LegendrePolynomials.java

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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];
    }

}