com.opengamma.analytics.math.function.special.OrthonormalHermitePolynomialFunction.java Source code

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Here is the source code for com.opengamma.analytics.math.function.special.OrthonormalHermitePolynomialFunction.java

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/**
 * 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;
    }
}