/* Copyright 2002-2017 CS Systèmes d'Information
* Licensed to CS Systèmes d'Information (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.data;
import java.util.HashMap;
import java.util.Map;
import org.hipparchus.RealFieldElement;
import org.hipparchus.util.MathArrays;
/**
* Class representing a Poisson series for nutation or ephemeris computations.
* <p>
* A Poisson series is composed of a time polynomial part and a non-polynomial
* part which consist in summation series. The {@link SeriesTerm series terms}
* are harmonic functions (combination of sines and cosines) of polynomial
* <em>arguments</em>. The polynomial arguments are combinations of luni-solar or
* planetary {@link BodiesElements elements}.
* </p>
* @author Luc Maisonobe
* @see PoissonSeriesParser
* @see SeriesTerm
* @see PolynomialNutation
*/
public class PoissonSeries {
/** Polynomial part. */
private final PolynomialNutation polynomial;
/** Non-polynomial series. */
private final Map<Long, SeriesTerm> series;
/** Build a Poisson series from an IERS table file.
* @param polynomial polynomial part (may be null)
* @param series non-polynomial part
*/
public PoissonSeries(final PolynomialNutation polynomial, final Map<Long, SeriesTerm> series) {
this.polynomial = polynomial;
this.series = series;
}
/** Get the polynomial part of the series.
* @return polynomial part of the series.
*/
public PolynomialNutation getPolynomial() {
return polynomial;
}
/** Get the number of different terms in the non-polynomial part.
* @return number of different terms in the non-polynomial part
*/
public int getNonPolynomialSize() {
return series.size();
}
/** Evaluate the value of the series.
* @param elements bodies elements for nutation
* @return value of the series
*/
public double value(final BodiesElements elements) {
// polynomial part
final double p = polynomial.value(elements.getTC());
// non-polynomial part
// compute sum accurately, using Møller-Knuth TwoSum algorithm without branching
// the following statements must NOT be simplified, they rely on floating point
// arithmetic properties (rounding and representable numbers)
double npHigh = 0;
double npLow = 0;
for (final SeriesTerm term : series.values()) {
final double v = term.value(elements)[0];
final double sum = npHigh + v;
final double sPrime = sum - v;
final double tPrime = sum - sPrime;
final double deltaS = npHigh - sPrime;
final double deltaT = v - tPrime;
npLow += deltaS + deltaT;
npHigh = sum;
}
// add the polynomial and the non-polynomial parts
return p + (npHigh + npLow);
}
/** Evaluate the value of the series.
* @param elements bodies elements for nutation
* @param <T> type fo the field elements
* @return value of the series
*/
public <T extends RealFieldElement<T>> T value(final FieldBodiesElements<T> elements) {
// polynomial part
final T tc = elements.getTC();
final T p = polynomial.value(tc);
// non-polynomial part
T sum = tc.getField().getZero();
for (final SeriesTerm term : series.values()) {
sum = sum.add(term.value(elements)[0]);
}
// add the polynomial and the non-polynomial parts
return p.add(sum);
}
/** This interface represents a fast evaluator for Poisson series.
* @see PoissonSeries#compile(PoissonSeries...)
* @since 6.1
*/
public interface CompiledSeries {
/** Evaluate a set of Poisson series.
* @param elements bodies elements for nutation
* @return value of the series
*/
double[] value(BodiesElements elements);
/** Evaluate time derivative of a set of Poisson series.
* @param elements bodies elements for nutation
* @return time derivative of the series
*/
double[] derivative(BodiesElements elements);
/** Evaluate a set of Poisson series.
* @param elements bodies elements for nutation
* @param <S> the type of the field elements
* @return value of the series
*/
<S extends RealFieldElement<S>> S[] value(FieldBodiesElements<S> elements);
/** Evaluate time derivative of a set of Poisson series.
* @param elements bodies elements for nutation
* @param <S> the type of the field elements
* @return time derivative of the series
*/
<S extends RealFieldElement<S>> S[] derivative(FieldBodiesElements<S> elements);
}
/** Join several nutation series, for fast simultaneous evaluation.
* @param poissonSeries Poisson series to join
* @return a single function that evaluates all series together
* @since 6.1
*/
@SafeVarargs
public static CompiledSeries compile(final PoissonSeries... poissonSeries) {
// store all polynomials
final PolynomialNutation[] polynomials = new PolynomialNutation[poissonSeries.length];
for (int i = 0; i < polynomials.length; ++i) {
polynomials[i] = poissonSeries[i].polynomial;
}
// gather all series terms
final Map<Long, SeriesTerm> joinedMap = new HashMap<Long, SeriesTerm>();
for (final PoissonSeries ps : poissonSeries) {
for (Map.Entry<Long, SeriesTerm> entry : ps.series.entrySet()) {
final long key = entry.getKey();
if (!joinedMap.containsKey(key)) {
// retrieve all Delaunay and planetary multipliers from the key
final int[] m = NutationCodec.decode(key);
// prepare a new term, ready to handle the required dimension
final SeriesTerm term =
SeriesTerm.buildTerm(m[0],
m[1], m[2], m[3], m[4], m[5],
m[6], m[7], m[8], m[9], m[10], m[11], m[12], m[13], m[14]);
term.add(poissonSeries.length - 1, -1, Double.NaN, Double.NaN);
// store it
joinedMap.put(key, term);
}
}
}
// join series by sharing terms, in order to speed up evaluation
// which is dominated by the computation of sine/cosine in each term
for (int i = 0; i < poissonSeries.length; ++i) {
for (final Map.Entry<Long, SeriesTerm> entry : poissonSeries[i].series.entrySet()) {
final SeriesTerm singleTerm = entry.getValue();
final SeriesTerm joinedTerm = joinedMap.get(entry.getKey());
for (int degree = 0; degree <= singleTerm.getDegree(0); ++degree) {
joinedTerm.add(i, degree,
singleTerm.getSinCoeff(0, degree),
singleTerm.getCosCoeff(0, degree));
}
}
}
// use a single array for faster access
final SeriesTerm[] joinedTerms = new SeriesTerm[joinedMap.size()];
int index = 0;
for (final Map.Entry<Long, SeriesTerm> entry : joinedMap.entrySet()) {
joinedTerms[index++] = entry.getValue();
}
return new CompiledSeries() {
/** {@inheritDoc} */
@Override
public double[] value(final BodiesElements elements) {
// non-polynomial part
// compute sum accurately, using Møller-Knuth TwoSum algorithm without branching
// the following statements must NOT be simplified, they rely on floating point
// arithmetic properties (rounding and representable numbers)
final double[] npHigh = new double[polynomials.length];
final double[] npLow = new double[polynomials.length];
for (final SeriesTerm term : joinedTerms) {
final double[] termValue = term.value(elements);
for (int i = 0; i < termValue.length; ++i) {
final double v = termValue[i];
final double sum = npHigh[i] + v;
final double sPrime = sum - v;
final double tPrime = sum - sPrime;
final double deltaS = npHigh[i] - sPrime;
final double deltaT = v - tPrime;
npLow[i] += deltaS + deltaT;
npHigh[i] = sum;
}
}
// add residual and polynomial part
for (int i = 0; i < npHigh.length; ++i) {
npHigh[i] += npLow[i] + polynomials[i].value(elements.getTC());
}
return npHigh;
}
/** {@inheritDoc} */
@Override
public double[] derivative(final BodiesElements elements) {
// non-polynomial part
final double[] v = new double[polynomials.length];
for (final SeriesTerm term : joinedTerms) {
final double[] termDerivative = term.derivative(elements);
for (int i = 0; i < termDerivative.length; ++i) {
v[i] += termDerivative[i];
}
}
// add polynomial part
for (int i = 0; i < v.length; ++i) {
v[i] += polynomials[i].derivative(elements.getTC());
}
return v;
}
/** {@inheritDoc} */
@Override
public <S extends RealFieldElement<S>> S[] value(final FieldBodiesElements<S> elements) {
// non-polynomial part
final S[] v = MathArrays.buildArray(elements.getTC().getField(), polynomials.length);
for (final SeriesTerm term : joinedTerms) {
final S[] termValue = term.value(elements);
for (int i = 0; i < termValue.length; ++i) {
v[i] = v[i].add(termValue[i]);
}
}
// add polynomial part
final S tc = elements.getTC();
for (int i = 0; i < v.length; ++i) {
v[i] = v[i].add(polynomials[i].value(tc));
}
return v;
}
/** {@inheritDoc} */
@Override
public <S extends RealFieldElement<S>> S[] derivative(final FieldBodiesElements<S> elements) {
// non-polynomial part
final S[] v = MathArrays.buildArray(elements.getTC().getField(), polynomials.length);
for (final SeriesTerm term : joinedTerms) {
final S[] termDerivative = term.derivative(elements);
for (int i = 0; i < termDerivative.length; ++i) {
v[i] = v[i].add(termDerivative[i]);
}
}
// add polynomial part
final S tc = elements.getTC();
for (int i = 0; i < v.length; ++i) {
v[i] = v[i].add(polynomials[i].derivative(tc));
}
return v;
}
};
}
}