FieldLegendrePolynomials.java
/* Copyright 2002-2022 CS GROUP
* Licensed to CS GROUP (CS) under one or more
* contributor license agreements. See the NOTICE file distributed with
* 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,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.orekit.utils;
import org.hipparchus.Field;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.util.CombinatoricsUtils;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;
/**
* 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 FieldLegendrePolynomials<T extends CalculusFieldElement<T>> {
/** Array for the Legendre polynomials. */
private T[][] 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 FieldLegendrePolynomials(final int degree, final int order,
final T t) {
// Field
final Field<T> field = t.getField();
// Initialize array
this.pCoef = MathArrays.buildArray(field, degree + 1, order + 1);
final T t2 = t.multiply(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;
T sum = field.getZero();
for (int k = 0; k <= r; k++) {
final T term = FastMath.pow(t, n - m - 2 * k).
multiply(FastMath.pow(-1.0, k) * CombinatoricsUtils.factorialDouble(2 * n - 2 * k) /
(CombinatoricsUtils.factorialDouble(k) * CombinatoricsUtils.factorialDouble(n - k) *
CombinatoricsUtils.factorialDouble(n - m - 2 * k)));
sum = sum.add(term);
}
pCoef[n][m] = FastMath.pow(t2.negate().add(1.0), 0.5 * m).multiply(FastMath.pow(2, -n)).multiply(sum);
}
}
}
/** Return the coefficient P<sub>nm</sub>.
* @param n index
* @param m index
* @return The coefficient P<sub>nm</sub>
*/
public T getPnm(final int n, final int m) {
return pCoef[n][m];
}
}