/* 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,
   * 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.propagation.semianalytical.dsst.utilities;
  
  import java.util.Map;
  import java.util.TreeMap;
  
  import org.hipparchus.Field;
  import org.hipparchus.RealFieldElement;
  import org.hipparchus.analysis.polynomials.PolynomialFunction;
  import org.hipparchus.analysis.polynomials.PolynomialsUtils;
  import org.hipparchus.complex.Complex;
  import org.hipparchus.exception.NullArgumentException;
  import org.hipparchus.random.MersenneTwister;
  import org.hipparchus.util.CombinatoricsUtils;
  import org.hipparchus.util.Decimal64Field;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.MathArrays;
  import org.junit.Assert;
  import org.junit.Test;
  import org.orekit.errors.OrekitException;
  import org.orekit.propagation.semianalytical.dsst.utilities.CoefficientsFactory.NSKey;
  
  public class CoefficientFactoryTest {
  
      private static final double eps0  = 0.;
      private static final double eps10 = 1e-10;
      private static final double eps12 = 1e-12;
  
      /** Map of the Qns derivatives, for each (n, s) couple. */
      private static Map<NSKey, PolynomialFunction> QNS_MAP = new TreeMap<NSKey, PolynomialFunction>();
  
      @Test
      public void testVns() {
          final int order = 100;
          TreeMap<NSKey, Double> Vns = CoefficientsFactory.computeVns(order);
  
          // Odd terms are null
          for (int i = 0; i < order; i++) {
              for (int j = 0; j < i + 1; j++) {
                  if ((i - j) % 2 != 0) {
                      Assert.assertEquals(0d, Vns.get(new NSKey(i, j)), eps0);
                  }
              }
          }
  
          // Check the first coefficients :
          Assert.assertEquals(1, Vns.get(new NSKey(0, 0)), eps0);
          Assert.assertEquals(0.5, Vns.get(new NSKey(1, 1)), eps0);
          Assert.assertEquals(-0.5, Vns.get(new NSKey(2, 0)), eps0);
          Assert.assertEquals(1 / 8d, Vns.get(new NSKey(2, 2)), eps0);
          Assert.assertEquals(-1 / 8d, Vns.get(new NSKey(3, 1)), eps0);
          Assert.assertEquals(1 / 48d, Vns.get(new NSKey(3, 3)), eps0);
          Assert.assertEquals(3 / 8d, Vns.get(new NSKey(4, 0)), eps0);
          Assert.assertEquals(-1 / 48d, Vns.get(new NSKey(4, 2)), eps0);
          Assert.assertEquals(1 / 384d, Vns.get(new NSKey(4, 4)), eps0);
          Assert.assertEquals(1 / 16d, Vns.get(new NSKey(5, 1)), eps0);
          Assert.assertEquals(-1 / 384d, Vns.get(new NSKey(5, 3)), eps0);
          Assert.assertEquals(1 / 3840d, Vns.get(new NSKey(5, 5)), eps0);
          Assert.assertEquals(Vns.lastKey().getN(), order - 1);
          Assert.assertEquals(Vns.lastKey().getS(), order - 1);
      }
  
      /**
       * Test the direct computation method : the getVmns is using the Vns computation to compute the
       * current element
       */
      @Test
      public void testVmns() {
          Assert.assertEquals(getVmns2(0, 0, 0), CoefficientsFactory.getVmns(0, 0, 0), eps0);
          Assert.assertEquals(getVmns2(0, 1, 1), CoefficientsFactory.getVmns(0, 1, 1), eps0);
          Assert.assertEquals(getVmns2(0, 2, 2), CoefficientsFactory.getVmns(0, 2, 2), eps0);
          Assert.assertEquals(getVmns2(0, 3, 1), CoefficientsFactory.getVmns(0, 3, 1), eps0);
          Assert.assertEquals(getVmns2(0, 3, 3), CoefficientsFactory.getVmns(0, 3, 3), eps0);
          Assert.assertEquals(getVmns2(2, 2, 2), CoefficientsFactory.getVmns(2, 2, 2), eps0);
          final double vmnsp = getVmns2(12, 26, 20);
          Assert.assertEquals(vmnsp,
                              CoefficientsFactory.getVmns(12, 26, 20),
                              FastMath.abs(eps12 * vmnsp));
          final double vmnsm = getVmns2(12, 27, -21);
          Assert.assertEquals(vmnsm,
                              CoefficientsFactory.getVmns(12, 27, -21),
                              Math.abs(eps12 * vmnsm));
      }
  
     /** Error if m > n */
     @Test(expected = OrekitException.class)
     public void testVmnsError() {
         // if m > n
         CoefficientsFactory.getVmns(3, 2, 1);
     }
 
     /**
      * Qns test based on two computation method. As methods are independent, if they give the same
      * results, we assume them to be consistent.
      */
     @Test
     public void testQns() {
         Assert.assertEquals(1., getQnsPolynomialValue(0, 0, 0), 0.);
         // Method comparison :
         final int nmax = 10;
         final int smax = 10;
         final MersenneTwister random = new MersenneTwister(123456789);
         for (int g = 0; g < 1000; g++) {
             final double gamma = random.nextDouble();
             double[][] qns = CoefficientsFactory.computeQns(gamma, nmax, smax);
             for (int n = 0; n <= nmax; n++) {
                 final int sdim = FastMath.min(smax + 2, n);
                 for (int s = 0; s <= sdim; s++) {
                     final double qp = getQnsPolynomialValue(gamma, n, s);
                     Assert.assertEquals(qns[n][s], qp, FastMath.abs(eps10 * qns[n][s]));
                 }
             }
         }
     }
 
     @Test
     public void testQnsField() {
         doTestQnsField(Decimal64Field.getInstance());
     }
 
     /**
      * Qns test based on two computation method. As methods are independent, if they give the same
      * results, we assume them to be consistent.
      */
     private <T extends RealFieldElement<T>> void doTestQnsField(Field<T> field) {
         final T zero = field.getZero();
         Assert.assertEquals(1., getQnsPolynomialValue(0, 0, 0), 0.);
         // Method comparison :
         final int nmax = 10;
         final int smax = 10;
         final MersenneTwister random = new MersenneTwister(123456789);
         for (int g = 0; g < 1000; g++) {
             final T gamma = zero.add(random.nextDouble());
             T[][] qns = CoefficientsFactory.computeQns(gamma, nmax, smax);
             for (int n = 0; n <= nmax; n++) {
                 final int sdim = FastMath.min(smax + 2, n);
                 for (int s = 0; s <= sdim; s++) {
                     final T qp = getQnsPolynomialValue(gamma, n, s);
                     Assert.assertEquals(qns[n][s].getReal(), qp.getReal(), FastMath.abs(qns[n][s].multiply(eps10)).getReal());
                 }
             }
         }
     }
 
     /** Gs and Hs computation test based on 2 independent methods.
      *  If they give same results, we assume them to be consistent.
      */
     @Test
     public void testGsHs() {
         final int s = 50;
         final MersenneTwister random = new MersenneTwister(123456789);
         for (int i = 0; i < 10; i++) {
             final double k = random.nextDouble();
             final double h = random.nextDouble();
             final double a = random.nextDouble();
             final double b = random.nextDouble();
             final double[][] GH = CoefficientsFactory.computeGsHs(k, h, a, b, s);
             for (int j = 1; j < s; j++) {
                 final double[] GsHs = getGsHs(k, h, a, b, j);
                 Assert.assertEquals(GsHs[0], GH[0][j], FastMath.abs(eps12 * GsHs[0]));
                 Assert.assertEquals(GsHs[1], GH[1][j], FastMath.abs(eps12 * GsHs[1]));
             }
         }
     }
 
     @Test
     public void testGsHsField() {
         doTestGsHsField(Decimal64Field.getInstance());
     }
 
     /** Gs and Hs computation test based on 2 independent methods.
      *  If they give same results, we assume them to be consistent.
      */
     private <T extends RealFieldElement<T>> void doTestGsHsField(Field<T> field) {
         final T zero = field.getZero();
         final int s = 50;
         final MersenneTwister random = new MersenneTwister(123456789);
         for (int i = 0; i < 10; i++) {
             final T k = zero.add(random.nextDouble());
             final T h = zero.add(random.nextDouble());
             final T a = zero.add(random.nextDouble());
             final T b = zero.add(random.nextDouble());
             final T[][] GH = CoefficientsFactory.computeGsHs(k, h, a, b, s, field);
             for (int j = 1; j < s; j++) {
                 final T[] GsHs = getGsHs(k, h, a, b, j, field);
                 Assert.assertEquals(GsHs[0].getReal(), GH[0][j].getReal(), FastMath.abs(GsHs[0].multiply(eps12)).getReal());
                 Assert.assertEquals(GsHs[1].getReal(), GH[1][j].getReal(), FastMath.abs(GsHs[1].multiply(eps12)).getReal());
             }
         }
     }
 
     /**
      * Direct computation for the Vmns coefficient from equation 2.7.1 - (6)
      */
     private static double getVmns2(final int m,
                                    final int n,
                                    final int s) {
         double vmsn = 0d;
         if ((n - s) % 2 == 0) {
             final int coef = (s > 0 || s % 2 == 0) ? 1 : -1;
             final int ss = (s > 0) ? s : -s;
             final double num = FastMath.pow(-1, (n - ss) / 2) *
                                CombinatoricsUtils.factorialDouble(n + ss) *
                                CombinatoricsUtils.factorialDouble(n - ss);
             final double den = FastMath.pow(2, n) *
                                CombinatoricsUtils.factorialDouble(n - m) *
                                CombinatoricsUtils.factorialDouble((n + ss) / 2) *
                                CombinatoricsUtils.factorialDouble((n - ss) / 2);
             vmsn = coef * num / den;
         }
         return vmsn;
     }
 
     /** Get the Q<sub>ns</sub> value from 2.8.1-(4) evaluated in γ This method is using the
      * Legendre polynomial to compute the Q<sub>ns</sub>'s one. This direct computation method
      * allows to store the polynomials value in a static map. If the Q<sub>ns</sub> had been
      * computed already, they just will be evaluated at γ
      *
      * @param gamma γ angle for which Q<sub>ns</sub> is evaluated
      * @param n n value
      * @param s s value
      * @return the polynomial value evaluated at γ
      */
     private static double getQnsPolynomialValue(final double gamma, final int n, final int s) {
         PolynomialFunction derivative;
         if (QNS_MAP.containsKey(new NSKey(n, s))) {
             derivative = QNS_MAP.get(new NSKey(n, s));
         } else {
             final PolynomialFunction legendre = PolynomialsUtils.createLegendrePolynomial(n);
             derivative = legendre;
             for (int i = 0; i < s; i++) {
                 derivative = (PolynomialFunction) derivative.polynomialDerivative();
             }
             QNS_MAP.put(new NSKey(n, s), derivative);
         }
         return derivative.value(gamma);
     }
 
     /** Get the Q<sub>ns</sub> value from 2.8.1-(4) evaluated in γ This method is using the
      * Legendre polynomial to compute the Q<sub>ns</sub>'s one. This direct computation method
      * allows to store the polynomials value in a static map. If the Q<sub>ns</sub> had been
      * computed already, they just will be evaluated at γ
      *
      * @param gamma γ angle for which Q<sub>ns</sub> is evaluated
      * @param n n value
      * @param s s value
      * @return the polynomial value evaluated at γ
      */
     private static <T extends RealFieldElement<T>> T getQnsPolynomialValue(final T gamma, final int n, final int s) {
         PolynomialFunction derivative;
         if (QNS_MAP.containsKey(new NSKey(n, s))) {
             derivative = QNS_MAP.get(new NSKey(n, s));
         } else {
             final PolynomialFunction legendre = PolynomialsUtils.createLegendrePolynomial(n);
             derivative = legendre;
             for (int i = 0; i < s; i++) {
                 derivative = (PolynomialFunction) derivative.polynomialDerivative();
             }
             QNS_MAP.put(new NSKey(n, s), derivative);
         }
         return derivative.value(gamma);
     }
 
     /** Compute directly G<sub>s</sub> and H<sub>s</sub> coefficients from equation 3.1-(4).
      * @param k x-component of the eccentricity vector
      * @param h y-component of the eccentricity vector
      * @param a 1st direction cosine
      * @param b 2nd direction cosine
      * @param s development order
      * @return Array of G<sub>s</sub> and H<sub>s</sub> values for s.<br>
      *         The 1st element contains the G<sub>s</sub> value.
      *         The 2nd element contains the H<sub>s</sub> value.
      */
     private static double[] getGsHs(final double k, final double h,
                                     final double a, final double b, final int s) {
         final Complex as   = new Complex(k, h).pow(s);
         final Complex bs   = new Complex(a, -b).pow(s);
         final Complex asbs = as.multiply(bs);
         return new double[] {asbs.getReal(), asbs.getImaginary()};
     }
     
     /** Compute directly G<sub>s</sub> and H<sub>s</sub> coefficients from equation 3.1-(4).
      * @param k x-component of the eccentricity vector
      * @param h y-component of the eccentricity vector
      * @param a 1st direction cosine
      * @param b 2nd direction cosine
      * @param s development order
      * @return Array of G<sub>s</sub> and H<sub>s</sub> values for s.<br>
      *         The 1st element contains the G<sub>s</sub> value.
      *         The 2nd element contains the H<sub>s</sub> value.
      */
     private static <T extends RealFieldElement<T>> T[] getGsHs(final T k, final T h,
                                     final T a, final T b, final int s,
                                     final Field<T> field) {
         final FieldComplex<T> as   = new FieldComplex<>(k, h).pow(s);
         final FieldComplex<T> bs   = new FieldComplex<>(a, b.negate()).pow(s);
         final FieldComplex<T> asbs = as.multiply(bs);
         final T[] values = MathArrays.buildArray(field, 2);
         values[0] = asbs.getReal();
         values[1] = asbs.getImaginary();
         return values;
     }
     
     private static class FieldComplex <T extends RealFieldElement<T>> {
 
         /** The imaginary part. */
         private final T imaginary;
 
         /** The real part. */
         private final T real;
        
         /**
          * Create a complex number given the real and imaginary parts.
          *
          * @param real Real part.
          * @param imaginary Imaginary part.
          */
         FieldComplex(final T real, final T imaginary) {
             this.real = real;
             this.imaginary = imaginary;
         }
 
         /**
          * Access the real part.
          *
          * @return the real part.
          */
         public T getReal() {
             return real;
         }
 
         /**
          * Access the imaginary part.
          *
          * @return the imaginary part.
          */
         public T getImaginary() {
             return imaginary;
         }
 
         /**
          * Create a complex number given the real and imaginary parts.
          *
          * @param realPart Real part.
          * @param imaginaryPart Imaginary part.
          * @return a new complex number instance.
          *
          * @see #valueOf(double, double)
          */
         protected FieldComplex<T> createComplex(final T realPart, final T imaginaryPart) {
             return new FieldComplex<>(realPart, imaginaryPart);
         }
 
         /**
          * Returns a {@code Complex} whose value is {@code this * factor}.
          * Implements preliminary checks for {@code NaN} and infinity followed by
          * the definitional formula:
          * <p>
          *   {@code (a + bi)(c + di) = (ac - bd) + (ad + bc)i}
          * </p>
          * <p>
          * Returns finite values in components of the result per the definitional
          * formula in all remaining cases.</p>
          *
          * @param  factor value to be multiplied by this {@code Complex}.
          * @return {@code this * factor}.
          * @throws NullArgumentException if {@code factor} is {@code null}.
          */
         public FieldComplex<T> multiply(final FieldComplex<T> factor) throws NullArgumentException {
             return createComplex(real.multiply(factor.real).subtract(imaginary.multiply(factor.imaginary)),
                                  real.multiply(factor.imaginary).add(imaginary.multiply(factor.real)));
         }
         
         /**
          * Returns a {@code Complex} whose value is {@code this * factor}, with {@code factor}
          * interpreted as a integer number.
          *
          * @param  factor value to be multiplied by this {@code Complex}.
          * @return {@code this * factor}.
          * @see #multiply(Complex)
          */
         public FieldComplex<T> multiply(final int factor) {
             return createComplex(real.multiply(factor), imaginary.multiply(factor));
         }
 
         /**
          * Returns of value of this complex number raised to the power of {@code x}.
          *
          * @param  x exponent to which this {@code Complex} is to be raised.
          * @return <code>this<sup>x</sup></code>.
          * @see #pow(Complex)
          */
          public FieldComplex<T> pow(int x) {
             return this.log().multiply(x).exp();
         }
          
          /**
           * Compute the
           * <a href="http://mathworld.wolfram.com/NaturalLogarithm.html" TARGET="_top">
           * natural logarithm</a> of this complex number.
           * Implements the formula:
           * <pre>
           *  <code>
           *   log(a + bi) = ln(|a + bi|) + arg(a + bi)i
           *  </code>
           * </pre>
           * where ln on the right hand side is {@link FastMath#log},
           * {@code |a + bi|} is the modulus, {@link Complex#abs},  and
           * {@code arg(a + bi) = }{@link FastMath#atan2}(b, a).
           * <p>
           * Returns {@link Complex#NaN} if either real or imaginary part of the
           * input argument is {@code NaN}.
           * </p>
           * Infinite (or critical) values in real or imaginary parts of the input may
           * result in infinite or NaN values returned in parts of the result.
           * <pre>
           *  Examples:
           *  <code>
           *   log(1 &plusmn; INFINITY i) = INFINITY &plusmn; (&pi;/2)i
           *   log(INFINITY + i) = INFINITY + 0i
           *   log(-INFINITY + i) = INFINITY + &pi;i
           *   log(INFINITY &plusmn; INFINITY i) = INFINITY &plusmn; (&pi;/4)i
           *   log(-INFINITY &plusmn; INFINITY i) = INFINITY &plusmn; (3&pi;/4)i
           *   log(0 + 0i) = -INFINITY + 0i
           *  </code>
           * </pre>
           *
           * @return the value <code>ln &nbsp; this</code>, the natural logarithm
           * of {@code this}.
           */
          public FieldComplex<T> log() {
              return createComplex(FastMath.log(abs()),
                                   FastMath.atan2(imaginary, real));
          }
 
          /**
           * Compute the
           * <a href="http://mathworld.wolfram.com/ExponentialFunction.html" TARGET="_top">
           * exponential function</a> of this complex number.
           * Implements the formula:
           * <pre>
           *  <code>
           *   exp(a + bi) = exp(a)cos(b) + exp(a)sin(b)i
           *  </code>
           * </pre>
           * where the (real) functions on the right-hand side are
           * {@link FastMath#exp}, {@link FastMath#cos}, and
           * {@link FastMath#sin}.
           * <p>
           * Returns {@link Complex#NaN} if either real or imaginary part of the
           * input argument is {@code NaN}.
           * </p>
           * Infinite values in real or imaginary parts of the input may result in
           * infinite or NaN values returned in parts of the result.
           * <pre>
           *  Examples:
           *  <code>
           *   exp(1 &plusmn; INFINITY i) = NaN + NaN i
           *   exp(INFINITY + i) = INFINITY + INFINITY i
           *   exp(-INFINITY + i) = 0 + 0i
           *   exp(&plusmn;INFINITY &plusmn; INFINITY i) = NaN + NaN i
           *  </code>
           * </pre>
           *
           * @return <code><i>e</i><sup>this</sup></code>.
           */
          public FieldComplex<T> exp() {
              T expReal = FastMath.exp(real);
              return createComplex(expReal.multiply(FastMath.cos(imaginary)),
                                   expReal.multiply(FastMath.sin(imaginary)));
          }
 
          /**
           * Return the absolute value of this complex number.
           * Returns {@code NaN} if either real or imaginary part is {@code NaN}
           * and {@code Double.POSITIVE_INFINITY} if neither part is {@code NaN},
           * but at least one part is infinite.
           *
           * @return the absolute value.
           */
          public T abs() {
              if (FastMath.abs(real).getReal() < FastMath.abs(imaginary).getReal()) {
                  if (imaginary.getReal() == 0.0) {
                      return FastMath.abs(real);
                  }
                  T q = real.divide(imaginary);
                  return FastMath.abs(imaginary).multiply(FastMath.sqrt(q.multiply(q).add(1.)));
              } else {
                  if (real.getReal() == 0.0) {
                      return FastMath.abs(imaginary);
                  }
                  T q = imaginary.divide(real);
                  return FastMath.abs(real).multiply(FastMath.sqrt(q.multiply(q).add(1.)));
              }
          }
 
     }
 }