GammaMnsFunction.java

/* Copyright 2002-2020 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,
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 * See the License for the specific language governing permissions and
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package org.orekit.propagation.semianalytical.dsst.utilities;

import java.util.Arrays;

import org.hipparchus.fraction.BigFraction;
import org.hipparchus.util.FastMath;

/** Compute the &Gamma;<sup>m</sup><sub>n,s</sub>(γ) function from equation 2.7.1-(13).
 *
 *  @author Romain Di Costanzo
 */
public class GammaMnsFunction {

    /** Factorial ratios. */
    private static double[] PRECOMPUTED_RATIOS;

    /** Factorial ratios. */
    private final double[] ratios;

    /** Storage array. */
    private final double[] values;

    /** 1 + I * γ. */
    private final double opIg;

    /** I = +1 for a prograde orbit, -1 otherwise. */
    private final int    I;

    /** Simple constructor.
     *  @param nMax max value for n
     *  @param gamma γ
     *  @param I retrograde factor
     */
    public GammaMnsFunction(final int nMax, final double gamma, final int I) {
        final int size = (nMax + 1) * (nMax + 2) * (4 * nMax + 3) / 6;
        this.values = new double[size];
        this.ratios = getRatios(nMax, size);
        Arrays.fill(values, Double.NaN);
        this.opIg   = 1. + I * gamma;
        this.I      = I;
    }

    /** Compute the array index.
     *  @param m m
     *  @param n n
     *  @param s s
     *  @return index for element m, n, s
     */
    private static int index(final int m, final int n, final int s) {
        return n * (n + 1) * (4 * n - 1) / 6 + // index for 0, n, 0
               m * (2 * n + 1) +               // index for m, n, 0
               s + n;                          // index for m, n, s
    }

    /** Get the ratios for the given size.
     * @param nMax max value for n
     * @param size ratio size array
     * @return factorial ratios
     */
    private static double[] getRatios(final int nMax, final int size) {
        synchronized (GammaMnsFunction.class) {
            if (PRECOMPUTED_RATIOS == null || PRECOMPUTED_RATIOS.length < size) {
                // we need to compute a larger reference array

                final BigFraction[] bF = new BigFraction[size];
                for (int n = 0; n <= nMax; ++n) {

                    // populate ratios for s = 0
                    bF[index(0, n, 0)] = BigFraction.ONE;
                    for (int m = 1; m <= n; ++m) {
                        bF[index(m, n, 0)] = bF[index(m - 1, n, 0)].multiply(n + m).divide(n - (m - 1));
                    }

                    // populate ratios for s != 0
                    for (int absS = 1; absS <= n; ++absS) {
                        for (int m = 0; m <= n; ++m) {
                            bF[index(m, n, +absS)] = bF[index(m, n, absS - 1)].divide(n + absS).multiply(n - (absS - 1));
                            bF[index(m, n, -absS)] = bF[index(m, n, absS)];
                        }
                    }

                }

                // convert to double
                PRECOMPUTED_RATIOS = new double[size];
                for (int i = 0; i < bF.length; ++i) {
                    PRECOMPUTED_RATIOS[i] = bF[i].doubleValue();
                }

            }
            return PRECOMPUTED_RATIOS;
        }
    }

    /** Get &Gamma; function value.
     *  @param m m
     *  @param n n
     *  @param s s
     *  @return &Gamma;<sup>m</sup><sub>n, s</sub>(γ)
     */
    public double getValue(final int m, final int n, final int s) {
        final int i = index(m, n, s);
        if (Double.isNaN(values[i])) {
            if (s <= -m) {
                values[i] = (((m - s) & 0x1) == 0 ? +1 : -1) * FastMath.scalb(FastMath.pow(opIg, -I * m), s);
            } else if (s <= m) {
                values[i] = (((m - s) & 0x1) == 0 ? +1 : -1) * FastMath.scalb(FastMath.pow(opIg, I * s), -m) * ratios[i];
            } else {
                values[i] = FastMath.scalb(FastMath.pow(opIg, I * m), -s);
            }
        }
        return values[i];
    }

    /** Get &Gamma; function derivative.
     * @param m m
     * @param n n
     * @param s s
     * @return d&Gamma;<sup>m</sup><sub>n,s</sub>(γ)/dγ
     */
    public double getDerivative(final int m, final int n, final int s) {
        double res = 0.;
        if (s <= -m) {
            res = -m * I * getValue(m, n, s) / opIg;
        } else if (s >= m) {
            res =  m * I * getValue(m, n, s) / opIg;
        } else {
            res =  s * I * getValue(m, n, s) / opIg;
        }
        return res;
    }

}