/**
* 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.util.tuple.Pair;
/**
*
*/
public class LegendrePolynomialFunction extends OrthogonalPolynomialFunctionGenerator {
@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] = getOne();
} else if (i == 1) {
polynomials[i] = getX();
} else {
polynomials[i] = (polynomials[i - 1].multiply(getX()).multiply(2 * i - 1).subtract(polynomials[i - 2].multiply(i - 1))).multiply(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;
for (int i = 0; i <= n; i++) {
if (i == 0) {
polynomials[i] = Pair.of(getOne(), getZero());
} else if (i == 1) {
polynomials[i] = Pair.of(getX(), getOne());
} else {
p = (polynomials[i - 1].getFirst().multiply(getX()).multiply(2 * i - 1).subtract(polynomials[i - 2].getFirst().multiply(i - 1))).multiply(1. / i);
dp = p.derivative();
polynomials[i] = Pair.of(p, dp);
}
}
return polynomials;
}
}