/**
* 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 LaguerrePolynomialFunction extends OrthogonalPolynomialFunctionGenerator {
private static final DoubleFunction1D F1 = new RealPolynomialFunction1D(new double[] {1, -1});
private static final DoubleFunction1D DF1 = new RealPolynomialFunction1D(new double[] {-1});
@Override
public DoubleFunction1D[] getPolynomials(final int n) {
return getPolynomials(n, 0);
}
@Override
public Pair<DoubleFunction1D, DoubleFunction1D>[] getPolynomialsAndFirstDerivative(final int n) {
return getPolynomialsAndFirstDerivative(n, 0);
}
public DoubleFunction1D[] getPolynomials(final int n, final double alpha) {
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[] {1 + alpha, -1});
} else {
polynomials[i] = (polynomials[i - 1].multiply(2. * i + alpha - 1).subtract(polynomials[i - 1].multiply(getX())).subtract(polynomials[i - 2].multiply((i - 1. + alpha))).divide(i));
}
}
return polynomials;
}
public Pair<DoubleFunction1D, DoubleFunction1D>[] getPolynomialsAndFirstDerivative(final int n, final double alpha) {
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) {
polynomials[i] = Pair.of(F1, DF1);
} else {
p1 = polynomials[i - 1].getFirst();
p2 = polynomials[i - 2].getFirst();
p = (p1.multiply(2. * i + alpha - 1).subtract(p1.multiply(getX())).subtract(p2.multiply((i - 1. + alpha))).divide(i));
dp = (p.multiply(i).subtract(p1.multiply(i + alpha))).divide(getX());
polynomials[i] = Pair.of(p, dp);
}
}
return polynomials;
}
}