LegendrePolynomials.java
/* Copyright 2002-2022 CS GROUP
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* this work for additional information regarding copyright ownership.
* CS licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
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package org.orekit.utils;
import org.hipparchus.util.CombinatoricsUtils;
import org.hipparchus.util.FastMath;
/**
* Computes the P<sub>nm</sub>(t) coefficients.
* <p>
* The computation of the Legendre polynomials is performed following:
* Heiskanen and Moritz, Physical Geodesy, 1967, eq. 1-62
* </p>
* @since 11.0
* @author Bryan Cazabonne
*/
public class LegendrePolynomials {
/** Array for the Legendre polynomials. */
private double[][] pCoef;
/** Create Legendre polynomials for the given degree and order.
* @param degree degree of the spherical harmonics
* @param order order of the spherical harmonics
* @param t argument for polynomials calculation
*/
public LegendrePolynomials(final int degree, final int order,
final double t) {
// Initialize array
this.pCoef = new double[degree + 1][order + 1];
final double t2 = t * t;
for (int n = 0; n <= degree; n++) {
// m shall be <= n (Heiskanen and Moritz, 1967, pp 21)
for (int m = 0; m <= FastMath.min(n, order); m++) {
// r = int((n - m) / 2)
final int r = (int) (n - m) / 2;
double sum = 0.;
for (int k = 0; k <= r; k++) {
final double term = FastMath.pow(-1.0, k) * CombinatoricsUtils.factorialDouble(2 * n - 2 * k) /
(CombinatoricsUtils.factorialDouble(k) * CombinatoricsUtils.factorialDouble(n - k) *
CombinatoricsUtils.factorialDouble(n - m - 2 * k)) *
FastMath.pow(t, n - m - 2 * k);
sum = sum + term;
}
pCoef[n][m] = FastMath.pow(2, -n) * FastMath.pow(1.0 - t2, 0.5 * m) * sum;
}
}
}
/** Return the coefficient P<sub>nm</sub>.
* @param n index
* @param m index
* @return The coefficient P<sub>nm</sub>
*/
public double getPnm(final int n, final int m) {
return pCoef[n][m];
}
}