials = new Pair[n + 1];
DoubleFunction1D p, dp, p1, p2;
final double divisor = Math.sqrt(2 * n);
final double sqrt2 = Math.sqrt(2);
final DoubleFunction1D x = getX();
for (int i = 0; i <= n; i++) {
if (i == 0) {
polynomials[i] = Pair.of((DoubleFunction1D) F0, getZero());
} else if (i == 1) {
polynomials[i] = Pair.of(polynomials[0].getFirst().multiply(sqrt2).multiply(x), (DoubleFunction1D) DF1);
} else {
p1 = polynomials[i - 1].getFirst();
p2 = polynomials[i - 2].getFirst();
p = p1.multiply(x).multiply(Math.sqrt(2. / i)).subtract(p2.multiply(Math.sqrt((i - 1.) / i)));
dp = p1.multiply(divisor);
polynomials[i] = Pair.of(p, dp);
}
}
return polynomials;
}
}